LMFDB - Embedded newform 5077.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, 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("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74765 q^{2} +1.79689 q^{3} +5.54960 q^{4} -1.53731 q^{5} -4.93723 q^{6} -2.66154 q^{7} -9.75307 q^{8} +0.228810 q^{9} +O(q^{10})$	\(q-2.74765 q^{2} +1.79689 q^{3} +5.54960 q^{4} -1.53731 q^{5} -4.93723 q^{6} -2.66154 q^{7} -9.75307 q^{8} +0.228810 q^{9} +4.22399 q^{10} +6.00651 q^{11} +9.97201 q^{12} +2.63805 q^{13} +7.31298 q^{14} -2.76237 q^{15} +15.6988 q^{16} -2.14393 q^{17} -0.628690 q^{18} -5.68526 q^{19} -8.53145 q^{20} -4.78248 q^{21} -16.5038 q^{22} +5.77175 q^{23} -17.5252 q^{24} -2.63668 q^{25} -7.24846 q^{26} -4.97952 q^{27} -14.7705 q^{28} -5.82907 q^{29} +7.59004 q^{30} -1.12302 q^{31} -23.6289 q^{32} +10.7930 q^{33} +5.89077 q^{34} +4.09160 q^{35} +1.26980 q^{36} -0.852256 q^{37} +15.6211 q^{38} +4.74029 q^{39} +14.9935 q^{40} -7.11031 q^{41} +13.1406 q^{42} +6.82774 q^{43} +33.3337 q^{44} -0.351751 q^{45} -15.8588 q^{46} +11.9169 q^{47} +28.2091 q^{48} +0.0837686 q^{49} +7.24469 q^{50} -3.85240 q^{51} +14.6401 q^{52} +4.95543 q^{53} +13.6820 q^{54} -9.23386 q^{55} +25.9581 q^{56} -10.2158 q^{57} +16.0163 q^{58} +12.5895 q^{59} -15.3301 q^{60} -6.82849 q^{61} +3.08567 q^{62} -0.608986 q^{63} +33.5262 q^{64} -4.05550 q^{65} -29.6555 q^{66} +3.64999 q^{67} -11.8979 q^{68} +10.3712 q^{69} -11.2423 q^{70} -1.60799 q^{71} -2.23160 q^{72} +13.2649 q^{73} +2.34170 q^{74} -4.73783 q^{75} -31.5509 q^{76} -15.9865 q^{77} -13.0247 q^{78} -0.221411 q^{79} -24.1340 q^{80} -9.63408 q^{81} +19.5367 q^{82} -10.5305 q^{83} -26.5409 q^{84} +3.29588 q^{85} -18.7603 q^{86} -10.4742 q^{87} -58.5819 q^{88} +12.2722 q^{89} +0.966491 q^{90} -7.02127 q^{91} +32.0309 q^{92} -2.01794 q^{93} -32.7436 q^{94} +8.73999 q^{95} -42.4584 q^{96} +13.4558 q^{97} -0.230167 q^{98} +1.37435 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * 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 $

$2$	−2.74765	−1.94288	−0.971442	−	0.237277i	$-0.923745\pi$
$2$	−2.74765	−1.94288	−0.971442	+	0.237277i	$0.923745\pi$
$3$	1.79689	1.03743	0.518717	−	0.854946i	$-0.326410\pi$
$3$	1.79689	1.03743	0.518717	+	0.854946i	$0.326410\pi$
$4$	5.54960	2.77480
$5$	−1.53731	−0.687505	−0.343753	−	0.939060i	$-0.611698\pi$
$5$	−1.53731	−0.687505	−0.343753	+	0.939060i	$0.611698\pi$
$6$	−4.93723	−2.01561
$7$	−2.66154	−1.00597	−0.502983	−	0.864296i	$-0.667764\pi$
$7$	−2.66154	−1.00597	−0.502983	+	0.864296i	$0.667764\pi$
$8$	−9.75307	−3.44823
$9$	0.228810	0.0762700
$10$	4.22399	1.33574
$11$	6.00651	1.81103	0.905516	−	0.424312i	$-0.139484\pi$
$11$	6.00651	1.81103	0.905516	+	0.424312i	$0.139484\pi$
$12$	9.97201	2.87867
$13$	2.63805	0.731664	0.365832	−	0.930681i	$-0.380784\pi$
$13$	2.63805	0.731664	0.365832	+	0.930681i	$0.380784\pi$
$14$	7.31298	1.95447
$15$	−2.76237	−0.713242
$16$	15.6988	3.92471
$17$	−2.14393	−0.519979	−0.259989	−	0.965612i	$-0.583719\pi$
$17$	−2.14393	−0.519979	−0.259989	+	0.965612i	$0.583719\pi$
$18$	−0.628690	−0.148184
$19$	−5.68526	−1.30429	−0.652144	−	0.758095i	$-0.726130\pi$
$19$	−5.68526	−1.30429	−0.652144	+	0.758095i	$0.726130\pi$
$20$	−8.53145	−1.90769
$21$	−4.78248	−1.04362
$22$	−16.5038	−3.51863
$23$	5.77175	1.20349	0.601746	−	0.798687i	$-0.294472\pi$
$23$	5.77175	1.20349	0.601746	+	0.798687i	$0.294472\pi$
$24$	−17.5252	−3.57731
$25$	−2.63668	−0.527337
$26$	−7.24846	−1.42154
$27$	−4.97952	−0.958309
$28$	−14.7705	−2.79135
$29$	−5.82907	−1.08243	−0.541215	−	0.840884i	$-0.682036\pi$
$29$	−5.82907	−1.08243	−0.541215	+	0.840884i	$0.682036\pi$
$30$	7.59004	1.38575
$31$	−1.12302	−0.201700	−0.100850	−	0.994902i	$-0.532156\pi$
$31$	−1.12302	−0.201700	−0.100850	+	0.994902i	$0.532156\pi$
$32$	−23.6289	−4.17703
$33$	10.7930	1.87883
$34$	5.89077	1.01026
$35$	4.09160	0.691607
$36$	1.26980	0.211634
$37$	−0.852256	−0.140110	−0.0700550	−	0.997543i	$-0.522317\pi$
$37$	−0.852256	−0.140110	−0.0700550	+	0.997543i	$0.522317\pi$
$38$	15.6211	2.53408
$39$	4.74029	0.759054
$40$	14.9935	2.37068
$41$	−7.11031	−1.11044	−0.555222	−	0.831702i	$-0.687367\pi$
$41$	−7.11031	−1.11044	−0.555222	+	0.831702i	$0.687367\pi$
$42$	13.1406	2.02764
$43$	6.82774	1.04122	0.520610	−	0.853794i	$-0.325704\pi$
$43$	6.82774	1.04122	0.520610	+	0.853794i	$0.325704\pi$
$44$	33.3337	5.02525
$45$	−0.351751	−0.0524360
$46$	−15.8588	−2.33825
$47$	11.9169	1.73826	0.869132	−	0.494581i	$-0.164678\pi$
$47$	11.9169	1.73826	0.869132	+	0.494581i	$0.164678\pi$
$48$	28.2091	4.07163
$49$	0.0837686	0.0119669
$50$	7.24469	1.02455
$51$	−3.85240	−0.539444
$52$	14.6401	2.03022
$53$	4.95543	0.680681	0.340340	−	0.940302i	$-0.389458\pi$
$53$	4.95543	0.680681	0.340340	+	0.940302i	$0.389458\pi$
$54$	13.6820	1.86188
$55$	−9.23386	−1.24509
$56$	25.9581	3.46880
$57$	−10.2158	−1.35311
$58$	16.0163	2.10304
$59$	12.5895	1.63901	0.819505	−	0.573072i	$-0.194248\pi$
$59$	12.5895	1.63901	0.819505	+	0.573072i	$0.194248\pi$
$60$	−15.3301	−1.97910
$61$	−6.82849	−0.874298	−0.437149	−	0.899389i	$-0.644012\pi$
$61$	−6.82849	−0.874298	−0.437149	+	0.899389i	$0.644012\pi$
$62$	3.08567	0.391880
$63$	−0.608986	−0.0767250
$64$	33.5262	4.19078
$65$	−4.05550	−0.503023
$66$	−29.6555	−3.65034
$67$	3.64999	0.445917	0.222959	−	0.974828i	$-0.428429\pi$
$67$	3.64999	0.445917	0.222959	+	0.974828i	$0.428429\pi$
$68$	−11.8979	−1.44284
$69$	10.3712	1.24854
$70$	−11.2423	−1.34371
$71$	−1.60799	−0.190833	−0.0954165	−	0.995437i	$-0.530418\pi$
$71$	−1.60799	−0.190833	−0.0954165	+	0.995437i	$0.530418\pi$
$72$	−2.23160	−0.262996
$73$	13.2649	1.55254	0.776270	−	0.630401i	$-0.217109\pi$
$73$	13.2649	1.55254	0.776270	+	0.630401i	$0.217109\pi$
$74$	2.34170	0.272218
$75$	−4.73783	−0.547077
$76$	−31.5509	−3.61914
$77$	−15.9865	−1.82184
$78$	−13.0247	−1.47475
$79$	−0.221411	−0.0249107	−0.0124554	−	0.999922i	$-0.503965\pi$
$79$	−0.221411	−0.0249107	−0.0124554	+	0.999922i	$0.503965\pi$
$80$	−24.1340	−2.69826
$81$	−9.63408	−1.07045
$82$	19.5367	2.15746
$83$	−10.5305	−1.15588	−0.577938	−	0.816081i	$-0.696142\pi$
$83$	−10.5305	−1.15588	−0.577938	+	0.816081i	$0.696142\pi$
$84$	−26.5409	−2.89585
$85$	3.29588	0.357488
$86$	−18.7603	−2.02297
$87$	−10.4742	−1.12295
$88$	−58.5819	−6.24485
$89$	12.2722	1.30085	0.650427	−	0.759569i	$-0.274590\pi$
$89$	12.2722	1.30085	0.650427	+	0.759569i	$0.274590\pi$
$90$	0.966491	0.101877
$91$	−7.02127	−0.736029
$92$	32.0309	3.33945
$93$	−2.01794	−0.209251
$94$	−32.7436	−3.37724
$95$	8.73999	0.896704
$96$	−42.4584	−4.33340
$97$	13.4558	1.36623	0.683113	−	0.730313i	$-0.260626\pi$
$97$	13.4558	1.36623	0.683113	+	0.730313i	$0.260626\pi$
$98$	−0.230167	−0.0232504
$99$	1.37435	0.138127
$100$	−14.6325	−1.46325
$101$	6.44246	0.641049	0.320524	−	0.947240i	$-0.396141\pi$
$101$	6.44246	0.641049	0.320524	+	0.947240i	$0.396141\pi$
$102$	10.5851	1.04808
$103$	−7.61928	−0.750750	−0.375375	−	0.926873i	$-0.622486\pi$
$103$	−7.61928	−0.750750	−0.375375	+	0.926873i	$0.622486\pi$
$104$	−25.7291	−2.52295
$105$	7.35215	0.717497
$106$	−13.6158	−1.32248
$107$	−11.8935	−1.14979	−0.574894	−	0.818228i	$-0.694957\pi$
$107$	−11.8935	−1.14979	−0.574894	+	0.818228i	$0.694957\pi$
$108$	−27.6343	−2.65912
$109$	16.6514	1.59492	0.797458	−	0.603374i	$-0.206177\pi$
$109$	16.6514	1.59492	0.797458	+	0.603374i	$0.206177\pi$
$110$	25.3715	2.41907
$111$	−1.53141	−0.145355
$112$	−41.7830	−3.94813
$113$	−2.48707	−0.233964	−0.116982	−	0.993134i	$-0.537322\pi$
$113$	−2.48707	−0.233964	−0.116982	+	0.993134i	$0.537322\pi$
$114$	28.0694	2.62894
$115$	−8.87295	−0.827407
$116$	−32.3490	−3.00353
$117$	0.603613	0.0558040
$118$	−34.5915	−3.18441
$119$	5.70614	0.523081
$120$	26.9416	2.45942
$121$	25.0782	2.27984
$122$	18.7623	1.69866
$123$	−12.7764	−1.15201
$124$	−6.23231	−0.559678
$125$	11.7399	1.05005
$126$	1.67328	0.149068
$127$	−15.9885	−1.41875	−0.709373	−	0.704833i	$-0.751022\pi$
$127$	−15.9885	−1.41875	−0.709373	+	0.704833i	$0.751022\pi$
$128$	−44.8607	−3.96516
$129$	12.2687	1.08020
$130$	11.1431	0.977316
$131$	5.53406	0.483513	0.241756	−	0.970337i	$-0.422276\pi$
$131$	5.53406	0.483513	0.241756	+	0.970337i	$0.422276\pi$
$132$	59.8970	5.21337
$133$	15.1315	1.31207
$134$	−10.0289	−0.866366
$135$	7.65506	0.658843
$136$	20.9099	1.79301
$137$	5.30114	0.452907	0.226453	−	0.974022i	$-0.427287\pi$
$137$	5.30114	0.452907	0.226453	+	0.974022i	$0.427287\pi$
$138$	−28.4964	−2.42578
$139$	−3.68073	−0.312196	−0.156098	−	0.987742i	$-0.549892\pi$
$139$	−3.68073	−0.312196	−0.156098	+	0.987742i	$0.549892\pi$
$140$	22.7067	1.91907
$141$	21.4134	1.80333
$142$	4.41819	0.370766
$143$	15.8455	1.32507
$144$	3.59205	0.299338
$145$	8.96107	0.744177
$146$	−36.4474	−3.01640
$147$	0.150523	0.0124149
$148$	−4.72968	−0.388777
$149$	0.816180	0.0668641	0.0334320	−	0.999441i	$-0.489356\pi$
$149$	0.816180	0.0668641	0.0334320	+	0.999441i	$0.489356\pi$
$150$	13.0179	1.06291
$151$	−16.8816	−1.37380	−0.686901	−	0.726751i	$-0.741029\pi$
$151$	−16.8816	−1.37380	−0.686901	+	0.726751i	$0.741029\pi$
$152$	55.4487	4.49748
$153$	−0.490552	−0.0396588
$154$	43.9255	3.53962
$155$	1.72643	0.138670
$156$	26.3067	2.10622
$157$	−11.9217	−0.951454	−0.475727	−	0.879593i	$-0.657815\pi$
$157$	−11.9217	−0.951454	−0.475727	+	0.879593i	$0.657815\pi$
$158$	0.608362	0.0483987
$159$	8.90436	0.706161
$160$	36.3248	2.87173
$161$	−15.3617	−1.21067
$162$	26.4711	2.07977
$163$	−7.80839	−0.611600	−0.305800	−	0.952096i	$-0.598924\pi$
$163$	−7.80839	−0.611600	−0.305800	+	0.952096i	$0.598924\pi$
$164$	−39.4593	−3.08126
$165$	−16.5922	−1.29170
$166$	28.9342	2.24573
$167$	7.73195	0.598316	0.299158	−	0.954204i	$-0.403294\pi$
$167$	7.73195	0.598316	0.299158	+	0.954204i	$0.403294\pi$
$168$	46.6439	3.59865
$169$	−6.04068	−0.464667
$170$	−9.05593	−0.694558
$171$	−1.30084	−0.0994780
$172$	37.8912	2.88918
$173$	18.7775	1.42763	0.713813	−	0.700336i	$-0.246967\pi$
$173$	18.7775	1.42763	0.713813	+	0.700336i	$0.246967\pi$
$174$	28.7794	2.18176
$175$	7.01762	0.530482
$176$	94.2953	7.10778
$177$	22.6219	1.70037
$178$	−33.7198	−2.52741
$179$	7.70770	0.576101	0.288050	−	0.957615i	$-0.406993\pi$
$179$	7.70770	0.576101	0.288050	+	0.957615i	$0.406993\pi$
$180$	−1.95208	−0.145499
$181$	−16.2930	−1.21105	−0.605526	−	0.795825i	$-0.707037\pi$
$181$	−16.2930	−1.21105	−0.605526	+	0.795825i	$0.707037\pi$
$182$	19.2920	1.43002
$183$	−12.2700	−0.907027
$184$	−56.2922	−4.14992
$185$	1.31018	0.0963264
$186$	5.54461	0.406550
$187$	−12.8775	−0.941698
$188$	66.1342	4.82333
$189$	13.2532	0.964026
$190$	−24.0145	−1.74219
$191$	5.01655	0.362985	0.181493	−	0.983392i	$-0.441907\pi$
$191$	5.01655	0.362985	0.181493	+	0.983392i	$0.441907\pi$
$192$	60.2429	4.34766
$193$	−6.14579	−0.442384	−0.221192	−	0.975230i	$-0.570995\pi$
$193$	−6.14579	−0.442384	−0.221192	+	0.975230i	$0.570995\pi$
$194$	−36.9718	−2.65442
$195$	−7.28729	−0.521853
$196$	0.464882	0.0332059
$197$	19.7033	1.40380	0.701902	−	0.712274i	$-0.252335\pi$
$197$	19.7033	1.40380	0.701902	+	0.712274i	$0.252335\pi$
$198$	−3.77624	−0.268365
$199$	−16.7423	−1.18683	−0.593415	−	0.804896i	$-0.702221\pi$
$199$	−16.7423	−1.18683	−0.593415	+	0.804896i	$0.702221\pi$
$200$	25.7157	1.81838
$201$	6.55863	0.462610
$202$	−17.7016	−1.24548
$203$	15.5143	1.08889
$204$	−21.3793	−1.49685
$205$	10.9307	0.763436
$206$	20.9351	1.45862
$207$	1.32063	0.0917903
$208$	41.4144	2.87157
$209$	−34.1486	−2.36211
$210$	−20.2012	−1.39401
$211$	−2.20807	−0.152010	−0.0760048	−	0.997107i	$-0.524216\pi$
$211$	−2.20807	−0.152010	−0.0760048	+	0.997107i	$0.524216\pi$
$212$	27.5006	1.88875
$213$	−2.88938	−0.197977
$214$	32.6792	2.23391
$215$	−10.4963	−0.715845
$216$	48.5656	3.30447
$217$	2.98896	0.202904
$218$	−45.7523	−3.09874
$219$	23.8356	1.61066
$220$	−51.2442	−3.45489
$221$	−5.65579	−0.380450
$222$	4.20778	0.282408
$223$	11.2610	0.754094	0.377047	−	0.926194i	$-0.376939\pi$
$223$	11.2610	0.754094	0.377047	+	0.926194i	$0.376939\pi$
$224$	62.8890	4.20195
$225$	−0.603299	−0.0402199
$226$	6.83360	0.454565
$227$	22.0937	1.46641	0.733204	−	0.680008i	$-0.238024\pi$
$227$	22.0937	1.46641	0.733204	+	0.680008i	$0.238024\pi$
$228$	−56.6935	−3.75462
$229$	−3.92434	−0.259328	−0.129664	−	0.991558i	$-0.541390\pi$
$229$	−3.92434	−0.259328	−0.129664	+	0.991558i	$0.541390\pi$
$230$	24.3798	1.60756
$231$	−28.7260	−1.89003
$232$	56.8513	3.73247
$233$	22.8343	1.49593	0.747963	−	0.663740i	$-0.231032\pi$
$233$	22.8343	1.49593	0.747963	+	0.663740i	$0.231032\pi$
$234$	−1.65852	−0.108421
$235$	−18.3200	−1.19507
$236$	69.8665	4.54792
$237$	−0.397852	−0.0258432
$238$	−15.6785	−1.01628
$239$	27.2646	1.76360	0.881800	−	0.471624i	$-0.156332\pi$
$239$	27.2646	1.76360	0.881800	+	0.471624i	$0.156332\pi$
$240$	−43.3661	−2.79927
$241$	−24.9771	−1.60891	−0.804457	−	0.594011i	$-0.797543\pi$
$241$	−24.9771	−1.60891	−0.804457	+	0.594011i	$0.797543\pi$
$242$	−68.9062	−4.42946
$243$	−2.37280	−0.152215
$244$	−37.8954	−2.42600
$245$	−0.128778	−0.00822733
$246$	35.1052	2.23823
$247$	−14.9980	−0.954300
$248$	10.9529	0.695509
$249$	−18.9222	−1.19915
$250$	−32.2573	−2.04013
$251$	19.6007	1.23719	0.618593	−	0.785711i	$-0.287703\pi$
$251$	19.6007	1.23719	0.618593	+	0.785711i	$0.287703\pi$
$252$	−3.37963	−0.212896
$253$	34.6681	2.17956
$254$	43.9307	2.75646
$255$	5.92232	0.370870
$256$	56.2092	3.51308
$257$	−1.96280	−0.122436	−0.0612179	−	0.998124i	$-0.519498\pi$
$257$	−1.96280	−0.122436	−0.0612179	+	0.998124i	$0.519498\pi$
$258$	−33.7101	−2.09870
$259$	2.26831	0.140946
$260$	−22.5064	−1.39579
$261$	−1.33375	−0.0825569
$262$	−15.2057	−0.939410
$263$	−21.0955	−1.30080	−0.650401	−	0.759591i	$-0.725399\pi$
$263$	−21.0955	−1.30080	−0.650401	+	0.759591i	$0.725399\pi$
$264$	−105.265	−6.47863
$265$	−7.61802	−0.467971
$266$	−41.5761	−2.54920
$267$	22.0518	1.34955
$268$	20.2560	1.23733
$269$	19.3251	1.17827	0.589135	−	0.808034i	$-0.299469\pi$
$269$	19.3251	1.17827	0.589135	+	0.808034i	$0.299469\pi$
$270$	−21.0335	−1.28006
$271$	12.3351	0.749305	0.374652	−	0.927165i	$-0.377762\pi$
$271$	12.3351	0.749305	0.374652	+	0.927165i	$0.377762\pi$
$272$	−33.6572	−2.04077
$273$	−12.6164	−0.763582
$274$	−14.5657	−0.879946
$275$	−15.8373	−0.955023
$276$	57.5559	3.46446
$277$	−5.99215	−0.360034	−0.180017	−	0.983664i	$-0.557615\pi$
$277$	−5.99215	−0.360034	−0.180017	+	0.983664i	$0.557615\pi$
$278$	10.1134	0.606560
$279$	−0.256958	−0.0153837
$280$	−39.9057	−2.38482
$281$	−8.17397	−0.487618	−0.243809	−	0.969823i	$-0.578397\pi$
$281$	−8.17397	−0.487618	−0.243809	+	0.969823i	$0.578397\pi$
$282$	−58.8366	−3.50367
$283$	−16.1185	−0.958144	−0.479072	−	0.877776i	$-0.659027\pi$
$283$	−16.1185	−0.958144	−0.479072	+	0.877776i	$0.659027\pi$
$284$	−8.92369	−0.529523
$285$	15.7048	0.930272
$286$	−43.5379	−2.57445
$287$	18.9243	1.11707
$288$	−5.40652	−0.318582
$289$	−12.4036	−0.729622
$290$	−24.6219	−1.44585
$291$	24.1785	1.41737
$292$	73.6149	4.30799
$293$	18.4366	1.07708	0.538540	−	0.842600i	$-0.318976\pi$
$293$	18.4366	1.07708	0.538540	+	0.842600i	$0.318976\pi$
$294$	−0.413585	−0.0241207
$295$	−19.3539	−1.12683
$296$	8.31211	0.483131
$297$	−29.9096	−1.73553
$298$	−2.24258	−0.129909
$299$	15.2262	0.880552
$300$	−26.2930	−1.51803
$301$	−18.1723	−1.04743
$302$	46.3847	2.66914
$303$	11.5764	0.665046
$304$	−89.2520	−5.11895
$305$	10.4975	0.601085
$306$	1.34787	0.0770524
$307$	19.0580	1.08770	0.543848	−	0.839184i	$-0.316967\pi$
$307$	19.0580	1.08770	0.543848	+	0.839184i	$0.316967\pi$
$308$	−88.7189	−5.05523
$309$	−13.6910	−0.778853
$310$	−4.74363	−0.269420
$311$	−27.6210	−1.56624	−0.783120	−	0.621870i	$-0.786373\pi$
$311$	−27.6210	−1.56624	−0.783120	+	0.621870i	$0.786373\pi$
$312$	−46.2323	−2.61739
$313$	31.9583	1.80639	0.903196	−	0.429229i	$-0.141215\pi$
$313$	31.9583	1.80639	0.903196	+	0.429229i	$0.141215\pi$
$314$	32.7567	1.84857
$315$	0.936199	0.0527488
$316$	−1.22874	−0.0691223
$317$	−26.2116	−1.47219	−0.736094	−	0.676880i	$-0.763332\pi$
$317$	−26.2116	−1.47219	−0.736094	+	0.676880i	$0.763332\pi$
$318$	−24.4661	−1.37199
$319$	−35.0124	−1.96032
$320$	−51.5401	−2.88118
$321$	−21.3713	−1.19283
$322$	42.2086	2.35220
$323$	12.1888	0.678201
$324$	−53.4653	−2.97029
$325$	−6.95571	−0.385833
$326$	21.4548	1.18827
$327$	29.9207	1.65462
$328$	69.3473	3.82906
$329$	−31.7173	−1.74863
$330$	45.5897	2.50963
$331$	23.5932	1.29680	0.648400	−	0.761300i	$-0.275438\pi$
$331$	23.5932	1.29680	0.648400	+	0.761300i	$0.275438\pi$
$332$	−58.4402	−3.20732
$333$	−0.195005	−0.0106862
$334$	−21.2447	−1.16246
$335$	−5.61116	−0.306570
$336$	−75.0795	−4.09592
$337$	23.8780	1.30072	0.650360	−	0.759626i	$-0.274618\pi$
$337$	23.8780	1.30072	0.650360	+	0.759626i	$0.274618\pi$
$338$	16.5977	0.902795
$339$	−4.46899	−0.242722
$340$	18.2908	0.991957
$341$	−6.74543	−0.365286
$342$	3.57427	0.193274
$343$	18.4078	0.993927
$344$	−66.5914	−3.59037
$345$	−15.9437	−0.858381
$346$	−51.5940	−2.77371
$347$	17.6057	0.945124	0.472562	−	0.881297i	$-0.343329\pi$
$347$	17.6057	0.945124	0.472562	+	0.881297i	$0.343329\pi$
$348$	−58.1275	−3.11596
$349$	12.5489	0.671725	0.335862	−	0.941911i	$-0.390972\pi$
$349$	12.5489	0.671725	0.335862	+	0.941911i	$0.390972\pi$
$350$	−19.2820	−1.03067
$351$	−13.1362	−0.701161
$352$	−141.927	−7.56474
$353$	11.8941	0.633059	0.316529	−	0.948583i	$-0.397482\pi$
$353$	11.8941	0.633059	0.316529	+	0.948583i	$0.397482\pi$
$354$	−62.1571	−3.30361
$355$	2.47197	0.131199
$356$	68.1060	3.60961
$357$	10.2533	0.542662
$358$	−21.1781	−1.11930
$359$	−25.0803	−1.32369	−0.661844	−	0.749642i	$-0.730226\pi$
$359$	−25.0803	−1.32369	−0.661844	+	0.749642i	$0.730226\pi$
$360$	3.43066	0.180811
$361$	13.3221	0.701165
$362$	44.7676	2.35294
$363$	45.0627	2.36518
$364$	−38.9652	−2.04233
$365$	−20.3922	−1.06738
$366$	33.7138	1.76225
$367$	10.8592	0.566844	0.283422	−	0.958995i	$-0.408530\pi$
$367$	10.8592	0.566844	0.283422	+	0.958995i	$0.408530\pi$
$368$	90.6098	4.72336
$369$	−1.62691	−0.0846935
$370$	−3.59992	−0.187151
$371$	−13.1890	−0.684741
$372$	−11.1988	−0.580629
$373$	22.7268	1.17675	0.588375	−	0.808588i	$-0.299768\pi$
$373$	22.7268	1.17675	0.588375	+	0.808588i	$0.299768\pi$
$374$	35.3830	1.82961
$375$	21.0954	1.08936
$376$	−116.227	−5.99393
$377$	−15.3774	−0.791976
$378$	−36.4151	−1.87299
$379$	15.4174	0.791938	0.395969	−	0.918264i	$-0.370409\pi$
$379$	15.4174	0.791938	0.395969	+	0.918264i	$0.370409\pi$
$380$	48.5035	2.48817
$381$	−28.7295	−1.47186
$382$	−13.7838	−0.705238
$383$	16.0382	0.819512	0.409756	−	0.912195i	$-0.365614\pi$
$383$	16.0382	0.819512	0.409756	+	0.912195i	$0.365614\pi$
$384$	−80.6097	−4.11360
$385$	24.5763	1.25252
$386$	16.8865	0.859500
$387$	1.56225	0.0794139
$388$	74.6741	3.79100
$389$	−8.86877	−0.449664	−0.224832	−	0.974398i	$-0.572183\pi$
$389$	−8.86877	−0.449664	−0.224832	+	0.974398i	$0.572183\pi$
$390$	20.0229	1.01390
$391$	−12.3742	−0.625790
$392$	−0.817000	−0.0412648
$393$	9.94409	0.501613
$394$	−54.1379	−2.72743
$395$	0.340378	0.0171263
$396$	7.62709	0.383276
$397$	−5.93564	−0.297901	−0.148951	−	0.988845i	$-0.547590\pi$
$397$	−5.93564	−0.297901	−0.148951	+	0.988845i	$0.547590\pi$
$398$	46.0021	2.30587
$399$	27.1896	1.36118
$400$	−41.3929	−2.06964
$401$	−5.73143	−0.286214	−0.143107	−	0.989707i	$-0.545709\pi$
$401$	−5.73143	−0.286214	−0.143107	+	0.989707i	$0.545709\pi$
$402$	−18.0208	−0.898798
$403$	−2.96259	−0.147577
$404$	35.7531	1.77878
$405$	14.8105	0.735942
$406$	−42.6278	−2.11558
$407$	−5.11909	−0.253744
$408$	37.5727	1.86013
$409$	28.4758	1.40804	0.704018	−	0.710182i	$-0.251388\pi$
$409$	28.4758	1.40804	0.704018	+	0.710182i	$0.251388\pi$
$410$	−30.0339	−1.48327
$411$	9.52556	0.469861
$412$	−42.2839	−2.08318
$413$	−33.5073	−1.64879
$414$	−3.62864	−0.178338
$415$	16.1887	0.794671
$416$	−62.3342	−3.05618
$417$	−6.61387	−0.323883
$418$	93.8284	4.58930
$419$	−0.262449	−0.0128215	−0.00641073	−	0.999979i	$-0.502041\pi$
$419$	−0.262449	−0.0128215	−0.00641073	+	0.999979i	$0.502041\pi$
$420$	40.8015	1.99091
$421$	2.33993	0.114041	0.0570205	−	0.998373i	$-0.481840\pi$
$421$	2.33993	0.114041	0.0570205	+	0.998373i	$0.481840\pi$
$422$	6.06700	0.295337
$423$	2.72671	0.132577
$424$	−48.3306	−2.34714
$425$	5.65285	0.274204
$426$	7.93900	0.384646
$427$	18.1743	0.879514
$428$	−66.0042	−3.19043
$429$	28.4726	1.37467
$430$	28.8403	1.39080
$431$	31.6224	1.52320	0.761599	−	0.648049i	$-0.224415\pi$
$431$	31.6224	1.52320	0.761599	+	0.648049i	$0.224415\pi$
$432$	−78.1727	−3.76109
$433$	36.3318	1.74599	0.872997	−	0.487725i	$-0.162173\pi$
$433$	36.3318	1.74599	0.872997	+	0.487725i	$0.162173\pi$
$434$	−8.21262	−0.394218
$435$	16.1021	0.772034
$436$	92.4087	4.42557
$437$	−32.8139	−1.56970
$438$	−65.4919	−3.12932
$439$	−4.87129	−0.232494	−0.116247	−	0.993220i	$-0.537086\pi$
$439$	−4.87129	−0.232494	−0.116247	+	0.993220i	$0.537086\pi$
$440$	90.0585	4.29337
$441$	0.0191671	0.000912718 0
$442$	15.5402	0.739170
$443$	28.8189	1.36923	0.684613	−	0.728907i	$-0.259971\pi$
$443$	28.8189	1.36923	0.684613	+	0.728907i	$0.259971\pi$
$444$	−8.49871	−0.403331
$445$	−18.8662	−0.894344
$446$	−30.9414	−1.46512
$447$	1.46658	0.0693671
$448$	−89.2312	−4.21578
$449$	38.6122	1.82222	0.911112	−	0.412159i	$-0.135225\pi$
$449$	38.6122	1.82222	0.911112	+	0.412159i	$0.135225\pi$
$450$	1.65766	0.0781427
$451$	−42.7081	−2.01105
$452$	−13.8022	−0.649203
$453$	−30.3343	−1.42523
$454$	−60.7058	−2.84906
$455$	10.7939	0.506024
$456$	99.6351	4.66584
$457$	19.9686	0.934091	0.467046	−	0.884233i	$-0.345318\pi$
$457$	19.9686	0.934091	0.467046	+	0.884233i	$0.345318\pi$
$458$	10.7827	0.503844
$459$	10.6757	0.498300
$460$	−49.2413	−2.29589
$461$	−31.6643	−1.47475	−0.737377	−	0.675481i	$-0.763936\pi$
$461$	−31.6643	−1.47475	−0.737377	+	0.675481i	$0.763936\pi$
$462$	78.9292	3.67212
$463$	−5.32366	−0.247411	−0.123706	−	0.992319i	$-0.539478\pi$
$463$	−5.32366	−0.247411	−0.123706	+	0.992319i	$0.539478\pi$
$464$	−91.5096	−4.24823
$465$	3.10220	0.143861
$466$	−62.7408	−2.90641
$467$	35.1204	1.62518	0.812589	−	0.582837i	$-0.198057\pi$
$467$	35.1204	1.62518	0.812589	+	0.582837i	$0.198057\pi$
$468$	3.34981	0.154845
$469$	−9.71458	−0.448577
$470$	50.3370	2.32187
$471$	−21.4219	−0.987071
$472$	−122.786	−5.65168
$473$	41.0109	1.88568
$474$	1.09316	0.0502104
$475$	14.9902	0.687798
$476$	31.6668	1.45144
$477$	1.13385	0.0519155
$478$	−74.9136	−3.42647
$479$	−15.4434	−0.705625	−0.352813	−	0.935694i	$-0.614775\pi$
$479$	−15.4434	−0.705625	−0.352813	+	0.935694i	$0.614775\pi$
$480$	65.2717	2.97923
$481$	−2.24830	−0.102513
$482$	68.6283	3.12593
$483$	−27.6033	−1.25599
$484$	139.174	6.32609
$485$	−20.6857	−0.939288
$486$	6.51964	0.295737
$487$	36.2029	1.64051	0.820255	−	0.571998i	$-0.193831\pi$
$487$	36.2029	1.64051	0.820255	+	0.571998i	$0.193831\pi$
$488$	66.5987	3.01478
$489$	−14.0308	−0.634495
$490$	0.353838	0.0159848
$491$	28.9409	1.30608	0.653042	−	0.757322i	$-0.273493\pi$
$491$	28.9409	1.30608	0.653042	+	0.757322i	$0.273493\pi$
$492$	−70.9041	−3.19660
$493$	12.4971	0.562841
$494$	41.2093	1.85410
$495$	−2.11280	−0.0949633
$496$	−17.6301	−0.791616
$497$	4.27972	0.191971
$498$	51.9916	2.32980
$499$	−1.67147	−0.0748251	−0.0374126	−	0.999300i	$-0.511912\pi$
$499$	−1.67147	−0.0748251	−0.0374126	+	0.999300i	$0.511912\pi$
$500$	65.1519	2.91368
$501$	13.8935	0.620714
$502$	−53.8560	−2.40371
$503$	−14.5452	−0.648537	−0.324268	−	0.945965i	$-0.605118\pi$
$503$	−14.5452	−0.648537	−0.324268	+	0.945965i	$0.605118\pi$
$504$	5.93948	0.264565
$505$	−9.90405	−0.440724
$506$	−95.2558	−4.23464
$507$	−10.8544	−0.482062
$508$	−88.7295	−3.93674
$509$	19.5158	0.865024	0.432512	−	0.901628i	$-0.357627\pi$
$509$	19.5158	0.865024	0.432512	+	0.901628i	$0.357627\pi$
$510$	−16.2725	−0.720558
$511$	−35.3050	−1.56180
$512$	−64.7220	−2.86034
$513$	28.3099	1.24991
$514$	5.39308	0.237879
$515$	11.7132	0.516144
$516$	68.0863	2.99733
$517$	71.5792	3.14805
$518$	−6.23253	−0.273841
$519$	33.7411	1.48107
$520$	39.5536	1.73454
$521$	10.0222	0.439080	0.219540	−	0.975604i	$-0.429544\pi$
$521$	10.0222	0.439080	0.219540	+	0.975604i	$0.429544\pi$
$522$	3.66468	0.160399
$523$	−10.3345	−0.451896	−0.225948	−	0.974139i	$-0.572548\pi$
$523$	−10.3345	−0.451896	−0.225948	+	0.974139i	$0.572548\pi$
$524$	30.7118	1.34165
$525$	12.6099	0.550341
$526$	57.9630	2.52731
$527$	2.40767	0.104880
$528$	169.438	7.37385
$529$	10.3130	0.448393
$530$	20.9317	0.909214
$531$	2.88060	0.125007
$532$	83.9738	3.64073
$533$	−18.7574	−0.812472
$534$	−60.5908	−2.62202
$535$	18.2840	0.790486
$536$	−35.5986	−1.53763
$537$	13.8499	0.597667
$538$	−53.0986	−2.28924
$539$	0.503157	0.0216725
$540$	42.4825	1.82816
$541$	−23.3728	−1.00488	−0.502439	−	0.864613i	$-0.667564\pi$
$541$	−23.3728	−1.00488	−0.502439	+	0.864613i	$0.667564\pi$
$542$	−33.8926	−1.45581
$543$	−29.2768	−1.25639
$544$	50.6585	2.17197
$545$	−25.5984	−1.09651
$546$	34.6656	1.48355
$547$	10.1669	0.434706	0.217353	−	0.976093i	$-0.430258\pi$
$547$	10.1669	0.434706	0.217353	+	0.976093i	$0.430258\pi$
$548$	29.4192	1.25673
$549$	−1.56243	−0.0666827
$550$	43.5153	1.85550
$551$	33.1397	1.41180
$552$	−101.151	−4.30527
$553$	0.589294	0.0250593
$554$	16.4644	0.699503
$555$	2.35425	0.0999323
$556$	−20.4266	−0.866280
$557$	20.5719	0.871658	0.435829	−	0.900030i	$-0.356455\pi$
$557$	20.5719	0.871658	0.435829	+	0.900030i	$0.356455\pi$
$558$	0.706032	0.0298887
$559$	18.0119	0.761824
$560$	64.2334	2.71436
$561$	−23.1395	−0.976949
$562$	22.4592	0.947386
$563$	−17.5320	−0.738886	−0.369443	−	0.929253i	$-0.620452\pi$
$563$	−17.5320	−0.738886	−0.369443	+	0.929253i	$0.620452\pi$
$564$	118.836	5.00389
$565$	3.82339	0.160851
$566$	44.2880	1.86156
$567$	25.6414	1.07684
$568$	15.6828	0.658036
$569$	7.49755	0.314314	0.157157	−	0.987574i	$-0.449767\pi$
$569$	7.49755	0.314314	0.157157	+	0.987574i	$0.449767\pi$
$570$	−43.1513	−1.80741
$571$	−5.90334	−0.247047	−0.123524	−	0.992342i	$-0.539419\pi$
$571$	−5.90334	−0.247047	−0.123524	+	0.992342i	$0.539419\pi$
$572$	87.9362	3.67680
$573$	9.01419	0.376573
$574$	−51.9975	−2.17033
$575$	−15.2183	−0.634645
$576$	7.67113	0.319630
$577$	−27.6448	−1.15087	−0.575433	−	0.817849i	$-0.695167\pi$
$577$	−27.6448	−1.15087	−0.575433	+	0.817849i	$0.695167\pi$
$578$	34.0807	1.41757
$579$	−11.0433	−0.458944
$580$	49.7304	2.06494
$581$	28.0274	1.16277
$582$	−66.4342	−2.75379
$583$	29.7648	1.23273
$584$	−129.373	−5.35351
$585$	−0.927939	−0.0383656
$586$	−50.6575	−2.09264
$587$	−46.3180	−1.91175	−0.955875	−	0.293773i	$-0.905089\pi$
$587$	−46.3180	−1.91175	−0.955875	+	0.293773i	$0.905089\pi$
$588$	0.835341	0.0344489
$589$	6.38466	0.263075
$590$	53.1778	2.18930
$591$	35.4047	1.45635
$592$	−13.3794	−0.549891
$593$	30.9064	1.26917	0.634587	−	0.772852i	$-0.281170\pi$
$593$	30.9064	1.26917	0.634587	+	0.772852i	$0.281170\pi$
$594$	82.1811	3.37193
$595$	−8.77209	−0.359621
$596$	4.52947	0.185534
$597$	−30.0841	−1.23126
$598$	−41.8362	−1.71081
$599$	−10.3533	−0.423024	−0.211512	−	0.977375i	$-0.567839\pi$
$599$	−10.3533	−0.423024	−0.211512	+	0.977375i	$0.567839\pi$
$600$	46.2083	1.88645
$601$	−15.9140	−0.649145	−0.324572	−	0.945861i	$-0.605220\pi$
$601$	−15.9140	−0.649145	−0.324572	+	0.945861i	$0.605220\pi$
$602$	49.9311	2.03504
$603$	0.835154	0.0340101
$604$	−93.6858	−3.81202
$605$	−38.5529	−1.56740
$606$	−31.8079	−1.29211
$607$	30.0623	1.22019	0.610096	−	0.792327i	$-0.291131\pi$
$607$	30.0623	1.22019	0.610096	+	0.792327i	$0.291131\pi$
$608$	134.336	5.44805
$609$	27.8774	1.12965
$610$	−28.8435	−1.16784
$611$	31.4375	1.27183
$612$	−2.72236	−0.110045
$613$	−7.40276	−0.298994	−0.149497	−	0.988762i	$-0.547766\pi$
$613$	−7.40276	−0.298994	−0.149497	+	0.988762i	$0.547766\pi$
$614$	−52.3647	−2.11327
$615$	19.6413	0.792014
$616$	155.918	6.28211
$617$	−0.862925	−0.0347401	−0.0173700	−	0.999849i	$-0.505529\pi$
$617$	−0.862925	−0.0347401	−0.0173700	+	0.999849i	$0.505529\pi$
$618$	37.6181	1.51322
$619$	11.0332	0.443462	0.221731	−	0.975108i	$-0.428829\pi$
$619$	11.0332	0.443462	0.221731	+	0.975108i	$0.428829\pi$
$620$	9.58098	0.384782
$621$	−28.7405	−1.15332
$622$	75.8928	3.04302
$623$	−32.6630	−1.30861
$624$	74.4171	2.97907
$625$	−4.86449	−0.194580
$626$	−87.8104	−3.50961
$627$	−61.3612	−2.45053
$628$	−66.1606	−2.64009
$629$	1.82717	0.0728542
$630$	−2.57235	−0.102485
$631$	19.7789	0.787386	0.393693	−	0.919242i	$-0.371197\pi$
$631$	19.7789	0.787386	0.393693	+	0.919242i	$0.371197\pi$
$632$	2.15944	0.0858979
$633$	−3.96765	−0.157700
$634$	72.0203	2.86029
$635$	24.5792	0.975396
$636$	49.4156	1.95946
$637$	0.220986	0.00875578
$638$	96.2018	3.80867
$639$	−0.367924	−0.0145548
$640$	68.9647	2.72607
$641$	−13.4011	−0.529312	−0.264656	−	0.964343i	$-0.585258\pi$
$641$	−13.4011	−0.529312	−0.264656	+	0.964343i	$0.585258\pi$
$642$	58.7210	2.31753
$643$	2.51171	0.0990523	0.0495262	−	0.998773i	$-0.484229\pi$
$643$	2.51171	0.0990523	0.0495262	+	0.998773i	$0.484229\pi$
$644$	−85.2513	−3.35937
$645$	−18.8608	−0.742642
$646$	−33.4905	−1.31767
$647$	−38.0294	−1.49509	−0.747545	−	0.664211i	$-0.768768\pi$
$647$	−38.0294	−1.49509	−0.747545	+	0.664211i	$0.768768\pi$
$648$	93.9618	3.69117
$649$	75.6188	2.96830
$650$	19.1119	0.749629
$651$	5.37082	0.210499
$652$	−43.3334	−1.69707
$653$	−20.6623	−0.808579	−0.404290	−	0.914631i	$-0.632481\pi$
$653$	−20.6623	−0.808579	−0.404290	+	0.914631i	$0.632481\pi$
$654$	−82.2118	−3.21474
$655$	−8.50755	−0.332418
$656$	−111.624	−4.35817
$657$	3.03514	0.118412
$658$	87.1482	3.39739
$659$	−38.0504	−1.48224	−0.741118	−	0.671375i	$-0.765704\pi$
$659$	−38.0504	−1.48224	−0.741118	+	0.671375i	$0.765704\pi$
$660$	−92.0802	−3.58422
$661$	39.9475	1.55378	0.776889	−	0.629637i	$-0.216796\pi$
$661$	39.9475	1.55378	0.776889	+	0.629637i	$0.216796\pi$
$662$	−64.8260	−2.51953
$663$	−10.1628	−0.394692
$664$	102.705	3.98573
$665$	−23.2618	−0.902054
$666$	0.535805	0.0207620
$667$	−33.6439	−1.30270
$668$	42.9092	1.66021
$669$	20.2348	0.782323
$670$	15.4175	0.595631
$671$	−41.0154	−1.58338
$672$	113.005	4.35925
$673$	45.4721	1.75282	0.876410	−	0.481565i	$-0.159931\pi$
$673$	45.4721	1.75282	0.876410	+	0.481565i	$0.159931\pi$
$674$	−65.6086	−2.52715
$675$	13.1294	0.505351
$676$	−33.5233	−1.28936
$677$	13.8720	0.533145	0.266573	−	0.963815i	$-0.414109\pi$
$677$	13.8720	0.533145	0.266573	+	0.963815i	$0.414109\pi$
$678$	12.2792	0.471581
$679$	−35.8130	−1.37438
$680$	−32.1449	−1.23270
$681$	39.6999	1.52130
$682$	18.5341	0.709708
$683$	9.88924	0.378401	0.189201	−	0.981938i	$-0.439410\pi$
$683$	9.88924	0.378401	0.189201	+	0.981938i	$0.439410\pi$
$684$	−7.21916	−0.276031
$685$	−8.14949	−0.311376
$686$	−50.5782	−1.93109
$687$	−7.05161	−0.269036
$688$	107.188	4.08649
$689$	13.0727	0.498030
$690$	43.8078	1.66773
$691$	−42.2294	−1.60648	−0.803241	−	0.595655i	$-0.796893\pi$
$691$	−42.2294	−1.60648	−0.803241	+	0.595655i	$0.796893\pi$
$692$	104.208	3.96138
$693$	−3.65788	−0.138951
$694$	−48.3744	−1.83627
$695$	5.65842	0.214636
$696$	102.155	3.87219
$697$	15.2440	0.577407
$698$	−34.4799	−1.30508
$699$	41.0307	1.55192
$700$	38.9450	1.47198
$701$	18.5998	0.702505	0.351253	−	0.936281i	$-0.385756\pi$
$701$	18.5998	0.702505	0.351253	+	0.936281i	$0.385756\pi$
$702$	36.0938	1.36227
$703$	4.84529	0.182744
$704$	201.376	7.58963
$705$	−32.9190	−1.23980
$706$	−32.6809	−1.22996
$707$	−17.1468	−0.644873
$708$	125.542	4.71817
$709$	−30.6046	−1.14938	−0.574690	−	0.818371i	$-0.694877\pi$
$709$	−30.6046	−1.14938	−0.574690	+	0.818371i	$0.694877\pi$
$710$	−6.79213	−0.254904
$711$	−0.0506611	−0.00189994
$712$	−119.692	−4.48564
$713$	−6.48179	−0.242745
$714$	−28.1725	−1.05433
$715$	−24.3594	−0.910991
$716$	42.7746	1.59856
$717$	48.9914	1.82962
$718$	68.9120	2.57177
$719$	−29.2485	−1.09079	−0.545393	−	0.838181i	$-0.683619\pi$
$719$	−29.2485	−1.09079	−0.545393	+	0.838181i	$0.683619\pi$
$720$	−5.52209	−0.205796
$721$	20.2790	0.755228
$722$	−36.6046	−1.36228
$723$	−44.8810	−1.66914
$724$	−90.4199	−3.36043
$725$	15.3694	0.570805
$726$	−123.817	−4.59527
$727$	−12.0050	−0.445239	−0.222620	−	0.974905i	$-0.571461\pi$
$727$	−12.0050	−0.445239	−0.222620	+	0.974905i	$0.571461\pi$
$728$	68.4789	2.53800
$729$	24.6386	0.912539
$730$	56.0308	2.07379
$731$	−14.6382	−0.541412
$732$	−68.0938	−2.51682
$733$	14.5821	0.538604	0.269302	−	0.963056i	$-0.413207\pi$
$733$	14.5821	0.538604	0.269302	+	0.963056i	$0.413207\pi$
$734$	−29.8372	−1.10131
$735$	−0.231400	−0.00853532
$736$	−136.380	−5.02702
$737$	21.9237	0.807570
$738$	4.47018	0.164550
$739$	−13.4481	−0.494698	−0.247349	−	0.968926i	$-0.579559\pi$
$739$	−13.4481	−0.494698	−0.247349	+	0.968926i	$0.579559\pi$
$740$	7.27097	0.267286
$741$	−26.9498	−0.990024
$742$	36.2389	1.33037
$743$	−35.5887	−1.30562	−0.652812	−	0.757520i	$-0.726411\pi$
$743$	−35.5887	−1.30562	−0.652812	+	0.757520i	$0.726411\pi$
$744$	19.6811	0.721545
$745$	−1.25472	−0.0459694
$746$	−62.4454	−2.28629
$747$	−2.40949	−0.0881586
$748$	−71.4651	−2.61302
$749$	31.6550	1.15665
$750$	−57.9627	−2.11650
$751$	48.3330	1.76370	0.881848	−	0.471534i	$-0.156300\pi$
$751$	48.3330	1.76370	0.881848	+	0.471534i	$0.156300\pi$
$752$	187.082	6.82218
$753$	35.2203	1.28350
$754$	42.2517	1.53872
$755$	25.9522	0.944496
$756$	73.5498	2.67498
$757$	21.6110	0.785465	0.392733	−	0.919653i	$-0.371530\pi$
$757$	21.6110	0.785465	0.392733	+	0.919653i	$0.371530\pi$
$758$	−42.3617	−1.53864
$759$	62.2947	2.26115
$760$	−85.2417	−3.09204
$761$	−40.2274	−1.45824	−0.729121	−	0.684385i	$-0.760071\pi$
$761$	−40.2274	−1.45824	−0.729121	+	0.684385i	$0.760071\pi$
$762$	78.9387	2.85965
$763$	−44.3183	−1.60443
$764$	27.8399	1.00721
$765$	0.754129	0.0272656
$766$	−44.0673	−1.59222
$767$	33.2117	1.19921
$768$	101.002	3.64459
$769$	5.16990	0.186432	0.0932158	−	0.995646i	$-0.470285\pi$
$769$	5.16990	0.186432	0.0932158	+	0.995646i	$0.470285\pi$
$770$	−67.5270	−2.43350
$771$	−3.52693	−0.127019
$772$	−34.1067	−1.22753
$773$	−21.8922	−0.787407	−0.393703	−	0.919237i	$-0.628806\pi$
$773$	−21.8922	−0.787407	−0.393703	+	0.919237i	$0.628806\pi$
$774$	−4.29253	−0.154292
$775$	2.96105	0.106364
$776$	−131.235	−4.71106
$777$	4.07590	0.146222
$778$	24.3683	0.873646
$779$	40.4239	1.44834
$780$	−40.4415	−1.44804
$781$	−9.65840	−0.345605
$782$	34.0000	1.21584
$783$	29.0260	1.03730
$784$	1.31507	0.0469668
$785$	18.3273	0.654130
$786$	−27.3229	−0.974576
$787$	−32.4625	−1.15716	−0.578582	−	0.815625i	$-0.696394\pi$
$787$	−32.4625	−1.15716	−0.578582	+	0.815625i	$0.696394\pi$
$788$	109.346	3.89527
$789$	−37.9062	−1.34950
$790$	−0.935240	−0.0332743
$791$	6.61942	0.235360
$792$	−13.4041	−0.476295
$793$	−18.0139	−0.639693
$794$	16.3091	0.578788
$795$	−13.6887	−0.485490
$796$	−92.9131	−3.29322
$797$	−11.2539	−0.398634	−0.199317	−	0.979935i	$-0.563872\pi$
$797$	−11.2539	−0.398634	−0.199317	+	0.979935i	$0.563872\pi$
$798$	−74.7077	−2.64462
$799$	−25.5490	−0.903860
$800$	62.3018	2.20270
$801$	2.80801	0.0992161
$802$	15.7480	0.556080
$803$	79.6758	2.81170
$804$	36.3977	1.28365
$805$	23.6157	0.832343
$806$	8.14016	0.286725
$807$	34.7250	1.22238
$808$	−62.8337	−2.21048
$809$	12.3184	0.433092	0.216546	−	0.976272i	$-0.430521\pi$
$809$	12.3184	0.433092	0.216546	+	0.976272i	$0.430521\pi$
$810$	−40.6942	−1.42985
$811$	28.7023	1.00788	0.503938	−	0.863740i	$-0.331884\pi$
$811$	28.7023	1.00788	0.503938	+	0.863740i	$0.331884\pi$
$812$	86.0979	3.02145
$813$	22.1648	0.777354
$814$	14.0655	0.492995
$815$	12.0039	0.420478
$816$	−60.4782	−2.11716
$817$	−38.8175	−1.35805
$818$	−78.2415	−2.73565
$819$	−1.60654	−0.0561369
$820$	60.6612	2.11838
$821$	−11.8770	−0.414509	−0.207255	−	0.978287i	$-0.566453\pi$
$821$	−11.8770	−0.414509	−0.207255	+	0.978287i	$0.566453\pi$
$822$	−26.1729	−0.912886
$823$	8.67871	0.302521	0.151260	−	0.988494i	$-0.451667\pi$
$823$	8.67871	0.302521	0.151260	+	0.988494i	$0.451667\pi$
$824$	74.3113	2.58876
$825$	−28.4578	−0.990774
$826$	92.0665	3.20340
$827$	−30.6964	−1.06742	−0.533709	−	0.845668i	$-0.679202\pi$
$827$	−30.6964	−1.06742	−0.533709	+	0.845668i	$0.679202\pi$
$828$	7.32898	0.254700
$829$	8.66405	0.300915	0.150458	−	0.988616i	$-0.451925\pi$
$829$	8.66405	0.300915	0.150458	+	0.988616i	$0.451925\pi$
$830$	−44.4809	−1.54395
$831$	−10.7672	−0.373511
$832$	88.4439	3.06624
$833$	−0.179594	−0.00622255
$834$	18.1726	0.629266
$835$	−11.8864	−0.411345
$836$	−189.511	−6.55437
$837$	5.59210	0.193291
$838$	0.721118	0.0249106
$839$	−37.6271	−1.29903	−0.649516	−	0.760348i	$-0.725029\pi$
$839$	−37.6271	−1.29903	−0.649516	+	0.760348i	$0.725029\pi$
$840$	−71.7060	−2.47409
$841$	4.97801	0.171656
$842$	−6.42930	−0.221568
$843$	−14.6877	−0.505872
$844$	−12.2539	−0.421796
$845$	9.28638	0.319461
$846$	−7.49206	−0.257582
$847$	−66.7465	−2.29344
$848$	77.7945	2.67147
$849$	−28.9631	−0.994011
$850$	−15.5321	−0.532746
$851$	−4.91900	−0.168621
$852$	−16.0349	−0.549346
$853$	43.1768	1.47834	0.739172	−	0.673517i	$-0.235217\pi$
$853$	43.1768	1.47834	0.739172	+	0.673517i	$0.235217\pi$
$854$	−49.9366	−1.70879
$855$	1.99980	0.0683916
$856$	115.998	3.96474
$857$	0.907335	0.0309940	0.0154970	−	0.999880i	$-0.495067\pi$
$857$	0.907335	0.0309940	0.0154970	+	0.999880i	$0.495067\pi$
$858$	−78.2328	−2.67083
$859$	6.25521	0.213425	0.106712	−	0.994290i	$-0.465968\pi$
$859$	6.25521	0.213425	0.106712	+	0.994290i	$0.465968\pi$
$860$	−58.2505	−1.98633
$861$	34.0049	1.15888
$862$	−86.8874	−2.95940
$863$	19.0895	0.649813	0.324906	−	0.945746i	$-0.394667\pi$
$863$	19.0895	0.649813	0.324906	+	0.945746i	$0.394667\pi$
$864$	117.660	4.00289
$865$	−28.8668	−0.981500
$866$	−99.8271	−3.39226
$867$	−22.2879	−0.756935
$868$	16.5875	0.563017
$869$	−1.32991	−0.0451141
$870$	−44.2429	−1.49997
$871$	9.62887	0.326262
$872$	−162.402	−5.49964
$873$	3.07881	0.104202
$874$	90.1611	3.04974
$875$	−31.2463	−1.05632
$876$	132.278	4.46925
$877$	−9.38810	−0.317014	−0.158507	−	0.987358i	$-0.550668\pi$
$877$	−9.38810	−0.317014	−0.158507	+	0.987358i	$0.550668\pi$
$878$	13.3846	0.451709
$879$	33.1286	1.11740
$880$	−144.961	−4.88663
$881$	11.4529	0.385858	0.192929	−	0.981213i	$-0.438201\pi$
$881$	11.4529	0.385858	0.192929	+	0.981213i	$0.438201\pi$
$882$	−0.0526645	−0.00177331
$883$	5.60765	0.188712	0.0943562	−	0.995538i	$-0.469921\pi$
$883$	5.60765	0.188712	0.0943562	+	0.995538i	$0.469921\pi$
$884$	−31.3874	−1.05567
$885$	−34.7768	−1.16901
$886$	−79.1843	−2.66025
$887$	38.2123	1.28304	0.641522	−	0.767105i	$-0.278303\pi$
$887$	38.2123	1.28304	0.641522	+	0.767105i	$0.278303\pi$
$888$	14.9359	0.501217
$889$	42.5538	1.42721
$890$	51.8378	1.73761
$891$	−57.8672	−1.93862
$892$	62.4942	2.09246
$893$	−67.7508	−2.26719
$894$	−4.02967	−0.134772
$895$	−11.8491	−0.396072
$896$	119.398	3.98882
$897$	27.3597	0.913515
$898$	−106.093	−3.54037
$899$	6.54616	0.218327
$900$	−3.34807	−0.111602
$901$	−10.6241	−0.353939
$902$	117.347	3.90723
$903$	−32.6536	−1.08664
$904$	24.2566	0.806761
$905$	25.0474	0.832605
$906$	83.3481	2.76905
$907$	−4.23550	−0.140637	−0.0703187	−	0.997525i	$-0.522402\pi$
$907$	−4.23550	−0.140637	−0.0703187	+	0.997525i	$0.522402\pi$
$908$	122.611	4.06899
$909$	1.47410	0.0488928
$910$	−29.6578	−0.983146
$911$	44.3546	1.46953	0.734767	−	0.678320i	$-0.237292\pi$
$911$	44.3546	1.46953	0.734767	+	0.678320i	$0.237292\pi$
$912$	−160.376	−5.31058
$913$	−63.2518	−2.09333
$914$	−54.8668	−1.81483
$915$	18.8628	0.623586
$916$	−21.7785	−0.719583
$917$	−14.7291	−0.486397
$918$	−29.3332	−0.968140
$919$	−6.53978	−0.215728	−0.107864	−	0.994166i	$-0.534401\pi$
$919$	−6.53978	−0.215728	−0.107864	+	0.994166i	$0.534401\pi$
$920$	86.5385	2.85309
$921$	34.2450	1.12841
$922$	87.0026	2.86528
$923$	−4.24196	−0.139626
$924$	−159.418	−5.24447
$925$	2.24713	0.0738851
$926$	14.6276	0.480692
$927$	−1.74337	−0.0572597
$928$	137.734	4.52135
$929$	12.6105	0.413738	0.206869	−	0.978369i	$-0.433673\pi$
$929$	12.6105	0.413738	0.206869	+	0.978369i	$0.433673\pi$
$930$	−8.52377	−0.279505
$931$	−0.476246	−0.0156083
$932$	126.721	4.15089
$933$	−49.6318	−1.62487
$934$	−96.4987	−3.15753
$935$	19.7967	0.647422
$936$	−5.88708	−0.192425
$937$	−3.84677	−0.125669	−0.0628343	−	0.998024i	$-0.520014\pi$
$937$	−3.84677	−0.125669	−0.0628343	+	0.998024i	$0.520014\pi$
$938$	26.6923	0.871534
$939$	57.4256	1.87401
$940$	−101.669	−3.31607
$941$	−7.15469	−0.233236	−0.116618	−	0.993177i	$-0.537205\pi$
$941$	−7.15469	−0.233236	−0.116618	+	0.993177i	$0.537205\pi$
$942$	58.8601	1.91777
$943$	−41.0389	−1.33641
$944$	197.640	6.43264
$945$	−20.3742	−0.662773
$946$	−112.684	−3.66367
$947$	38.7238	1.25835	0.629177	−	0.777262i	$-0.283392\pi$
$947$	38.7238	1.25835	0.629177	+	0.777262i	$0.283392\pi$
$948$	−2.20792	−0.0717098
$949$	34.9935	1.13594
$950$	−41.1879	−1.33631
$951$	−47.0993	−1.52730
$952$	−55.6523	−1.80370
$953$	−46.0828	−1.49277	−0.746384	−	0.665516i	$-0.768212\pi$
$953$	−46.0828	−1.49277	−0.746384	+	0.665516i	$0.768212\pi$
$954$	−3.11543	−0.100866
$955$	−7.71199	−0.249554
$956$	151.308	4.89364
$957$	−62.9133	−2.03370
$958$	42.4330	1.37095
$959$	−14.1092	−0.455609
$960$	−92.6119	−2.98904
$961$	−29.7388	−0.959317
$962$	6.17754	0.199172
$963$	−2.72135	−0.0876944
$964$	−138.613	−4.46441
$965$	9.44798	0.304141
$966$	75.8442	2.44025
$967$	−17.4409	−0.560863	−0.280432	−	0.959874i	$-0.590478\pi$
$967$	−17.4409	−0.560863	−0.280432	+	0.959874i	$0.590478\pi$
$968$	−244.589	−7.86140
$969$	21.9019	0.703589
$970$	56.8370	1.82493
$971$	−18.9143	−0.606987	−0.303494	−	0.952833i	$-0.598153\pi$
$971$	−18.9143	−0.606987	−0.303494	+	0.952833i	$0.598153\pi$
$972$	−13.1681	−0.422367
$973$	9.79640	0.314058
$974$	−99.4731	−3.18732
$975$	−12.4986	−0.400277
$976$	−107.199	−3.43137
$977$	39.3981	1.26046	0.630229	−	0.776410i	$-0.282961\pi$
$977$	39.3981	1.26046	0.630229	+	0.776410i	$0.282961\pi$
$978$	38.5518	1.23275
$979$	73.7133	2.35589
$980$	−0.714667	−0.0228292
$981$	3.81001	0.121644
$982$	−79.5195	−2.53757
$983$	−10.5169	−0.335437	−0.167718	−	0.985835i	$-0.553640\pi$
$983$	−10.5169	−0.335437	−0.167718	+	0.985835i	$0.553640\pi$
$984$	124.609	3.97240
$985$	−30.2901	−0.965122
$986$	−34.3377	−1.09353
$987$	−56.9925	−1.81409
$988$	−83.2329	−2.64799
$989$	39.4080	1.25310
$990$	5.80524	0.184503
$991$	1.91125	0.0607128	0.0303564	−	0.999539i	$-0.490336\pi$
$991$	1.91125	0.0607128	0.0303564	+	0.999539i	$0.490336\pi$
$992$	26.5357	0.842509
$993$	42.3944	1.34534
$994$	−11.7592	−0.372978
$995$	25.7381	0.815952
$996$	−105.011	−3.32739
$997$	34.4346	1.09055	0.545277	−	0.838256i	$-0.316425\pi$
$997$	34.4346	1.09055	0.545277	+	0.838256i	$0.316425\pi$
$998$	4.59261	0.145377
$999$	4.24383	0.134269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.1	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.1	✓	216	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74765 q^{2} +1.79689 q^{3} +5.54960 q^{4} -1.53731 q^{5} -4.93723 q^{6} -2.66154 q^{7} -9.75307 q^{8} +0.228810 q^{9} +O(q^{10})\)	\(q-2.74765 q^{2} +1.79689 q^{3} +5.54960 q^{4} -1.53731 q^{5} -4.93723 q^{6} -2.66154 q^{7} -9.75307 q^{8} +0.228810 q^{9} +4.22399 q^{10} +6.00651 q^{11} +9.97201 q^{12} +2.63805 q^{13} +7.31298 q^{14} -2.76237 q^{15} +15.6988 q^{16} -2.14393 q^{17} -0.628690 q^{18} -5.68526 q^{19} -8.53145 q^{20} -4.78248 q^{21} -16.5038 q^{22} +5.77175 q^{23} -17.5252 q^{24} -2.63668 q^{25} -7.24846 q^{26} -4.97952 q^{27} -14.7705 q^{28} -5.82907 q^{29} +7.59004 q^{30} -1.12302 q^{31} -23.6289 q^{32} +10.7930 q^{33} +5.89077 q^{34} +4.09160 q^{35} +1.26980 q^{36} -0.852256 q^{37} +15.6211 q^{38} +4.74029 q^{39} +14.9935 q^{40} -7.11031 q^{41} +13.1406 q^{42} +6.82774 q^{43} +33.3337 q^{44} -0.351751 q^{45} -15.8588 q^{46} +11.9169 q^{47} +28.2091 q^{48} +0.0837686 q^{49} +7.24469 q^{50} -3.85240 q^{51} +14.6401 q^{52} +4.95543 q^{53} +13.6820 q^{54} -9.23386 q^{55} +25.9581 q^{56} -10.2158 q^{57} +16.0163 q^{58} +12.5895 q^{59} -15.3301 q^{60} -6.82849 q^{61} +3.08567 q^{62} -0.608986 q^{63} +33.5262 q^{64} -4.05550 q^{65} -29.6555 q^{66} +3.64999 q^{67} -11.8979 q^{68} +10.3712 q^{69} -11.2423 q^{70} -1.60799 q^{71} -2.23160 q^{72} +13.2649 q^{73} +2.34170 q^{74} -4.73783 q^{75} -31.5509 q^{76} -15.9865 q^{77} -13.0247 q^{78} -0.221411 q^{79} -24.1340 q^{80} -9.63408 q^{81} +19.5367 q^{82} -10.5305 q^{83} -26.5409 q^{84} +3.29588 q^{85} -18.7603 q^{86} -10.4742 q^{87} -58.5819 q^{88} +12.2722 q^{89} +0.966491 q^{90} -7.02127 q^{91} +32.0309 q^{92} -2.01794 q^{93} -32.7436 q^{94} +8.73999 q^{95} -42.4584 q^{96} +13.4558 q^{97} -0.230167 q^{98} +1.37435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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