LMFDB - Embedded newform 6011.2.a.f.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.68457 q^{2} +2.63672 q^{3} +5.20694 q^{4} +0.421516 q^{5} -7.07847 q^{6} -3.33953 q^{7} -8.60926 q^{8} +3.95229 q^{9} +O(q^{10})$	\(q-2.68457 q^{2} +2.63672 q^{3} +5.20694 q^{4} +0.421516 q^{5} -7.07847 q^{6} -3.33953 q^{7} -8.60926 q^{8} +3.95229 q^{9} -1.13159 q^{10} -0.193213 q^{11} +13.7292 q^{12} +2.52862 q^{13} +8.96522 q^{14} +1.11142 q^{15} +12.6983 q^{16} -1.31056 q^{17} -10.6102 q^{18} +6.30580 q^{19} +2.19481 q^{20} -8.80541 q^{21} +0.518695 q^{22} -4.04455 q^{23} -22.7002 q^{24} -4.82232 q^{25} -6.78827 q^{26} +2.51093 q^{27} -17.3887 q^{28} +3.09910 q^{29} -2.98369 q^{30} +9.79736 q^{31} -16.8711 q^{32} -0.509449 q^{33} +3.51830 q^{34} -1.40767 q^{35} +20.5793 q^{36} -7.46223 q^{37} -16.9284 q^{38} +6.66727 q^{39} -3.62894 q^{40} +4.68719 q^{41} +23.6388 q^{42} +3.11988 q^{43} -1.00605 q^{44} +1.66596 q^{45} +10.8579 q^{46} -8.81047 q^{47} +33.4819 q^{48} +4.15246 q^{49} +12.9459 q^{50} -3.45558 q^{51} +13.1664 q^{52} +4.49344 q^{53} -6.74078 q^{54} -0.0814425 q^{55} +28.7509 q^{56} +16.6266 q^{57} -8.31977 q^{58} -5.34136 q^{59} +5.78709 q^{60} +14.2168 q^{61} -26.3017 q^{62} -13.1988 q^{63} +19.8950 q^{64} +1.06585 q^{65} +1.36765 q^{66} -0.977568 q^{67} -6.82401 q^{68} -10.6643 q^{69} +3.77898 q^{70} +15.2855 q^{71} -34.0263 q^{72} +14.1383 q^{73} +20.0329 q^{74} -12.7151 q^{75} +32.8339 q^{76} +0.645241 q^{77} -17.8988 q^{78} -4.25907 q^{79} +5.35255 q^{80} -5.23626 q^{81} -12.5831 q^{82} -1.91091 q^{83} -45.8492 q^{84} -0.552423 q^{85} -8.37554 q^{86} +8.17146 q^{87} +1.66342 q^{88} +14.2828 q^{89} -4.47238 q^{90} -8.44441 q^{91} -21.0597 q^{92} +25.8329 q^{93} +23.6524 q^{94} +2.65799 q^{95} -44.4843 q^{96} -7.16853 q^{97} -11.1476 q^{98} -0.763635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.68457	−1.89828	−0.949140	−	0.314854i	$-0.898045\pi$
$2$	−2.68457	−1.89828	−0.949140	+	0.314854i	$0.898045\pi$
$3$	2.63672	1.52231	0.761156	−	0.648569i	$-0.224632\pi$
$3$	2.63672	1.52231	0.761156	+	0.648569i	$0.224632\pi$
$4$	5.20694	2.60347
$5$	0.421516	0.188508	0.0942539	−	0.995548i	$-0.469953\pi$
$5$	0.421516	0.188508	0.0942539	+	0.995548i	$0.469953\pi$
$6$	−7.07847	−2.88977
$7$	−3.33953	−1.26222	−0.631112	−	0.775692i	$-0.717401\pi$
$7$	−3.33953	−1.26222	−0.631112	+	0.775692i	$0.717401\pi$
$8$	−8.60926	−3.04383
$9$	3.95229	1.31743
$10$	−1.13159	−0.357841
$11$	−0.193213	−0.0582560	−0.0291280	−	0.999576i	$-0.509273\pi$
$11$	−0.193213	−0.0582560	−0.0291280	+	0.999576i	$0.509273\pi$
$12$	13.7292	3.96329
$13$	2.52862	0.701313	0.350657	−	0.936504i	$-0.385958\pi$
$13$	2.52862	0.701313	0.350657	+	0.936504i	$0.385958\pi$
$14$	8.96522	2.39605
$15$	1.11142	0.286967
$16$	12.6983	3.17458
$17$	−1.31056	−0.317858	−0.158929	−	0.987290i	$-0.550804\pi$
$17$	−1.31056	−0.317858	−0.158929	+	0.987290i	$0.550804\pi$
$18$	−10.6102	−2.50085
$19$	6.30580	1.44665	0.723324	−	0.690508i	$-0.242613\pi$
$19$	6.30580	1.44665	0.723324	+	0.690508i	$0.242613\pi$
$20$	2.19481	0.490774
$21$	−8.80541	−1.92150
$22$	0.518695	0.110586
$23$	−4.04455	−0.843347	−0.421673	−	0.906748i	$-0.638557\pi$
$23$	−4.04455	−0.843347	−0.421673	+	0.906748i	$0.638557\pi$
$24$	−22.7002	−4.63366
$25$	−4.82232	−0.964465
$26$	−6.78827	−1.33129
$27$	2.51093	0.483229
$28$	−17.3887	−3.28616
$29$	3.09910	0.575489	0.287744	−	0.957707i	$-0.407095\pi$
$29$	3.09910	0.575489	0.287744	+	0.957707i	$0.407095\pi$
$30$	−2.98369	−0.544745
$31$	9.79736	1.75966	0.879829	−	0.475291i	$-0.157657\pi$
$31$	9.79736	1.75966	0.879829	+	0.475291i	$0.157657\pi$
$32$	−16.8711	−2.98241
$33$	−0.509449	−0.0886837
$34$	3.51830	0.603383
$35$	−1.40767	−0.237939
$36$	20.5793	3.42989
$37$	−7.46223	−1.22678	−0.613391	−	0.789779i	$-0.710195\pi$
$37$	−7.46223	−1.22678	−0.613391	+	0.789779i	$0.710195\pi$
$38$	−16.9284	−2.74615
$39$	6.66727	1.06762
$40$	−3.62894	−0.573786
$41$	4.68719	0.732016	0.366008	−	0.930612i	$-0.380724\pi$
$41$	4.68719	0.732016	0.366008	+	0.930612i	$0.380724\pi$
$42$	23.6388	3.64754
$43$	3.11988	0.475777	0.237888	−	0.971292i	$-0.423545\pi$
$43$	3.11988	0.475777	0.237888	+	0.971292i	$0.423545\pi$
$44$	−1.00605	−0.151668
$45$	1.66596	0.248346
$46$	10.8579	1.60091
$47$	−8.81047	−1.28514	−0.642570	−	0.766227i	$-0.722132\pi$
$47$	−8.81047	−1.28514	−0.642570	+	0.766227i	$0.722132\pi$
$48$	33.4819	4.83270
$49$	4.15246	0.593208
$50$	12.9459	1.83082
$51$	−3.45558	−0.483878
$52$	13.1664	1.82585
$53$	4.49344	0.617222	0.308611	−	0.951188i	$-0.400136\pi$
$53$	4.49344	0.617222	0.308611	+	0.951188i	$0.400136\pi$
$54$	−6.74078	−0.917304
$55$	−0.0814425	−0.0109817
$56$	28.7509	3.84200
$57$	16.6266	2.20225
$58$	−8.31977	−1.09244
$59$	−5.34136	−0.695386	−0.347693	−	0.937608i	$-0.613035\pi$
$59$	−5.34136	−0.695386	−0.347693	+	0.937608i	$0.613035\pi$
$60$	5.78709	0.747111
$61$	14.2168	1.82028	0.910140	−	0.414300i	$-0.135974\pi$
$61$	14.2168	1.82028	0.910140	+	0.414300i	$0.135974\pi$
$62$	−26.3017	−3.34032
$63$	−13.1988	−1.66289
$64$	19.8950	2.48687
$65$	1.06585	0.132203
$66$	1.36765	0.168347
$67$	−0.977568	−0.119429	−0.0597145	−	0.998215i	$-0.519019\pi$
$67$	−0.977568	−0.119429	−0.0597145	+	0.998215i	$0.519019\pi$
$68$	−6.82401	−0.827533
$69$	−10.6643	−1.28384
$70$	3.77898	0.451675
$71$	15.2855	1.81405	0.907027	−	0.421072i	$-0.138346\pi$
$71$	15.2855	1.81405	0.907027	+	0.421072i	$0.138346\pi$
$72$	−34.0263	−4.01004
$73$	14.1383	1.65477	0.827383	−	0.561638i	$-0.189829\pi$
$73$	14.1383	1.65477	0.827383	+	0.561638i	$0.189829\pi$
$74$	20.0329	2.32878
$75$	−12.7151	−1.46822
$76$	32.8339	3.76631
$77$	0.645241	0.0735321
$78$	−17.8988	−2.02664
$79$	−4.25907	−0.479183	−0.239591	−	0.970874i	$-0.577013\pi$
$79$	−4.25907	−0.479183	−0.239591	+	0.970874i	$0.577013\pi$
$80$	5.35255	0.598433
$81$	−5.23626	−0.581807
$82$	−12.5831	−1.38957
$83$	−1.91091	−0.209750	−0.104875	−	0.994485i	$-0.533444\pi$
$83$	−1.91091	−0.209750	−0.104875	+	0.994485i	$0.533444\pi$
$84$	−45.8492	−5.00256
$85$	−0.552423	−0.0599187
$86$	−8.37554	−0.903158
$87$	8.17146	0.876073
$88$	1.66342	0.177322
$89$	14.2828	1.51397	0.756985	−	0.653432i	$-0.226671\pi$
$89$	14.2828	1.51397	0.756985	+	0.653432i	$0.226671\pi$
$90$	−4.47238	−0.471430
$91$	−8.44441	−0.885214
$92$	−21.0597	−2.19563
$93$	25.8329	2.67875
$94$	23.6524	2.43955
$95$	2.65799	0.272704
$96$	−44.4843	−4.54016
$97$	−7.16853	−0.727853	−0.363927	−	0.931428i	$-0.618564\pi$
$97$	−7.16853	−0.727853	−0.363927	+	0.931428i	$0.618564\pi$
$98$	−11.1476	−1.12608
$99$	−0.763635	−0.0767483
$100$	−25.1095	−2.51095
$101$	−8.15825	−0.811776	−0.405888	−	0.913923i	$-0.633038\pi$
$101$	−8.15825	−0.811776	−0.405888	+	0.913923i	$0.633038\pi$
$102$	9.27677	0.918537
$103$	−14.5981	−1.43839	−0.719195	−	0.694809i	$-0.755489\pi$
$103$	−14.5981	−1.43839	−0.719195	+	0.694809i	$0.755489\pi$
$104$	−21.7696	−2.13468
$105$	−3.71162	−0.362217
$106$	−12.0630	−1.17166
$107$	−12.6302	−1.22101	−0.610504	−	0.792013i	$-0.709033\pi$
$107$	−12.6302	−1.22101	−0.610504	+	0.792013i	$0.709033\pi$
$108$	13.0743	1.25807
$109$	7.41309	0.710046	0.355023	−	0.934858i	$-0.384473\pi$
$109$	7.41309	0.710046	0.355023	+	0.934858i	$0.384473\pi$
$110$	0.218638	0.0208464
$111$	−19.6758	−1.86755
$112$	−42.4064	−4.00703
$113$	6.79908	0.639603	0.319802	−	0.947485i	$-0.396384\pi$
$113$	6.79908	0.639603	0.319802	+	0.947485i	$0.396384\pi$
$114$	−44.6354	−4.18049
$115$	−1.70484	−0.158977
$116$	16.1368	1.49827
$117$	9.99385	0.923932
$118$	14.3393	1.32004
$119$	4.37666	0.401208
$120$	−9.56851	−0.873481
$121$	−10.9627	−0.996606
$122$	−38.1662	−3.45540
$123$	12.3588	1.11436
$124$	51.0142	4.58121
$125$	−4.14027	−0.370317
$126$	35.4332	3.15664
$127$	14.6041	1.29591	0.647954	−	0.761680i	$-0.275625\pi$
$127$	14.6041	1.29591	0.647954	+	0.761680i	$0.275625\pi$
$128$	−19.6674	−1.73837
$129$	8.22624	0.724280
$130$	−2.86137	−0.250958
$131$	−19.9282	−1.74114	−0.870569	−	0.492047i	$-0.836249\pi$
$131$	−19.9282	−1.74114	−0.870569	+	0.492047i	$0.836249\pi$
$132$	−2.65267	−0.230885
$133$	−21.0584	−1.82599
$134$	2.62435	0.226710
$135$	1.05840	0.0910923
$136$	11.2830	0.967506
$137$	9.11036	0.778351	0.389175	−	0.921164i	$-0.372760\pi$
$137$	9.11036	0.778351	0.389175	+	0.921164i	$0.372760\pi$
$138$	28.6292	2.43708
$139$	11.1274	0.943810	0.471905	−	0.881649i	$-0.343567\pi$
$139$	11.1274	0.943810	0.471905	+	0.881649i	$0.343567\pi$
$140$	−7.32963	−0.619467
$141$	−23.2307	−1.95638
$142$	−41.0350	−3.44358
$143$	−0.488563	−0.0408557
$144$	50.1875	4.18229
$145$	1.30632	0.108484
$146$	−37.9554	−3.14121
$147$	10.9489	0.903048
$148$	−38.8554	−3.19389
$149$	11.4319	0.936542	0.468271	−	0.883585i	$-0.344877\pi$
$149$	11.4319	0.936542	0.468271	+	0.883585i	$0.344877\pi$
$150$	34.1347	2.78708
$151$	10.5310	0.857002	0.428501	−	0.903541i	$-0.359042\pi$
$151$	10.5310	0.857002	0.428501	+	0.903541i	$0.359042\pi$
$152$	−54.2883	−4.40336
$153$	−5.17972	−0.418756
$154$	−1.73220	−0.139585
$155$	4.12974	0.331709
$156$	34.7160	2.77951
$157$	5.72832	0.457170	0.228585	−	0.973524i	$-0.426590\pi$
$157$	5.72832	0.457170	0.228585	+	0.973524i	$0.426590\pi$
$158$	11.4338	0.909623
$159$	11.8479	0.939603
$160$	−7.11143	−0.562208
$161$	13.5069	1.06449
$162$	14.0571	1.10443
$163$	14.2417	1.11550	0.557749	−	0.830010i	$-0.311665\pi$
$163$	14.2417	1.11550	0.557749	+	0.830010i	$0.311665\pi$
$164$	24.4059	1.90578
$165$	−0.214741	−0.0167176
$166$	5.12998	0.398163
$167$	−13.1298	−1.01602	−0.508009	−	0.861352i	$-0.669618\pi$
$167$	−13.1298	−1.01602	−0.508009	+	0.861352i	$0.669618\pi$
$168$	75.8080	5.84872
$169$	−6.60607	−0.508160
$170$	1.48302	0.113742
$171$	24.9224	1.90586
$172$	16.2450	1.23867
$173$	9.73972	0.740497	0.370249	−	0.928933i	$-0.379273\pi$
$173$	9.73972	0.740497	0.370249	+	0.928933i	$0.379273\pi$
$174$	−21.9369	−1.66303
$175$	16.1043	1.21737
$176$	−2.45349	−0.184938
$177$	−14.0837	−1.05859
$178$	−38.3432	−2.87394
$179$	1.67320	0.125061	0.0625304	−	0.998043i	$-0.480083\pi$
$179$	1.67320	0.125061	0.0625304	+	0.998043i	$0.480083\pi$
$180$	8.67452	0.646561
$181$	21.1599	1.57280	0.786402	−	0.617716i	$-0.211942\pi$
$181$	21.1599	1.57280	0.786402	+	0.617716i	$0.211942\pi$
$182$	22.6696	1.68039
$183$	37.4858	2.77103
$184$	34.8206	2.56701
$185$	−3.14545	−0.231258
$186$	−69.3503	−5.08501
$187$	0.253218	0.0185171
$188$	−45.8756	−3.34582
$189$	−8.38533	−0.609943
$190$	−7.13558	−0.517670
$191$	11.1864	0.809423	0.404711	−	0.914444i	$-0.367372\pi$
$191$	11.1864	0.809423	0.404711	+	0.914444i	$0.367372\pi$
$192$	52.4575	3.78580
$193$	−11.6853	−0.841124	−0.420562	−	0.907264i	$-0.638167\pi$
$193$	−11.6853	−0.841124	−0.420562	+	0.907264i	$0.638167\pi$
$194$	19.2444	1.38167
$195$	2.81036	0.201254
$196$	21.6216	1.54440
$197$	16.9095	1.20475	0.602377	−	0.798212i	$-0.294220\pi$
$197$	16.9095	1.20475	0.602377	+	0.798212i	$0.294220\pi$
$198$	2.05004	0.145690
$199$	11.2561	0.797926	0.398963	−	0.916967i	$-0.369370\pi$
$199$	11.2561	0.797926	0.398963	+	0.916967i	$0.369370\pi$
$200$	41.5167	2.93567
$201$	−2.57757	−0.181808
$202$	21.9014	1.54098
$203$	−10.3495	−0.726396
$204$	−17.9930	−1.25976
$205$	1.97573	0.137991
$206$	39.1896	2.73047
$207$	−15.9852	−1.11105
$208$	32.1093	2.22638
$209$	−1.21836	−0.0842760
$210$	9.96412	0.687590
$211$	22.6977	1.56257	0.781287	−	0.624173i	$-0.214564\pi$
$211$	22.6977	1.56257	0.781287	+	0.624173i	$0.214564\pi$
$212$	23.3971	1.60692
$213$	40.3036	2.76156
$214$	33.9067	2.31782
$215$	1.31508	0.0896876
$216$	−21.6173	−1.47087
$217$	−32.7186	−2.22108
$218$	−19.9010	−1.34787
$219$	37.2788	2.51907
$220$	−0.424066	−0.0285905
$221$	−3.31391	−0.222918
$222$	52.8212	3.54512
$223$	4.52443	0.302978	0.151489	−	0.988459i	$-0.451593\pi$
$223$	4.52443	0.302978	0.151489	+	0.988459i	$0.451593\pi$
$224$	56.3415	3.76447
$225$	−19.0592	−1.27062
$226$	−18.2526	−1.21415
$227$	21.9679	1.45806	0.729030	−	0.684481i	$-0.239971\pi$
$227$	21.9679	1.45806	0.729030	+	0.684481i	$0.239971\pi$
$228$	86.5738	5.73349
$229$	13.2926	0.878396	0.439198	−	0.898390i	$-0.355263\pi$
$229$	13.2926	0.878396	0.439198	+	0.898390i	$0.355263\pi$
$230$	4.57677	0.301784
$231$	1.70132	0.111939
$232$	−26.6810	−1.75169
$233$	15.1406	0.991896	0.495948	−	0.868352i	$-0.334821\pi$
$233$	15.1406	0.991896	0.495948	+	0.868352i	$0.334821\pi$
$234$	−26.8292	−1.75388
$235$	−3.71376	−0.242259
$236$	−27.8121	−1.81042
$237$	−11.2300	−0.729465
$238$	−11.7495	−0.761605
$239$	21.1940	1.37092	0.685462	−	0.728109i	$-0.259600\pi$
$239$	21.1940	1.37092	0.685462	+	0.728109i	$0.259600\pi$
$240$	14.1132	0.911001
$241$	−13.7597	−0.886339	−0.443170	−	0.896438i	$-0.646146\pi$
$241$	−13.7597	−0.886339	−0.443170	+	0.896438i	$0.646146\pi$
$242$	29.4301	1.89184
$243$	−21.3393	−1.36892
$244$	74.0262	4.73904
$245$	1.75033	0.111824
$246$	−33.1781	−2.11536
$247$	15.9450	1.01455
$248$	−84.3480	−5.35611
$249$	−5.03853	−0.319304
$250$	11.1149	0.702965
$251$	−9.59506	−0.605635	−0.302817	−	0.953049i	$-0.597927\pi$
$251$	−9.59506	−0.605635	−0.302817	+	0.953049i	$0.597927\pi$
$252$	−68.7253	−4.32929
$253$	0.781460	0.0491300
$254$	−39.2059	−2.46000
$255$	−1.45658	−0.0912148
$256$	13.0087	0.813044
$257$	−9.78728	−0.610513	−0.305257	−	0.952270i	$-0.598742\pi$
$257$	−9.78728	−0.610513	−0.305257	+	0.952270i	$0.598742\pi$
$258$	−22.0840	−1.37489
$259$	24.9203	1.54847
$260$	5.54984	0.344186
$261$	12.2486	0.758167
$262$	53.4988	3.30517
$263$	−28.0616	−1.73035	−0.865175	−	0.501471i	$-0.832793\pi$
$263$	−28.0616	−1.73035	−0.865175	+	0.501471i	$0.832793\pi$
$264$	4.38598	0.269939
$265$	1.89406	0.116351
$266$	56.5328	3.46625
$267$	37.6597	2.30473
$268$	−5.09014	−0.310930
$269$	−22.6366	−1.38018	−0.690089	−	0.723725i	$-0.742429\pi$
$269$	−22.6366	−1.38018	−0.690089	+	0.723725i	$0.742429\pi$
$270$	−2.84135	−0.172919
$271$	−9.34111	−0.567432	−0.283716	−	0.958908i	$-0.591567\pi$
$271$	−9.34111	−0.567432	−0.283716	+	0.958908i	$0.591567\pi$
$272$	−16.6419	−1.00907
$273$	−22.2655	−1.34757
$274$	−24.4574	−1.47753
$275$	0.931737	0.0561859
$276$	−55.5286	−3.34243
$277$	−23.2506	−1.39699	−0.698497	−	0.715613i	$-0.746147\pi$
$277$	−23.2506	−1.39699	−0.698497	+	0.715613i	$0.746147\pi$
$278$	−29.8722	−1.79162
$279$	38.7220	2.31823
$280$	12.1190	0.724247
$281$	−5.80028	−0.346016	−0.173008	−	0.984920i	$-0.555349\pi$
$281$	−5.80028	−0.346016	−0.173008	+	0.984920i	$0.555349\pi$
$282$	62.3647	3.71376
$283$	15.7900	0.938617	0.469308	−	0.883034i	$-0.344503\pi$
$283$	15.7900	0.938617	0.469308	+	0.883034i	$0.344503\pi$
$284$	79.5906	4.72283
$285$	7.00839	0.415141
$286$	1.31158	0.0775556
$287$	−15.6530	−0.923968
$288$	−66.6794	−3.92912
$289$	−15.2824	−0.898966
$290$	−3.50692	−0.205933
$291$	−18.9014	−1.10802
$292$	73.6174	4.30813
$293$	−2.69728	−0.157577	−0.0787883	−	0.996891i	$-0.525105\pi$
$293$	−2.69728	−0.157577	−0.0787883	+	0.996891i	$0.525105\pi$
$294$	−29.3931	−1.71424
$295$	−2.25147	−0.131086
$296$	64.2443	3.73412
$297$	−0.485145	−0.0281510
$298$	−30.6899	−1.77782
$299$	−10.2271	−0.591450
$300$	−66.2068	−3.82245
$301$	−10.4189	−0.600537
$302$	−28.2713	−1.62683
$303$	−21.5110	−1.23578
$304$	80.0731	4.59251
$305$	5.99263	0.343137
$306$	13.9053	0.794916
$307$	15.6892	0.895430	0.447715	−	0.894176i	$-0.352238\pi$
$307$	15.6892	0.895430	0.447715	+	0.894176i	$0.352238\pi$
$308$	3.35973	0.191439
$309$	−38.4910	−2.18968
$310$	−11.0866	−0.629677
$311$	−24.6052	−1.39523	−0.697616	−	0.716472i	$-0.745756\pi$
$311$	−24.6052	−1.39523	−0.697616	+	0.716472i	$0.745756\pi$
$312$	−57.4002	−3.24965
$313$	11.1517	0.630331	0.315166	−	0.949037i	$-0.397940\pi$
$313$	11.1517	0.630331	0.315166	+	0.949037i	$0.397940\pi$
$314$	−15.3781	−0.867837
$315$	−5.56351	−0.313468
$316$	−22.1767	−1.24754
$317$	26.0765	1.46460	0.732302	−	0.680980i	$-0.238446\pi$
$317$	26.0765	1.46460	0.732302	+	0.680980i	$0.238446\pi$
$318$	−31.8067	−1.78363
$319$	−0.598788	−0.0335257
$320$	8.38606	0.468795
$321$	−33.3023	−1.85876
$322$	−36.2602	−2.02070
$323$	−8.26413	−0.459829
$324$	−27.2649	−1.51472
$325$	−12.1938	−0.676392
$326$	−38.2329	−2.11753
$327$	19.5463	1.08091
$328$	−40.3532	−2.22813
$329$	29.4228	1.62213
$330$	0.576488	0.0317346
$331$	4.60761	0.253257	0.126628	−	0.991950i	$-0.459584\pi$
$331$	4.60761	0.253257	0.126628	+	0.991950i	$0.459584\pi$
$332$	−9.94998	−0.546076
$333$	−29.4929	−1.61620
$334$	35.2480	1.92869
$335$	−0.412061	−0.0225133
$336$	−111.814	−6.09995
$337$	30.0740	1.63824	0.819118	−	0.573626i	$-0.194464\pi$
$337$	30.0740	1.63824	0.819118	+	0.573626i	$0.194464\pi$
$338$	17.7345	0.964629
$339$	17.9273	0.973675
$340$	−2.87643	−0.155996
$341$	−1.89298	−0.102511
$342$	−66.9059	−3.61786
$343$	9.50945	0.513462
$344$	−26.8598	−1.44819
$345$	−4.49519	−0.242013
$346$	−26.1470	−1.40567
$347$	26.4389	1.41931	0.709657	−	0.704547i	$-0.248850\pi$
$347$	26.4389	1.41931	0.709657	+	0.704547i	$0.248850\pi$
$348$	42.5483	2.28083
$349$	5.69442	0.304815	0.152408	−	0.988318i	$-0.451297\pi$
$349$	5.69442	0.304815	0.152408	+	0.988318i	$0.451297\pi$
$350$	−43.2332	−2.31091
$351$	6.34919	0.338895
$352$	3.25972	0.173743
$353$	−18.6803	−0.994252	−0.497126	−	0.867678i	$-0.665611\pi$
$353$	−18.6803	−0.994252	−0.497126	+	0.867678i	$0.665611\pi$
$354$	37.8087	2.00951
$355$	6.44308	0.341963
$356$	74.3695	3.94158
$357$	11.5400	0.610763
$358$	−4.49183	−0.237400
$359$	18.4316	0.972783	0.486391	−	0.873741i	$-0.338313\pi$
$359$	18.4316	0.972783	0.486391	+	0.873741i	$0.338313\pi$
$360$	−14.3426	−0.755924
$361$	20.7631	1.09279
$362$	−56.8053	−2.98562
$363$	−28.9055	−1.51714
$364$	−43.9695	−2.30463
$365$	5.95953	0.311936
$366$	−100.634	−5.26020
$367$	−7.38654	−0.385574	−0.192787	−	0.981241i	$-0.561753\pi$
$367$	−7.38654	−0.385574	−0.192787	+	0.981241i	$0.561753\pi$
$368$	−51.3590	−2.67727
$369$	18.5251	0.964380
$370$	8.44419	0.438993
$371$	−15.0060	−0.779072
$372$	134.510	6.97403
$373$	25.9537	1.34383	0.671917	−	0.740627i	$-0.265471\pi$
$373$	25.9537	1.34383	0.671917	+	0.740627i	$0.265471\pi$
$374$	−0.679782	−0.0351507
$375$	−10.9167	−0.563737
$376$	75.8517	3.91175
$377$	7.83646	0.403598
$378$	22.5110	1.15784
$379$	−3.18695	−0.163703	−0.0818514	−	0.996645i	$-0.526083\pi$
$379$	−3.18695	−0.163703	−0.0818514	+	0.996645i	$0.526083\pi$
$380$	13.8400	0.709978
$381$	38.5070	1.97277
$382$	−30.0308	−1.53651
$383$	3.12403	0.159630	0.0798152	−	0.996810i	$-0.474567\pi$
$383$	3.12403	0.159630	0.0798152	+	0.996810i	$0.474567\pi$
$384$	−51.8575	−2.64634
$385$	0.271980	0.0138614
$386$	31.3700	1.59669
$387$	12.3307	0.626803
$388$	−37.3261	−1.89494
$389$	12.8841	0.653248	0.326624	−	0.945154i	$-0.394089\pi$
$389$	12.8841	0.653248	0.326624	+	0.945154i	$0.394089\pi$
$390$	−7.54462	−0.382037
$391$	5.30063	0.268064
$392$	−35.7496	−1.80563
$393$	−52.5452	−2.65055
$394$	−45.3949	−2.28696
$395$	−1.79527	−0.0903296
$396$	−3.97620	−0.199812
$397$	−5.52484	−0.277284	−0.138642	−	0.990343i	$-0.544274\pi$
$397$	−5.52484	−0.277284	−0.138642	+	0.990343i	$0.544274\pi$
$398$	−30.2179	−1.51469
$399$	−55.5251	−2.77973
$400$	−61.2354	−3.06177
$401$	−1.95554	−0.0976552	−0.0488276	−	0.998807i	$-0.515548\pi$
$401$	−1.95554	−0.0976552	−0.0488276	+	0.998807i	$0.515548\pi$
$402$	6.91969	0.345123
$403$	24.7738	1.23407
$404$	−42.4795	−2.11343
$405$	−2.20717	−0.109675
$406$	27.7841	1.37890
$407$	1.44180	0.0714675
$408$	29.7500	1.47285
$409$	−17.5189	−0.866253	−0.433126	−	0.901333i	$-0.642590\pi$
$409$	−17.5189	−0.866253	−0.433126	+	0.901333i	$0.642590\pi$
$410$	−5.30398	−0.261945
$411$	24.0215	1.18489
$412$	−76.0112	−3.74480
$413$	17.8376	0.877732
$414$	42.9136	2.10909
$415$	−0.805479	−0.0395394
$416$	−42.6606	−2.09161
$417$	29.3397	1.43677
$418$	3.27079	0.159979
$419$	−6.96861	−0.340439	−0.170219	−	0.985406i	$-0.554448\pi$
$419$	−6.96861	−0.340439	−0.170219	+	0.985406i	$0.554448\pi$
$420$	−19.3262	−0.943021
$421$	−0.0736207	−0.00358805	−0.00179403	−	0.999998i	$-0.500571\pi$
$421$	−0.0736207	−0.00358805	−0.00179403	+	0.999998i	$0.500571\pi$
$422$	−60.9336	−2.96620
$423$	−34.8216	−1.69308
$424$	−38.6852	−1.87872
$425$	6.31995	0.306563
$426$	−108.198	−5.24221
$427$	−47.4776	−2.29760
$428$	−65.7647	−3.17886
$429$	−1.28820	−0.0621951
$430$	−3.53043	−0.170252
$431$	−31.3086	−1.50808	−0.754041	−	0.656828i	$-0.771898\pi$
$431$	−31.3086	−1.50808	−0.754041	+	0.656828i	$0.771898\pi$
$432$	31.8846	1.53405
$433$	26.4452	1.27088	0.635438	−	0.772152i	$-0.280820\pi$
$433$	26.4452	1.27088	0.635438	+	0.772152i	$0.280820\pi$
$434$	87.8354	4.21624
$435$	3.44440	0.165147
$436$	38.5995	1.84858
$437$	−25.5041	−1.22003
$438$	−100.078	−4.78190
$439$	9.48729	0.452803	0.226402	−	0.974034i	$-0.427304\pi$
$439$	9.48729	0.452803	0.226402	+	0.974034i	$0.427304\pi$
$440$	0.701160	0.0334265
$441$	16.4117	0.781511
$442$	8.89645	0.423161
$443$	15.5768	0.740075	0.370037	−	0.929017i	$-0.379345\pi$
$443$	15.5768	0.740075	0.370037	+	0.929017i	$0.379345\pi$
$444$	−102.451	−4.86210
$445$	6.02042	0.285395
$446$	−12.1462	−0.575138
$447$	30.1428	1.42571
$448$	−66.4399	−3.13899
$449$	−22.9266	−1.08197	−0.540987	−	0.841031i	$-0.681949\pi$
$449$	−22.9266	−1.08197	−0.540987	+	0.841031i	$0.681949\pi$
$450$	51.1659	2.41199
$451$	−0.905627	−0.0426443
$452$	35.4024	1.66519
$453$	27.7674	1.30462
$454$	−58.9745	−2.76781
$455$	−3.55945	−0.166870
$456$	−143.143	−6.70328
$457$	36.9139	1.72676	0.863381	−	0.504553i	$-0.168343\pi$
$457$	36.9139	1.72676	0.863381	+	0.504553i	$0.168343\pi$
$458$	−35.6848	−1.66744
$459$	−3.29073	−0.153598
$460$	−8.87701	−0.413893
$461$	29.9878	1.39667	0.698336	−	0.715770i	$-0.253924\pi$
$461$	29.9878	1.39667	0.698336	+	0.715770i	$0.253924\pi$
$462$	−4.56732	−0.212491
$463$	33.3954	1.55201	0.776007	−	0.630724i	$-0.217242\pi$
$463$	33.3954	1.55201	0.776007	+	0.630724i	$0.217242\pi$
$464$	39.3534	1.82694
$465$	10.8890	0.504964
$466$	−40.6462	−1.88290
$467$	−3.35753	−0.155368	−0.0776840	−	0.996978i	$-0.524753\pi$
$467$	−3.35753	−0.155368	−0.0776840	+	0.996978i	$0.524753\pi$
$468$	52.0374	2.40543
$469$	3.26462	0.150746
$470$	9.96985	0.459875
$471$	15.1040	0.695955
$472$	45.9852	2.11664
$473$	−0.602802	−0.0277168
$474$	30.1477	1.38473
$475$	−30.4086	−1.39524
$476$	22.7890	1.04453
$477$	17.7594	0.813147
$478$	−56.8968	−2.60240
$479$	−26.0855	−1.19188	−0.595939	−	0.803030i	$-0.703220\pi$
$479$	−26.0855	−1.19188	−0.595939	+	0.803030i	$0.703220\pi$
$480$	−18.7508	−0.855855
$481$	−18.8692	−0.860359
$482$	36.9389	1.68252
$483$	35.6139	1.62049
$484$	−57.0819	−2.59463
$485$	−3.02165	−0.137206
$486$	57.2870	2.59859
$487$	14.9329	0.676673	0.338336	−	0.941025i	$-0.390136\pi$
$487$	14.9329	0.676673	0.338336	+	0.941025i	$0.390136\pi$
$488$	−122.397	−5.54063
$489$	37.5514	1.69813
$490$	−4.69889	−0.212274
$491$	19.4121	0.876057	0.438028	−	0.898961i	$-0.355677\pi$
$491$	19.4121	0.876057	0.438028	+	0.898961i	$0.355677\pi$
$492$	64.3515	2.90119
$493$	−4.06156	−0.182924
$494$	−42.8055	−1.92591
$495$	−0.321885	−0.0144676
$496$	124.410	5.58618
$497$	−51.0464	−2.28974
$498$	13.5263	0.606129
$499$	27.9928	1.25313	0.626566	−	0.779368i	$-0.284460\pi$
$499$	27.9928	1.25313	0.626566	+	0.779368i	$0.284460\pi$
$500$	−21.5581	−0.964108
$501$	−34.6197	−1.54669
$502$	25.7587	1.14966
$503$	16.1442	0.719835	0.359918	−	0.932984i	$-0.382805\pi$
$503$	16.1442	0.719835	0.359918	+	0.932984i	$0.382805\pi$
$504$	113.632	5.06157
$505$	−3.43883	−0.153026
$506$	−2.09789	−0.0932625
$507$	−17.4184	−0.773577
$508$	76.0428	3.37385
$509$	29.4792	1.30664	0.653322	−	0.757081i	$-0.273375\pi$
$509$	29.4792	1.30664	0.653322	+	0.757081i	$0.273375\pi$
$510$	3.91031	0.173151
$511$	−47.2154	−2.08869
$512$	4.41205	0.194987
$513$	15.8334	0.699062
$514$	26.2747	1.15893
$515$	−6.15332	−0.271147
$516$	42.8335	1.88564
$517$	1.70230	0.0748671
$518$	−66.9005	−2.93944
$519$	25.6809	1.12727
$520$	−9.17622	−0.402404
$521$	−32.9895	−1.44530	−0.722649	−	0.691215i	$-0.757076\pi$
$521$	−32.9895	−1.44530	−0.722649	+	0.691215i	$0.757076\pi$
$522$	−32.8822	−1.43921
$523$	12.6169	0.551699	0.275850	−	0.961201i	$-0.411041\pi$
$523$	12.6169	0.551699	0.275850	+	0.961201i	$0.411041\pi$
$524$	−103.765	−4.53300
$525$	42.4625	1.85322
$526$	75.3333	3.28469
$527$	−12.8400	−0.559321
$528$	−6.46915	−0.281534
$529$	−6.64163	−0.288767
$530$	−5.08474	−0.220867
$531$	−21.1106	−0.916123
$532$	−109.650	−4.75392
$533$	11.8521	0.513372
$534$	−101.100	−4.37503
$535$	−5.32384	−0.230170
$536$	8.41614	0.363522
$537$	4.41176	0.190381
$538$	60.7696	2.61996
$539$	−0.802310	−0.0345579
$540$	5.51101	0.237156
$541$	−11.0694	−0.475910	−0.237955	−	0.971276i	$-0.576477\pi$
$541$	−11.0694	−0.475910	−0.237955	+	0.971276i	$0.576477\pi$
$542$	25.0769	1.07714
$543$	55.7927	2.39430
$544$	22.1106	0.947983
$545$	3.12474	0.133849
$546$	59.7735	2.55807
$547$	−19.8451	−0.848514	−0.424257	−	0.905542i	$-0.639465\pi$
$547$	−19.8451	−0.848514	−0.424257	+	0.905542i	$0.639465\pi$
$548$	47.4371	2.02641
$549$	56.1891	2.39809
$550$	−2.50132	−0.106657
$551$	19.5423	0.832530
$552$	91.8121	3.90778
$553$	14.2233	0.604836
$554$	62.4180	2.65189
$555$	−8.29367	−0.352047
$556$	57.9394	2.45718
$557$	−25.3661	−1.07479	−0.537397	−	0.843329i	$-0.680592\pi$
$557$	−25.3661	−1.07479	−0.537397	+	0.843329i	$0.680592\pi$
$558$	−103.952	−4.40065
$559$	7.88899	0.333669
$560$	−17.8750	−0.755356
$561$	0.667665	0.0281888
$562$	15.5713	0.656835
$563$	−22.3974	−0.943939	−0.471970	−	0.881615i	$-0.656457\pi$
$563$	−22.3974	−0.943939	−0.471970	+	0.881615i	$0.656457\pi$
$564$	−120.961	−5.09338
$565$	2.86592	0.120570
$566$	−42.3894	−1.78176
$567$	17.4866	0.734370
$568$	−131.597	−5.52168
$569$	−10.8967	−0.456815	−0.228408	−	0.973566i	$-0.573352\pi$
$569$	−10.8967	−0.456815	−0.228408	+	0.973566i	$0.573352\pi$
$570$	−18.8145	−0.788054
$571$	−20.2128	−0.845879	−0.422939	−	0.906158i	$-0.639002\pi$
$571$	−20.2128	−0.845879	−0.422939	+	0.906158i	$0.639002\pi$
$572$	−2.54392	−0.106367
$573$	29.4955	1.23219
$574$	42.0217	1.75395
$575$	19.5041	0.813378
$576$	78.6308	3.27629
$577$	22.6257	0.941921	0.470960	−	0.882154i	$-0.343907\pi$
$577$	22.6257	0.941921	0.470960	+	0.882154i	$0.343907\pi$
$578$	41.0268	1.70649
$579$	−30.8108	−1.28045
$580$	6.80193	0.282435
$581$	6.38154	0.264751
$582$	50.7422	2.10333
$583$	−0.868192	−0.0359569
$584$	−121.721	−5.03683
$585$	4.21257	0.174168
$586$	7.24104	0.299124
$587$	−27.8791	−1.15069	−0.575346	−	0.817910i	$-0.695133\pi$
$587$	−27.8791	−1.15069	−0.575346	+	0.817910i	$0.695133\pi$
$588$	57.0101	2.35106
$589$	61.7802	2.54561
$590$	6.04423	0.248837
$591$	44.5857	1.83401
$592$	−94.7578	−3.89452
$593$	30.8180	1.26554	0.632772	−	0.774338i	$-0.281917\pi$
$593$	30.8180	1.26554	0.632772	+	0.774338i	$0.281917\pi$
$594$	1.30241	0.0534384
$595$	1.84483	0.0756307
$596$	59.5254	2.43826
$597$	29.6793	1.21469
$598$	27.4555	1.12274
$599$	−27.4103	−1.11995	−0.559977	−	0.828508i	$-0.689190\pi$
$599$	−27.4103	−1.11995	−0.559977	+	0.828508i	$0.689190\pi$
$600$	109.468	4.46900
$601$	−43.0652	−1.75667	−0.878333	−	0.478050i	$-0.841344\pi$
$601$	−43.0652	−1.75667	−0.878333	+	0.478050i	$0.841344\pi$
$602$	27.9704	1.13999
$603$	−3.86364	−0.157339
$604$	54.8344	2.23118
$605$	−4.62094	−0.187868
$606$	57.7479	2.34585
$607$	2.03385	0.0825512	0.0412756	−	0.999148i	$-0.486858\pi$
$607$	2.03385	0.0825512	0.0412756	+	0.999148i	$0.486858\pi$
$608$	−106.386	−4.31450
$609$	−27.2888	−1.10580
$610$	−16.0877	−0.651370
$611$	−22.2783	−0.901285
$612$	−26.9705	−1.09022
$613$	−23.1186	−0.933751	−0.466876	−	0.884323i	$-0.654620\pi$
$613$	−23.1186	−0.933751	−0.466876	+	0.884323i	$0.654620\pi$
$614$	−42.1188	−1.69978
$615$	5.20943	0.210065
$616$	−5.55505	−0.223819
$617$	−14.2414	−0.573339	−0.286670	−	0.958030i	$-0.592548\pi$
$617$	−14.2414	−0.573339	−0.286670	+	0.958030i	$0.592548\pi$
$618$	103.332	4.15662
$619$	−11.4646	−0.460802	−0.230401	−	0.973096i	$-0.574004\pi$
$619$	−11.4646	−0.460802	−0.230401	+	0.973096i	$0.574004\pi$
$620$	21.5033	0.863594
$621$	−10.1556	−0.407529
$622$	66.0544	2.64854
$623$	−47.6977	−1.91097
$624$	84.6631	3.38924
$625$	22.3664	0.894657
$626$	−29.9376	−1.19655
$627$	−3.21248	−0.128294
$628$	29.8270	1.19023
$629$	9.77971	0.389943
$630$	14.9356	0.595050
$631$	40.0963	1.59621	0.798103	−	0.602521i	$-0.205837\pi$
$631$	40.0963	1.59621	0.798103	+	0.602521i	$0.205837\pi$
$632$	36.6674	1.45855
$633$	59.8474	2.37872
$634$	−70.0044	−2.78023
$635$	6.15588	0.244289
$636$	61.6915	2.44623
$637$	10.5000	0.416025
$638$	1.60749	0.0636411
$639$	60.4128	2.38989
$640$	−8.29014	−0.327697
$641$	−31.8260	−1.25705	−0.628527	−	0.777788i	$-0.716342\pi$
$641$	−31.8260	−1.25705	−0.628527	+	0.777788i	$0.716342\pi$
$642$	89.4026	3.52844
$643$	−43.8779	−1.73037	−0.865187	−	0.501449i	$-0.832800\pi$
$643$	−43.8779	−1.73037	−0.865187	+	0.501449i	$0.832800\pi$
$644$	70.3295	2.77137
$645$	3.46749	0.136532
$646$	22.1857	0.872884
$647$	48.1188	1.89174	0.945872	−	0.324540i	$-0.105209\pi$
$647$	48.1188	1.89174	0.945872	+	0.324540i	$0.105209\pi$
$648$	45.0803	1.77092
$649$	1.03202	0.0405104
$650$	32.7352	1.28398
$651$	−86.2697	−3.38118
$652$	74.1557	2.90416
$653$	33.6695	1.31759	0.658795	−	0.752322i	$-0.271066\pi$
$653$	33.6695	1.31759	0.658795	+	0.752322i	$0.271066\pi$
$654$	−52.4734	−2.05187
$655$	−8.40007	−0.328218
$656$	59.5194	2.32384
$657$	55.8788	2.18004
$658$	−78.9878	−3.07926
$659$	−13.2174	−0.514876	−0.257438	−	0.966295i	$-0.582878\pi$
$659$	−13.2174	−0.514876	−0.257438	+	0.966295i	$0.582878\pi$
$660$	−1.11814	−0.0435237
$661$	−1.62518	−0.0632122	−0.0316061	−	0.999500i	$-0.510062\pi$
$661$	−1.62518	−0.0632122	−0.0316061	+	0.999500i	$0.510062\pi$
$662$	−12.3695	−0.480753
$663$	−8.73786	−0.339350
$664$	16.4515	0.638443
$665$	−8.87645	−0.344214
$666$	79.1759	3.06800
$667$	−12.5345	−0.485336
$668$	−68.3663	−2.64517
$669$	11.9297	0.461227
$670$	1.10621	0.0427365
$671$	−2.74688	−0.106042
$672$	148.557	5.73070
$673$	−17.7195	−0.683035	−0.341518	−	0.939875i	$-0.610941\pi$
$673$	−17.7195	−0.683035	−0.341518	+	0.939875i	$0.610941\pi$
$674$	−80.7359	−3.10983
$675$	−12.1085	−0.466057
$676$	−34.3974	−1.32298
$677$	6.27519	0.241175	0.120588	−	0.992703i	$-0.461522\pi$
$677$	6.27519	0.241175	0.120588	+	0.992703i	$0.461522\pi$
$678$	−48.1271	−1.84831
$679$	23.9395	0.918714
$680$	4.75595	0.182382
$681$	57.9232	2.21962
$682$	5.08184	0.194594
$683$	−50.5075	−1.93261	−0.966307	−	0.257391i	$-0.917137\pi$
$683$	−50.5075	−1.93261	−0.966307	+	0.257391i	$0.917137\pi$
$684$	129.769	4.96185
$685$	3.84016	0.146725
$686$	−25.5288	−0.974695
$687$	35.0487	1.33719
$688$	39.6172	1.51039
$689$	11.3622	0.432866
$690$	12.0677	0.459408
$691$	−14.9793	−0.569841	−0.284920	−	0.958551i	$-0.591967\pi$
$691$	−14.9793	−0.569841	−0.284920	+	0.958551i	$0.591967\pi$
$692$	50.7141	1.92786
$693$	2.55018	0.0968735
$694$	−70.9772	−2.69426
$695$	4.69036	0.177915
$696$	−70.3503	−2.66662
$697$	−6.14285	−0.232677
$698$	−15.2871	−0.578625
$699$	39.9216	1.50997
$700$	83.8541	3.16939
$701$	7.04733	0.266174	0.133087	−	0.991104i	$-0.457511\pi$
$701$	7.04733	0.266174	0.133087	+	0.991104i	$0.457511\pi$
$702$	−17.0449	−0.643317
$703$	−47.0553	−1.77472
$704$	−3.84398	−0.144875
$705$	−9.79213	−0.368793
$706$	50.1486	1.88737
$707$	27.2447	1.02464
$708$	−73.3328	−2.75602
$709$	4.62534	0.173708	0.0868541	−	0.996221i	$-0.472319\pi$
$709$	4.62534	0.173708	0.0868541	+	0.996221i	$0.472319\pi$
$710$	−17.2969	−0.649142
$711$	−16.8331	−0.631290
$712$	−122.964	−4.60828
$713$	−39.6259	−1.48400
$714$	−30.9800	−1.15940
$715$	−0.205937	−0.00770162
$716$	8.71224	0.325592
$717$	55.8825	2.08697
$718$	−49.4810	−1.84661
$719$	−5.60429	−0.209005	−0.104502	−	0.994525i	$-0.533325\pi$
$719$	−5.60429	−0.209005	−0.104502	+	0.994525i	$0.533325\pi$
$720$	21.1548	0.788394
$721$	48.7506	1.81557
$722$	−55.7400	−2.07443
$723$	−36.2804	−1.34928
$724$	110.178	4.09474
$725$	−14.9449	−0.555039
$726$	77.5989	2.87997
$727$	30.1044	1.11651	0.558255	−	0.829670i	$-0.311471\pi$
$727$	30.1044	1.11651	0.558255	+	0.829670i	$0.311471\pi$
$728$	72.7001	2.69445
$729$	−40.5571	−1.50211
$730$	−15.9988	−0.592142
$731$	−4.08879	−0.151229
$732$	195.186	7.21430
$733$	17.0092	0.628248	0.314124	−	0.949382i	$-0.398289\pi$
$733$	17.0092	0.628248	0.314124	+	0.949382i	$0.398289\pi$
$734$	19.8297	0.731928
$735$	4.61513	0.170231
$736$	68.2359	2.51521
$737$	0.188879	0.00695745
$738$	−49.7321	−1.83066
$739$	23.9152	0.879734	0.439867	−	0.898063i	$-0.355026\pi$
$739$	23.9152	0.879734	0.439867	+	0.898063i	$0.355026\pi$
$740$	−16.3782	−0.602073
$741$	42.0424	1.54447
$742$	40.2847	1.47890
$743$	−7.03805	−0.258201	−0.129100	−	0.991632i	$-0.541209\pi$
$743$	−7.03805	−0.258201	−0.129100	+	0.991632i	$0.541209\pi$
$744$	−222.402	−8.15366
$745$	4.81875	0.176545
$746$	−69.6747	−2.55097
$747$	−7.55247	−0.276330
$748$	1.31849	0.0482088
$749$	42.1790	1.54119
$750$	29.3068	1.07013
$751$	29.5496	1.07828	0.539140	−	0.842216i	$-0.318750\pi$
$751$	29.5496	1.07828	0.539140	+	0.842216i	$0.318750\pi$
$752$	−111.878	−4.07978
$753$	−25.2995	−0.921965
$754$	−21.0375	−0.766142
$755$	4.43900	0.161552
$756$	−43.6619	−1.58797
$757$	−15.4655	−0.562103	−0.281052	−	0.959693i	$-0.590683\pi$
$757$	−15.4655	−0.562103	−0.281052	+	0.959693i	$0.590683\pi$
$758$	8.55561	0.310754
$759$	2.06049	0.0747911
$760$	−22.8834	−0.830067
$761$	−22.2599	−0.806921	−0.403461	−	0.914997i	$-0.632193\pi$
$761$	−22.2599	−0.806921	−0.403461	+	0.914997i	$0.632193\pi$
$762$	−103.375	−3.74488
$763$	−24.7562	−0.896236
$764$	58.2471	2.10731
$765$	−2.18334	−0.0789387
$766$	−8.38668	−0.303023
$767$	−13.5063	−0.487683
$768$	34.3003	1.23771
$769$	4.37280	0.157687	0.0788436	−	0.996887i	$-0.474877\pi$
$769$	4.37280	0.157687	0.0788436	+	0.996887i	$0.474877\pi$
$770$	−0.730150	−0.0263128
$771$	−25.8063	−0.929391
$772$	−60.8444	−2.18984
$773$	10.1895	0.366491	0.183245	−	0.983067i	$-0.441340\pi$
$773$	10.1895	0.366491	0.183245	+	0.983067i	$0.441340\pi$
$774$	−33.1026	−1.18985
$775$	−47.2460	−1.69713
$776$	61.7157	2.21547
$777$	65.7079	2.35726
$778$	−34.5882	−1.24005
$779$	29.5565	1.05897
$780$	14.6334	0.523959
$781$	−2.95336	−0.105680
$782$	−14.2299	−0.508861
$783$	7.78163	0.278093
$784$	52.7293	1.88319
$785$	2.41458	0.0861801
$786$	141.061	5.03149
$787$	22.8169	0.813335	0.406667	−	0.913576i	$-0.366691\pi$
$787$	22.8169	0.813335	0.406667	+	0.913576i	$0.366691\pi$
$788$	88.0468	3.13654
$789$	−73.9905	−2.63413
$790$	4.81952	0.171471
$791$	−22.7057	−0.807322
$792$	6.57434	0.233609
$793$	35.9490	1.27659
$794$	14.8319	0.526363
$795$	4.99410	0.177122
$796$	58.6099	2.07737
$797$	−11.6476	−0.412578	−0.206289	−	0.978491i	$-0.566139\pi$
$797$	−11.6476	−0.412578	−0.206289	+	0.978491i	$0.566139\pi$
$798$	149.061	5.27671
$799$	11.5467	0.408492
$800$	81.3578	2.87643
$801$	56.4497	1.99455
$802$	5.24980	0.185377
$803$	−2.73171	−0.0964001
$804$	−13.4213	−0.473332
$805$	5.69337	0.200665
$806$	−66.5071	−2.34261
$807$	−59.6864	−2.10106
$808$	70.2365	2.47091
$809$	25.9833	0.913524	0.456762	−	0.889589i	$-0.349009\pi$
$809$	25.9833	0.913524	0.456762	+	0.889589i	$0.349009\pi$
$810$	5.92530	0.208194
$811$	−18.0979	−0.635502	−0.317751	−	0.948174i	$-0.602928\pi$
$811$	−18.0979	−0.635502	−0.317751	+	0.948174i	$0.602928\pi$
$812$	−53.8894	−1.89115
$813$	−24.6299	−0.863808
$814$	−3.87062	−0.135665
$815$	6.00311	0.210280
$816$	−43.8801	−1.53611
$817$	19.6733	0.688282
$818$	47.0307	1.64439
$819$	−33.3748	−1.16621
$820$	10.2875	0.359254
$821$	7.19739	0.251191	0.125595	−	0.992082i	$-0.459916\pi$
$821$	7.19739	0.251191	0.125595	+	0.992082i	$0.459916\pi$
$822$	−64.4874	−2.24926
$823$	−2.15477	−0.0751106	−0.0375553	−	0.999295i	$-0.511957\pi$
$823$	−2.15477	−0.0751106	−0.0375553	+	0.999295i	$0.511957\pi$
$824$	125.678	4.37822
$825$	2.45673	0.0855324
$826$	−47.8864	−1.66618
$827$	12.8754	0.447721	0.223861	−	0.974621i	$-0.428134\pi$
$827$	12.8754	0.447721	0.223861	+	0.974621i	$0.428134\pi$
$828$	−83.2341	−2.89259
$829$	−50.6911	−1.76057	−0.880287	−	0.474442i	$-0.842650\pi$
$829$	−50.6911	−1.76057	−0.880287	+	0.474442i	$0.842650\pi$
$830$	2.16237	0.0750569
$831$	−61.3054	−2.12666
$832$	50.3069	1.74408
$833$	−5.44205	−0.188556
$834$	−78.7646	−2.72740
$835$	−5.53444	−0.191527
$836$	−6.34394	−0.219410
$837$	24.6005	0.850317
$838$	18.7077	0.646248
$839$	−11.2144	−0.387162	−0.193581	−	0.981084i	$-0.562010\pi$
$839$	−11.2144	−0.387162	−0.193581	+	0.981084i	$0.562010\pi$
$840$	31.9543	1.10253
$841$	−19.3956	−0.668813
$842$	0.197640	0.00681113
$843$	−15.2937	−0.526744
$844$	118.185	4.06811
$845$	−2.78457	−0.0957920
$846$	93.4811	3.21394
$847$	36.6102	1.25794
$848$	57.0592	1.95942
$849$	41.6337	1.42887
$850$	−16.9664	−0.581942
$851$	30.1813	1.03460
$852$	209.858	7.18962
$853$	−3.50665	−0.120065	−0.0600327	−	0.998196i	$-0.519120\pi$
$853$	−3.50665	−0.120065	−0.0600327	+	0.998196i	$0.519120\pi$
$854$	127.457	4.36149
$855$	10.5052	0.359269
$856$	108.737	3.71655
$857$	20.4727	0.699336	0.349668	−	0.936874i	$-0.386294\pi$
$857$	20.4727	0.699336	0.349668	+	0.936874i	$0.386294\pi$
$858$	3.45828	0.118064
$859$	−4.50349	−0.153657	−0.0768286	−	0.997044i	$-0.524479\pi$
$859$	−4.50349	−0.153657	−0.0768286	+	0.997044i	$0.524479\pi$
$860$	6.84753	0.233499
$861$	−41.2726	−1.40657
$862$	84.0502	2.86276
$863$	−39.0823	−1.33038	−0.665188	−	0.746676i	$-0.731649\pi$
$863$	−39.0823	−1.33038	−0.665188	+	0.746676i	$0.731649\pi$
$864$	−42.3621	−1.44119
$865$	4.10545	0.139589
$866$	−70.9941	−2.41248
$867$	−40.2955	−1.36851
$868$	−170.364	−5.78252
$869$	0.822908	0.0279153
$870$	−9.24676	−0.313494
$871$	−2.47190	−0.0837571
$872$	−63.8213	−2.16126
$873$	−28.3321	−0.958897
$874$	68.4676	2.31595
$875$	13.8265	0.467423
$876$	194.108	6.55832
$877$	34.2512	1.15658	0.578290	−	0.815831i	$-0.303720\pi$
$877$	34.2512	1.15658	0.578290	+	0.815831i	$0.303720\pi$
$878$	−25.4693	−0.859548
$879$	−7.11196	−0.239880
$880$	−1.03418	−0.0348623
$881$	−44.6117	−1.50301	−0.751504	−	0.659729i	$-0.770671\pi$
$881$	−44.6117	−1.50301	−0.751504	+	0.659729i	$0.770671\pi$
$882$	−44.0585	−1.48353
$883$	−51.2601	−1.72504	−0.862520	−	0.506023i	$-0.831115\pi$
$883$	−51.2601	−1.72504	−0.862520	+	0.506023i	$0.831115\pi$
$884$	−17.2553	−0.580360
$885$	−5.93649	−0.199553
$886$	−41.8170	−1.40487
$887$	22.7809	0.764909	0.382454	−	0.923974i	$-0.375079\pi$
$887$	22.7809	0.764909	0.382454	+	0.923974i	$0.375079\pi$
$888$	169.394	5.68450
$889$	−48.7709	−1.63572
$890$	−16.1623	−0.541760
$891$	1.01171	0.0338937
$892$	23.5584	0.788795
$893$	−55.5570	−1.85915
$894$	−80.9207	−2.70639
$895$	0.705280	0.0235749
$896$	65.6800	2.19421
$897$	−26.9661	−0.900371
$898$	61.5482	2.05389
$899$	30.3630	1.01266
$900$	−99.2403	−3.30801
$901$	−5.88893	−0.196189
$902$	2.43122	0.0809509
$903$	−27.4718	−0.914204
$904$	−58.5350	−1.94685
$905$	8.91924	0.296486
$906$	−74.5435	−2.47654
$907$	19.0064	0.631098	0.315549	−	0.948909i	$-0.397811\pi$
$907$	19.0064	0.631098	0.315549	+	0.948909i	$0.397811\pi$
$908$	114.385	3.79602
$909$	−32.2438	−1.06946
$910$	9.55562	0.316766
$911$	23.5514	0.780294	0.390147	−	0.920753i	$-0.372424\pi$
$911$	23.5514	0.780294	0.390147	+	0.920753i	$0.372424\pi$
$912$	211.130	6.99122
$913$	0.369213	0.0122192
$914$	−99.0982	−3.27788
$915$	15.8009	0.522361
$916$	69.2135	2.28688
$917$	66.5509	2.19770
$918$	8.83420	0.291572
$919$	14.2469	0.469962	0.234981	−	0.972000i	$-0.424497\pi$
$919$	14.2469	0.469962	0.234981	+	0.972000i	$0.424497\pi$
$920$	14.6774	0.483901
$921$	41.3680	1.36312
$922$	−80.5045	−2.65127
$923$	38.6512	1.27222
$924$	8.85867	0.291429
$925$	35.9853	1.18319
$926$	−89.6523	−2.94616
$927$	−57.6958	−1.89498
$928$	−52.2852	−1.71635
$929$	−7.55706	−0.247939	−0.123970	−	0.992286i	$-0.539563\pi$
$929$	−7.55706	−0.247939	−0.123970	+	0.992286i	$0.539563\pi$
$930$	−29.2323	−0.958564
$931$	26.1846	0.858164
$932$	78.8363	2.58237
$933$	−64.8770	−2.12398
$934$	9.01354	0.294932
$935$	0.106735	0.00349062
$936$	−86.0397	−2.81230
$937$	−5.43539	−0.177566	−0.0887832	−	0.996051i	$-0.528298\pi$
$937$	−5.43539	−0.177566	−0.0887832	+	0.996051i	$0.528298\pi$
$938$	−8.76411	−0.286158
$939$	29.4039	0.959561
$940$	−19.3373	−0.630713
$941$	−39.0714	−1.27369	−0.636845	−	0.770992i	$-0.719761\pi$
$941$	−39.0714	−1.27369	−0.636845	+	0.770992i	$0.719761\pi$
$942$	−40.5478	−1.32112
$943$	−18.9576	−0.617343
$944$	−67.8263	−2.20756
$945$	−3.53455	−0.114979
$946$	1.61827	0.0526144
$947$	−9.90748	−0.321950	−0.160975	−	0.986958i	$-0.551464\pi$
$947$	−9.90748	−0.321950	−0.160975	+	0.986958i	$0.551464\pi$
$948$	−58.4738	−1.89914
$949$	35.7505	1.16051
$950$	81.6341	2.64856
$951$	68.7565	2.22958
$952$	−37.6798	−1.22121
$953$	55.5429	1.79921	0.899606	−	0.436702i	$-0.143854\pi$
$953$	55.5429	1.79921	0.899606	+	0.436702i	$0.143854\pi$
$954$	−47.6764	−1.54358
$955$	4.71527	0.152582
$956$	110.356	3.56916
$957$	−1.57884	−0.0510365
$958$	70.0285	2.26252
$959$	−30.4243	−0.982453
$960$	22.1117	0.713652
$961$	64.9882	2.09640
$962$	50.6556	1.63320
$963$	−49.9183	−1.60859
$964$	−71.6458	−2.30756
$965$	−4.92553	−0.158558
$966$	−95.6081	−3.07614
$967$	23.4971	0.755617	0.377808	−	0.925884i	$-0.376678\pi$
$967$	23.4971	0.755617	0.377808	+	0.925884i	$0.376678\pi$
$968$	94.3805	3.03350
$969$	−21.7902	−0.700002
$970$	8.11184	0.260455
$971$	8.82860	0.283323	0.141662	−	0.989915i	$-0.454756\pi$
$971$	8.82860	0.283323	0.141662	+	0.989915i	$0.454756\pi$
$972$	−111.113	−3.56394
$973$	−37.1601	−1.19130
$974$	−40.0884	−1.28451
$975$	−32.1517	−1.02968
$976$	180.530	5.77863
$977$	20.7425	0.663610	0.331805	−	0.943348i	$-0.392342\pi$
$977$	20.7425	0.663610	0.331805	+	0.943348i	$0.392342\pi$
$978$	−100.810	−3.22353
$979$	−2.75962	−0.0881979
$980$	9.11385	0.291131
$981$	29.2987	0.935436
$982$	−52.1133	−1.66300
$983$	26.2848	0.838355	0.419177	−	0.907904i	$-0.362319\pi$
$983$	26.2848	0.838355	0.419177	+	0.907904i	$0.362319\pi$
$984$	−106.400	−3.39191
$985$	7.12764	0.227105
$986$	10.9036	0.347240
$987$	77.5798	2.46939
$988$	83.0245	2.64136
$989$	−12.6185	−0.401245
$990$	0.864123	0.0274636
$991$	−36.3122	−1.15350	−0.576748	−	0.816922i	$-0.695679\pi$
$991$	−36.3122	−1.15350	−0.576748	+	0.816922i	$0.695679\pi$
$992$	−165.292	−5.24803
$993$	12.1490	0.385536
$994$	137.038	4.34657
$995$	4.74464	0.150415
$996$	−26.2353	−0.831298
$997$	0.857077	0.0271439	0.0135719	−	0.999908i	$-0.495680\pi$
$997$	0.857077	0.0271439	0.0135719	+	0.999908i	$0.495680\pi$
$998$	−75.1489	−2.37880
$999$	−18.7371	−0.592817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.9	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.68457 q^{2} +2.63672 q^{3} +5.20694 q^{4} +0.421516 q^{5} -7.07847 q^{6} -3.33953 q^{7} -8.60926 q^{8} +3.95229 q^{9} +O(q^{10})\)	\(q-2.68457 q^{2} +2.63672 q^{3} +5.20694 q^{4} +0.421516 q^{5} -7.07847 q^{6} -3.33953 q^{7} -8.60926 q^{8} +3.95229 q^{9} -1.13159 q^{10} -0.193213 q^{11} +13.7292 q^{12} +2.52862 q^{13} +8.96522 q^{14} +1.11142 q^{15} +12.6983 q^{16} -1.31056 q^{17} -10.6102 q^{18} +6.30580 q^{19} +2.19481 q^{20} -8.80541 q^{21} +0.518695 q^{22} -4.04455 q^{23} -22.7002 q^{24} -4.82232 q^{25} -6.78827 q^{26} +2.51093 q^{27} -17.3887 q^{28} +3.09910 q^{29} -2.98369 q^{30} +9.79736 q^{31} -16.8711 q^{32} -0.509449 q^{33} +3.51830 q^{34} -1.40767 q^{35} +20.5793 q^{36} -7.46223 q^{37} -16.9284 q^{38} +6.66727 q^{39} -3.62894 q^{40} +4.68719 q^{41} +23.6388 q^{42} +3.11988 q^{43} -1.00605 q^{44} +1.66596 q^{45} +10.8579 q^{46} -8.81047 q^{47} +33.4819 q^{48} +4.15246 q^{49} +12.9459 q^{50} -3.45558 q^{51} +13.1664 q^{52} +4.49344 q^{53} -6.74078 q^{54} -0.0814425 q^{55} +28.7509 q^{56} +16.6266 q^{57} -8.31977 q^{58} -5.34136 q^{59} +5.78709 q^{60} +14.2168 q^{61} -26.3017 q^{62} -13.1988 q^{63} +19.8950 q^{64} +1.06585 q^{65} +1.36765 q^{66} -0.977568 q^{67} -6.82401 q^{68} -10.6643 q^{69} +3.77898 q^{70} +15.2855 q^{71} -34.0263 q^{72} +14.1383 q^{73} +20.0329 q^{74} -12.7151 q^{75} +32.8339 q^{76} +0.645241 q^{77} -17.8988 q^{78} -4.25907 q^{79} +5.35255 q^{80} -5.23626 q^{81} -12.5831 q^{82} -1.91091 q^{83} -45.8492 q^{84} -0.552423 q^{85} -8.37554 q^{86} +8.17146 q^{87} +1.66342 q^{88} +14.2828 q^{89} -4.47238 q^{90} -8.44441 q^{91} -21.0597 q^{92} +25.8329 q^{93} +23.6524 q^{94} +2.65799 q^{95} -44.4843 q^{96} -7.16853 q^{97} -11.1476 q^{98} -0.763635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 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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