LMFDB - Embedded newform 983.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55366 q^{2} +2.02223 q^{3} +4.52118 q^{4} -4.30555 q^{5} -5.16409 q^{6} +1.54441 q^{7} -6.43825 q^{8} +1.08942 q^{9} +O(q^{10})$	\(q-2.55366 q^{2} +2.02223 q^{3} +4.52118 q^{4} -4.30555 q^{5} -5.16409 q^{6} +1.54441 q^{7} -6.43825 q^{8} +1.08942 q^{9} +10.9949 q^{10} +5.86317 q^{11} +9.14288 q^{12} +3.29053 q^{13} -3.94389 q^{14} -8.70681 q^{15} +7.39873 q^{16} -2.14214 q^{17} -2.78201 q^{18} -1.66799 q^{19} -19.4662 q^{20} +3.12315 q^{21} -14.9726 q^{22} -1.83179 q^{23} -13.0196 q^{24} +13.5377 q^{25} -8.40290 q^{26} -3.86364 q^{27} +6.98255 q^{28} -5.51761 q^{29} +22.2342 q^{30} -4.59229 q^{31} -6.01735 q^{32} +11.8567 q^{33} +5.47031 q^{34} -6.64952 q^{35} +4.92546 q^{36} +6.32726 q^{37} +4.25949 q^{38} +6.65422 q^{39} +27.7202 q^{40} +8.97167 q^{41} -7.97546 q^{42} +5.34134 q^{43} +26.5085 q^{44} -4.69055 q^{45} +4.67776 q^{46} +3.44412 q^{47} +14.9619 q^{48} -4.61481 q^{49} -34.5708 q^{50} -4.33191 q^{51} +14.8771 q^{52} +5.89587 q^{53} +9.86642 q^{54} -25.2442 q^{55} -9.94327 q^{56} -3.37307 q^{57} +14.0901 q^{58} +10.5848 q^{59} -39.3651 q^{60} -0.264241 q^{61} +11.7272 q^{62} +1.68251 q^{63} +0.568814 q^{64} -14.1675 q^{65} -30.2780 q^{66} +16.2266 q^{67} -9.68502 q^{68} -3.70429 q^{69} +16.9806 q^{70} +8.77180 q^{71} -7.01395 q^{72} -15.2163 q^{73} -16.1577 q^{74} +27.3764 q^{75} -7.54130 q^{76} +9.05513 q^{77} -16.9926 q^{78} +7.82890 q^{79} -31.8556 q^{80} -11.0814 q^{81} -22.9106 q^{82} +7.54474 q^{83} +14.1203 q^{84} +9.22310 q^{85} -13.6400 q^{86} -11.1579 q^{87} -37.7485 q^{88} -3.32813 q^{89} +11.9781 q^{90} +5.08192 q^{91} -8.28184 q^{92} -9.28668 q^{93} -8.79511 q^{94} +7.18163 q^{95} -12.1685 q^{96} +17.0197 q^{97} +11.7846 q^{98} +6.38745 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	−2.55366	−1.80571	−0.902855	−	0.429944i	$-0.858533\pi$
$2$	−2.55366	−1.80571	−0.902855	+	0.429944i	$0.858533\pi$
$3$	2.02223	1.16754	0.583768	−	0.811921i	$-0.301578\pi$
$3$	2.02223	1.16754	0.583768	+	0.811921i	$0.301578\pi$
$4$	4.52118	2.26059
$5$	−4.30555	−1.92550	−0.962750	−	0.270394i	$-0.912846\pi$
$5$	−4.30555	−1.92550	−0.962750	+	0.270394i	$0.912846\pi$
$6$	−5.16409	−2.10823
$7$	1.54441	0.583731	0.291866	−	0.956459i	$-0.405724\pi$
$7$	1.54441	0.583731	0.291866	+	0.956459i	$0.405724\pi$
$8$	−6.43825	−2.27626
$9$	1.08942	0.363140
$10$	10.9949	3.47689
$11$	5.86317	1.76781	0.883906	−	0.467664i	$-0.154904\pi$
$11$	5.86317	1.76781	0.883906	+	0.467664i	$0.154904\pi$
$12$	9.14288	2.63932
$13$	3.29053	0.912630	0.456315	−	0.889818i	$-0.349169\pi$
$13$	3.29053	0.912630	0.456315	+	0.889818i	$0.349169\pi$
$14$	−3.94389	−1.05405
$15$	−8.70681	−2.24809
$16$	7.39873	1.84968
$17$	−2.14214	−0.519546	−0.259773	−	0.965670i	$-0.583648\pi$
$17$	−2.14214	−0.519546	−0.259773	+	0.965670i	$0.583648\pi$
$18$	−2.78201	−0.655725
$19$	−1.66799	−0.382664	−0.191332	−	0.981525i	$-0.561281\pi$
$19$	−1.66799	−0.382664	−0.191332	+	0.981525i	$0.561281\pi$
$20$	−19.4662	−4.35277
$21$	3.12315	0.681527
$22$	−14.9726	−3.19216
$23$	−1.83179	−0.381954	−0.190977	−	0.981595i	$-0.561166\pi$
$23$	−1.83179	−0.381954	−0.190977	+	0.981595i	$0.561166\pi$
$24$	−13.0196	−2.65762
$25$	13.5377	2.70755
$26$	−8.40290	−1.64795
$27$	−3.86364	−0.743557
$28$	6.98255	1.31958
$29$	−5.51761	−1.02460	−0.512298	−	0.858808i	$-0.671205\pi$
$29$	−5.51761	−1.02460	−0.512298	+	0.858808i	$0.671205\pi$
$30$	22.2342	4.05940
$31$	−4.59229	−0.824800	−0.412400	−	0.911003i	$-0.635309\pi$
$31$	−4.59229	−0.824800	−0.412400	+	0.911003i	$0.635309\pi$
$32$	−6.01735	−1.06373
$33$	11.8567	2.06398
$34$	5.47031	0.938150
$35$	−6.64952	−1.12397
$36$	4.92546	0.820911
$37$	6.32726	1.04019	0.520097	−	0.854107i	$-0.325896\pi$
$37$	6.32726	1.04019	0.520097	+	0.854107i	$0.325896\pi$
$38$	4.25949	0.690980
$39$	6.65422	1.06553
$40$	27.7202	4.38294
$41$	8.97167	1.40114	0.700569	−	0.713584i	$-0.252929\pi$
$41$	8.97167	1.40114	0.700569	+	0.713584i	$0.252929\pi$
$42$	−7.97546	−1.23064
$43$	5.34134	0.814547	0.407274	−	0.913306i	$-0.366480\pi$
$43$	5.34134	0.814547	0.407274	+	0.913306i	$0.366480\pi$
$44$	26.5085	3.99630
$45$	−4.69055	−0.699225
$46$	4.67776	0.689698
$47$	3.44412	0.502376	0.251188	−	0.967938i	$-0.419179\pi$
$47$	3.44412	0.502376	0.251188	+	0.967938i	$0.419179\pi$
$48$	14.9619	2.15957
$49$	−4.61481	−0.659258
$50$	−34.5708	−4.88905
$51$	−4.33191	−0.606588
$52$	14.8771	2.06308
$53$	5.89587	0.809861	0.404930	−	0.914348i	$-0.367296\pi$
$53$	5.89587	0.809861	0.404930	+	0.914348i	$0.367296\pi$
$54$	9.86642	1.34265
$55$	−25.2442	−3.40392
$56$	−9.94327	−1.32873
$57$	−3.37307	−0.446774
$58$	14.0901	1.85012
$59$	10.5848	1.37803	0.689015	−	0.724747i	$-0.258044\pi$
$59$	10.5848	1.37803	0.689015	+	0.724747i	$0.258044\pi$
$60$	−39.3651	−5.08201
$61$	−0.264241	−0.0338326	−0.0169163	−	0.999857i	$-0.505385\pi$
$61$	−0.264241	−0.0338326	−0.0169163	+	0.999857i	$0.505385\pi$
$62$	11.7272	1.48935
$63$	1.68251	0.211976
$64$	0.568814	0.0711017
$65$	−14.1675	−1.75727
$66$	−30.2780	−3.72696
$67$	16.2266	1.98239	0.991196	−	0.132402i	$-0.0422691\pi$
$67$	16.2266	1.98239	0.991196	+	0.132402i	$0.0422691\pi$
$68$	−9.68502	−1.17448
$69$	−3.70429	−0.445945
$70$	16.9806	2.02957
$71$	8.77180	1.04102	0.520511	−	0.853855i	$-0.325742\pi$
$71$	8.77180	1.04102	0.520511	+	0.853855i	$0.325742\pi$
$72$	−7.01395	−0.826602
$73$	−15.2163	−1.78094	−0.890469	−	0.455045i	$-0.849623\pi$
$73$	−15.2163	−1.78094	−0.890469	+	0.455045i	$0.849623\pi$
$74$	−16.1577	−1.87829
$75$	27.3764	3.16116
$76$	−7.54130	−0.865047
$77$	9.05513	1.03193
$78$	−16.9926	−1.92403
$79$	7.82890	0.880821	0.440410	−	0.897797i	$-0.354833\pi$
$79$	7.82890	0.880821	0.440410	+	0.897797i	$0.354833\pi$
$80$	−31.8556	−3.56156
$81$	−11.0814	−1.23127
$82$	−22.9106	−2.53005
$83$	7.54474	0.828143	0.414072	−	0.910244i	$-0.364106\pi$
$83$	7.54474	0.828143	0.414072	+	0.910244i	$0.364106\pi$
$84$	14.1203	1.54065
$85$	9.22310	1.00039
$86$	−13.6400	−1.47084
$87$	−11.1579	−1.19625
$88$	−37.7485	−4.02401
$89$	−3.32813	−0.352781	−0.176390	−	0.984320i	$-0.556442\pi$
$89$	−3.32813	−0.352781	−0.176390	+	0.984320i	$0.556442\pi$
$90$	11.9781	1.26260
$91$	5.08192	0.532730
$92$	−8.28184	−0.863441
$93$	−9.28668	−0.962984
$94$	−8.79511	−0.907146
$95$	7.18163	0.736819
$96$	−12.1685	−1.24194
$97$	17.0197	1.72809	0.864046	−	0.503413i	$-0.167923\pi$
$97$	17.0197	1.72809	0.864046	+	0.503413i	$0.167923\pi$
$98$	11.7846	1.19043
$99$	6.38745	0.641963
$100$	61.2066	6.12066
$101$	2.37123	0.235946	0.117973	−	0.993017i	$-0.462360\pi$
$101$	2.37123	0.235946	0.117973	+	0.993017i	$0.462360\pi$
$102$	11.0622	1.09532
$103$	13.9828	1.37777	0.688884	−	0.724872i	$-0.258101\pi$
$103$	13.9828	1.37777	0.688884	+	0.724872i	$0.258101\pi$
$104$	−21.1853	−2.07739
$105$	−13.4469	−1.31228
$106$	−15.0561	−1.46237
$107$	7.69251	0.743663	0.371831	−	0.928300i	$-0.378730\pi$
$107$	7.69251	0.743663	0.371831	+	0.928300i	$0.378730\pi$
$108$	−17.4682	−1.68088
$109$	−3.25693	−0.311958	−0.155979	−	0.987760i	$-0.549853\pi$
$109$	−3.25693	−0.311958	−0.155979	+	0.987760i	$0.549853\pi$
$110$	64.4650	6.14650
$111$	12.7952	1.21446
$112$	11.4267	1.07972
$113$	−5.76782	−0.542591	−0.271295	−	0.962496i	$-0.587452\pi$
$113$	−5.76782	−0.542591	−0.271295	+	0.962496i	$0.587452\pi$
$114$	8.61367	0.806744
$115$	7.88684	0.735452
$116$	−24.9461	−2.31619
$117$	3.58477	0.331412
$118$	−27.0301	−2.48832
$119$	−3.30834	−0.303275
$120$	56.0566	5.11724
$121$	23.3768	2.12516
$122$	0.674782	0.0610919
$123$	18.1428	1.63588
$124$	−20.7626	−1.86454
$125$	−36.7596	−3.28788
$126$	−4.29655	−0.382767
$127$	−4.05546	−0.359864	−0.179932	−	0.983679i	$-0.557588\pi$
$127$	−4.05546	−0.359864	−0.179932	+	0.983679i	$0.557588\pi$
$128$	10.5821	0.935338
$129$	10.8014	0.951013
$130$	36.1791	3.17312
$131$	11.3729	0.993657	0.496829	−	0.867849i	$-0.334498\pi$
$131$	11.3729	0.993657	0.496829	+	0.867849i	$0.334498\pi$
$132$	53.6063	4.66583
$133$	−2.57606	−0.223373
$134$	−41.4372	−3.57963
$135$	16.6351	1.43172
$136$	13.7916	1.18262
$137$	−3.46466	−0.296006	−0.148003	−	0.988987i	$-0.547285\pi$
$137$	−3.46466	−0.296006	−0.148003	+	0.988987i	$0.547285\pi$
$138$	9.45951	0.805247
$139$	−12.6077	−1.06937	−0.534687	−	0.845050i	$-0.679570\pi$
$139$	−12.6077	−1.06937	−0.534687	+	0.845050i	$0.679570\pi$
$140$	−30.0637	−2.54085
$141$	6.96480	0.586542
$142$	−22.4002	−1.87978
$143$	19.2930	1.61336
$144$	8.06032	0.671693
$145$	23.7563	1.97286
$146$	38.8574	3.21586
$147$	−9.33220	−0.769707
$148$	28.6067	2.35145
$149$	−2.63576	−0.215930	−0.107965	−	0.994155i	$-0.534433\pi$
$149$	−2.63576	−0.215930	−0.107965	+	0.994155i	$0.534433\pi$
$150$	−69.9101	−5.70814
$151$	4.38271	0.356660	0.178330	−	0.983971i	$-0.442931\pi$
$151$	4.38271	0.356660	0.178330	+	0.983971i	$0.442931\pi$
$152$	10.7390	0.871044
$153$	−2.33369	−0.188668
$154$	−23.1237	−1.86336
$155$	19.7723	1.58815
$156$	30.0849	2.40872
$157$	−16.3122	−1.30186	−0.650928	−	0.759139i	$-0.725620\pi$
$157$	−16.3122	−1.30186	−0.650928	+	0.759139i	$0.725620\pi$
$158$	−19.9924	−1.59051
$159$	11.9228	0.945541
$160$	25.9080	2.04821
$161$	−2.82902	−0.222958
$162$	28.2982	2.22332
$163$	8.90417	0.697429	0.348714	−	0.937229i	$-0.386618\pi$
$163$	8.90417	0.697429	0.348714	+	0.937229i	$0.386618\pi$
$164$	40.5625	3.16740
$165$	−51.0495	−3.97420
$166$	−19.2667	−1.49539
$167$	−7.36475	−0.569901	−0.284951	−	0.958542i	$-0.591977\pi$
$167$	−7.36475	−0.569901	−0.284951	+	0.958542i	$0.591977\pi$
$168$	−20.1076	−1.55133
$169$	−2.17239	−0.167107
$170$	−23.5527	−1.80641
$171$	−1.81714	−0.138961
$172$	24.1492	1.84136
$173$	−12.9388	−0.983722	−0.491861	−	0.870674i	$-0.663683\pi$
$173$	−12.9388	−0.983722	−0.491861	+	0.870674i	$0.663683\pi$
$174$	28.4935	2.16008
$175$	20.9078	1.58048
$176$	43.3800	3.26989
$177$	21.4050	1.60890
$178$	8.49891	0.637020
$179$	−9.36019	−0.699614	−0.349807	−	0.936822i	$-0.613753\pi$
$179$	−9.36019	−0.699614	−0.349807	+	0.936822i	$0.613753\pi$
$180$	−21.2068	−1.58066
$181$	−10.5046	−0.780800	−0.390400	−	0.920645i	$-0.627663\pi$
$181$	−10.5046	−0.780800	−0.390400	+	0.920645i	$0.627663\pi$
$182$	−12.9775	−0.961957
$183$	−0.534357	−0.0395008
$184$	11.7935	0.869427
$185$	−27.2423	−2.00289
$186$	23.7150	1.73887
$187$	−12.5598	−0.918460
$188$	15.5715	1.13567
$189$	−5.96703	−0.434037
$190$	−18.3394	−1.33048
$191$	−5.23407	−0.378724	−0.189362	−	0.981907i	$-0.560642\pi$
$191$	−5.23407	−0.378724	−0.189362	+	0.981907i	$0.560642\pi$
$192$	1.15027	0.0830138
$193$	13.9188	1.00190	0.500949	−	0.865477i	$-0.332985\pi$
$193$	13.9188	1.00190	0.500949	+	0.865477i	$0.332985\pi$
$194$	−43.4626	−3.12043
$195$	−28.6501	−2.05167
$196$	−20.8644	−1.49031
$197$	20.9748	1.49439	0.747195	−	0.664605i	$-0.231400\pi$
$197$	20.9748	1.49439	0.747195	+	0.664605i	$0.231400\pi$
$198$	−16.3114	−1.15920
$199$	−23.3759	−1.65707	−0.828535	−	0.559937i	$-0.810825\pi$
$199$	−23.3759	−1.65707	−0.828535	+	0.559937i	$0.810825\pi$
$200$	−87.1593	−6.16309
$201$	32.8139	2.31451
$202$	−6.05531	−0.426050
$203$	−8.52144	−0.598088
$204$	−19.5853	−1.37125
$205$	−38.6279	−2.69789
$206$	−35.7074	−2.48785
$207$	−1.99558	−0.138703
$208$	24.3458	1.68807
$209$	−9.77973	−0.676478
$210$	34.3387	2.36960
$211$	11.9442	0.822271	0.411136	−	0.911574i	$-0.365132\pi$
$211$	11.9442	0.822271	0.411136	+	0.911574i	$0.365132\pi$
$212$	26.6563	1.83076
$213$	17.7386	1.21543
$214$	−19.6441	−1.34284
$215$	−22.9974	−1.56841
$216$	24.8750	1.69253
$217$	−7.09237	−0.481462
$218$	8.31711	0.563306
$219$	−30.7709	−2.07931
$220$	−114.133	−7.69488
$221$	−7.04879	−0.474153
$222$	−32.6745	−2.19297
$223$	−15.2922	−1.02404	−0.512022	−	0.858973i	$-0.671103\pi$
$223$	−15.2922	−1.02404	−0.512022	+	0.858973i	$0.671103\pi$
$224$	−9.29324	−0.620931
$225$	14.7483	0.983218
$226$	14.7291	0.979762
$227$	−7.46348	−0.495369	−0.247684	−	0.968841i	$-0.579670\pi$
$227$	−7.46348	−0.495369	−0.247684	+	0.968841i	$0.579670\pi$
$228$	−15.2503	−1.00997
$229$	−4.44835	−0.293955	−0.146978	−	0.989140i	$-0.546955\pi$
$229$	−4.44835	−0.293955	−0.146978	+	0.989140i	$0.546955\pi$
$230$	−20.1403	−1.32801
$231$	18.3116	1.20481
$232$	35.5237	2.33225
$233$	18.5538	1.21550	0.607750	−	0.794128i	$-0.292072\pi$
$233$	18.5538	1.21550	0.607750	+	0.794128i	$0.292072\pi$
$234$	−9.15429	−0.598434
$235$	−14.8288	−0.967325
$236$	47.8560	3.11516
$237$	15.8319	1.02839
$238$	8.44838	0.547627
$239$	−1.20476	−0.0779291	−0.0389646	−	0.999241i	$-0.512406\pi$
$239$	−1.20476	−0.0779291	−0.0389646	+	0.999241i	$0.512406\pi$
$240$	−64.4193	−4.15825
$241$	24.7776	1.59606	0.798032	−	0.602616i	$-0.205875\pi$
$241$	24.7776	1.59606	0.798032	+	0.602616i	$0.205875\pi$
$242$	−59.6964	−3.83743
$243$	−10.8183	−0.693994
$244$	−1.19468	−0.0764817
$245$	19.8693	1.26940
$246$	−46.3305	−2.95393
$247$	−5.48859	−0.349230
$248$	29.5663	1.87746
$249$	15.2572	0.966887
$250$	93.8716	5.93696
$251$	9.27348	0.585337	0.292668	−	0.956214i	$-0.405457\pi$
$251$	9.27348	0.585337	0.292668	+	0.956214i	$0.405457\pi$
$252$	7.60692	0.479191
$253$	−10.7401	−0.675223
$254$	10.3563	0.649810
$255$	18.6512	1.16799
$256$	−28.1608	−1.76005
$257$	10.4339	0.650848	0.325424	−	0.945568i	$-0.394493\pi$
$257$	10.4339	0.650848	0.325424	+	0.945568i	$0.394493\pi$
$258$	−27.5832	−1.71725
$259$	9.77186	0.607194
$260$	−64.0541	−3.97246
$261$	−6.01099	−0.372071
$262$	−29.0426	−1.79426
$263$	30.7730	1.89754	0.948772	−	0.315961i	$-0.102327\pi$
$263$	30.7730	1.89754	0.948772	+	0.315961i	$0.102327\pi$
$264$	−76.3363	−4.69817
$265$	−25.3850	−1.55939
$266$	6.57839	0.403347
$267$	−6.73024	−0.411884
$268$	73.3633	4.48138
$269$	16.8132	1.02512	0.512560	−	0.858652i	$-0.328697\pi$
$269$	16.8132	1.02512	0.512560	+	0.858652i	$0.328697\pi$
$270$	−42.4803	−2.58527
$271$	−0.400659	−0.0243383	−0.0121692	−	0.999926i	$-0.503874\pi$
$271$	−0.400659	−0.0243383	−0.0121692	+	0.999926i	$0.503874\pi$
$272$	−15.8491	−0.960995
$273$	10.2768	0.621982
$274$	8.84757	0.534501
$275$	79.3741	4.78644
$276$	−16.7478	−1.00810
$277$	−22.1355	−1.32999	−0.664997	−	0.746846i	$-0.731567\pi$
$277$	−22.1355	−1.32999	−0.664997	+	0.746846i	$0.731567\pi$
$278$	32.1959	1.93098
$279$	−5.00293	−0.299518
$280$	42.8112	2.55846
$281$	−11.6299	−0.693783	−0.346891	−	0.937905i	$-0.612763\pi$
$281$	−11.6299	−0.693783	−0.346891	+	0.937905i	$0.612763\pi$
$282$	−17.7857	−1.05913
$283$	25.4557	1.51318	0.756592	−	0.653887i	$-0.226863\pi$
$283$	25.4557	1.51318	0.756592	+	0.653887i	$0.226863\pi$
$284$	39.6589	2.35332
$285$	14.5229	0.860263
$286$	−49.2677	−2.91326
$287$	13.8559	0.817888
$288$	−6.55542	−0.386282
$289$	−12.4112	−0.730072
$290$	−60.6656	−3.56241
$291$	34.4178	2.01761
$292$	−68.7958	−4.02597
$293$	−29.3138	−1.71253	−0.856266	−	0.516535i	$-0.827221\pi$
$293$	−29.3138	−1.71253	−0.856266	+	0.516535i	$0.827221\pi$
$294$	23.8313	1.38987
$295$	−45.5735	−2.65339
$296$	−40.7364	−2.36776
$297$	−22.6532	−1.31447
$298$	6.73084	0.389907
$299$	−6.02755	−0.348582
$300$	123.774	7.14609
$301$	8.24921	0.475477
$302$	−11.1920	−0.644025
$303$	4.79517	0.275475
$304$	−12.3410	−0.707807
$305$	1.13770	0.0651447
$306$	5.95946	0.340679
$307$	14.1383	0.806915	0.403457	−	0.914998i	$-0.367808\pi$
$307$	14.1383	0.806915	0.403457	+	0.914998i	$0.367808\pi$
$308$	40.9399	2.33277
$309$	28.2765	1.60859
$310$	−50.4918	−2.86774
$311$	−7.28499	−0.413094	−0.206547	−	0.978437i	$-0.566223\pi$
$311$	−7.28499	−0.413094	−0.206547	+	0.978437i	$0.566223\pi$
$312$	−42.8415	−2.42542
$313$	−23.9429	−1.35334	−0.676668	−	0.736289i	$-0.736577\pi$
$313$	−23.9429	−1.35334	−0.676668	+	0.736289i	$0.736577\pi$
$314$	41.6559	2.35078
$315$	−7.24411	−0.408160
$316$	35.3959	1.99118
$317$	−30.9775	−1.73987	−0.869935	−	0.493166i	$-0.835839\pi$
$317$	−30.9775	−1.73987	−0.869935	+	0.493166i	$0.835839\pi$
$318$	−30.4468	−1.70737
$319$	−32.3507	−1.81129
$320$	−2.44906	−0.136906
$321$	15.5560	0.868253
$322$	7.22437	0.402598
$323$	3.57308	0.198812
$324$	−50.1011	−2.78340
$325$	44.5464	2.47099
$326$	−22.7382	−1.25935
$327$	−6.58628	−0.364222
$328$	−57.7618	−3.18936
$329$	5.31912	0.293253
$330$	130.363	7.17626
$331$	−25.2108	−1.38571	−0.692855	−	0.721077i	$-0.743647\pi$
$331$	−25.2108	−1.38571	−0.692855	+	0.721077i	$0.743647\pi$
$332$	34.1112	1.87209
$333$	6.89303	0.377736
$334$	18.8071	1.02908
$335$	−69.8643	−3.81709
$336$	23.1073	1.26061
$337$	10.8011	0.588374	0.294187	−	0.955748i	$-0.404951\pi$
$337$	10.8011	0.588374	0.294187	+	0.955748i	$0.404951\pi$
$338$	5.54755	0.301747
$339$	−11.6639	−0.633494
$340$	41.6993	2.26146
$341$	−26.9254	−1.45809
$342$	4.64037	0.250922
$343$	−17.9380	−0.968561
$344$	−34.3889	−1.85412
$345$	15.9490	0.858666
$346$	33.0414	1.77632
$347$	4.28903	0.230247	0.115123	−	0.993351i	$-0.463274\pi$
$347$	4.28903	0.230247	0.115123	+	0.993351i	$0.463274\pi$
$348$	−50.4469	−2.70424
$349$	6.88638	0.368619	0.184310	−	0.982868i	$-0.440995\pi$
$349$	6.88638	0.368619	0.184310	+	0.982868i	$0.440995\pi$
$350$	−53.3914	−2.85389
$351$	−12.7134	−0.678592
$352$	−35.2808	−1.88047
$353$	−9.33176	−0.496680	−0.248340	−	0.968673i	$-0.579885\pi$
$353$	−9.33176	−0.496680	−0.248340	+	0.968673i	$0.579885\pi$
$354$	−54.6611	−2.90521
$355$	−37.7674	−2.00449
$356$	−15.0471	−0.797493
$357$	−6.69023	−0.354085
$358$	23.9028	1.26330
$359$	−0.581190	−0.0306740	−0.0153370	−	0.999882i	$-0.504882\pi$
$359$	−0.581190	−0.0306740	−0.0153370	+	0.999882i	$0.504882\pi$
$360$	30.1989	1.59162
$361$	−16.2178	−0.853568
$362$	26.8251	1.40990
$363$	47.2733	2.48120
$364$	22.9763	1.20429
$365$	65.5146	3.42919
$366$	1.36457	0.0713270
$367$	25.0469	1.30744	0.653718	−	0.756738i	$-0.273208\pi$
$367$	25.0469	1.30744	0.653718	+	0.756738i	$0.273208\pi$
$368$	−13.5529	−0.706493
$369$	9.77391	0.508809
$370$	69.5676	3.61665
$371$	9.10563	0.472741
$372$	−41.9868	−2.17691
$373$	−20.0130	−1.03623	−0.518117	−	0.855310i	$-0.673367\pi$
$373$	−20.0130	−1.03623	−0.518117	+	0.855310i	$0.673367\pi$
$374$	32.0733	1.65847
$375$	−74.3365	−3.83872
$376$	−22.1741	−1.14354
$377$	−18.1559	−0.935076
$378$	15.2378	0.783746
$379$	−17.3703	−0.892253	−0.446126	−	0.894970i	$-0.647197\pi$
$379$	−17.3703	−0.892253	−0.446126	+	0.894970i	$0.647197\pi$
$380$	32.4694	1.66565
$381$	−8.20108	−0.420154
$382$	13.3660	0.683866
$383$	31.2502	1.59681	0.798406	−	0.602120i	$-0.205677\pi$
$383$	31.2502	1.59681	0.798406	+	0.602120i	$0.205677\pi$
$384$	21.3995	1.09204
$385$	−38.9873	−1.98698
$386$	−35.5439	−1.80914
$387$	5.81896	0.295794
$388$	76.9493	3.90651
$389$	−27.7573	−1.40735	−0.703675	−	0.710522i	$-0.748459\pi$
$389$	−27.7573	−1.40735	−0.703675	+	0.710522i	$0.748459\pi$
$390$	73.1625	3.70473
$391$	3.92395	0.198443
$392$	29.7112	1.50064
$393$	22.9987	1.16013
$394$	−53.5624	−2.69844
$395$	−33.7077	−1.69602
$396$	28.8788	1.45122
$397$	−6.82018	−0.342295	−0.171148	−	0.985245i	$-0.554747\pi$
$397$	−6.82018	−0.342295	−0.171148	+	0.985245i	$0.554747\pi$
$398$	59.6940	2.99219
$399$	−5.20939	−0.260796
$400$	100.162	5.00810
$401$	−4.34899	−0.217178	−0.108589	−	0.994087i	$-0.534633\pi$
$401$	−4.34899	−0.217178	−0.108589	+	0.994087i	$0.534633\pi$
$402$	−83.7956	−4.17934
$403$	−15.1111	−0.752737
$404$	10.7207	0.533377
$405$	47.7116	2.37081
$406$	21.7609	1.07997
$407$	37.0978	1.83887
$408$	27.8899	1.38076
$409$	−21.4090	−1.05861	−0.529304	−	0.848432i	$-0.677547\pi$
$409$	−21.4090	−1.05861	−0.529304	+	0.848432i	$0.677547\pi$
$410$	98.6426	4.87161
$411$	−7.00635	−0.345598
$412$	63.2189	3.11457
$413$	16.3473	0.804399
$414$	5.09604	0.250457
$415$	−32.4842	−1.59459
$416$	−19.8003	−0.970789
$417$	−25.4957	−1.24853
$418$	24.9741	1.22152
$419$	−31.0298	−1.51590	−0.757952	−	0.652311i	$-0.773800\pi$
$419$	−31.0298	−1.51590	−0.757952	+	0.652311i	$0.773800\pi$
$420$	−60.7957	−2.96653
$421$	0.298655	0.0145555	0.00727777	−	0.999974i	$-0.497683\pi$
$421$	0.298655	0.0145555	0.00727777	+	0.999974i	$0.497683\pi$
$422$	−30.5014	−1.48478
$423$	3.75209	0.182433
$424$	−37.9591	−1.84346
$425$	−28.9998	−1.40670
$426$	−45.2984	−2.19471
$427$	−0.408096	−0.0197492
$428$	34.7792	1.68112
$429$	39.0148	1.88365
$430$	58.7276	2.83209
$431$	10.8909	0.524598	0.262299	−	0.964987i	$-0.415519\pi$
$431$	10.8909	0.524598	0.262299	+	0.964987i	$0.415519\pi$
$432$	−28.5860	−1.37534
$433$	6.93722	0.333382	0.166691	−	0.986009i	$-0.446692\pi$
$433$	6.93722	0.333382	0.166691	+	0.986009i	$0.446692\pi$
$434$	18.1115	0.869381
$435$	48.0408	2.30338
$436$	−14.7252	−0.705209
$437$	3.05541	0.146160
$438$	78.5786	3.75463
$439$	3.95183	0.188611	0.0943054	−	0.995543i	$-0.469937\pi$
$439$	3.95183	0.188611	0.0943054	+	0.995543i	$0.469937\pi$
$440$	162.528	7.74822
$441$	−5.02746	−0.239403
$442$	18.0002	0.856183
$443$	15.7742	0.749454	0.374727	−	0.927135i	$-0.377736\pi$
$443$	15.7742	0.749454	0.374727	+	0.927135i	$0.377736\pi$
$444$	57.8493	2.74541
$445$	14.3294	0.679279
$446$	39.0512	1.84913
$447$	−5.33012	−0.252106
$448$	0.878481	0.0415043
$449$	−22.6024	−1.06668	−0.533338	−	0.845902i	$-0.679063\pi$
$449$	−22.6024	−1.06668	−0.533338	+	0.845902i	$0.679063\pi$
$450$	−37.6621	−1.77541
$451$	52.6024	2.47695
$452$	−26.0774	−1.22658
$453$	8.86285	0.416413
$454$	19.0592	0.894493
$455$	−21.8805	−1.02577
$456$	21.7166	1.01698
$457$	32.5656	1.52336	0.761678	−	0.647956i	$-0.224376\pi$
$457$	32.5656	1.52336	0.761678	+	0.647956i	$0.224376\pi$
$458$	11.3596	0.530798
$459$	8.27646	0.386312
$460$	35.6578	1.66256
$461$	−12.2392	−0.570038	−0.285019	−	0.958522i	$-0.592000\pi$
$461$	−12.2392	−0.570038	−0.285019	+	0.958522i	$0.592000\pi$
$462$	−46.7615	−2.17554
$463$	−27.1558	−1.26204	−0.631018	−	0.775768i	$-0.717363\pi$
$463$	−27.1558	−1.26204	−0.631018	+	0.775768i	$0.717363\pi$
$464$	−40.8233	−1.89518
$465$	39.9842	1.85422
$466$	−47.3801	−2.19484
$467$	−0.523009	−0.0242020	−0.0121010	−	0.999927i	$-0.503852\pi$
$467$	−0.523009	−0.0242020	−0.0121010	+	0.999927i	$0.503852\pi$
$468$	16.2074	0.749187
$469$	25.0604	1.15718
$470$	37.8678	1.74671
$471$	−32.9871	−1.51996
$472$	−68.1478	−3.13676
$473$	31.3172	1.43997
$474$	−40.4292	−1.85697
$475$	−22.5809	−1.03608
$476$	−14.9576	−0.685581
$477$	6.42308	0.294093
$478$	3.07654	0.140717
$479$	−1.94297	−0.0887764	−0.0443882	−	0.999014i	$-0.514134\pi$
$479$	−1.94297	−0.0887764	−0.0443882	+	0.999014i	$0.514134\pi$
$480$	52.3919	2.39135
$481$	20.8200	0.949312
$482$	−63.2735	−2.88203
$483$	−5.72094	−0.260312
$484$	105.691	4.80412
$485$	−73.2792	−3.32744
$486$	27.6262	1.25315
$487$	11.7672	0.533221	0.266611	−	0.963804i	$-0.414096\pi$
$487$	11.7672	0.533221	0.266611	+	0.963804i	$0.414096\pi$
$488$	1.70125	0.0770119
$489$	18.0063	0.814273
$490$	−50.7394	−2.29217
$491$	−10.4808	−0.472994	−0.236497	−	0.971632i	$-0.575999\pi$
$491$	−10.4808	−0.472994	−0.236497	+	0.971632i	$0.575999\pi$
$492$	82.0268	3.69806
$493$	11.8195	0.532324
$494$	14.0160	0.630609
$495$	−27.5015	−1.23610
$496$	−33.9771	−1.52562
$497$	13.5472	0.607677
$498$	−38.9617	−1.74592
$499$	32.4259	1.45158	0.725791	−	0.687916i	$-0.241474\pi$
$499$	32.4259	1.45158	0.725791	+	0.687916i	$0.241474\pi$
$500$	−166.197	−7.43256
$501$	−14.8932	−0.665380
$502$	−23.6813	−1.05695
$503$	27.5191	1.22701	0.613507	−	0.789689i	$-0.289758\pi$
$503$	27.5191	1.22701	0.613507	+	0.789689i	$0.289758\pi$
$504$	−10.8324	−0.482513
$505$	−10.2094	−0.454313
$506$	27.4265	1.21926
$507$	−4.39308	−0.195104
$508$	−18.3355	−0.813505
$509$	9.90524	0.439042	0.219521	−	0.975608i	$-0.429551\pi$
$509$	9.90524	0.439042	0.219521	+	0.975608i	$0.429551\pi$
$510$	−47.6289	−2.10904
$511$	−23.5002	−1.03959
$512$	50.7489	2.24281
$513$	6.44452	0.284533
$514$	−26.6446	−1.17524
$515$	−60.2037	−2.65289
$516$	48.8352	2.14985
$517$	20.1935	0.888107
$518$	−24.9540	−1.09642
$519$	−26.1653	−1.14853
$520$	91.2141	4.00000
$521$	−8.31099	−0.364111	−0.182056	−	0.983288i	$-0.558275\pi$
$521$	−8.31099	−0.364111	−0.182056	+	0.983288i	$0.558275\pi$
$522$	15.3500	0.671853
$523$	−22.9386	−1.00304	−0.501518	−	0.865147i	$-0.667225\pi$
$523$	−22.9386	−1.00304	−0.501518	+	0.865147i	$0.667225\pi$
$524$	51.4191	2.24625
$525$	42.2804	1.84527
$526$	−78.5838	−3.42642
$527$	9.83735	0.428522
$528$	87.7244	3.81772
$529$	−19.6446	−0.854111
$530$	64.8246	2.81580
$531$	11.5313	0.500417
$532$	−11.6468	−0.504955
$533$	29.5216	1.27872
$534$	17.1868	0.743744
$535$	−33.1204	−1.43192
$536$	−104.471	−4.51245
$537$	−18.9285	−0.816824
$538$	−42.9352	−1.85107
$539$	−27.0574	−1.16544
$540$	75.2102	3.23653
$541$	23.1913	0.997070	0.498535	−	0.866870i	$-0.333872\pi$
$541$	23.1913	0.997070	0.498535	+	0.866870i	$0.333872\pi$
$542$	1.02315	0.0439479
$543$	−21.2427	−0.911611
$544$	12.8900	0.552655
$545$	14.0229	0.600675
$546$	−26.2435	−1.12312
$547$	−29.8381	−1.27578	−0.637892	−	0.770126i	$-0.720193\pi$
$547$	−29.8381	−1.27578	−0.637892	+	0.770126i	$0.720193\pi$
$548$	−15.6644	−0.669149
$549$	−0.287869	−0.0122860
$550$	−202.694	−8.64292
$551$	9.20334	0.392076
$552$	23.8492	1.01509
$553$	12.0910	0.514162
$554$	56.5266	2.40158
$555$	−55.0902	−2.33845
$556$	−57.0018	−2.41742
$557$	−28.2527	−1.19711	−0.598553	−	0.801083i	$-0.704258\pi$
$557$	−28.2527	−1.19711	−0.598553	+	0.801083i	$0.704258\pi$
$558$	12.7758	0.540843
$559$	17.5759	0.743380
$560$	−49.1980	−2.07899
$561$	−25.3987	−1.07233
$562$	29.6989	1.25277
$563$	4.45022	0.187554	0.0937771	−	0.995593i	$-0.470106\pi$
$563$	4.45022	0.187554	0.0937771	+	0.995593i	$0.470106\pi$
$564$	31.4892	1.32593
$565$	24.8336	1.04476
$566$	−65.0052	−2.73237
$567$	−17.1142	−0.718730
$568$	−56.4750	−2.36964
$569$	−28.0393	−1.17547	−0.587734	−	0.809054i	$-0.699980\pi$
$569$	−28.0393	−1.17547	−0.587734	+	0.809054i	$0.699980\pi$
$570$	−37.0866	−1.55339
$571$	39.6145	1.65782	0.828908	−	0.559385i	$-0.188962\pi$
$571$	39.6145	1.65782	0.828908	+	0.559385i	$0.188962\pi$
$572$	87.2270	3.64714
$573$	−10.5845	−0.442174
$574$	−35.3833	−1.47687
$575$	−24.7982	−1.03416
$576$	0.619677	0.0258199
$577$	30.6068	1.27418	0.637089	−	0.770790i	$-0.280138\pi$
$577$	30.6068	1.27418	0.637089	+	0.770790i	$0.280138\pi$
$578$	31.6941	1.31830
$579$	28.1470	1.16975
$580$	107.407	4.45982
$581$	11.6522	0.483413
$582$	−87.8914	−3.64322
$583$	34.5685	1.43168
$584$	97.9665	4.05388
$585$	−15.4344	−0.638134
$586$	74.8575	3.09234
$587$	23.4561	0.968138	0.484069	−	0.875030i	$-0.339158\pi$
$587$	23.4561	0.968138	0.484069	+	0.875030i	$0.339158\pi$
$588$	−42.1926	−1.73999
$589$	7.65992	0.315621
$590$	116.379	4.79126
$591$	42.4158	1.74475
$592$	46.8136	1.92403
$593$	10.0162	0.411318	0.205659	−	0.978624i	$-0.434066\pi$
$593$	10.0162	0.411318	0.205659	+	0.978624i	$0.434066\pi$
$594$	57.8485	2.37355
$595$	14.2442	0.583956
$596$	−11.9168	−0.488130
$597$	−47.2714	−1.93469
$598$	15.3923	0.629439
$599$	−10.5874	−0.432591	−0.216296	−	0.976328i	$-0.569397\pi$
$599$	−10.5874	−0.432591	−0.216296	+	0.976328i	$0.569397\pi$
$600$	−176.256	−7.19563
$601$	−34.4856	−1.40670	−0.703349	−	0.710844i	$-0.748313\pi$
$601$	−34.4856	−1.40670	−0.703349	+	0.710844i	$0.748313\pi$
$602$	−21.0657	−0.858573
$603$	17.6775	0.719885
$604$	19.8150	0.806262
$605$	−100.650	−4.09200
$606$	−12.2452	−0.497428
$607$	−32.7533	−1.32941	−0.664707	−	0.747104i	$-0.731444\pi$
$607$	−32.7533	−1.32941	−0.664707	+	0.747104i	$0.731444\pi$
$608$	10.0369	0.407050
$609$	−17.2323	−0.698289
$610$	−2.90531	−0.117632
$611$	11.3330	0.458484
$612$	−10.5510	−0.426501
$613$	17.9610	0.725438	0.362719	−	0.931899i	$-0.381849\pi$
$613$	17.9610	0.725438	0.362719	+	0.931899i	$0.381849\pi$
$614$	−36.1044	−1.45705
$615$	−78.1146	−3.14989
$616$	−58.2991	−2.34894
$617$	−15.2736	−0.614890	−0.307445	−	0.951566i	$-0.599474\pi$
$617$	−15.2736	−0.614890	−0.307445	+	0.951566i	$0.599474\pi$
$618$	−72.2085	−2.90465
$619$	8.27163	0.332465	0.166232	−	0.986087i	$-0.446840\pi$
$619$	8.27163	0.332465	0.166232	+	0.986087i	$0.446840\pi$
$620$	89.3944	3.59016
$621$	7.07735	0.284004
$622$	18.6034	0.745928
$623$	−5.13999	−0.205929
$624$	49.2328	1.97089
$625$	90.5817	3.62327
$626$	61.1422	2.44373
$627$	−19.7769	−0.789813
$628$	−73.7505	−2.94297
$629$	−13.5539	−0.540429
$630$	18.4990	0.737018
$631$	−4.78409	−0.190452	−0.0952259	−	0.995456i	$-0.530357\pi$
$631$	−4.78409	−0.190452	−0.0952259	+	0.995456i	$0.530357\pi$
$632$	−50.4044	−2.00498
$633$	24.1539	0.960031
$634$	79.1060	3.14170
$635$	17.4610	0.692918
$636$	53.9052	2.13748
$637$	−15.1852	−0.601658
$638$	82.6128	3.27067
$639$	9.55617	0.378036
$640$	−45.5619	−1.80099
$641$	−20.1063	−0.794150	−0.397075	−	0.917786i	$-0.629975\pi$
$641$	−20.1063	−0.794150	−0.397075	+	0.917786i	$0.629975\pi$
$642$	−39.7248	−1.56781
$643$	−47.1143	−1.85801	−0.929003	−	0.370072i	$-0.879333\pi$
$643$	−47.1143	−1.85801	−0.929003	+	0.370072i	$0.879333\pi$
$644$	−12.7905	−0.504018
$645$	−46.5061	−1.83117
$646$	−9.12444	−0.358996
$647$	−3.94841	−0.155228	−0.0776141	−	0.996983i	$-0.524730\pi$
$647$	−3.94841	−0.155228	−0.0776141	+	0.996983i	$0.524730\pi$
$648$	71.3449	2.80269
$649$	62.0608	2.43610
$650$	−113.756	−4.46189
$651$	−14.3424	−0.562124
$652$	40.2574	1.57660
$653$	38.3115	1.49925	0.749623	−	0.661865i	$-0.230235\pi$
$653$	38.3115	1.49925	0.749623	+	0.661865i	$0.230235\pi$
$654$	16.8191	0.657679
$655$	−48.9667	−1.91329
$656$	66.3789	2.59166
$657$	−16.5770	−0.646729
$658$	−13.5832	−0.529530
$659$	15.9817	0.622560	0.311280	−	0.950318i	$-0.399242\pi$
$659$	15.9817	0.622560	0.311280	+	0.950318i	$0.399242\pi$
$660$	−230.804	−8.98404
$661$	−6.61541	−0.257309	−0.128655	−	0.991689i	$-0.541066\pi$
$661$	−6.61541	−0.257309	−0.128655	+	0.991689i	$0.541066\pi$
$662$	64.3798	2.50219
$663$	−14.2543	−0.553591
$664$	−48.5749	−1.88507
$665$	11.0914	0.430104
$666$	−17.6025	−0.682082
$667$	10.1071	0.391348
$668$	−33.2974	−1.28831
$669$	−30.9244	−1.19561
$670$	178.410	6.89257
$671$	−1.54929	−0.0598097
$672$	−18.7931	−0.724959
$673$	31.5354	1.21560	0.607799	−	0.794091i	$-0.292052\pi$
$673$	31.5354	1.21560	0.607799	+	0.794091i	$0.292052\pi$
$674$	−27.5824	−1.06243
$675$	−52.3049	−2.01322
$676$	−9.82179	−0.377761
$677$	−38.8091	−1.49156	−0.745778	−	0.666194i	$-0.767922\pi$
$677$	−38.8091	−1.49156	−0.745778	+	0.666194i	$0.767922\pi$
$678$	29.7855	1.14391
$679$	26.2854	1.00874
$680$	−59.3806	−2.27714
$681$	−15.0929	−0.578361
$682$	68.7584	2.63289
$683$	18.8603	0.721671	0.360835	−	0.932630i	$-0.382492\pi$
$683$	18.8603	0.721671	0.360835	+	0.932630i	$0.382492\pi$
$684$	−8.21564	−0.314133
$685$	14.9173	0.569960
$686$	45.8075	1.74894
$687$	−8.99559	−0.343203
$688$	39.5191	1.50665
$689$	19.4006	0.739103
$690$	−40.7284	−1.55050
$691$	−43.9618	−1.67239	−0.836193	−	0.548435i	$-0.815224\pi$
$691$	−43.9618	−1.67239	−0.836193	+	0.548435i	$0.815224\pi$
$692$	−58.4989	−2.22379
$693$	9.86483	0.374734
$694$	−10.9527	−0.415759
$695$	54.2832	2.05908
$696$	71.8372	2.72298
$697$	−19.2186	−0.727956
$698$	−17.5855	−0.665620
$699$	37.5201	1.41914
$700$	94.5279	3.57282
$701$	2.34385	0.0885260	0.0442630	−	0.999020i	$-0.485906\pi$
$701$	2.34385	0.0885260	0.0442630	+	0.999020i	$0.485906\pi$
$702$	32.4658	1.22534
$703$	−10.5538	−0.398045
$704$	3.33505	0.125695
$705$	−29.9873	−1.12939
$706$	23.8302	0.896860
$707$	3.66214	0.137729
$708$	96.7759	3.63706
$709$	−30.8821	−1.15980	−0.579901	−	0.814687i	$-0.696909\pi$
$709$	−30.8821	−1.15980	−0.579901	+	0.814687i	$0.696909\pi$
$710$	96.4452	3.61952
$711$	8.52896	0.319861
$712$	21.4273	0.803022
$713$	8.41210	0.315036
$714$	17.0846	0.639374
$715$	−83.0668	−3.10652
$716$	−42.3191	−1.58154
$717$	−2.43629	−0.0909851
$718$	1.48416	0.0553884
$719$	−11.5612	−0.431160	−0.215580	−	0.976486i	$-0.569164\pi$
$719$	−11.5612	−0.431160	−0.215580	+	0.976486i	$0.569164\pi$
$720$	−34.7041	−1.29334
$721$	21.5952	0.804246
$722$	41.4148	1.54130
$723$	50.1060	1.86346
$724$	−47.4931	−1.76507
$725$	−74.6960	−2.77414
$726$	−120.720	−4.48033
$727$	44.2986	1.64294	0.821472	−	0.570249i	$-0.193153\pi$
$727$	44.2986	1.64294	0.821472	+	0.570249i	$0.193153\pi$
$728$	−32.7187	−1.21263
$729$	11.3672	0.421007
$730$	−167.302	−6.19213
$731$	−11.4419	−0.423195
$732$	−2.41592	−0.0892951
$733$	−2.33820	−0.0863635	−0.0431818	−	0.999067i	$-0.513749\pi$
$733$	−2.33820	−0.0863635	−0.0431818	+	0.999067i	$0.513749\pi$
$734$	−63.9612	−2.36085
$735$	40.1802	1.48207
$736$	11.0225	0.406295
$737$	95.1392	3.50450
$738$	−24.9592	−0.918762
$739$	8.31643	0.305925	0.152962	−	0.988232i	$-0.451119\pi$
$739$	8.31643	0.305925	0.152962	+	0.988232i	$0.451119\pi$
$740$	−123.167	−4.52772
$741$	−11.0992	−0.407739
$742$	−23.2527	−0.853633
$743$	18.7650	0.688423	0.344211	−	0.938892i	$-0.388146\pi$
$743$	18.7650	0.688423	0.344211	+	0.938892i	$0.388146\pi$
$744$	59.7899	2.19201
$745$	11.3484	0.415773
$746$	51.1064	1.87114
$747$	8.21939	0.300732
$748$	−56.7849	−2.07626
$749$	11.8804	0.434099
$750$	189.830	6.93162
$751$	37.5996	1.37203	0.686014	−	0.727589i	$-0.259359\pi$
$751$	37.5996	1.37203	0.686014	+	0.727589i	$0.259359\pi$
$752$	25.4821	0.929237
$753$	18.7531	0.683402
$754$	46.3640	1.68848
$755$	−18.8700	−0.686748
$756$	−26.9780	−0.981181
$757$	16.6421	0.604869	0.302434	−	0.953170i	$-0.402201\pi$
$757$	16.6421	0.604869	0.302434	+	0.953170i	$0.402201\pi$
$758$	44.3579	1.61115
$759$	−21.7189	−0.788347
$760$	−46.2371	−1.67719
$761$	−31.3201	−1.13535	−0.567676	−	0.823252i	$-0.692158\pi$
$761$	−31.3201	−1.13535	−0.567676	+	0.823252i	$0.692158\pi$
$762$	20.9428	0.758677
$763$	−5.03003	−0.182099
$764$	−23.6642	−0.856140
$765$	10.0478	0.363280
$766$	−79.8025	−2.88338
$767$	34.8298	1.25763
$768$	−56.9477	−2.05492
$769$	−41.4689	−1.49541	−0.747703	−	0.664034i	$-0.768843\pi$
$769$	−41.4689	−1.49541	−0.747703	+	0.664034i	$0.768843\pi$
$770$	99.5603	3.58790
$771$	21.0997	0.759889
$772$	62.9294	2.26488
$773$	−9.08663	−0.326823	−0.163412	−	0.986558i	$-0.552250\pi$
$773$	−9.08663	−0.326823	−0.163412	+	0.986558i	$0.552250\pi$
$774$	−14.8597	−0.534119
$775$	−62.1693	−2.23319
$776$	−109.577	−3.93359
$777$	19.7610	0.708921
$778$	70.8827	2.54127
$779$	−14.9647	−0.536165
$780$	−129.532	−4.63799
$781$	51.4306	1.84033
$782$	−10.0204	−0.358330
$783$	21.3181	0.761845
$784$	−34.1437	−1.21942
$785$	70.2330	2.50672
$786$	−58.7309	−2.09486
$787$	25.9535	0.925141	0.462571	−	0.886582i	$-0.346927\pi$
$787$	25.9535	0.925141	0.462571	+	0.886582i	$0.346927\pi$
$788$	94.8307	3.37820
$789$	62.2301	2.21545
$790$	86.0781	3.06252
$791$	−8.90786	−0.316727
$792$	−41.1240	−1.46128
$793$	−0.869494	−0.0308766
$794$	17.4164	0.618086
$795$	−51.3343	−1.82064
$796$	−105.687	−3.74596
$797$	−29.5158	−1.04550	−0.522751	−	0.852485i	$-0.675094\pi$
$797$	−29.5158	−1.04550	−0.522751	+	0.852485i	$0.675094\pi$
$798$	13.3030	0.470922
$799$	−7.37779	−0.261008
$800$	−81.4613	−2.88009
$801$	−3.62573	−0.128109
$802$	11.1058	0.392161
$803$	−89.2160	−3.14836
$804$	148.358	5.23217
$805$	12.1805	0.429306
$806$	38.5886	1.35923
$807$	34.0002	1.19686
$808$	−15.2665	−0.537075
$809$	19.2030	0.675140	0.337570	−	0.941300i	$-0.390395\pi$
$809$	19.2030	0.675140	0.337570	+	0.941300i	$0.390395\pi$
$810$	−121.839	−4.28099
$811$	48.5731	1.70563	0.852816	−	0.522211i	$-0.174893\pi$
$811$	48.5731	1.70563	0.852816	+	0.522211i	$0.174893\pi$
$812$	−38.5270	−1.35203
$813$	−0.810225	−0.0284158
$814$	−94.7352	−3.32047
$815$	−38.3373	−1.34290
$816$	−32.0506	−1.12200
$817$	−8.90933	−0.311698
$818$	54.6714	1.91154
$819$	5.53635	0.193456
$820$	−174.644	−6.09883
$821$	−8.25274	−0.288023	−0.144011	−	0.989576i	$-0.546000\pi$
$821$	−8.25274	−0.288023	−0.144011	+	0.989576i	$0.546000\pi$
$822$	17.8918	0.624050
$823$	−1.67415	−0.0583573	−0.0291786	−	0.999574i	$-0.509289\pi$
$823$	−1.67415	−0.0583573	−0.0291786	+	0.999574i	$0.509289\pi$
$824$	−90.0248	−3.13616
$825$	160.513	5.58834
$826$	−41.7455	−1.45251
$827$	−35.2356	−1.22526	−0.612631	−	0.790369i	$-0.709889\pi$
$827$	−35.2356	−1.22526	−0.612631	+	0.790369i	$0.709889\pi$
$828$	−9.02240	−0.313550
$829$	16.7418	0.581467	0.290734	−	0.956804i	$-0.406101\pi$
$829$	16.7418	0.581467	0.290734	+	0.956804i	$0.406101\pi$
$830$	82.9537	2.87937
$831$	−44.7631	−1.55281
$832$	1.87170	0.0648896
$833$	9.88557	0.342515
$834$	65.1075	2.25449
$835$	31.7093	1.09734
$836$	−44.2160	−1.52924
$837$	17.7430	0.613286
$838$	79.2395	2.73728
$839$	41.4546	1.43117	0.715586	−	0.698525i	$-0.246160\pi$
$839$	41.4546	1.43117	0.715586	+	0.698525i	$0.246160\pi$
$840$	86.5742	2.98709
$841$	1.44406	0.0497951
$842$	−0.762663	−0.0262831
$843$	−23.5184	−0.810016
$844$	54.0018	1.85882
$845$	9.35334	0.321765
$846$	−9.58156	−0.329421
$847$	36.1033	1.24052
$848$	43.6220	1.49798
$849$	51.4773	1.76670
$850$	74.0556	2.54009
$851$	−11.5902	−0.397306
$852$	80.1995	2.74759
$853$	−4.88259	−0.167177	−0.0835883	−	0.996500i	$-0.526638\pi$
$853$	−4.88259	−0.167177	−0.0835883	+	0.996500i	$0.526638\pi$
$854$	1.04214	0.0356613
$855$	7.82380	0.267568
$856$	−49.5262	−1.69277
$857$	12.2333	0.417880	0.208940	−	0.977928i	$-0.432999\pi$
$857$	12.2333	0.417880	0.208940	+	0.977928i	$0.432999\pi$
$858$	−99.6306	−3.40133
$859$	−29.4010	−1.00315	−0.501574	−	0.865115i	$-0.667246\pi$
$859$	−29.4010	−1.00315	−0.501574	+	0.865115i	$0.667246\pi$
$860$	−103.975	−3.54553
$861$	28.0199	0.954914
$862$	−27.8117	−0.947272
$863$	45.3599	1.54407	0.772035	−	0.635580i	$-0.219239\pi$
$863$	45.3599	1.54407	0.772035	+	0.635580i	$0.219239\pi$
$864$	23.2488	0.790942
$865$	55.7088	1.89416
$866$	−17.7153	−0.601991
$867$	−25.0984	−0.852385
$868$	−32.0659	−1.08839
$869$	45.9022	1.55713
$870$	−122.680	−4.15924
$871$	53.3941	1.80919
$872$	20.9689	0.710098
$873$	18.5416	0.627539
$874$	−7.80247	−0.263923
$875$	−56.7719	−1.91924
$876$	−139.121	−4.70047
$877$	−1.49599	−0.0505158	−0.0252579	−	0.999681i	$-0.508041\pi$
$877$	−1.49599	−0.0505158	−0.0252579	+	0.999681i	$0.508041\pi$
$878$	−10.0916	−0.340576
$879$	−59.2793	−1.99944
$880$	−186.775	−6.29617
$881$	−0.803803	−0.0270808	−0.0135404	−	0.999908i	$-0.504310\pi$
$881$	−0.803803	−0.0270808	−0.0135404	+	0.999908i	$0.504310\pi$
$882$	12.8384	0.432292
$883$	−18.1813	−0.611849	−0.305924	−	0.952056i	$-0.598965\pi$
$883$	−18.1813	−0.611849	−0.305924	+	0.952056i	$0.598965\pi$
$884$	−31.8689	−1.07187
$885$	−92.1602	−3.09793
$886$	−40.2819	−1.35330
$887$	9.73208	0.326771	0.163386	−	0.986562i	$-0.447759\pi$
$887$	9.73208	0.326771	0.163386	+	0.986562i	$0.447759\pi$
$888$	−82.3785	−2.76444
$889$	−6.26328	−0.210064
$890$	−36.5925	−1.22658
$891$	−64.9723	−2.17665
$892$	−69.1390	−2.31494
$893$	−5.74477	−0.192241
$894$	13.6113	0.455231
$895$	40.3008	1.34711
$896$	16.3431	0.545986
$897$	−12.1891	−0.406982
$898$	57.7190	1.92611
$899$	25.3385	0.845086
$900$	66.6796	2.22265
$901$	−12.6298	−0.420760
$902$	−134.329	−4.47266
$903$	16.6818	0.555136
$904$	37.1346	1.23508
$905$	45.2280	1.50343
$906$	−22.6327	−0.751922
$907$	−8.34467	−0.277080	−0.138540	−	0.990357i	$-0.544241\pi$
$907$	−8.34467	−0.277080	−0.138540	+	0.990357i	$0.544241\pi$
$908$	−33.7438	−1.11983
$909$	2.58326	0.0856813
$910$	55.8753	1.85225
$911$	−45.9166	−1.52129	−0.760643	−	0.649170i	$-0.775116\pi$
$911$	−45.9166	−1.52129	−0.760643	+	0.649170i	$0.775116\pi$
$912$	−24.9564	−0.826390
$913$	44.2361	1.46400
$914$	−83.1615	−2.75074
$915$	2.30070	0.0760587
$916$	−20.1118	−0.664512
$917$	17.5644	0.580029
$918$	−21.1353	−0.697568
$919$	−37.4705	−1.23604	−0.618018	−	0.786164i	$-0.712064\pi$
$919$	−37.4705	−1.23604	−0.618018	+	0.786164i	$0.712064\pi$
$920$	−50.7774	−1.67408
$921$	28.5909	0.942102
$922$	31.2548	1.02932
$923$	28.8639	0.950067
$924$	82.7899	2.72359
$925$	85.6567	2.81638
$926$	69.3467	2.27887
$927$	15.2331	0.500322
$928$	33.2014	1.08989
$929$	−6.46610	−0.212146	−0.106073	−	0.994358i	$-0.533828\pi$
$929$	−6.46610	−0.212146	−0.106073	+	0.994358i	$0.533828\pi$
$930$	−102.106	−3.34819
$931$	7.69747	0.252274
$932$	83.8851	2.74775
$933$	−14.7319	−0.482302
$934$	1.33559	0.0437018
$935$	54.0766	1.76849
$936$	−23.0796	−0.754381
$937$	−20.8327	−0.680575	−0.340287	−	0.940322i	$-0.610524\pi$
$937$	−20.8327	−0.680575	−0.340287	+	0.940322i	$0.610524\pi$
$938$	−63.9959	−2.08954
$939$	−48.4182	−1.58007
$940$	−67.0438	−2.18673
$941$	15.6486	0.510131	0.255066	−	0.966924i	$-0.417903\pi$
$941$	15.6486	0.510131	0.255066	+	0.966924i	$0.417903\pi$
$942$	84.2378	2.74462
$943$	−16.4342	−0.535170
$944$	78.3144	2.54892
$945$	25.6913	0.835739
$946$	−79.9735	−2.60016
$947$	4.68772	0.152330	0.0761651	−	0.997095i	$-0.475732\pi$
$947$	4.68772	0.152330	0.0761651	+	0.997095i	$0.475732\pi$
$948$	71.5787	2.32477
$949$	−50.0698	−1.62534
$950$	57.6639	1.87086
$951$	−62.6437	−2.03136
$952$	21.2999	0.690334
$953$	−24.2203	−0.784574	−0.392287	−	0.919843i	$-0.628316\pi$
$953$	−24.2203	−0.784574	−0.392287	+	0.919843i	$0.628316\pi$
$954$	−16.4024	−0.531046
$955$	22.5355	0.729233
$956$	−5.44692	−0.176166
$957$	−65.4206	−2.11475
$958$	4.96168	0.160305
$959$	−5.35085	−0.172788
$960$	−4.95256	−0.159843
$961$	−9.91083	−0.319704
$962$	−53.1673	−1.71418
$963$	8.38036	0.270053
$964$	112.024	3.60805
$965$	−59.9281	−1.92915
$966$	14.6093	0.470048
$967$	−2.49217	−0.0801429	−0.0400714	−	0.999197i	$-0.512759\pi$
$967$	−2.49217	−0.0801429	−0.0400714	+	0.999197i	$0.512759\pi$
$968$	−150.505	−4.83743
$969$	7.22560	0.232120
$970$	187.130	6.00839
$971$	−51.7458	−1.66060	−0.830300	−	0.557316i	$-0.811831\pi$
$971$	−51.7458	−1.66060	−0.830300	+	0.557316i	$0.811831\pi$
$972$	−48.9115	−1.56884
$973$	−19.4715	−0.624227
$974$	−30.0493	−0.962843
$975$	90.0831	2.88497
$976$	−1.95505	−0.0625796
$977$	19.3724	0.619778	0.309889	−	0.950773i	$-0.399708\pi$
$977$	19.3724	0.619778	0.309889	+	0.950773i	$0.399708\pi$
$978$	−45.9820	−1.47034
$979$	−19.5134	−0.623650
$980$	89.8326	2.86960
$981$	−3.54817	−0.113284
$982$	26.7645	0.854090
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−116.808	−3.72369
$985$	−90.3078	−2.87745
$986$	−30.1830	−0.961224
$987$	10.7565	0.342383
$988$	−24.8149	−0.789467
$989$	−9.78420	−0.311119
$990$	70.2294	2.23204
$991$	4.74977	0.150881	0.0754407	−	0.997150i	$-0.475964\pi$
$991$	4.74977	0.150881	0.0754407	+	0.997150i	$0.475964\pi$
$992$	27.6334	0.877363
$993$	−50.9820	−1.61787
$994$	−34.5951	−1.09729
$995$	100.646	3.19069
$996$	68.9807	2.18574
$997$	0.151969	0.00481292	0.00240646	−	0.999997i	$-0.499234\pi$
$997$	0.151969	0.00481292	0.00240646	+	0.999997i	$0.499234\pi$
$998$	−82.8047	−2.62114
$999$	−24.4462	−0.773444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.4	✓	54
3.2	odd	2		8847.2.a.g.1.51		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.4	✓	54	1.1	even	1	trivial
8847.2.a.g.1.51		54	3.2	odd	2

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55366 q^{2} +2.02223 q^{3} +4.52118 q^{4} -4.30555 q^{5} -5.16409 q^{6} +1.54441 q^{7} -6.43825 q^{8} +1.08942 q^{9} +O(q^{10})\)	\(q-2.55366 q^{2} +2.02223 q^{3} +4.52118 q^{4} -4.30555 q^{5} -5.16409 q^{6} +1.54441 q^{7} -6.43825 q^{8} +1.08942 q^{9} +10.9949 q^{10} +5.86317 q^{11} +9.14288 q^{12} +3.29053 q^{13} -3.94389 q^{14} -8.70681 q^{15} +7.39873 q^{16} -2.14214 q^{17} -2.78201 q^{18} -1.66799 q^{19} -19.4662 q^{20} +3.12315 q^{21} -14.9726 q^{22} -1.83179 q^{23} -13.0196 q^{24} +13.5377 q^{25} -8.40290 q^{26} -3.86364 q^{27} +6.98255 q^{28} -5.51761 q^{29} +22.2342 q^{30} -4.59229 q^{31} -6.01735 q^{32} +11.8567 q^{33} +5.47031 q^{34} -6.64952 q^{35} +4.92546 q^{36} +6.32726 q^{37} +4.25949 q^{38} +6.65422 q^{39} +27.7202 q^{40} +8.97167 q^{41} -7.97546 q^{42} +5.34134 q^{43} +26.5085 q^{44} -4.69055 q^{45} +4.67776 q^{46} +3.44412 q^{47} +14.9619 q^{48} -4.61481 q^{49} -34.5708 q^{50} -4.33191 q^{51} +14.8771 q^{52} +5.89587 q^{53} +9.86642 q^{54} -25.2442 q^{55} -9.94327 q^{56} -3.37307 q^{57} +14.0901 q^{58} +10.5848 q^{59} -39.3651 q^{60} -0.264241 q^{61} +11.7272 q^{62} +1.68251 q^{63} +0.568814 q^{64} -14.1675 q^{65} -30.2780 q^{66} +16.2266 q^{67} -9.68502 q^{68} -3.70429 q^{69} +16.9806 q^{70} +8.77180 q^{71} -7.01395 q^{72} -15.2163 q^{73} -16.1577 q^{74} +27.3764 q^{75} -7.54130 q^{76} +9.05513 q^{77} -16.9926 q^{78} +7.82890 q^{79} -31.8556 q^{80} -11.0814 q^{81} -22.9106 q^{82} +7.54474 q^{83} +14.1203 q^{84} +9.22310 q^{85} -13.6400 q^{86} -11.1579 q^{87} -37.7485 q^{88} -3.32813 q^{89} +11.9781 q^{90} +5.08192 q^{91} -8.28184 q^{92} -9.28668 q^{93} -8.79511 q^{94} +7.18163 q^{95} -12.1685 q^{96} +17.0197 q^{97} +11.7846 q^{98} +6.38745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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