LMFDB - Embedded newform 6011.2.a.f.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.70543 q^{2} +2.79292 q^{3} +5.31937 q^{4} +2.92654 q^{5} -7.55605 q^{6} -0.481988 q^{7} -8.98033 q^{8} +4.80038 q^{9} +O(q^{10})$	\(q-2.70543 q^{2} +2.79292 q^{3} +5.31937 q^{4} +2.92654 q^{5} -7.55605 q^{6} -0.481988 q^{7} -8.98033 q^{8} +4.80038 q^{9} -7.91756 q^{10} +5.14330 q^{11} +14.8566 q^{12} +5.68360 q^{13} +1.30399 q^{14} +8.17358 q^{15} +13.6569 q^{16} +6.36247 q^{17} -12.9871 q^{18} -4.77039 q^{19} +15.5673 q^{20} -1.34615 q^{21} -13.9148 q^{22} -5.38084 q^{23} -25.0813 q^{24} +3.56464 q^{25} -15.3766 q^{26} +5.02831 q^{27} -2.56387 q^{28} -0.451451 q^{29} -22.1131 q^{30} -7.85066 q^{31} -18.9873 q^{32} +14.3648 q^{33} -17.2132 q^{34} -1.41056 q^{35} +25.5350 q^{36} +6.20899 q^{37} +12.9060 q^{38} +15.8738 q^{39} -26.2813 q^{40} +5.21230 q^{41} +3.64192 q^{42} -5.01942 q^{43} +27.3591 q^{44} +14.0485 q^{45} +14.5575 q^{46} -5.13394 q^{47} +38.1427 q^{48} -6.76769 q^{49} -9.64389 q^{50} +17.7698 q^{51} +30.2332 q^{52} -5.52263 q^{53} -13.6037 q^{54} +15.0521 q^{55} +4.32841 q^{56} -13.3233 q^{57} +1.22137 q^{58} +10.1300 q^{59} +43.4783 q^{60} +12.1748 q^{61} +21.2394 q^{62} -2.31372 q^{63} +24.0550 q^{64} +16.6333 q^{65} -38.8630 q^{66} +2.16921 q^{67} +33.8443 q^{68} -15.0282 q^{69} +3.81617 q^{70} -5.11241 q^{71} -43.1090 q^{72} -12.3074 q^{73} -16.7980 q^{74} +9.95573 q^{75} -25.3755 q^{76} -2.47900 q^{77} -42.9455 q^{78} +17.2529 q^{79} +39.9676 q^{80} -0.357500 q^{81} -14.1015 q^{82} +16.6812 q^{83} -7.16067 q^{84} +18.6200 q^{85} +13.5797 q^{86} -1.26086 q^{87} -46.1885 q^{88} -14.9732 q^{89} -38.0073 q^{90} -2.73942 q^{91} -28.6227 q^{92} -21.9262 q^{93} +13.8895 q^{94} -13.9607 q^{95} -53.0299 q^{96} +10.0897 q^{97} +18.3095 q^{98} +24.6898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.70543	−1.91303	−0.956515	−	0.291683i	$-0.905785\pi$
$2$	−2.70543	−1.91303	−0.956515	+	0.291683i	$0.905785\pi$
$3$	2.79292	1.61249	0.806245	−	0.591581i	$-0.201496\pi$
$3$	2.79292	1.61249	0.806245	+	0.591581i	$0.201496\pi$
$4$	5.31937	2.65968
$5$	2.92654	1.30879	0.654394	−	0.756154i	$-0.272924\pi$
$5$	2.92654	1.30879	0.654394	+	0.756154i	$0.272924\pi$
$6$	−7.55605	−3.08474
$7$	−0.481988	−0.182174	−0.0910871	−	0.995843i	$-0.529034\pi$
$7$	−0.481988	−0.182174	−0.0910871	+	0.995843i	$0.529034\pi$
$8$	−8.98033	−3.17503
$9$	4.80038	1.60013
$10$	−7.91756	−2.50375
$11$	5.14330	1.55076	0.775381	−	0.631494i	$-0.217558\pi$
$11$	5.14330	1.55076	0.775381	+	0.631494i	$0.217558\pi$
$12$	14.8566	4.28872
$13$	5.68360	1.57635	0.788173	−	0.615454i	$-0.211027\pi$
$13$	5.68360	1.57635	0.788173	+	0.615454i	$0.211027\pi$
$14$	1.30399	0.348505
$15$	8.17358	2.11041
$16$	13.6569	3.41424
$17$	6.36247	1.54313	0.771563	−	0.636153i	$-0.219475\pi$
$17$	6.36247	1.54313	0.771563	+	0.636153i	$0.219475\pi$
$18$	−12.9871	−3.06109
$19$	−4.77039	−1.09440	−0.547201	−	0.837001i	$-0.684307\pi$
$19$	−4.77039	−1.09440	−0.547201	+	0.837001i	$0.684307\pi$
$20$	15.5673	3.48096
$21$	−1.34615	−0.293754
$22$	−13.9148	−2.96665
$23$	−5.38084	−1.12198	−0.560992	−	0.827822i	$-0.689580\pi$
$23$	−5.38084	−1.12198	−0.560992	+	0.827822i	$0.689580\pi$
$24$	−25.0813	−5.11970
$25$	3.56464	0.712928
$26$	−15.3766	−3.01560
$27$	5.02831	0.967698
$28$	−2.56387	−0.484526
$29$	−0.451451	−0.0838323	−0.0419162	−	0.999121i	$-0.513346\pi$
$29$	−0.451451	−0.0838323	−0.0419162	+	0.999121i	$0.513346\pi$
$30$	−22.1131	−4.03728
$31$	−7.85066	−1.41002	−0.705010	−	0.709197i	$-0.749058\pi$
$31$	−7.85066	−1.41002	−0.705010	+	0.709197i	$0.749058\pi$
$32$	−18.9873	−3.35651
$33$	14.3648	2.50059
$34$	−17.2132	−2.95205
$35$	−1.41056	−0.238428
$36$	25.5350	4.25583
$37$	6.20899	1.02075	0.510376	−	0.859951i	$-0.329506\pi$
$37$	6.20899	1.02075	0.510376	+	0.859951i	$0.329506\pi$
$38$	12.9060	2.09362
$39$	15.8738	2.54184
$40$	−26.2813	−4.15544
$41$	5.21230	0.814025	0.407012	−	0.913423i	$-0.366571\pi$
$41$	5.21230	0.814025	0.407012	+	0.913423i	$0.366571\pi$
$42$	3.64192	0.561961
$43$	−5.01942	−0.765454	−0.382727	−	0.923861i	$-0.625015\pi$
$43$	−5.01942	−0.765454	−0.382727	+	0.923861i	$0.625015\pi$
$44$	27.3591	4.12454
$45$	14.0485	2.09423
$46$	14.5575	2.14639
$47$	−5.13394	−0.748863	−0.374431	−	0.927255i	$-0.622162\pi$
$47$	−5.13394	−0.748863	−0.374431	+	0.927255i	$0.622162\pi$
$48$	38.1427	5.50543
$49$	−6.76769	−0.966813
$50$	−9.64389	−1.36385
$51$	17.7698	2.48828
$52$	30.2332	4.19258
$53$	−5.52263	−0.758591	−0.379296	−	0.925276i	$-0.623834\pi$
$53$	−5.52263	−0.758591	−0.379296	+	0.925276i	$0.623834\pi$
$54$	−13.6037	−1.85124
$55$	15.0521	2.02962
$56$	4.32841	0.578408
$57$	−13.3233	−1.76471
$58$	1.22137	0.160374
$59$	10.1300	1.31881	0.659407	−	0.751786i	$-0.270807\pi$
$59$	10.1300	1.31881	0.659407	+	0.751786i	$0.270807\pi$
$60$	43.4783	5.61302
$61$	12.1748	1.55883	0.779414	−	0.626509i	$-0.215517\pi$
$61$	12.1748	1.55883	0.779414	+	0.626509i	$0.215517\pi$
$62$	21.2394	2.69741
$63$	−2.31372	−0.291502
$64$	24.0550	3.00687
$65$	16.6333	2.06310
$66$	−38.8630	−4.78370
$67$	2.16921	0.265011	0.132506	−	0.991182i	$-0.457698\pi$
$67$	2.16921	0.265011	0.132506	+	0.991182i	$0.457698\pi$
$68$	33.8443	4.10423
$69$	−15.0282	−1.80919
$70$	3.81617	0.456119
$71$	−5.11241	−0.606732	−0.303366	−	0.952874i	$-0.598110\pi$
$71$	−5.11241	−0.606732	−0.303366	+	0.952874i	$0.598110\pi$
$72$	−43.1090	−5.08044
$73$	−12.3074	−1.44047	−0.720237	−	0.693728i	$-0.755967\pi$
$73$	−12.3074	−1.44047	−0.720237	+	0.693728i	$0.755967\pi$
$74$	−16.7980	−1.95273
$75$	9.95573	1.14959
$76$	−25.3755	−2.91076
$77$	−2.47900	−0.282509
$78$	−42.9455	−4.86262
$79$	17.2529	1.94110	0.970552	−	0.240892i	$-0.0774400\pi$
$79$	17.2529	1.94110	0.970552	+	0.240892i	$0.0774400\pi$
$80$	39.9676	4.46851
$81$	−0.357500	−0.0397222
$82$	−14.1015	−1.55725
$83$	16.6812	1.83099	0.915497	−	0.402324i	$-0.131798\pi$
$83$	16.6812	1.83099	0.915497	+	0.402324i	$0.131798\pi$
$84$	−7.16067	−0.781294
$85$	18.6200	2.01962
$86$	13.5797	1.46434
$87$	−1.26086	−0.135179
$88$	−46.1885	−4.92371
$89$	−14.9732	−1.58716	−0.793579	−	0.608467i	$-0.791785\pi$
$89$	−14.9732	−1.58716	−0.793579	+	0.608467i	$0.791785\pi$
$90$	−38.0073	−4.00632
$91$	−2.73942	−0.287170
$92$	−28.6227	−2.98412
$93$	−21.9262	−2.27364
$94$	13.8895	1.43260
$95$	−13.9607	−1.43234
$96$	−53.0299	−5.41235
$97$	10.0897	1.02445	0.512226	−	0.858851i	$-0.328821\pi$
$97$	10.0897	1.02445	0.512226	+	0.858851i	$0.328821\pi$
$98$	18.3095	1.84954
$99$	24.6898	2.48141
$100$	18.9616	1.89616
$101$	7.84109	0.780218	0.390109	−	0.920769i	$-0.372437\pi$
$101$	7.84109	0.780218	0.390109	+	0.920769i	$0.372437\pi$
$102$	−48.0751	−4.76015
$103$	−2.43360	−0.239790	−0.119895	−	0.992787i	$-0.538256\pi$
$103$	−2.43360	−0.239790	−0.119895	+	0.992787i	$0.538256\pi$
$104$	−51.0406	−5.00494
$105$	−3.93957	−0.384462
$106$	14.9411	1.45121
$107$	−9.06608	−0.876451	−0.438226	−	0.898865i	$-0.644393\pi$
$107$	−9.06608	−0.876451	−0.438226	+	0.898865i	$0.644393\pi$
$108$	26.7474	2.57377
$109$	12.3323	1.18122	0.590608	−	0.806959i	$-0.298888\pi$
$109$	12.3323	1.18122	0.590608	+	0.806959i	$0.298888\pi$
$110$	−40.7223	−3.88272
$111$	17.3412	1.64595
$112$	−6.58248	−0.621986
$113$	−7.24561	−0.681609	−0.340805	−	0.940134i	$-0.610699\pi$
$113$	−7.24561	−0.681609	−0.340805	+	0.940134i	$0.610699\pi$
$114$	36.0453	3.37595
$115$	−15.7472	−1.46844
$116$	−2.40143	−0.222968
$117$	27.2834	2.52235
$118$	−27.4061	−2.52293
$119$	−3.06663	−0.281118
$120$	−73.4015	−6.70061
$121$	15.4535	1.40486
$122$	−32.9382	−2.98209
$123$	14.5575	1.31261
$124$	−41.7606	−3.75021
$125$	−4.20065	−0.375717
$126$	6.25962	0.557652
$127$	−7.46605	−0.662505	−0.331252	−	0.943542i	$-0.607471\pi$
$127$	−7.46605	−0.662505	−0.331252	+	0.943542i	$0.607471\pi$
$128$	−27.1045	−2.39573
$129$	−14.0188	−1.23429
$130$	−45.0002	−3.94678
$131$	−9.47887	−0.828173	−0.414086	−	0.910238i	$-0.635899\pi$
$131$	−9.47887	−0.828173	−0.414086	+	0.910238i	$0.635899\pi$
$132$	76.4116	6.65078
$133$	2.29927	0.199372
$134$	−5.86865	−0.506974
$135$	14.7155	1.26651
$136$	−57.1371	−4.89946
$137$	1.76662	0.150933	0.0754664	−	0.997148i	$-0.475955\pi$
$137$	1.76662	0.150933	0.0754664	+	0.997148i	$0.475955\pi$
$138$	40.6579	3.46103
$139$	−5.33759	−0.452729	−0.226364	−	0.974043i	$-0.572684\pi$
$139$	−5.33759	−0.452729	−0.226364	+	0.974043i	$0.572684\pi$
$140$	−7.50327	−0.634142
$141$	−14.3387	−1.20753
$142$	13.8313	1.16070
$143$	29.2324	2.44454
$144$	65.5585	5.46321
$145$	−1.32119	−0.109719
$146$	33.2969	2.75567
$147$	−18.9016	−1.55898
$148$	33.0279	2.71488
$149$	−16.2241	−1.32913	−0.664566	−	0.747230i	$-0.731383\pi$
$149$	−16.2241	−1.32913	−0.664566	+	0.747230i	$0.731383\pi$
$150$	−26.9346	−2.19920
$151$	22.7819	1.85396	0.926982	−	0.375106i	$-0.122394\pi$
$151$	22.7819	1.85396	0.926982	+	0.375106i	$0.122394\pi$
$152$	42.8397	3.47476
$153$	30.5423	2.46920
$154$	6.70678	0.540448
$155$	−22.9753	−1.84542
$156$	84.4387	6.76050
$157$	−16.3459	−1.30454	−0.652272	−	0.757985i	$-0.726184\pi$
$157$	−16.3459	−1.30454	−0.652272	+	0.757985i	$0.726184\pi$
$158$	−46.6766	−3.71339
$159$	−15.4242	−1.22322
$160$	−55.5671	−4.39297
$161$	2.59350	0.204396
$162$	0.967191	0.0759897
$163$	17.4654	1.36799	0.683996	−	0.729485i	$-0.260240\pi$
$163$	17.4654	1.36799	0.683996	+	0.729485i	$0.260240\pi$
$164$	27.7261	2.16505
$165$	42.0391	3.27274
$166$	−45.1297	−3.50275
$167$	−7.81355	−0.604631	−0.302315	−	0.953208i	$-0.597760\pi$
$167$	−7.81355	−0.604631	−0.302315	+	0.953208i	$0.597760\pi$
$168$	12.0889	0.932678
$169$	19.3033	1.48487
$170$	−50.3752	−3.86360
$171$	−22.8997	−1.75118
$172$	−26.7001	−2.03587
$173$	6.17667	0.469604	0.234802	−	0.972043i	$-0.424556\pi$
$173$	6.17667	0.469604	0.234802	+	0.972043i	$0.424556\pi$
$174$	3.41118	0.258601
$175$	−1.71811	−0.129877
$176$	70.2417	5.29467
$177$	28.2922	2.12658
$178$	40.5090	3.03628
$179$	−9.32540	−0.697013	−0.348507	−	0.937306i	$-0.613311\pi$
$179$	−9.32540	−0.697013	−0.348507	+	0.937306i	$0.613311\pi$
$180$	74.7292	5.56998
$181$	7.92400	0.588986	0.294493	−	0.955654i	$-0.404849\pi$
$181$	7.92400	0.588986	0.294493	+	0.955654i	$0.404849\pi$
$182$	7.41133	0.549364
$183$	34.0033	2.51360
$184$	48.3217	3.56233
$185$	18.1709	1.33595
$186$	59.3200	4.34955
$187$	32.7241	2.39302
$188$	−27.3093	−1.99174
$189$	−2.42358	−0.176290
$190$	37.7698	2.74011
$191$	−11.2176	−0.811675	−0.405838	−	0.913945i	$-0.633020\pi$
$191$	−11.2176	−0.811675	−0.405838	+	0.913945i	$0.633020\pi$
$192$	67.1835	4.84855
$193$	4.07761	0.293513	0.146756	−	0.989173i	$-0.453117\pi$
$193$	4.07761	0.293513	0.146756	+	0.989173i	$0.453117\pi$
$194$	−27.2969	−1.95981
$195$	46.4553	3.32674
$196$	−35.9998	−2.57142
$197$	12.8814	0.917765	0.458882	−	0.888497i	$-0.348250\pi$
$197$	12.8814	0.917765	0.458882	+	0.888497i	$0.348250\pi$
$198$	−66.7965	−4.74702
$199$	−3.12406	−0.221459	−0.110729	−	0.993851i	$-0.535319\pi$
$199$	−3.12406	−0.221459	−0.110729	+	0.993851i	$0.535319\pi$
$200$	−32.0116	−2.26356
$201$	6.05842	0.427328
$202$	−21.2136	−1.49258
$203$	0.217594	0.0152721
$204$	94.5243	6.61803
$205$	15.2540	1.06539
$206$	6.58395	0.458726
$207$	−25.8301	−1.79531
$208$	77.6206	5.38202
$209$	−24.5355	−1.69716
$210$	10.6582	0.735488
$211$	−5.55504	−0.382425	−0.191212	−	0.981549i	$-0.561242\pi$
$211$	−5.55504	−0.382425	−0.191212	+	0.981549i	$0.561242\pi$
$212$	−29.3769	−2.01761
$213$	−14.2785	−0.978349
$214$	24.5277	1.67668
$215$	−14.6895	−1.00182
$216$	−45.1559	−3.07247
$217$	3.78392	0.256869
$218$	−33.3641	−2.25970
$219$	−34.3736	−2.32275
$220$	80.0675	5.39815
$221$	36.1617	2.43250
$222$	−46.9154	−3.14876
$223$	−23.8945	−1.60010	−0.800049	−	0.599935i	$-0.795193\pi$
$223$	−23.8945	−1.60010	−0.800049	+	0.599935i	$0.795193\pi$
$224$	9.15165	0.611470
$225$	17.1116	1.14077
$226$	19.6025	1.30394
$227$	−0.382503	−0.0253876	−0.0126938	−	0.999919i	$-0.504041\pi$
$227$	−0.382503	−0.0253876	−0.0126938	+	0.999919i	$0.504041\pi$
$228$	−70.8715	−4.69358
$229$	11.0481	0.730082	0.365041	−	0.930991i	$-0.381055\pi$
$229$	11.0481	0.730082	0.365041	+	0.930991i	$0.381055\pi$
$230$	42.6031	2.80917
$231$	−6.92365	−0.455543
$232$	4.05418	0.266170
$233$	11.2822	0.739121	0.369561	−	0.929207i	$-0.379508\pi$
$233$	11.2822	0.739121	0.369561	+	0.929207i	$0.379508\pi$
$234$	−73.8135	−4.82534
$235$	−15.0247	−0.980103
$236$	53.8852	3.50763
$237$	48.1859	3.13001
$238$	8.29657	0.537787
$239$	−28.2116	−1.82485	−0.912427	−	0.409239i	$-0.865794\pi$
$239$	−28.2116	−1.82485	−0.912427	+	0.409239i	$0.865794\pi$
$240$	111.626	7.20544
$241$	−15.1736	−0.977417	−0.488708	−	0.872447i	$-0.662532\pi$
$241$	−15.1736	−0.977417	−0.488708	+	0.872447i	$0.662532\pi$
$242$	−41.8084	−2.68754
$243$	−16.0834	−1.03175
$244$	64.7624	4.14599
$245$	−19.8059	−1.26535
$246$	−39.3844	−2.51106
$247$	−27.1130	−1.72516
$248$	70.5015	4.47685
$249$	46.5891	2.95246
$250$	11.3646	0.718758
$251$	−16.1629	−1.02019	−0.510096	−	0.860117i	$-0.670390\pi$
$251$	−16.1629	−1.02019	−0.510096	+	0.860117i	$0.670390\pi$
$252$	−12.3075	−0.775303
$253$	−27.6753	−1.73993
$254$	20.1989	1.26739
$255$	52.0042	3.25663
$256$	25.2196	1.57622
$257$	7.84051	0.489078	0.244539	−	0.969639i	$-0.421363\pi$
$257$	7.84051	0.489078	0.244539	+	0.969639i	$0.421363\pi$
$258$	37.9270	2.36123
$259$	−2.99266	−0.185955
$260$	88.4785	5.48721
$261$	−2.16714	−0.134142
$262$	25.6444	1.58432
$263$	−19.3255	−1.19166	−0.595832	−	0.803109i	$-0.703178\pi$
$263$	−19.3255	−1.19166	−0.595832	+	0.803109i	$0.703178\pi$
$264$	−129.001	−7.93944
$265$	−16.1622	−0.992836
$266$	−6.22052	−0.381404
$267$	−41.8189	−2.55928
$268$	11.5388	0.704846
$269$	−6.93682	−0.422946	−0.211473	−	0.977384i	$-0.567826\pi$
$269$	−6.93682	−0.422946	−0.211473	+	0.977384i	$0.567826\pi$
$270$	−39.8119	−2.42288
$271$	−15.0007	−0.911228	−0.455614	−	0.890177i	$-0.650580\pi$
$271$	−15.0007	−0.911228	−0.455614	+	0.890177i	$0.650580\pi$
$272$	86.8919	5.26860
$273$	−7.65098	−0.463058
$274$	−4.77948	−0.288739
$275$	18.3340	1.10558
$276$	−79.9407	−4.81187
$277$	17.5412	1.05395	0.526973	−	0.849882i	$-0.323327\pi$
$277$	17.5412	1.05395	0.526973	+	0.849882i	$0.323327\pi$
$278$	14.4405	0.866083
$279$	−37.6861	−2.25621
$280$	12.6673	0.757014
$281$	−14.3021	−0.853194	−0.426597	−	0.904442i	$-0.640288\pi$
$281$	−14.3021	−0.853194	−0.426597	+	0.904442i	$0.640288\pi$
$282$	38.7923	2.31005
$283$	−21.6143	−1.28484	−0.642418	−	0.766355i	$-0.722069\pi$
$283$	−21.6143	−1.28484	−0.642418	+	0.766355i	$0.722069\pi$
$284$	−27.1948	−1.61372
$285$	−38.9912	−2.30964
$286$	−79.0864	−4.67647
$287$	−2.51226	−0.148294
$288$	−91.1462	−5.37084
$289$	23.4810	1.38124
$290$	3.57439	0.209895
$291$	28.1796	1.65192
$292$	−65.4677	−3.83120
$293$	−8.62665	−0.503974	−0.251987	−	0.967731i	$-0.581084\pi$
$293$	−8.62665	−0.503974	−0.251987	+	0.967731i	$0.581084\pi$
$294$	51.1370	2.98237
$295$	29.6459	1.72605
$296$	−55.7588	−3.24092
$297$	25.8621	1.50067
$298$	43.8933	2.54267
$299$	−30.5825	−1.76863
$300$	52.9582	3.05754
$301$	2.41930	0.139446
$302$	−61.6349	−3.54669
$303$	21.8995	1.25809
$304$	−65.1490	−3.73655
$305$	35.6301	2.04018
$306$	−82.6300	−4.72365
$307$	−13.2763	−0.757719	−0.378859	−	0.925454i	$-0.623684\pi$
$307$	−13.2763	−0.757719	−0.378859	+	0.925454i	$0.623684\pi$
$308$	−13.1867	−0.751384
$309$	−6.79685	−0.386659
$310$	62.1581	3.53034
$311$	3.35797	0.190413	0.0952065	−	0.995458i	$-0.469649\pi$
$311$	3.35797	0.190413	0.0952065	+	0.995458i	$0.469649\pi$
$312$	−142.552	−8.07042
$313$	12.1649	0.687602	0.343801	−	0.939042i	$-0.388285\pi$
$313$	12.1649	0.687602	0.343801	+	0.939042i	$0.388285\pi$
$314$	44.2227	2.49563
$315$	−6.77120	−0.381514
$316$	91.7746	5.16272
$317$	30.2706	1.70017	0.850084	−	0.526647i	$-0.176551\pi$
$317$	30.2706	1.70017	0.850084	+	0.526647i	$0.176551\pi$
$318$	41.7292	2.34006
$319$	−2.32195	−0.130004
$320$	70.3979	3.93536
$321$	−25.3208	−1.41327
$322$	−7.01654	−0.391016
$323$	−30.3514	−1.68880
$324$	−1.90167	−0.105648
$325$	20.2600	1.12382
$326$	−47.2514	−2.61701
$327$	34.4430	1.90470
$328$	−46.8082	−2.58455
$329$	2.47450	0.136423
$330$	−113.734	−6.26086
$331$	−22.6711	−1.24612	−0.623058	−	0.782176i	$-0.714110\pi$
$331$	−22.6711	−1.24612	−0.623058	+	0.782176i	$0.714110\pi$
$332$	88.7332	4.86987
$333$	29.8055	1.63333
$334$	21.1390	1.15668
$335$	6.34828	0.346843
$336$	−18.3843	−1.00295
$337$	−15.5923	−0.849365	−0.424683	−	0.905342i	$-0.639614\pi$
$337$	−15.5923	−0.849365	−0.424683	+	0.905342i	$0.639614\pi$
$338$	−52.2237	−2.84060
$339$	−20.2364	−1.09909
$340$	99.0468	5.37156
$341$	−40.3783	−2.18661
$342$	61.9535	3.35006
$343$	6.63586	0.358303
$344$	45.0760	2.43034
$345$	−43.9807	−2.36784
$346$	−16.7106	−0.898366
$347$	0.107950	0.00579505	0.00289752	−	0.999996i	$-0.499078\pi$
$347$	0.107950	0.00579505	0.00289752	+	0.999996i	$0.499078\pi$
$348$	−6.70700	−0.359533
$349$	30.6172	1.63890	0.819451	−	0.573149i	$-0.194278\pi$
$349$	30.6172	1.63890	0.819451	+	0.573149i	$0.194278\pi$
$350$	4.64824	0.248459
$351$	28.5789	1.52543
$352$	−97.6573	−5.20515
$353$	−2.31548	−0.123240	−0.0616202	−	0.998100i	$-0.519627\pi$
$353$	−2.31548	−0.123240	−0.0616202	+	0.998100i	$0.519627\pi$
$354$	−76.5428	−4.06820
$355$	−14.9617	−0.794084
$356$	−79.6481	−4.22134
$357$	−8.56484	−0.453300
$358$	25.2292	1.33341
$359$	5.06691	0.267421	0.133711	−	0.991020i	$-0.457311\pi$
$359$	5.06691	0.267421	0.133711	+	0.991020i	$0.457311\pi$
$360$	−126.160	−6.64923
$361$	3.75661	0.197716
$362$	−21.4379	−1.12675
$363$	43.1603	2.26533
$364$	−14.5720	−0.763781
$365$	−36.0181	−1.88528
$366$	−91.9936	−4.80858
$367$	25.7631	1.34482	0.672410	−	0.740179i	$-0.265259\pi$
$367$	25.7631	1.34482	0.672410	+	0.740179i	$0.265259\pi$
$368$	−73.4859	−3.83072
$369$	25.0210	1.30254
$370$	−49.1601	−2.55571
$371$	2.66184	0.138196
$372$	−116.634	−6.04718
$373$	3.94686	0.204361	0.102180	−	0.994766i	$-0.467418\pi$
$373$	3.94686	0.204361	0.102180	+	0.994766i	$0.467418\pi$
$374$	−88.5327	−4.57792
$375$	−11.7321	−0.605840
$376$	46.1045	2.37766
$377$	−2.56587	−0.132149
$378$	6.55684	0.337247
$379$	17.9822	0.923686	0.461843	−	0.886962i	$-0.347188\pi$
$379$	17.9822	0.923686	0.461843	+	0.886962i	$0.347188\pi$
$380$	−74.2623	−3.80958
$381$	−20.8520	−1.06828
$382$	30.3484	1.55276
$383$	34.3858	1.75703	0.878516	−	0.477713i	$-0.158534\pi$
$383$	34.3858	1.75703	0.878516	+	0.477713i	$0.158534\pi$
$384$	−75.7007	−3.86308
$385$	−7.25491	−0.369744
$386$	−11.0317	−0.561499
$387$	−24.0951	−1.22482
$388$	53.6707	2.72472
$389$	−11.7444	−0.595464	−0.297732	−	0.954650i	$-0.596230\pi$
$389$	−11.7444	−0.595464	−0.297732	+	0.954650i	$0.596230\pi$
$390$	−125.682	−6.36415
$391$	−34.2354	−1.73136
$392$	60.7761	3.06966
$393$	−26.4737	−1.33542
$394$	−34.8499	−1.75571
$395$	50.4913	2.54049
$396$	131.334	6.59978
$397$	0.765484	0.0384185	0.0192093	−	0.999815i	$-0.493885\pi$
$397$	0.765484	0.0384185	0.0192093	+	0.999815i	$0.493885\pi$
$398$	8.45193	0.423657
$399$	6.42166	0.321485
$400$	48.6821	2.43410
$401$	−23.7833	−1.18768	−0.593842	−	0.804582i	$-0.702389\pi$
$401$	−23.7833	−1.18768	−0.593842	+	0.804582i	$0.702389\pi$
$402$	−16.3906	−0.817491
$403$	−44.6200	−2.22268
$404$	41.7097	2.07513
$405$	−1.04624	−0.0519879
$406$	−0.588686	−0.0292160
$407$	31.9347	1.58294
$408$	−159.579	−7.90034
$409$	19.3806	0.958307	0.479153	−	0.877731i	$-0.340944\pi$
$409$	19.3806	0.958307	0.479153	+	0.877731i	$0.340944\pi$
$410$	−41.2687	−2.03812
$411$	4.93403	0.243378
$412$	−12.9452	−0.637766
$413$	−4.88254	−0.240254
$414$	69.8816	3.43449
$415$	48.8181	2.39638
$416$	−107.916	−5.29103
$417$	−14.9074	−0.730021
$418$	66.3792	3.24671
$419$	2.60508	0.127266	0.0636332	−	0.997973i	$-0.479731\pi$
$419$	2.60508	0.127266	0.0636332	+	0.997973i	$0.479731\pi$
$420$	−20.9560	−1.02255
$421$	16.2663	0.792769	0.396385	−	0.918085i	$-0.370265\pi$
$421$	16.2663	0.792769	0.396385	+	0.918085i	$0.370265\pi$
$422$	15.0288	0.731590
$423$	−24.6449	−1.19828
$424$	49.5950	2.40855
$425$	22.6799	1.10014
$426$	38.6296	1.87161
$427$	−5.86812	−0.283978
$428$	−48.2258	−2.33108
$429$	81.6437	3.94179
$430$	39.7415	1.91651
$431$	8.14850	0.392500	0.196250	−	0.980554i	$-0.437124\pi$
$431$	8.14850	0.392500	0.196250	+	0.980554i	$0.437124\pi$
$432$	68.6713	3.30395
$433$	−25.4104	−1.22115	−0.610574	−	0.791959i	$-0.709061\pi$
$433$	−25.4104	−1.22115	−0.610574	+	0.791959i	$0.709061\pi$
$434$	−10.2371	−0.491399
$435$	−3.68997	−0.176921
$436$	65.5998	3.14166
$437$	25.6687	1.22790
$438$	92.9954	4.44349
$439$	22.8767	1.09184	0.545922	−	0.837836i	$-0.316179\pi$
$439$	22.8767	1.09184	0.545922	+	0.837836i	$0.316179\pi$
$440$	−135.172	−6.44410
$441$	−32.4875	−1.54702
$442$	−97.8331	−4.65345
$443$	−6.51523	−0.309548	−0.154774	−	0.987950i	$-0.549465\pi$
$443$	−6.51523	−0.309548	−0.154774	+	0.987950i	$0.549465\pi$
$444$	92.2442	4.37772
$445$	−43.8197	−2.07725
$446$	64.6451	3.06103
$447$	−45.3126	−2.14321
$448$	−11.5942	−0.547775
$449$	24.0494	1.13496	0.567480	−	0.823387i	$-0.307918\pi$
$449$	24.0494	1.13496	0.567480	+	0.823387i	$0.307918\pi$
$450$	−46.2943	−2.18234
$451$	26.8084	1.26236
$452$	−38.5421	−1.81287
$453$	63.6279	2.98950
$454$	1.03484	0.0485673
$455$	−8.01703	−0.375844
$456$	119.648	5.60301
$457$	16.8744	0.789352	0.394676	−	0.918820i	$-0.370857\pi$
$457$	16.8744	0.789352	0.394676	+	0.918820i	$0.370857\pi$
$458$	−29.8900	−1.39667
$459$	31.9924	1.49328
$460$	−83.7654	−3.90558
$461$	−34.2708	−1.59615	−0.798076	−	0.602557i	$-0.794149\pi$
$461$	−34.2708	−1.59615	−0.798076	+	0.602557i	$0.794149\pi$
$462$	18.7315	0.871467
$463$	−19.0613	−0.885856	−0.442928	−	0.896557i	$-0.646060\pi$
$463$	−19.0613	−0.885856	−0.442928	+	0.896557i	$0.646060\pi$
$464$	−6.16544	−0.286224
$465$	−64.1680	−2.97572
$466$	−30.5232	−1.41396
$467$	−0.345814	−0.0160024	−0.00800118	−	0.999968i	$-0.502547\pi$
$467$	−0.345814	−0.0160024	−0.00800118	+	0.999968i	$0.502547\pi$
$468$	145.131	6.70866
$469$	−1.04553	−0.0482782
$470$	40.6483	1.87497
$471$	−45.6527	−2.10357
$472$	−90.9708	−4.18727
$473$	−25.8163	−1.18704
$474$	−130.364	−5.98781
$475$	−17.0047	−0.780229
$476$	−16.3125	−0.747684
$477$	−26.5107	−1.21384
$478$	76.3245	3.49100
$479$	16.6285	0.759776	0.379888	−	0.925033i	$-0.375963\pi$
$479$	16.6285	0.759776	0.379888	+	0.925033i	$0.375963\pi$
$480$	−155.194	−7.08362
$481$	35.2894	1.60906
$482$	41.0511	1.86983
$483$	7.24343	0.329587
$484$	82.2028	3.73649
$485$	29.5278	1.34079
$486$	43.5125	1.97377
$487$	−26.0541	−1.18063	−0.590313	−	0.807175i	$-0.700996\pi$
$487$	−26.0541	−1.18063	−0.590313	+	0.807175i	$0.700996\pi$
$488$	−109.334	−4.94932
$489$	48.7793	2.20588
$490$	53.5836	2.42066
$491$	42.7722	1.93028	0.965140	−	0.261733i	$-0.0842939\pi$
$491$	42.7722	1.93028	0.965140	+	0.261733i	$0.0842939\pi$
$492$	77.4368	3.49112
$493$	−2.87234	−0.129364
$494$	73.3523	3.30028
$495$	72.2556	3.24765
$496$	−107.216	−4.81414
$497$	2.46412	0.110531
$498$	−126.044	−5.64815
$499$	23.8461	1.06750	0.533749	−	0.845643i	$-0.320783\pi$
$499$	23.8461	1.06750	0.533749	+	0.845643i	$0.320783\pi$
$500$	−22.3448	−0.999289
$501$	−21.8226	−0.974961
$502$	43.7276	1.95166
$503$	−40.5945	−1.81002	−0.905009	−	0.425392i	$-0.860136\pi$
$503$	−40.5945	−1.81002	−0.905009	+	0.425392i	$0.860136\pi$
$504$	20.7780	0.925526
$505$	22.9473	1.02114
$506$	74.8736	3.32854
$507$	53.9124	2.39434
$508$	−39.7147	−1.76205
$509$	−17.0548	−0.755943	−0.377971	−	0.925817i	$-0.623378\pi$
$509$	−17.0548	−0.755943	−0.377971	+	0.925817i	$0.623378\pi$
$510$	−140.694	−6.23002
$511$	5.93202	0.262417
$512$	−14.0208	−0.619636
$513$	−23.9870	−1.05905
$514$	−21.2120	−0.935620
$515$	−7.12204	−0.313834
$516$	−74.5712	−3.28282
$517$	−26.4054	−1.16131
$518$	8.09644	0.355737
$519$	17.2509	0.757232
$520$	−149.372	−6.55041
$521$	−23.2964	−1.02063	−0.510316	−	0.859987i	$-0.670472\pi$
$521$	−23.2964	−1.02063	−0.510316	+	0.859987i	$0.670472\pi$
$522$	5.86304	0.256618
$523$	−9.55893	−0.417983	−0.208991	−	0.977917i	$-0.567018\pi$
$523$	−9.55893	−0.417983	−0.208991	+	0.977917i	$0.567018\pi$
$524$	−50.4216	−2.20268
$525$	−4.79854	−0.209425
$526$	52.2840	2.27969
$527$	−49.9496	−2.17584
$528$	196.179	8.53760
$529$	5.95346	0.258846
$530$	43.7257	1.89932
$531$	48.6279	2.11027
$532$	12.2307	0.530266
$533$	29.6246	1.28318
$534$	113.138	4.89598
$535$	−26.5323	−1.14709
$536$	−19.4802	−0.841417
$537$	−26.0451	−1.12393
$538$	18.7671	0.809108
$539$	−34.8082	−1.49930
$540$	78.2774	3.36852
$541$	−31.1461	−1.33908	−0.669538	−	0.742778i	$-0.733508\pi$
$541$	−31.1461	−1.33908	−0.669538	+	0.742778i	$0.733508\pi$
$542$	40.5834	1.74321
$543$	22.1311	0.949735
$544$	−120.806	−5.17952
$545$	36.0908	1.54596
$546$	20.6992	0.885845
$547$	−29.8086	−1.27452	−0.637261	−	0.770648i	$-0.719933\pi$
$547$	−29.8086	−1.27452	−0.637261	+	0.770648i	$0.719933\pi$
$548$	9.39732	0.401434
$549$	58.4438	2.49432
$550$	−49.6014	−2.11501
$551$	2.15360	0.0917463
$552$	134.959	5.74422
$553$	−8.31569	−0.353619
$554$	−47.4564	−2.01623
$555$	50.7497	2.15421
$556$	−28.3926	−1.20412
$557$	12.7871	0.541809	0.270904	−	0.962606i	$-0.412677\pi$
$557$	12.7871	0.541809	0.270904	+	0.962606i	$0.412677\pi$
$558$	101.957	4.31620
$559$	−28.5284	−1.20662
$560$	−19.2639	−0.814048
$561$	91.3955	3.85872
$562$	38.6935	1.63219
$563$	−29.3573	−1.23726	−0.618632	−	0.785681i	$-0.712313\pi$
$563$	−29.3573	−1.23726	−0.618632	+	0.785681i	$0.712313\pi$
$564$	−76.2727	−3.21166
$565$	−21.2046	−0.892082
$566$	58.4760	2.45793
$567$	0.172310	0.00723636
$568$	45.9112	1.92639
$569$	13.0487	0.547028	0.273514	−	0.961868i	$-0.411814\pi$
$569$	13.0487	0.547028	0.273514	+	0.961868i	$0.411814\pi$
$570$	105.488	4.41840
$571$	−21.1931	−0.886905	−0.443453	−	0.896298i	$-0.646247\pi$
$571$	−21.1931	−0.886905	−0.443453	+	0.896298i	$0.646247\pi$
$572$	155.498	6.50170
$573$	−31.3297	−1.30882
$574$	6.79676	0.283691
$575$	−19.1808	−0.799893
$576$	115.473	4.81138
$577$	−11.2194	−0.467071	−0.233536	−	0.972348i	$-0.575030\pi$
$577$	−11.2194	−0.467071	−0.233536	+	0.972348i	$0.575030\pi$
$578$	−63.5263	−2.64235
$579$	11.3884	0.473287
$580$	−7.02789	−0.291817
$581$	−8.04011	−0.333560
$582$	−76.2381	−3.16017
$583$	−28.4045	−1.17639
$584$	110.525	4.57354
$585$	79.8460	3.30123
$586$	23.3388	0.964118
$587$	−46.5934	−1.92312	−0.961558	−	0.274600i	$-0.911454\pi$
$587$	−46.5934	−1.92312	−0.961558	+	0.274600i	$0.911454\pi$
$588$	−100.544	−4.14639
$589$	37.4507	1.54313
$590$	−80.2049	−3.30198
$591$	35.9768	1.47989
$592$	84.7959	3.48509
$593$	−26.8765	−1.10368	−0.551842	−	0.833949i	$-0.686075\pi$
$593$	−26.8765	−1.10368	−0.551842	+	0.833949i	$0.686075\pi$
$594$	−69.9681	−2.87083
$595$	−8.97462	−0.367924
$596$	−86.3021	−3.53507
$597$	−8.72523	−0.357100
$598$	82.7390	3.38345
$599$	33.0502	1.35039	0.675197	−	0.737637i	$-0.264059\pi$
$599$	33.0502	1.35039	0.675197	+	0.737637i	$0.264059\pi$
$600$	−89.4058	−3.64998
$601$	18.3722	0.749419	0.374710	−	0.927142i	$-0.377742\pi$
$601$	18.3722	0.749419	0.374710	+	0.927142i	$0.377742\pi$
$602$	−6.54525	−0.266764
$603$	10.4130	0.424051
$604$	121.185	4.93096
$605$	45.2252	1.83867
$606$	−59.2477	−2.40677
$607$	23.9507	0.972128	0.486064	−	0.873923i	$-0.338432\pi$
$607$	23.9507	0.972128	0.486064	+	0.873923i	$0.338432\pi$
$608$	90.5768	3.67337
$609$	0.607721	0.0246261
$610$	−96.3950	−3.90292
$611$	−29.1793	−1.18047
$612$	162.466	6.56728
$613$	−15.2917	−0.617625	−0.308812	−	0.951123i	$-0.599932\pi$
$613$	−15.2917	−0.617625	−0.308812	+	0.951123i	$0.599932\pi$
$614$	35.9182	1.44954
$615$	42.6032	1.71793
$616$	22.2623	0.896973
$617$	−6.02465	−0.242543	−0.121272	−	0.992619i	$-0.538697\pi$
$617$	−6.02465	−0.242543	−0.121272	+	0.992619i	$0.538697\pi$
$618$	18.3884	0.739691
$619$	43.9807	1.76773	0.883866	−	0.467740i	$-0.154931\pi$
$619$	43.9807	1.76773	0.883866	+	0.467740i	$0.154931\pi$
$620$	−122.214	−4.90823
$621$	−27.0565	−1.08574
$622$	−9.08476	−0.364266
$623$	7.21691	0.289139
$624$	216.788	8.67846
$625$	−30.1165	−1.20466
$626$	−32.9114	−1.31540
$627$	−68.5256	−2.73665
$628$	−86.9498	−3.46968
$629$	39.5045	1.57515
$630$	18.3190	0.729848
$631$	41.7561	1.66229	0.831143	−	0.556059i	$-0.187687\pi$
$631$	41.7561	1.66229	0.831143	+	0.556059i	$0.187687\pi$
$632$	−154.937	−6.16306
$633$	−15.5148	−0.616657
$634$	−81.8952	−3.25247
$635$	−21.8497	−0.867079
$636$	−82.0472	−3.25338
$637$	−38.4648	−1.52403
$638$	6.28187	0.248702
$639$	−24.5415	−0.970848
$640$	−79.3225	−3.13550
$641$	−31.8935	−1.25972	−0.629858	−	0.776710i	$-0.716887\pi$
$641$	−31.8935	−1.25972	−0.629858	+	0.776710i	$0.716887\pi$
$642$	68.5038	2.70363
$643$	4.65306	0.183499	0.0917494	−	0.995782i	$-0.470754\pi$
$643$	4.65306	0.183499	0.0917494	+	0.995782i	$0.470754\pi$
$644$	13.7958	0.543630
$645$	−41.0266	−1.61542
$646$	82.1138	3.23072
$647$	−32.3084	−1.27018	−0.635088	−	0.772440i	$-0.719036\pi$
$647$	−32.3084	−1.27018	−0.635088	+	0.772440i	$0.719036\pi$
$648$	3.21046	0.126119
$649$	52.1016	2.04517
$650$	−54.8120	−2.14990
$651$	10.5682	0.414199
$652$	92.9047	3.63843
$653$	−5.53670	−0.216668	−0.108334	−	0.994115i	$-0.534552\pi$
$653$	−5.53670	−0.216668	−0.108334	+	0.994115i	$0.534552\pi$
$654$	−93.1831	−3.64375
$655$	−27.7403	−1.08390
$656$	71.1841	2.77927
$657$	−59.0802	−2.30494
$658$	−6.69459	−0.260982
$659$	−12.1645	−0.473863	−0.236931	−	0.971526i	$-0.576142\pi$
$659$	−12.1645	−0.473863	−0.236931	+	0.971526i	$0.576142\pi$
$660$	223.622	8.70446
$661$	0.191320	0.00744147	0.00372074	−	0.999993i	$-0.498816\pi$
$661$	0.191320	0.00744147	0.00372074	+	0.999993i	$0.498816\pi$
$662$	61.3351	2.38386
$663$	100.997	3.92238
$664$	−149.802	−5.81346
$665$	6.72890	0.260936
$666$	−80.6368	−3.12461
$667$	2.42919	0.0940585
$668$	−41.5632	−1.60813
$669$	−66.7355	−2.58014
$670$	−17.1748	−0.663522
$671$	62.6188	2.41737
$672$	25.5598	0.985990
$673$	−18.4358	−0.710648	−0.355324	−	0.934743i	$-0.615630\pi$
$673$	−18.4358	−0.710648	−0.355324	+	0.934743i	$0.615630\pi$
$674$	42.1839	1.62486
$675$	17.9241	0.689899
$676$	102.681	3.94928
$677$	19.6307	0.754469	0.377234	−	0.926118i	$-0.376875\pi$
$677$	19.6307	0.754469	0.377234	+	0.926118i	$0.376875\pi$
$678$	54.7481	2.10259
$679$	−4.86310	−0.186629
$680$	−167.214	−6.41236
$681$	−1.06830	−0.0409373
$682$	109.241	4.18304
$683$	4.18485	0.160129	0.0800644	−	0.996790i	$-0.474487\pi$
$683$	4.18485	0.160129	0.0800644	+	0.996790i	$0.474487\pi$
$684$	−121.812	−4.65759
$685$	5.17009	0.197539
$686$	−17.9529	−0.685444
$687$	30.8565	1.17725
$688$	−68.5499	−2.61344
$689$	−31.3884	−1.19580
$690$	118.987	4.52976
$691$	−3.04084	−0.115679	−0.0578395	−	0.998326i	$-0.518421\pi$
$691$	−3.04084	−0.115679	−0.0578395	+	0.998326i	$0.518421\pi$
$692$	32.8560	1.24900
$693$	−11.9002	−0.452050
$694$	−0.292051	−0.0110861
$695$	−15.6207	−0.592526
$696$	11.3230	0.429197
$697$	33.1631	1.25614
$698$	−82.8329	−3.13527
$699$	31.5102	1.19183
$700$	−9.13927	−0.345432
$701$	48.1599	1.81897	0.909487	−	0.415732i	$-0.136474\pi$
$701$	48.1599	1.81897	0.909487	+	0.415732i	$0.136474\pi$
$702$	−77.3182	−2.91819
$703$	−29.6193	−1.11711
$704$	123.722	4.66294
$705$	−41.9627	−1.58041
$706$	6.26437	0.235763
$707$	−3.77931	−0.142136
$708$	150.497	5.65602
$709$	40.1640	1.50839	0.754195	−	0.656651i	$-0.228027\pi$
$709$	40.1640	1.50839	0.754195	+	0.656651i	$0.228027\pi$
$710$	40.4778	1.51911
$711$	82.8205	3.10601
$712$	134.464	5.03927
$713$	42.2432	1.58202
$714$	23.1716	0.867176
$715$	85.5499	3.19938
$716$	−49.6052	−1.85384
$717$	−78.7925	−2.94256
$718$	−13.7082	−0.511585
$719$	−8.63137	−0.321896	−0.160948	−	0.986963i	$-0.551455\pi$
$719$	−8.63137	−0.321896	−0.160948	+	0.986963i	$0.551455\pi$
$720$	191.860	7.15019
$721$	1.17297	0.0436836
$722$	−10.1632	−0.378237
$723$	−42.3786	−1.57608
$724$	42.1507	1.56652
$725$	−1.60926	−0.0597664
$726$	−116.767	−4.33364
$727$	−13.2350	−0.490857	−0.245429	−	0.969415i	$-0.578929\pi$
$727$	−13.2350	−0.490857	−0.245429	+	0.969415i	$0.578929\pi$
$728$	24.6009	0.911771
$729$	−43.8470	−1.62396
$730$	97.4447	3.60659
$731$	−31.9359	−1.18119
$732$	180.876	6.68537
$733$	32.8416	1.21303	0.606516	−	0.795072i	$-0.292567\pi$
$733$	32.8416	1.21303	0.606516	+	0.795072i	$0.292567\pi$
$734$	−69.7002	−2.57268
$735$	−55.3162	−2.04037
$736$	102.168	3.76595
$737$	11.1569	0.410969
$738$	−67.6927	−2.49180
$739$	53.8628	1.98137	0.990687	−	0.136160i	$-0.0434761\pi$
$739$	53.8628	1.98137	0.990687	+	0.136160i	$0.0434761\pi$
$740$	96.6576	3.55320
$741$	−75.7242	−2.78180
$742$	−7.20143	−0.264373
$743$	−3.45311	−0.126682	−0.0633412	−	0.997992i	$-0.520176\pi$
$743$	−3.45311	−0.126682	−0.0633412	+	0.997992i	$0.520176\pi$
$744$	196.905	7.21888
$745$	−47.4805	−1.73955
$746$	−10.6780	−0.390948
$747$	80.0759	2.92982
$748$	174.071	6.36468
$749$	4.36974	0.159667
$750$	31.7403	1.15899
$751$	20.1223	0.734273	0.367136	−	0.930167i	$-0.380338\pi$
$751$	20.1223	0.734273	0.367136	+	0.930167i	$0.380338\pi$
$752$	−70.1140	−2.55680
$753$	−45.1416	−1.64505
$754$	6.94178	0.252805
$755$	66.6721	2.42645
$756$	−12.8919	−0.468875
$757$	22.4047	0.814311	0.407156	−	0.913359i	$-0.366521\pi$
$757$	22.4047	0.814311	0.407156	+	0.913359i	$0.366521\pi$
$758$	−48.6498	−1.76704
$759$	−77.2947	−2.80562
$760$	125.372	4.54772
$761$	4.38084	0.158805	0.0794027	−	0.996843i	$-0.474699\pi$
$761$	4.38084	0.158805	0.0794027	+	0.996843i	$0.474699\pi$
$762$	56.4138	2.04366
$763$	−5.94400	−0.215187
$764$	−59.6704	−2.15880
$765$	89.3832	3.23165
$766$	−93.0285	−3.36125
$767$	57.5749	2.07891
$768$	70.4361	2.54164
$769$	9.63998	0.347626	0.173813	−	0.984779i	$-0.444391\pi$
$769$	9.63998	0.347626	0.173813	+	0.984779i	$0.444391\pi$
$770$	19.6277	0.707332
$771$	21.8979	0.788633
$772$	21.6903	0.780652
$773$	−16.8216	−0.605032	−0.302516	−	0.953144i	$-0.597826\pi$
$773$	−16.8216	−0.605032	−0.302516	+	0.953144i	$0.597826\pi$
$774$	65.1877	2.34312
$775$	−27.9848	−1.00524
$776$	−90.6086	−3.25266
$777$	−8.35824	−0.299850
$778$	31.7736	1.13914
$779$	−24.8647	−0.890870
$780$	247.113	8.84807
$781$	−26.2947	−0.940897
$782$	92.6217	3.31215
$783$	−2.27003	−0.0811244
$784$	−92.4260	−3.30093
$785$	−47.8369	−1.70737
$786$	71.6228	2.55470
$787$	−10.1340	−0.361238	−0.180619	−	0.983553i	$-0.557810\pi$
$787$	−10.1340	−0.361238	−0.180619	+	0.983553i	$0.557810\pi$
$788$	68.5211	2.44096
$789$	−53.9746	−1.92155
$790$	−136.601	−4.86004
$791$	3.49229	0.124172
$792$	−221.722	−7.87856
$793$	69.1969	2.45725
$794$	−2.07097	−0.0734958
$795$	−45.1397	−1.60094
$796$	−16.6180	−0.589010
$797$	33.0360	1.17020	0.585098	−	0.810963i	$-0.301056\pi$
$797$	33.0360	1.17020	0.585098	+	0.810963i	$0.301056\pi$
$798$	−17.3734	−0.615011
$799$	−32.6646	−1.15559
$800$	−67.6829	−2.39295
$801$	−71.8771	−2.53965
$802$	64.3443	2.27207
$803$	−63.3006	−2.23383
$804$	32.2270	1.13656
$805$	7.58998	0.267512
$806$	120.716	4.25205
$807$	−19.3740	−0.681996
$808$	−70.4156	−2.47721
$809$	−47.7609	−1.67918	−0.839591	−	0.543218i	$-0.817206\pi$
$809$	−47.7609	−1.67918	−0.839591	+	0.543218i	$0.817206\pi$
$810$	2.83052	0.0994545
$811$	18.0650	0.634348	0.317174	−	0.948367i	$-0.397266\pi$
$811$	18.0650	0.634348	0.317174	+	0.948367i	$0.397266\pi$
$812$	1.15746	0.0406189
$813$	−41.8957	−1.46935
$814$	−86.3972	−3.02822
$815$	51.1131	1.79041
$816$	242.682	8.49556
$817$	23.9446	0.837715
$818$	−52.4328	−1.83327
$819$	−13.1503	−0.459508
$820$	81.1417	2.83359
$821$	−6.41997	−0.224059	−0.112029	−	0.993705i	$-0.535735\pi$
$821$	−6.41997	−0.224059	−0.112029	+	0.993705i	$0.535735\pi$
$822$	−13.3487	−0.465589
$823$	17.2852	0.602525	0.301263	−	0.953541i	$-0.402592\pi$
$823$	17.2852	0.602525	0.301263	+	0.953541i	$0.402592\pi$
$824$	21.8546	0.761340
$825$	51.2053	1.78274
$826$	13.2094	0.459613
$827$	14.7930	0.514402	0.257201	−	0.966358i	$-0.417200\pi$
$827$	14.7930	0.514402	0.257201	+	0.966358i	$0.417200\pi$
$828$	−137.400	−4.77497
$829$	40.9601	1.42260	0.711302	−	0.702887i	$-0.248106\pi$
$829$	40.9601	1.42260	0.711302	+	0.702887i	$0.248106\pi$
$830$	−132.074	−4.58436
$831$	48.9910	1.69948
$832$	136.719	4.73987
$833$	−43.0592	−1.49191
$834$	40.3311	1.39655
$835$	−22.8667	−0.791334
$836$	−130.513	−4.51390
$837$	−39.4755	−1.36447
$838$	−7.04787	−0.243465
$839$	−14.7268	−0.508426	−0.254213	−	0.967148i	$-0.581816\pi$
$839$	−14.7268	−0.508426	−0.254213	+	0.967148i	$0.581816\pi$
$840$	35.3786	1.22068
$841$	−28.7962	−0.992972
$842$	−44.0073	−1.51659
$843$	−39.9447	−1.37577
$844$	−29.5493	−1.01713
$845$	56.4918	1.94338
$846$	66.6751	2.29234
$847$	−7.44839	−0.255930
$848$	−75.4223	−2.59001
$849$	−60.3669	−2.07178
$850$	−61.3589	−2.10459
$851$	−33.4096	−1.14527
$852$	−75.9528	−2.60210
$853$	−16.0996	−0.551240	−0.275620	−	0.961267i	$-0.588883\pi$
$853$	−16.0996	−0.551240	−0.275620	+	0.961267i	$0.588883\pi$
$854$	15.8758	0.543259
$855$	−67.0168	−2.29193
$856$	81.4164	2.78276
$857$	−19.9388	−0.681097	−0.340549	−	0.940227i	$-0.610613\pi$
$857$	−19.9388	−0.681097	−0.340549	+	0.940227i	$0.610613\pi$
$858$	−220.882	−7.54077
$859$	26.6936	0.910775	0.455388	−	0.890293i	$-0.349501\pi$
$859$	26.6936	0.910775	0.455388	+	0.890293i	$0.349501\pi$
$860$	−78.1390	−2.66452
$861$	−7.01654	−0.239123
$862$	−22.0452	−0.750863
$863$	−0.242152	−0.00824294	−0.00412147	−	0.999992i	$-0.501312\pi$
$863$	−0.242152	−0.00824294	−0.00412147	+	0.999992i	$0.501312\pi$
$864$	−95.4740	−3.24809
$865$	18.0763	0.614612
$866$	68.7463	2.33609
$867$	65.5805	2.22723
$868$	20.1281	0.683191
$869$	88.7368	3.01019
$870$	9.98297	0.338454
$871$	12.3289	0.417749
$872$	−110.748	−3.75039
$873$	48.4343	1.63925
$874$	−69.4450	−2.34901
$875$	2.02466	0.0684460
$876$	−182.846	−6.17778
$877$	14.4199	0.486925	0.243463	−	0.969910i	$-0.421717\pi$
$877$	14.4199	0.486925	0.243463	+	0.969910i	$0.421717\pi$
$878$	−61.8913	−2.08873
$879$	−24.0935	−0.812654
$880$	205.565	6.92960
$881$	−19.2838	−0.649688	−0.324844	−	0.945768i	$-0.605312\pi$
$881$	−19.2838	−0.649688	−0.324844	+	0.945768i	$0.605312\pi$
$882$	87.8927	2.95950
$883$	−21.4926	−0.723284	−0.361642	−	0.932317i	$-0.617784\pi$
$883$	−21.4926	−0.723284	−0.361642	+	0.932317i	$0.617784\pi$
$884$	192.357	6.46968
$885$	82.7984	2.78324
$886$	17.6265	0.592174
$887$	−49.5775	−1.66465	−0.832324	−	0.554289i	$-0.812990\pi$
$887$	−49.5775	−1.66465	−0.832324	+	0.554289i	$0.812990\pi$
$888$	−155.730	−5.22595
$889$	3.59854	0.120691
$890$	118.551	3.97385
$891$	−1.83873	−0.0615996
$892$	−127.104	−4.25575
$893$	24.4909	0.819557
$894$	122.590	4.10003
$895$	−27.2912	−0.912243
$896$	13.0641	0.436439
$897$	−85.4145	−2.85191
$898$	−65.0640	−2.17121
$899$	3.54419	0.118205
$900$	91.0230	3.03410
$901$	−35.1376	−1.17060
$902$	−72.5283	−2.41493
$903$	6.75689	0.224855
$904$	65.0679	2.16413
$905$	23.1899	0.770859
$906$	−172.141	−5.71900
$907$	26.5304	0.880927	0.440464	−	0.897770i	$-0.354814\pi$
$907$	26.5304	0.880927	0.440464	+	0.897770i	$0.354814\pi$
$908$	−2.03467	−0.0675231
$909$	37.6402	1.24845
$910$	21.6896	0.719002
$911$	52.6891	1.74567	0.872834	−	0.488017i	$-0.162280\pi$
$911$	52.6891	1.74567	0.872834	+	0.488017i	$0.162280\pi$
$912$	−181.956	−6.02515
$913$	85.7961	2.83944
$914$	−45.6526	−1.51005
$915$	99.5120	3.28977
$916$	58.7692	1.94179
$917$	4.56870	0.150872
$918$	−86.5534	−2.85669
$919$	−38.0234	−1.25428	−0.627138	−	0.778908i	$-0.715774\pi$
$919$	−38.0234	−1.25428	−0.627138	+	0.778908i	$0.715774\pi$
$920$	141.416	4.66233
$921$	−37.0796	−1.22181
$922$	92.7175	3.05349
$923$	−29.0569	−0.956419
$924$	−36.8295	−1.21160
$925$	22.1328	0.727722
$926$	51.5692	1.69467
$927$	−11.6822	−0.383694
$928$	8.57184	0.281384
$929$	−7.47431	−0.245224	−0.122612	−	0.992455i	$-0.539127\pi$
$929$	−7.47431	−0.245224	−0.122612	+	0.992455i	$0.539127\pi$
$930$	173.602	5.69264
$931$	32.2845	1.05808
$932$	60.0142	1.96583
$933$	9.37852	0.307039
$934$	0.935577	0.0306130
$935$	95.7683	3.13196
$936$	−245.014	−8.00854
$937$	−11.3555	−0.370967	−0.185484	−	0.982647i	$-0.559385\pi$
$937$	−11.3555	−0.370967	−0.185484	+	0.982647i	$0.559385\pi$
$938$	2.82862	0.0923576
$939$	33.9756	1.10875
$940$	−79.9219	−2.60676
$941$	−22.1607	−0.722417	−0.361208	−	0.932485i	$-0.617636\pi$
$941$	−22.1607	−0.722417	−0.361208	+	0.932485i	$0.617636\pi$
$942$	123.510	4.02418
$943$	−28.0466	−0.913322
$944$	138.345	4.50274
$945$	−7.09271	−0.230726
$946$	69.8444	2.27084
$947$	43.4393	1.41159	0.705793	−	0.708418i	$-0.250591\pi$
$947$	43.4393	1.41159	0.705793	+	0.708418i	$0.250591\pi$
$948$	256.319	8.32484
$949$	−69.9504	−2.27069
$950$	46.0051	1.49260
$951$	84.5433	2.74151
$952$	27.5394	0.892556
$953$	41.3974	1.34099	0.670496	−	0.741913i	$-0.266081\pi$
$953$	41.3974	1.34099	0.670496	+	0.741913i	$0.266081\pi$
$954$	71.7230	2.32212
$955$	−32.8287	−1.06231
$956$	−150.068	−4.85354
$957$	−6.48500	−0.209630
$958$	−44.9873	−1.45347
$959$	−0.851491	−0.0274961
$960$	196.615	6.34573
$961$	30.6329	0.988157
$962$	−95.4732	−3.07818
$963$	−43.5206	−1.40243
$964$	−80.7139	−2.59962
$965$	11.9333	0.384146
$966$	−19.5966	−0.630510
$967$	2.81892	0.0906504	0.0453252	−	0.998972i	$-0.485568\pi$
$967$	2.81892	0.0906504	0.0453252	+	0.998972i	$0.485568\pi$
$968$	−138.777	−4.46048
$969$	−84.7690	−2.72317
$970$	−79.8856	−2.56497
$971$	−9.46357	−0.303700	−0.151850	−	0.988404i	$-0.548523\pi$
$971$	−9.46357	−0.303700	−0.151850	+	0.988404i	$0.548523\pi$
$972$	−85.5535	−2.74413
$973$	2.57265	0.0824755
$974$	70.4877	2.25857
$975$	56.5844	1.81215
$976$	166.271	5.32221
$977$	−25.8232	−0.826158	−0.413079	−	0.910695i	$-0.635547\pi$
$977$	−25.8232	−0.826158	−0.413079	+	0.910695i	$0.635547\pi$
$978$	−131.969	−4.21991
$979$	−77.0117	−2.46130
$980$	−105.355	−3.36544
$981$	59.1995	1.89009
$982$	−115.717	−3.69269
$983$	45.2714	1.44393	0.721967	−	0.691927i	$-0.243238\pi$
$983$	45.2714	1.44393	0.721967	+	0.691927i	$0.243238\pi$
$984$	−130.731	−4.16756
$985$	37.6981	1.20116
$986$	7.77093	0.247477
$987$	6.91106	0.219982
$988$	−144.224	−4.58837
$989$	27.0087	0.858827
$990$	−195.483	−6.21285
$991$	−49.6818	−1.57819	−0.789097	−	0.614269i	$-0.789451\pi$
$991$	−49.6818	−1.57819	−0.789097	+	0.614269i	$0.789451\pi$
$992$	149.063	4.73275
$993$	−63.3185	−2.00935
$994$	−6.66651	−0.211449
$995$	−9.14268	−0.289843
$996$	247.824	7.85262
$997$	−7.19279	−0.227798	−0.113899	−	0.993492i	$-0.536334\pi$
$997$	−7.19279	−0.227798	−0.113899	+	0.993492i	$0.536334\pi$
$998$	−64.5140	−2.04216
$999$	31.2207	0.987780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.7	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.70543 q^{2} +2.79292 q^{3} +5.31937 q^{4} +2.92654 q^{5} -7.55605 q^{6} -0.481988 q^{7} -8.98033 q^{8} +4.80038 q^{9} +O(q^{10})\)	\(q-2.70543 q^{2} +2.79292 q^{3} +5.31937 q^{4} +2.92654 q^{5} -7.55605 q^{6} -0.481988 q^{7} -8.98033 q^{8} +4.80038 q^{9} -7.91756 q^{10} +5.14330 q^{11} +14.8566 q^{12} +5.68360 q^{13} +1.30399 q^{14} +8.17358 q^{15} +13.6569 q^{16} +6.36247 q^{17} -12.9871 q^{18} -4.77039 q^{19} +15.5673 q^{20} -1.34615 q^{21} -13.9148 q^{22} -5.38084 q^{23} -25.0813 q^{24} +3.56464 q^{25} -15.3766 q^{26} +5.02831 q^{27} -2.56387 q^{28} -0.451451 q^{29} -22.1131 q^{30} -7.85066 q^{31} -18.9873 q^{32} +14.3648 q^{33} -17.2132 q^{34} -1.41056 q^{35} +25.5350 q^{36} +6.20899 q^{37} +12.9060 q^{38} +15.8738 q^{39} -26.2813 q^{40} +5.21230 q^{41} +3.64192 q^{42} -5.01942 q^{43} +27.3591 q^{44} +14.0485 q^{45} +14.5575 q^{46} -5.13394 q^{47} +38.1427 q^{48} -6.76769 q^{49} -9.64389 q^{50} +17.7698 q^{51} +30.2332 q^{52} -5.52263 q^{53} -13.6037 q^{54} +15.0521 q^{55} +4.32841 q^{56} -13.3233 q^{57} +1.22137 q^{58} +10.1300 q^{59} +43.4783 q^{60} +12.1748 q^{61} +21.2394 q^{62} -2.31372 q^{63} +24.0550 q^{64} +16.6333 q^{65} -38.8630 q^{66} +2.16921 q^{67} +33.8443 q^{68} -15.0282 q^{69} +3.81617 q^{70} -5.11241 q^{71} -43.1090 q^{72} -12.3074 q^{73} -16.7980 q^{74} +9.95573 q^{75} -25.3755 q^{76} -2.47900 q^{77} -42.9455 q^{78} +17.2529 q^{79} +39.9676 q^{80} -0.357500 q^{81} -14.1015 q^{82} +16.6812 q^{83} -7.16067 q^{84} +18.6200 q^{85} +13.5797 q^{86} -1.26086 q^{87} -46.1885 q^{88} -14.9732 q^{89} -38.0073 q^{90} -2.73942 q^{91} -28.6227 q^{92} -21.9262 q^{93} +13.8895 q^{94} -13.9607 q^{95} -53.0299 q^{96} +10.0897 q^{97} +18.3095 q^{98} +24.6898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 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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