LMFDB - Embedded newform 983.2.a.a.1.6

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:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-1.91443 q^{2} +1.82487 q^{3} +1.66503 q^{4} +2.84047 q^{5} -3.49358 q^{6} -3.81993 q^{7} +0.641279 q^{8} +0.330154 q^{9} +O(q^{10})$	\(q-1.91443 q^{2} +1.82487 q^{3} +1.66503 q^{4} +2.84047 q^{5} -3.49358 q^{6} -3.81993 q^{7} +0.641279 q^{8} +0.330154 q^{9} -5.43787 q^{10} -2.90484 q^{11} +3.03846 q^{12} +0.331101 q^{13} +7.31298 q^{14} +5.18349 q^{15} -4.55774 q^{16} -6.31190 q^{17} -0.632056 q^{18} +0.291089 q^{19} +4.72947 q^{20} -6.97088 q^{21} +5.56111 q^{22} -7.19529 q^{23} +1.17025 q^{24} +3.06828 q^{25} -0.633868 q^{26} -4.87212 q^{27} -6.36029 q^{28} -5.72792 q^{29} -9.92342 q^{30} +7.82786 q^{31} +7.44290 q^{32} -5.30096 q^{33} +12.0837 q^{34} -10.8504 q^{35} +0.549716 q^{36} -10.9349 q^{37} -0.557268 q^{38} +0.604216 q^{39} +1.82153 q^{40} -1.90520 q^{41} +13.3452 q^{42} -4.31454 q^{43} -4.83664 q^{44} +0.937794 q^{45} +13.7749 q^{46} +6.95271 q^{47} -8.31728 q^{48} +7.59188 q^{49} -5.87399 q^{50} -11.5184 q^{51} +0.551292 q^{52} +11.9343 q^{53} +9.32732 q^{54} -8.25112 q^{55} -2.44964 q^{56} +0.531200 q^{57} +10.9657 q^{58} +14.1080 q^{59} +8.63066 q^{60} +3.94112 q^{61} -14.9859 q^{62} -1.26117 q^{63} -5.13340 q^{64} +0.940483 q^{65} +10.1483 q^{66} +9.70276 q^{67} -10.5095 q^{68} -13.1305 q^{69} +20.7723 q^{70} -10.4998 q^{71} +0.211721 q^{72} -16.6894 q^{73} +20.9340 q^{74} +5.59921 q^{75} +0.484671 q^{76} +11.0963 q^{77} -1.15673 q^{78} +2.17810 q^{79} -12.9461 q^{80} -9.88146 q^{81} +3.64737 q^{82} +17.4567 q^{83} -11.6067 q^{84} -17.9288 q^{85} +8.25987 q^{86} -10.4527 q^{87} -1.86281 q^{88} +0.154665 q^{89} -1.79534 q^{90} -1.26478 q^{91} -11.9804 q^{92} +14.2848 q^{93} -13.3105 q^{94} +0.826830 q^{95} +13.5823 q^{96} +3.35686 q^{97} -14.5341 q^{98} -0.959046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * 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 $

$2$	−1.91443	−1.35370	−0.676852	−	0.736119i	$-0.736656\pi$
$2$	−1.91443	−1.35370	−0.676852	+	0.736119i	$0.736656\pi$
$3$	1.82487	1.05359	0.526795	−	0.849992i	$-0.323394\pi$
$3$	1.82487	1.05359	0.526795	+	0.849992i	$0.323394\pi$
$4$	1.66503	0.832514
$5$	2.84047	1.27030	0.635149	−	0.772390i	$-0.280939\pi$
$5$	2.84047	1.27030	0.635149	+	0.772390i	$0.280939\pi$
$6$	−3.49358	−1.42625
$7$	−3.81993	−1.44380	−0.721899	−	0.691998i	$-0.756731\pi$
$7$	−3.81993	−1.44380	−0.721899	+	0.691998i	$0.756731\pi$
$8$	0.641279	0.226726
$9$	0.330154	0.110051
$10$	−5.43787	−1.71961
$11$	−2.90484	−0.875843	−0.437921	−	0.899013i	$-0.644285\pi$
$11$	−2.90484	−0.875843	−0.437921	+	0.899013i	$0.644285\pi$
$12$	3.03846	0.877128
$13$	0.331101	0.0918309	0.0459154	−	0.998945i	$-0.485380\pi$
$13$	0.331101	0.0918309	0.0459154	+	0.998945i	$0.485380\pi$
$14$	7.31298	1.95448
$15$	5.18349	1.33837
$16$	−4.55774	−1.13943
$17$	−6.31190	−1.53086	−0.765431	−	0.643518i	$-0.777474\pi$
$17$	−6.31190	−1.53086	−0.765431	+	0.643518i	$0.777474\pi$
$18$	−0.632056	−0.148977
$19$	0.291089	0.0667804	0.0333902	−	0.999442i	$-0.489370\pi$
$19$	0.291089	0.0667804	0.0333902	+	0.999442i	$0.489370\pi$
$20$	4.72947	1.05754
$21$	−6.97088	−1.52117
$22$	5.56111	1.18563
$23$	−7.19529	−1.50032	−0.750161	−	0.661255i	$-0.770024\pi$
$23$	−7.19529	−1.50032	−0.750161	+	0.661255i	$0.770024\pi$
$24$	1.17025	0.238876
$25$	3.06828	0.613655
$26$	−0.633868	−0.124312
$27$	−4.87212	−0.937641
$28$	−6.36029	−1.20198
$29$	−5.72792	−1.06365	−0.531824	−	0.846855i	$-0.678493\pi$
$29$	−5.72792	−1.06365	−0.531824	+	0.846855i	$0.678493\pi$
$30$	−9.92342	−1.81176
$31$	7.82786	1.40592	0.702962	−	0.711227i	$-0.251860\pi$
$31$	7.82786	1.40592	0.702962	+	0.711227i	$0.251860\pi$
$32$	7.44290	1.31573
$33$	−5.30096	−0.922779
$34$	12.0837	2.07233
$35$	−10.8504	−1.83405
$36$	0.549716	0.0916194
$37$	−10.9349	−1.79768	−0.898839	−	0.438278i	$-0.855589\pi$
$37$	−10.9349	−1.79768	−0.898839	+	0.438278i	$0.855589\pi$
$38$	−0.557268	−0.0904008
$39$	0.604216	0.0967521
$40$	1.82153	0.288010
$41$	−1.90520	−0.297543	−0.148771	−	0.988872i	$-0.547532\pi$
$41$	−1.90520	−0.297543	−0.148771	+	0.988872i	$0.547532\pi$
$42$	13.3452	2.05922
$43$	−4.31454	−0.657961	−0.328980	−	0.944337i	$-0.606705\pi$
$43$	−4.31454	−0.657961	−0.328980	+	0.944337i	$0.606705\pi$
$44$	−4.83664	−0.729151
$45$	0.937794	0.139798
$46$	13.7749	2.03099
$47$	6.95271	1.01416	0.507079	−	0.861900i	$-0.330725\pi$
$47$	6.95271	1.01416	0.507079	+	0.861900i	$0.330725\pi$
$48$	−8.31728	−1.20050
$49$	7.59188	1.08455
$50$	−5.87399	−0.830708
$51$	−11.5184	−1.61290
$52$	0.551292	0.0764505
$53$	11.9343	1.63930	0.819652	−	0.572862i	$-0.194167\pi$
$53$	11.9343	1.63930	0.819652	+	0.572862i	$0.194167\pi$
$54$	9.32732	1.26929
$55$	−8.25112	−1.11258
$56$	−2.44964	−0.327347
$57$	0.531200	0.0703591
$58$	10.9657	1.43987
$59$	14.1080	1.83671	0.918353	−	0.395762i	$-0.129519\pi$
$59$	14.1080	1.83671	0.918353	+	0.395762i	$0.129519\pi$
$60$	8.63066	1.11421
$61$	3.94112	0.504609	0.252304	−	0.967648i	$-0.418812\pi$
$61$	3.94112	0.504609	0.252304	+	0.967648i	$0.418812\pi$
$62$	−14.9859	−1.90321
$63$	−1.26117	−0.158892
$64$	−5.13340	−0.641675
$65$	0.940483	0.116653
$66$	10.1483	1.24917
$67$	9.70276	1.18538	0.592691	−	0.805430i	$-0.298066\pi$
$67$	9.70276	1.18538	0.592691	+	0.805430i	$0.298066\pi$
$68$	−10.5095	−1.27446
$69$	−13.1305	−1.58072
$70$	20.7723	2.48276
$71$	−10.4998	−1.24610	−0.623048	−	0.782184i	$-0.714106\pi$
$71$	−10.4998	−1.24610	−0.623048	+	0.782184i	$0.714106\pi$
$72$	0.211721	0.0249515
$73$	−16.6894	−1.95334	−0.976672	−	0.214737i	$-0.931111\pi$
$73$	−16.6894	−1.95334	−0.976672	+	0.214737i	$0.931111\pi$
$74$	20.9340	2.43352
$75$	5.59921	0.646541
$76$	0.484671	0.0555956
$77$	11.0963	1.26454
$78$	−1.15673	−0.130974
$79$	2.17810	0.245055	0.122528	−	0.992465i	$-0.460900\pi$
$79$	2.17810	0.245055	0.122528	+	0.992465i	$0.460900\pi$
$80$	−12.9461	−1.44742
$81$	−9.88146	−1.09794
$82$	3.64737	0.402784
$83$	17.4567	1.91612	0.958062	−	0.286560i	$-0.0925118\pi$
$83$	17.4567	1.91612	0.958062	+	0.286560i	$0.0925118\pi$
$84$	−11.6067	−1.26640
$85$	−17.9288	−1.94465
$86$	8.25987	0.890684
$87$	−10.4527	−1.12065
$88$	−1.86281	−0.198576
$89$	0.154665	0.0163945	0.00819724	−	0.999966i	$-0.497391\pi$
$89$	0.154665	0.0163945	0.00819724	+	0.999966i	$0.497391\pi$
$90$	−1.79534	−0.189245
$91$	−1.26478	−0.132585
$92$	−11.9804	−1.24904
$93$	14.2848	1.48127
$94$	−13.3105	−1.37287
$95$	0.826830	0.0848309
$96$	13.5823	1.38624
$97$	3.35686	0.340837	0.170419	−	0.985372i	$-0.445488\pi$
$97$	3.35686	0.340837	0.170419	+	0.985372i	$0.445488\pi$
$98$	−14.5341	−1.46816
$99$	−0.959046	−0.0963877
$100$	5.10877	0.510877
$101$	−12.4360	−1.23743	−0.618713	−	0.785617i	$-0.712346\pi$
$101$	−12.4360	−1.23743	−0.618713	+	0.785617i	$0.712346\pi$
$102$	22.0511	2.18339
$103$	−19.2220	−1.89400	−0.946998	−	0.321238i	$-0.895901\pi$
$103$	−19.2220	−1.89400	−0.946998	+	0.321238i	$0.895901\pi$
$104$	0.212328	0.0208205
$105$	−19.8006	−1.93234
$106$	−22.8474	−2.21913
$107$	8.37861	0.809991	0.404995	−	0.914319i	$-0.367273\pi$
$107$	8.37861	0.809991	0.404995	+	0.914319i	$0.367273\pi$
$108$	−8.11222	−0.780599
$109$	−7.18710	−0.688399	−0.344200	−	0.938897i	$-0.611850\pi$
$109$	−7.18710	−0.688399	−0.344200	+	0.938897i	$0.611850\pi$
$110$	15.7962	1.50610
$111$	−19.9547	−1.89402
$112$	17.4102	1.64511
$113$	4.43998	0.417678	0.208839	−	0.977950i	$-0.433032\pi$
$113$	4.43998	0.417678	0.208839	+	0.977950i	$0.433032\pi$
$114$	−1.01694	−0.0952454
$115$	−20.4380	−1.90586
$116$	−9.53715	−0.885502
$117$	0.109314	0.0101061
$118$	−27.0087	−2.48636
$119$	24.1110	2.21026
$120$	3.32406	0.303444
$121$	−2.56190	−0.232900
$122$	−7.54498	−0.683091
$123$	−3.47675	−0.313488
$124$	13.0336	1.17045
$125$	−5.48700	−0.490773
$126$	2.41441	0.215093
$127$	7.18132	0.637239	0.318620	−	0.947883i	$-0.396781\pi$
$127$	7.18132	0.637239	0.318620	+	0.947883i	$0.396781\pi$
$128$	−5.05827	−0.447092
$129$	−7.87348	−0.693221
$130$	−1.80048	−0.157913
$131$	−2.04751	−0.178892	−0.0894461	−	0.995992i	$-0.528510\pi$
$131$	−2.04751	−0.178892	−0.0894461	+	0.995992i	$0.528510\pi$
$132$	−8.82625	−0.768226
$133$	−1.11194	−0.0964174
$134$	−18.5752	−1.60466
$135$	−13.8391	−1.19108
$136$	−4.04769	−0.347086
$137$	−5.75671	−0.491829	−0.245915	−	0.969292i	$-0.579088\pi$
$137$	−5.75671	−0.491829	−0.245915	+	0.969292i	$0.579088\pi$
$138$	25.1373	2.13983
$139$	4.69006	0.397806	0.198903	−	0.980019i	$-0.436262\pi$
$139$	4.69006	0.397806	0.198903	+	0.980019i	$0.436262\pi$
$140$	−18.0662	−1.52688
$141$	12.6878	1.06851
$142$	20.1011	1.68684
$143$	−0.961796	−0.0804294
$144$	−1.50476	−0.125396
$145$	−16.2700	−1.35115
$146$	31.9506	2.64425
$147$	13.8542	1.14267
$148$	−18.2068	−1.49659
$149$	−1.15354	−0.0945016	−0.0472508	−	0.998883i	$-0.515046\pi$
$149$	−1.15354	−0.0945016	−0.0472508	+	0.998883i	$0.515046\pi$
$150$	−10.7193	−0.875225
$151$	−7.45459	−0.606646	−0.303323	−	0.952888i	$-0.598096\pi$
$151$	−7.45459	−0.606646	−0.303323	+	0.952888i	$0.598096\pi$
$152$	0.186669	0.0151409
$153$	−2.08390	−0.168473
$154$	−21.2430	−1.71181
$155$	22.2348	1.78594
$156$	1.00604	0.0805475
$157$	0.683926	0.0545833	0.0272916	−	0.999628i	$-0.491312\pi$
$157$	0.683926	0.0545833	0.0272916	+	0.999628i	$0.491312\pi$
$158$	−4.16981	−0.331732
$159$	21.7786	1.72715
$160$	21.1413	1.67137
$161$	27.4855	2.16616
$162$	18.9173	1.48629
$163$	0.319718	0.0250422	0.0125211	−	0.999922i	$-0.496014\pi$
$163$	0.319718	0.0250422	0.0125211	+	0.999922i	$0.496014\pi$
$164$	−3.17221	−0.247708
$165$	−15.0572	−1.17220
$166$	−33.4196	−2.59387
$167$	6.56027	0.507649	0.253824	−	0.967250i	$-0.418311\pi$
$167$	6.56027	0.507649	0.253824	+	0.967250i	$0.418311\pi$
$168$	−4.47028	−0.344889
$169$	−12.8904	−0.991567
$170$	34.3233	2.63248
$171$	0.0961042	0.00734927
$172$	−7.18383	−0.547762
$173$	−16.7364	−1.27244	−0.636222	−	0.771506i	$-0.719504\pi$
$173$	−16.7364	−1.27244	−0.636222	+	0.771506i	$0.719504\pi$
$174$	20.0110	1.51703
$175$	−11.7206	−0.885995
$176$	13.2395	0.997965
$177$	25.7453	1.93514
$178$	−0.296095	−0.0221933
$179$	6.11417	0.456995	0.228497	−	0.973545i	$-0.426619\pi$
$179$	6.11417	0.456995	0.228497	+	0.973545i	$0.426619\pi$
$180$	1.56145	0.116384
$181$	3.43947	0.255654	0.127827	−	0.991796i	$-0.459200\pi$
$181$	3.43947	0.255654	0.127827	+	0.991796i	$0.459200\pi$
$182$	2.42133	0.179481
$183$	7.19203	0.531650
$184$	−4.61419	−0.340162
$185$	−31.0601	−2.28359
$186$	−27.3472	−2.00520
$187$	18.3351	1.34079
$188$	11.5765	0.844300
$189$	18.6112	1.35376
$190$	−1.58290	−0.114836
$191$	17.3304	1.25398	0.626992	−	0.779026i	$-0.284286\pi$
$191$	17.3304	1.25398	0.626992	+	0.779026i	$0.284286\pi$
$192$	−9.36779	−0.676062
$193$	−19.9884	−1.43880	−0.719400	−	0.694596i	$-0.755583\pi$
$193$	−19.9884	−1.43880	−0.719400	+	0.694596i	$0.755583\pi$
$194$	−6.42646	−0.461393
$195$	1.71626	0.122904
$196$	12.6407	0.902906
$197$	−8.79528	−0.626638	−0.313319	−	0.949648i	$-0.601441\pi$
$197$	−8.79528	−0.626638	−0.313319	+	0.949648i	$0.601441\pi$
$198$	1.83602	0.130480
$199$	18.5575	1.31551	0.657753	−	0.753233i	$-0.271507\pi$
$199$	18.5575	1.31551	0.657753	+	0.753233i	$0.271507\pi$
$200$	1.96762	0.139132
$201$	17.7063	1.24891
$202$	23.8078	1.67511
$203$	21.8803	1.53569
$204$	−19.1785	−1.34276
$205$	−5.41167	−0.377967
$206$	36.7990	2.56391
$207$	−2.37556	−0.165113
$208$	−1.50907	−0.104635
$209$	−0.845567	−0.0584891
$210$	37.9068	2.61582
$211$	−9.20716	−0.633847	−0.316923	−	0.948451i	$-0.602650\pi$
$211$	−9.20716	−0.633847	−0.316923	+	0.948451i	$0.602650\pi$
$212$	19.8710	1.36474
$213$	−19.1608	−1.31287
$214$	−16.0402	−1.09649
$215$	−12.2553	−0.835806
$216$	−3.12439	−0.212588
$217$	−29.9019	−2.02987
$218$	13.7592	0.931889
$219$	−30.4560	−2.05802
$220$	−13.7383	−0.926239
$221$	−2.08988	−0.140580
$222$	38.2018	2.56394
$223$	−21.1567	−1.41676	−0.708379	−	0.705832i	$-0.750573\pi$
$223$	−21.1567	−1.41676	−0.708379	+	0.705832i	$0.750573\pi$
$224$	−28.4313	−1.89965
$225$	1.01300	0.0675336
$226$	−8.50001	−0.565412
$227$	−14.8791	−0.987564	−0.493782	−	0.869586i	$-0.664386\pi$
$227$	−14.8791	−0.987564	−0.493782	+	0.869586i	$0.664386\pi$
$228$	0.884462	0.0585750
$229$	−1.59275	−0.105252	−0.0526260	−	0.998614i	$-0.516759\pi$
$229$	−1.59275	−0.105252	−0.0526260	+	0.998614i	$0.516759\pi$
$230$	39.1271	2.57996
$231$	20.2493	1.33231
$232$	−3.67319	−0.241157
$233$	−6.79506	−0.445159	−0.222579	−	0.974915i	$-0.571448\pi$
$233$	−6.79506	−0.445159	−0.222579	+	0.974915i	$0.571448\pi$
$234$	−0.209274	−0.0136807
$235$	19.7490	1.28828
$236$	23.4902	1.52908
$237$	3.97475	0.258188
$238$	−46.1588	−2.99203
$239$	23.5944	1.52620	0.763099	−	0.646282i	$-0.223677\pi$
$239$	23.5944	1.52620	0.763099	+	0.646282i	$0.223677\pi$
$240$	−23.6250	−1.52499
$241$	4.54184	0.292565	0.146283	−	0.989243i	$-0.453269\pi$
$241$	4.54184	0.292565	0.146283	+	0.989243i	$0.453269\pi$
$242$	4.90456	0.315277
$243$	−3.41602	−0.219138
$244$	6.56208	0.420094
$245$	21.5645	1.37771
$246$	6.65598	0.424370
$247$	0.0963798	0.00613250
$248$	5.01984	0.318760
$249$	31.8563	2.01881
$250$	10.5045	0.664361
$251$	−9.98396	−0.630182	−0.315091	−	0.949062i	$-0.602035\pi$
$251$	−9.98396	−0.630182	−0.315091	+	0.949062i	$0.602035\pi$
$252$	−2.09988	−0.132280
$253$	20.9012	1.31405
$254$	−13.7481	−0.862633
$255$	−32.7177	−2.04886
$256$	19.9505	1.24691
$257$	30.8001	1.92126	0.960629	−	0.277833i	$-0.0896163\pi$
$257$	30.8001	1.92126	0.960629	+	0.277833i	$0.0896163\pi$
$258$	15.0732	0.938416
$259$	41.7704	2.59549
$260$	1.56593	0.0971149
$261$	−1.89110	−0.117056
$262$	3.91982	0.242167
$263$	5.45848	0.336584	0.168292	−	0.985737i	$-0.446175\pi$
$263$	5.45848	0.336584	0.168292	+	0.985737i	$0.446175\pi$
$264$	−3.39939	−0.209218
$265$	33.8991	2.08240
$266$	2.12873	0.130521
$267$	0.282244	0.0172731
$268$	16.1554	0.986847
$269$	28.8396	1.75838	0.879192	−	0.476468i	$-0.158083\pi$
$269$	28.8396	1.75838	0.879192	+	0.476468i	$0.158083\pi$
$270$	26.4940	1.61237
$271$	27.7146	1.68354	0.841770	−	0.539837i	$-0.181514\pi$
$271$	27.7146	1.68354	0.841770	+	0.539837i	$0.181514\pi$
$272$	28.7680	1.74432
$273$	−2.30807	−0.139690
$274$	11.0208	0.665791
$275$	−8.91286	−0.537466
$276$	−21.8626	−1.31598
$277$	−0.261332	−0.0157019	−0.00785095	−	0.999969i	$-0.502499\pi$
$277$	−0.261332	−0.0157019	−0.00785095	+	0.999969i	$0.502499\pi$
$278$	−8.97877	−0.538511
$279$	2.58440	0.154724
$280$	−6.95813	−0.415828
$281$	−7.38494	−0.440549	−0.220274	−	0.975438i	$-0.570695\pi$
$281$	−7.38494	−0.440549	−0.220274	+	0.975438i	$0.570695\pi$
$282$	−24.2899	−1.44644
$283$	−6.23845	−0.370837	−0.185419	−	0.982660i	$-0.559364\pi$
$283$	−6.23845	−0.370837	−0.185419	+	0.982660i	$0.559364\pi$
$284$	−17.4824	−1.03739
$285$	1.50886	0.0893770
$286$	1.84129	0.108878
$287$	7.27774	0.429591
$288$	2.45730	0.144798
$289$	22.8401	1.34354
$290$	31.1477	1.82906
$291$	6.12583	0.359103
$292$	−27.7883	−1.62619
$293$	−22.9556	−1.34108	−0.670539	−	0.741874i	$-0.733937\pi$
$293$	−22.9556	−1.34108	−0.670539	+	0.741874i	$0.733937\pi$
$294$	−26.5228	−1.54684
$295$	40.0734	2.33316
$296$	−7.01229	−0.407581
$297$	14.1527	0.821226
$298$	2.20837	0.127927
$299$	−2.38237	−0.137776
$300$	9.32284	0.538255
$301$	16.4812	0.949963
$302$	14.2713	0.821219
$303$	−22.6941	−1.30374
$304$	−1.32671	−0.0760918
$305$	11.1946	0.641003
$306$	3.98948	0.228063
$307$	−32.8446	−1.87454	−0.937271	−	0.348603i	$-0.886656\pi$
$307$	−32.8446	−1.87454	−0.937271	+	0.348603i	$0.886656\pi$
$308$	18.4756	1.05275
$309$	−35.0776	−1.99550
$310$	−42.5669	−2.41764
$311$	−7.90882	−0.448468	−0.224234	−	0.974535i	$-0.571988\pi$
$311$	−7.90882	−0.448468	−0.224234	+	0.974535i	$0.571988\pi$
$312$	0.387471	0.0219362
$313$	17.6274	0.996361	0.498181	−	0.867073i	$-0.334002\pi$
$313$	17.6274	0.996361	0.498181	+	0.867073i	$0.334002\pi$
$314$	−1.30933	−0.0738896
$315$	−3.58231	−0.201840
$316$	3.62659	0.204012
$317$	−0.337950	−0.0189811	−0.00949057	−	0.999955i	$-0.503021\pi$
$317$	−0.337950	−0.0189811	−0.00949057	+	0.999955i	$0.503021\pi$
$318$	−41.6935	−2.33805
$319$	16.6387	0.931589
$320$	−14.5813	−0.815118
$321$	15.2899	0.853398
$322$	−52.6190	−2.93234
$323$	−1.83732	−0.102231
$324$	−16.4529	−0.914051
$325$	1.01591	0.0563525
$326$	−0.612076	−0.0338998
$327$	−13.1155	−0.725290
$328$	−1.22176	−0.0674607
$329$	−26.5589	−1.46424
$330$	28.8260	1.58682
$331$	−25.5607	−1.40494	−0.702472	−	0.711712i	$-0.747920\pi$
$331$	−25.5607	−1.40494	−0.702472	+	0.711712i	$0.747920\pi$
$332$	29.0659	1.59520
$333$	−3.61019	−0.197837
$334$	−12.5592	−0.687206
$335$	27.5604	1.50579
$336$	31.7714	1.73327
$337$	−24.1684	−1.31654	−0.658268	−	0.752783i	$-0.728711\pi$
$337$	−24.1684	−1.31654	−0.658268	+	0.752783i	$0.728711\pi$
$338$	24.6777	1.34229
$339$	8.10239	0.440061
$340$	−29.8519	−1.61895
$341$	−22.7387	−1.23137
$342$	−0.183984	−0.00994874
$343$	−2.26093	−0.122079
$344$	−2.76682	−0.149177
$345$	−37.2967	−2.00799
$346$	32.0406	1.72251
$347$	−12.7956	−0.686906	−0.343453	−	0.939170i	$-0.611597\pi$
$347$	−12.7956	−0.686906	−0.343453	+	0.939170i	$0.611597\pi$
$348$	−17.4041	−0.932956
$349$	24.7500	1.32484	0.662418	−	0.749134i	$-0.269530\pi$
$349$	24.7500	1.32484	0.662418	+	0.749134i	$0.269530\pi$
$350$	22.4382	1.19937
$351$	−1.61316	−0.0861044
$352$	−21.6204	−1.15237
$353$	24.5160	1.30485	0.652427	−	0.757852i	$-0.273751\pi$
$353$	24.5160	1.30485	0.652427	+	0.757852i	$0.273751\pi$
$354$	−49.2875	−2.61960
$355$	−29.8243	−1.58291
$356$	0.257522	0.0136486
$357$	43.9995	2.32870
$358$	−11.7051	−0.618635
$359$	2.64059	0.139365	0.0696826	−	0.997569i	$-0.477801\pi$
$359$	2.64059	0.139365	0.0696826	+	0.997569i	$0.477801\pi$
$360$	0.601387	0.0316959
$361$	−18.9153	−0.995540
$362$	−6.58462	−0.346080
$363$	−4.67513	−0.245381
$364$	−2.10590	−0.110379
$365$	−47.4057	−2.48133
$366$	−13.7686	−0.719697
$367$	−27.2446	−1.42215	−0.711077	−	0.703114i	$-0.751792\pi$
$367$	−27.2446	−1.42215	−0.711077	+	0.703114i	$0.751792\pi$
$368$	32.7942	1.70952
$369$	−0.629010	−0.0327450
$370$	59.4623	3.09130
$371$	−45.5882	−2.36682
$372$	23.7846	1.23318
$373$	23.7831	1.23144	0.615721	−	0.787964i	$-0.288865\pi$
$373$	23.7831	1.23144	0.615721	+	0.787964i	$0.288865\pi$
$374$	−35.1012	−1.81504
$375$	−10.0131	−0.517073
$376$	4.45862	0.229936
$377$	−1.89652	−0.0976758
$378$	−35.6297	−1.83260
$379$	−25.9033	−1.33057	−0.665283	−	0.746591i	$-0.731689\pi$
$379$	−25.9033	−1.33057	−0.665283	+	0.746591i	$0.731689\pi$
$380$	1.37669	0.0706229
$381$	13.1050	0.671389
$382$	−33.1778	−1.69752
$383$	−12.4921	−0.638318	−0.319159	−	0.947701i	$-0.603400\pi$
$383$	−12.4921	−0.638318	−0.319159	+	0.947701i	$0.603400\pi$
$384$	−9.23070	−0.471052
$385$	31.5187	1.60634
$386$	38.2664	1.94771
$387$	−1.42446	−0.0724095
$388$	5.58926	0.283752
$389$	0.113379	0.00574854	0.00287427	−	0.999996i	$-0.499085\pi$
$389$	0.113379	0.00574854	0.00287427	+	0.999996i	$0.499085\pi$
$390$	−3.28565	−0.166375
$391$	45.4160	2.29679
$392$	4.86851	0.245897
$393$	−3.73645	−0.188479
$394$	16.8379	0.848282
$395$	6.18682	0.311293
$396$	−1.59684	−0.0802441
$397$	−8.50606	−0.426907	−0.213454	−	0.976953i	$-0.568471\pi$
$397$	−8.50606	−0.426907	−0.213454	+	0.976953i	$0.568471\pi$
$398$	−35.5270	−1.78081
$399$	−2.02915	−0.101584
$400$	−13.9844	−0.699220
$401$	16.0336	0.800680	0.400340	−	0.916367i	$-0.368892\pi$
$401$	16.0336	0.800680	0.400340	+	0.916367i	$0.368892\pi$
$402$	−33.8974	−1.69065
$403$	2.59181	0.129107
$404$	−20.7063	−1.03017
$405$	−28.0680	−1.39471
$406$	−41.8882	−2.07887
$407$	31.7640	1.57448
$408$	−7.38651	−0.365687
$409$	21.1661	1.04660	0.523299	−	0.852149i	$-0.324701\pi$
$409$	21.1661	1.04660	0.523299	+	0.852149i	$0.324701\pi$
$410$	10.3602	0.511656
$411$	−10.5053	−0.518186
$412$	−32.0051	−1.57678
$413$	−53.8916	−2.65183
$414$	4.54783	0.223514
$415$	49.5853	2.43405
$416$	2.46435	0.120825
$417$	8.55875	0.419124
$418$	1.61878	0.0791769
$419$	−34.5484	−1.68780	−0.843901	−	0.536499i	$-0.819746\pi$
$419$	−34.5484	−1.68780	−0.843901	+	0.536499i	$0.819746\pi$
$420$	−32.9685	−1.60870
$421$	7.85848	0.382999	0.191500	−	0.981493i	$-0.438665\pi$
$421$	7.85848	0.382999	0.191500	+	0.981493i	$0.438665\pi$
$422$	17.6264	0.858041
$423$	2.29547	0.111609
$424$	7.65322	0.371673
$425$	−19.3667	−0.939421
$426$	36.6819	1.77724
$427$	−15.0548	−0.728553
$428$	13.9506	0.674329
$429$	−1.75515	−0.0847396
$430$	23.4619	1.13143
$431$	11.2128	0.540100	0.270050	−	0.962846i	$-0.412960\pi$
$431$	11.2128	0.540100	0.270050	+	0.962846i	$0.412960\pi$
$432$	22.2059	1.06838
$433$	−19.2853	−0.926793	−0.463396	−	0.886151i	$-0.653369\pi$
$433$	−19.2853	−0.926793	−0.463396	+	0.886151i	$0.653369\pi$
$434$	57.2449	2.74784
$435$	−29.6906	−1.42356
$436$	−11.9667	−0.573102
$437$	−2.09447	−0.100192
$438$	58.3057	2.78595
$439$	15.0499	0.718295	0.359147	−	0.933281i	$-0.383068\pi$
$439$	15.0499	0.718295	0.359147	+	0.933281i	$0.383068\pi$
$440$	−5.29127	−0.252251
$441$	2.50649	0.119357
$442$	4.00092	0.190304
$443$	25.2379	1.19909	0.599545	−	0.800341i	$-0.295348\pi$
$443$	25.2379	1.19909	0.599545	+	0.800341i	$0.295348\pi$
$444$	−33.2251	−1.57680
$445$	0.439322	0.0208259
$446$	40.5030	1.91787
$447$	−2.10506	−0.0995659
$448$	19.6092	0.926449
$449$	−25.5223	−1.20447	−0.602237	−	0.798318i	$-0.705724\pi$
$449$	−25.5223	−1.20447	−0.602237	+	0.798318i	$0.705724\pi$
$450$	−1.93932	−0.0914206
$451$	5.53431	0.260600
$452$	7.39269	0.347723
$453$	−13.6037	−0.639156
$454$	28.4850	1.33687
$455$	−3.59258	−0.168423
$456$	0.340647	0.0159523
$457$	−13.7358	−0.642532	−0.321266	−	0.946989i	$-0.604108\pi$
$457$	−13.7358	−0.642532	−0.321266	+	0.946989i	$0.604108\pi$
$458$	3.04920	0.142480
$459$	30.7524	1.43540
$460$	−34.0299	−1.58665
$461$	−2.84883	−0.132683	−0.0663417	−	0.997797i	$-0.521133\pi$
$461$	−2.84883	−0.132683	−0.0663417	+	0.997797i	$0.521133\pi$
$462$	−38.7658	−1.80355
$463$	−30.6564	−1.42472	−0.712362	−	0.701813i	$-0.752374\pi$
$463$	−30.6564	−1.42472	−0.712362	+	0.701813i	$0.752374\pi$
$464$	26.1064	1.21196
$465$	40.5756	1.88165
$466$	13.0086	0.602613
$467$	−22.3130	−1.03252	−0.516261	−	0.856431i	$-0.672676\pi$
$467$	−22.3130	−1.03252	−0.516261	+	0.856431i	$0.672676\pi$
$468$	0.182012	0.00841349
$469$	−37.0639	−1.71145
$470$	−37.8080	−1.74395
$471$	1.24808	0.0575084
$472$	9.04716	0.416430
$473$	12.5330	0.576270
$474$	−7.60936	−0.349510
$475$	0.893141	0.0409801
$476$	40.1456	1.84007
$477$	3.94016	0.180408
$478$	−45.1698	−2.06602
$479$	−10.7178	−0.489707	−0.244854	−	0.969560i	$-0.578740\pi$
$479$	−10.7178	−0.489707	−0.244854	+	0.969560i	$0.578740\pi$
$480$	38.5802	1.76094
$481$	−3.62054	−0.165082
$482$	−8.69501	−0.396047
$483$	50.1575	2.28225
$484$	−4.26563	−0.193892
$485$	9.53506	0.432965
$486$	6.53972	0.296648
$487$	14.9964	0.679552	0.339776	−	0.940506i	$-0.389649\pi$
$487$	14.9964	0.679552	0.339776	+	0.940506i	$0.389649\pi$
$488$	2.52736	0.114408
$489$	0.583444	0.0263842
$490$	−41.2837	−1.86501
$491$	17.5111	0.790265	0.395132	−	0.918624i	$-0.370699\pi$
$491$	17.5111	0.790265	0.395132	+	0.918624i	$0.370699\pi$
$492$	−5.78888	−0.260983
$493$	36.1541	1.62830
$494$	−0.184512	−0.00830159
$495$	−2.72414	−0.122441
$496$	−35.6773	−1.60196
$497$	40.1085	1.79911
$498$	−60.9865	−2.73287
$499$	−4.16328	−0.186374	−0.0931871	−	0.995649i	$-0.529705\pi$
$499$	−4.16328	−0.186374	−0.0931871	+	0.995649i	$0.529705\pi$
$500$	−9.13602	−0.408575
$501$	11.9716	0.534854
$502$	19.1135	0.853079
$503$	36.1028	1.60974	0.804871	−	0.593450i	$-0.202234\pi$
$503$	36.1028	1.60974	0.804871	+	0.593450i	$0.202234\pi$
$504$	−0.808759	−0.0360250
$505$	−35.3240	−1.57190
$506$	−40.0138	−1.77883
$507$	−23.5233	−1.04470
$508$	11.9571	0.530511
$509$	12.1417	0.538170	0.269085	−	0.963116i	$-0.413279\pi$
$509$	12.1417	0.538170	0.269085	+	0.963116i	$0.413279\pi$
$510$	62.6357	2.77355
$511$	63.7523	2.82023
$512$	−28.0772	−1.24085
$513$	−1.41822	−0.0626160
$514$	−58.9646	−2.60082
$515$	−54.5994	−2.40594
$516$	−13.1096	−0.577116
$517$	−20.1965	−0.888242
$518$	−79.9663	−3.51352
$519$	−30.5417	−1.34063
$520$	0.603111	0.0264482
$521$	36.3372	1.59196	0.795981	−	0.605322i	$-0.206956\pi$
$521$	36.3372	1.59196	0.795981	+	0.605322i	$0.206956\pi$
$522$	3.62037	0.158459
$523$	−19.4530	−0.850622	−0.425311	−	0.905047i	$-0.639835\pi$
$523$	−19.4530	−0.850622	−0.425311	+	0.905047i	$0.639835\pi$
$524$	−3.40917	−0.148930
$525$	−21.3886	−0.933475
$526$	−10.4499	−0.455636
$527$	−49.4087	−2.15228
$528$	24.1604	1.05145
$529$	28.7722	1.25097
$530$	−64.8973	−2.81896
$531$	4.65782	0.202132
$532$	−1.85141	−0.0802688
$533$	−0.630814	−0.0273236
$534$	−0.540335	−0.0233826
$535$	23.7992	1.02893
$536$	6.22217	0.268757
$537$	11.1576	0.481485
$538$	−55.2113	−2.38033
$539$	−22.0532	−0.949898
$540$	−23.0425	−0.991593
$541$	−31.2793	−1.34480	−0.672401	−	0.740187i	$-0.734737\pi$
$541$	−31.2793	−1.34480	−0.672401	+	0.740187i	$0.734737\pi$
$542$	−53.0575	−2.27901
$543$	6.27660	0.269355
$544$	−46.9788	−2.01420
$545$	−20.4147	−0.874472
$546$	4.41862	0.189100
$547$	22.6630	0.969000	0.484500	−	0.874791i	$-0.339002\pi$
$547$	22.6630	0.969000	0.484500	+	0.874791i	$0.339002\pi$
$548$	−9.58509	−0.409455
$549$	1.30118	0.0555329
$550$	17.0630	0.727569
$551$	−1.66733	−0.0710308
$552$	−8.42029	−0.358392
$553$	−8.32018	−0.353810
$554$	0.500300	0.0212557
$555$	−56.6807	−2.40596
$556$	7.80908	0.331179
$557$	9.96659	0.422298	0.211149	−	0.977454i	$-0.432279\pi$
$557$	9.96659	0.422298	0.211149	+	0.977454i	$0.432279\pi$
$558$	−4.94764	−0.209450
$559$	−1.42855	−0.0604211
$560$	49.4533	2.08978
$561$	33.4592	1.41265
$562$	14.1379	0.596372
$563$	−37.0491	−1.56143	−0.780717	−	0.624885i	$-0.785146\pi$
$563$	−37.0491	−1.56143	−0.780717	+	0.624885i	$0.785146\pi$
$564$	21.1255	0.889546
$565$	12.6116	0.530575
$566$	11.9431	0.502004
$567$	37.7465	1.58520
$568$	−6.73329	−0.282523
$569$	11.4749	0.481053	0.240526	−	0.970643i	$-0.422680\pi$
$569$	11.4749	0.481053	0.240526	+	0.970643i	$0.422680\pi$
$570$	−2.88860	−0.120990
$571$	16.7649	0.701590	0.350795	−	0.936452i	$-0.385911\pi$
$571$	16.7649	0.701590	0.350795	+	0.936452i	$0.385911\pi$
$572$	−1.60142	−0.0669586
$573$	31.6257	1.32118
$574$	−13.9327	−0.581540
$575$	−22.0771	−0.920681
$576$	−1.69481	−0.0706173
$577$	−28.4976	−1.18637	−0.593186	−	0.805065i	$-0.702130\pi$
$577$	−28.4976	−1.18637	−0.593186	+	0.805065i	$0.702130\pi$
$578$	−43.7258	−1.81875
$579$	−36.4763	−1.51590
$580$	−27.0900	−1.12485
$581$	−66.6835	−2.76650
$582$	−11.7275	−0.486119
$583$	−34.6673	−1.43577
$584$	−10.7025	−0.442874
$585$	0.310504	0.0128378
$586$	43.9467	1.81542
$587$	−2.34829	−0.0969242	−0.0484621	−	0.998825i	$-0.515432\pi$
$587$	−2.34829	−0.0969242	−0.0484621	+	0.998825i	$0.515432\pi$
$588$	23.0676	0.951293
$589$	2.27860	0.0938881
$590$	−76.7176	−3.15841
$591$	−16.0503	−0.660219
$592$	49.8382	2.04834
$593$	30.3708	1.24718	0.623590	−	0.781752i	$-0.285673\pi$
$593$	30.3708	1.24718	0.623590	+	0.781752i	$0.285673\pi$
$594$	−27.0944	−1.11170
$595$	68.4867	2.80768
$596$	−1.92068	−0.0786739
$597$	33.8650	1.38600
$598$	4.56087	0.186508
$599$	40.0306	1.63561	0.817804	−	0.575497i	$-0.195192\pi$
$599$	40.0306	1.63561	0.817804	+	0.575497i	$0.195192\pi$
$600$	3.59065	0.146588
$601$	−24.6698	−1.00630	−0.503150	−	0.864199i	$-0.667826\pi$
$601$	−24.6698	−1.00630	−0.503150	+	0.864199i	$0.667826\pi$
$602$	−31.5521	−1.28597
$603$	3.20341	0.130453
$604$	−12.4121	−0.505042
$605$	−7.27699	−0.295852
$606$	43.4461	1.76488
$607$	−25.7689	−1.04593	−0.522965	−	0.852354i	$-0.675174\pi$
$607$	−25.7689	−1.04593	−0.522965	+	0.852354i	$0.675174\pi$
$608$	2.16654	0.0878650
$609$	39.9287	1.61799
$610$	−21.4313	−0.867728
$611$	2.30205	0.0931309
$612$	−3.46976	−0.140257
$613$	25.3710	1.02473	0.512363	−	0.858769i	$-0.328770\pi$
$613$	25.3710	1.02473	0.512363	+	0.858769i	$0.328770\pi$
$614$	62.8786	2.53757
$615$	−9.87560	−0.398223
$616$	7.11582	0.286704
$617$	32.5866	1.31189	0.655943	−	0.754810i	$-0.272271\pi$
$617$	32.5866	1.31189	0.655943	+	0.754810i	$0.272271\pi$
$618$	67.1535	2.70131
$619$	14.7658	0.593488	0.296744	−	0.954957i	$-0.404099\pi$
$619$	14.7658	0.593488	0.296744	+	0.954957i	$0.404099\pi$
$620$	37.0216	1.48682
$621$	35.0564	1.40676
$622$	15.1409	0.607093
$623$	−0.590810	−0.0236703
$624$	−2.75386	−0.110243
$625$	−30.9271	−1.23708
$626$	−33.7464	−1.34878
$627$	−1.54305	−0.0616235
$628$	1.13876	0.0454413
$629$	69.0197	2.75200
$630$	6.85806	0.273232
$631$	1.12129	0.0446377	0.0223189	−	0.999751i	$-0.492895\pi$
$631$	1.12129	0.0446377	0.0223189	+	0.999751i	$0.492895\pi$
$632$	1.39677	0.0555604
$633$	−16.8019	−0.667815
$634$	0.646980	0.0256948
$635$	20.3983	0.809483
$636$	36.2619	1.43788
$637$	2.51368	0.0995955
$638$	−31.8536	−1.26110
$639$	−3.46655	−0.137135
$640$	−14.3679	−0.567940
$641$	−9.90200	−0.391105	−0.195553	−	0.980693i	$-0.562650\pi$
$641$	−9.90200	−0.391105	−0.195553	+	0.980693i	$0.562650\pi$
$642$	−29.2714	−1.15525
$643$	−44.5538	−1.75703	−0.878515	−	0.477714i	$-0.841466\pi$
$643$	−44.5538	−1.75703	−0.878515	+	0.477714i	$0.841466\pi$
$644$	45.7642	1.80336
$645$	−22.3644	−0.880597
$646$	3.51742	0.138391
$647$	−18.2521	−0.717563	−0.358781	−	0.933422i	$-0.616808\pi$
$647$	−18.2521	−0.717563	−0.358781	+	0.933422i	$0.616808\pi$
$648$	−6.33677	−0.248932
$649$	−40.9815	−1.60867
$650$	−1.94488	−0.0762846
$651$	−54.5671	−2.13865
$652$	0.532339	0.0208480
$653$	26.3313	1.03042	0.515212	−	0.857063i	$-0.327713\pi$
$653$	26.3313	1.03042	0.515212	+	0.857063i	$0.327713\pi$
$654$	25.1087	0.981828
$655$	−5.81591	−0.227246
$656$	8.68341	0.339030
$657$	−5.51007	−0.214968
$658$	50.8450	1.98215
$659$	−9.44327	−0.367858	−0.183929	−	0.982940i	$-0.558882\pi$
$659$	−9.44327	−0.367858	−0.183929	+	0.982940i	$0.558882\pi$
$660$	−25.0707	−0.975876
$661$	−5.64887	−0.219716	−0.109858	−	0.993947i	$-0.535040\pi$
$661$	−5.64887	−0.219716	−0.109858	+	0.993947i	$0.535040\pi$
$662$	48.9341	1.90188
$663$	−3.81376	−0.148114
$664$	11.1946	0.434436
$665$	−3.15843	−0.122479
$666$	6.91144	0.267813
$667$	41.2141	1.59582
$668$	10.9230	0.422625
$669$	−38.6083	−1.49268
$670$	−52.7624	−2.03839
$671$	−11.4483	−0.441958
$672$	−51.8835	−2.00145
$673$	−2.74490	−0.105808	−0.0529041	−	0.998600i	$-0.516848\pi$
$673$	−2.74490	−0.105808	−0.0529041	+	0.998600i	$0.516848\pi$
$674$	46.2686	1.78220
$675$	−14.9490	−0.575388
$676$	−21.4628	−0.825494
$677$	11.9780	0.460351	0.230176	−	0.973149i	$-0.426070\pi$
$677$	11.9780	0.460351	0.230176	+	0.973149i	$0.426070\pi$
$678$	−15.5114	−0.595713
$679$	−12.8230	−0.492100
$680$	−11.4973	−0.440903
$681$	−27.1525	−1.04049
$682$	43.5315	1.66691
$683$	−11.3974	−0.436108	−0.218054	−	0.975937i	$-0.569971\pi$
$683$	−11.3974	−0.436108	−0.218054	+	0.975937i	$0.569971\pi$
$684$	0.160016	0.00611837
$685$	−16.3518	−0.624769
$686$	4.32838	0.165258
$687$	−2.90657	−0.110892
$688$	19.6645	0.749703
$689$	3.95146	0.150539
$690$	71.4019	2.71822
$691$	−14.7577	−0.561408	−0.280704	−	0.959794i	$-0.590568\pi$
$691$	−14.7577	−0.561408	−0.280704	+	0.959794i	$0.590568\pi$
$692$	−27.8666	−1.05933
$693$	3.66349	0.139164
$694$	24.4963	0.929867
$695$	13.3220	0.505331
$696$	−6.70310	−0.254081
$697$	12.0255	0.455496
$698$	−47.3820	−1.79344
$699$	−12.4001	−0.469015
$700$	−19.5151	−0.737603
$701$	−10.3010	−0.389063	−0.194532	−	0.980896i	$-0.562319\pi$
$701$	−10.3010	−0.389063	−0.194532	+	0.980896i	$0.562319\pi$
$702$	3.08829	0.116560
$703$	−3.18301	−0.120050
$704$	14.9117	0.562006
$705$	36.0393	1.35732
$706$	−46.9340	−1.76639
$707$	47.5046	1.78659
$708$	42.8667	1.61103
$709$	19.2858	0.724294	0.362147	−	0.932121i	$-0.382044\pi$
$709$	19.2858	0.724294	0.362147	+	0.932121i	$0.382044\pi$
$710$	57.0965	2.14279
$711$	0.719108	0.0269687
$712$	0.0991835	0.00371706
$713$	−56.3237	−2.10934
$714$	−84.2339	−3.15237
$715$	−2.73195	−0.102169
$716$	10.1803	0.380454
$717$	43.0568	1.60799
$718$	−5.05522	−0.188659
$719$	−0.0115219	−0.000429694 0	−0.000214847	−	1.00000i	$-0.500068\pi$
$719$	−0.0115219	−0.000429694 0	−0.000214847		1.00000i	$0.500068\pi$
$720$	−4.27422	−0.159291
$721$	73.4266	2.73455
$722$	36.2119	1.34767
$723$	8.28826	0.308244
$724$	5.72682	0.212836
$725$	−17.5749	−0.652714
$726$	8.95019	0.332173
$727$	−12.0323	−0.446254	−0.223127	−	0.974789i	$-0.571626\pi$
$727$	−12.0323	−0.446254	−0.223127	+	0.974789i	$0.571626\pi$
$728$	−0.811078	−0.0300606
$729$	23.4106	0.867059
$730$	90.7547	3.35898
$731$	27.2330	1.00725
$732$	11.9749	0.442607
$733$	−16.0553	−0.593017	−0.296508	−	0.955030i	$-0.595822\pi$
$733$	−16.0553	−0.593017	−0.296508	+	0.955030i	$0.595822\pi$
$734$	52.1577	1.92518
$735$	39.3524	1.45154
$736$	−53.5538	−1.97402
$737$	−28.1850	−1.03821
$738$	1.20419	0.0443270
$739$	34.5965	1.27265	0.636326	−	0.771420i	$-0.280453\pi$
$739$	34.5965	1.27265	0.636326	+	0.771420i	$0.280453\pi$
$740$	−51.7160	−1.90112
$741$	0.175881	0.00646114
$742$	87.2753	3.20398
$743$	11.0028	0.403655	0.201827	−	0.979421i	$-0.435312\pi$
$743$	11.0028	0.403655	0.201827	+	0.979421i	$0.435312\pi$
$744$	9.16055	0.335842
$745$	−3.27659	−0.120045
$746$	−45.5310	−1.66701
$747$	5.76341	0.210872
$748$	30.5284	1.11623
$749$	−32.0057	−1.16946
$750$	19.1693	0.699964
$751$	18.2415	0.665643	0.332821	−	0.942990i	$-0.391999\pi$
$751$	18.2415	0.665643	0.332821	+	0.942990i	$0.391999\pi$
$752$	−31.6886	−1.15557
$753$	−18.2194	−0.663953
$754$	3.63075	0.132224
$755$	−21.1746	−0.770621
$756$	30.9881	1.12703
$757$	−2.77028	−0.100688	−0.0503439	−	0.998732i	$-0.516032\pi$
$757$	−2.77028	−0.100688	−0.0503439	+	0.998732i	$0.516032\pi$
$758$	49.5901	1.80119
$759$	38.1420	1.38447
$760$	0.530228	0.0192334
$761$	21.6210	0.783760	0.391880	−	0.920016i	$-0.371825\pi$
$761$	21.6210	0.783760	0.391880	+	0.920016i	$0.371825\pi$
$762$	−25.0885	−0.908862
$763$	27.4542	0.993909
$764$	28.8556	1.04396
$765$	−5.91926	−0.214011
$766$	23.9153	0.864094
$767$	4.67118	0.168666
$768$	36.4071	1.31373
$769$	−33.0748	−1.19271	−0.596354	−	0.802721i	$-0.703385\pi$
$769$	−33.0748	−1.19271	−0.596354	+	0.802721i	$0.703385\pi$
$770$	−60.3402	−2.17451
$771$	56.2062	2.02422
$772$	−33.2813	−1.19782
$773$	−1.51648	−0.0545442	−0.0272721	−	0.999628i	$-0.508682\pi$
$773$	−1.51648	−0.0545442	−0.0272721	+	0.999628i	$0.508682\pi$
$774$	2.72703	0.0980211
$775$	24.0180	0.862753
$776$	2.15268	0.0772767
$777$	76.2256	2.73458
$778$	−0.217056	−0.00778182
$779$	−0.554583	−0.0198700
$780$	2.85762	0.102319
$781$	30.5002	1.09138
$782$	−86.9456	−3.10917
$783$	27.9071	0.997320
$784$	−34.6018	−1.23578
$785$	1.94267	0.0693370
$786$	7.15316	0.255145
$787$	−4.12722	−0.147120	−0.0735598	−	0.997291i	$-0.523436\pi$
$787$	−4.12722	−0.147120	−0.0735598	+	0.997291i	$0.523436\pi$
$788$	−14.6444	−0.521685
$789$	9.96103	0.354622
$790$	−11.8442	−0.421398
$791$	−16.9604	−0.603043
$792$	−0.615015	−0.0218536
$793$	1.30491	0.0463387
$794$	16.2842	0.577906
$795$	61.8614	2.19400
$796$	30.8988	1.09518
$797$	−27.0477	−0.958078	−0.479039	−	0.877794i	$-0.659015\pi$
$797$	−27.0477	−0.958078	−0.479039	+	0.877794i	$0.659015\pi$
$798$	3.88465	0.137515
$799$	−43.8848	−1.55253
$800$	22.8369	0.807405
$801$	0.0510634	0.00180424
$802$	−30.6952	−1.08388
$803$	48.4800	1.71082
$804$	29.4815	1.03973
$805$	78.0718	2.75167
$806$	−4.96183	−0.174773
$807$	52.6286	1.85261
$808$	−7.97493	−0.280557
$809$	−32.2842	−1.13505	−0.567525	−	0.823356i	$-0.692099\pi$
$809$	−32.2842	−1.13505	−0.567525	+	0.823356i	$0.692099\pi$
$810$	53.7341	1.88802
$811$	−14.4950	−0.508990	−0.254495	−	0.967074i	$-0.581909\pi$
$811$	−14.4950	−0.508990	−0.254495	+	0.967074i	$0.581909\pi$
$812$	36.4313	1.27849
$813$	50.5755	1.77376
$814$	−60.8099	−2.13138
$815$	0.908149	0.0318111
$816$	52.4979	1.83779
$817$	−1.25591	−0.0439389
$818$	−40.5210	−1.41678
$819$	−0.417573	−0.0145912
$820$	−9.01058	−0.314663
$821$	−55.8972	−1.95083	−0.975413	−	0.220386i	$-0.929268\pi$
$821$	−55.8972	−1.95083	−0.975413	+	0.220386i	$0.929268\pi$
$822$	20.1115	0.701471
$823$	12.2430	0.426763	0.213381	−	0.976969i	$-0.431552\pi$
$823$	12.2430	0.426763	0.213381	+	0.976969i	$0.431552\pi$
$824$	−12.3266	−0.429419
$825$	−16.2648	−0.566268
$826$	103.172	3.58980
$827$	−8.01421	−0.278681	−0.139341	−	0.990245i	$-0.544498\pi$
$827$	−8.01421	−0.278681	−0.139341	+	0.990245i	$0.544498\pi$
$828$	−3.95537	−0.137459
$829$	13.3921	0.465126	0.232563	−	0.972581i	$-0.425289\pi$
$829$	13.3921	0.465126	0.232563	+	0.972581i	$0.425289\pi$
$830$	−94.9275	−3.29498
$831$	−0.476897	−0.0165434
$832$	−1.69967	−0.0589256
$833$	−47.9192	−1.66030
$834$	−16.3851	−0.567370
$835$	18.6343	0.644865
$836$	−1.40789	−0.0486930
$837$	−38.1383	−1.31825
$838$	66.1404	2.28478
$839$	−45.0250	−1.55444	−0.777218	−	0.629232i	$-0.783370\pi$
$839$	−45.0250	−1.55444	−0.777218	+	0.629232i	$0.783370\pi$
$840$	−12.6977	−0.438112
$841$	3.80909	0.131348
$842$	−15.0445	−0.518467
$843$	−13.4766	−0.464157
$844$	−15.3302	−0.527687
$845$	−36.6147	−1.25959
$846$	−4.39450	−0.151086
$847$	9.78627	0.336260
$848$	−54.3934	−1.86788
$849$	−11.3844	−0.390710
$850$	37.0761	1.27170
$851$	78.6795	2.69710
$852$	−31.9032	−1.09299
$853$	−10.0423	−0.343842	−0.171921	−	0.985111i	$-0.554997\pi$
$853$	−10.0423	−0.343842	−0.171921	+	0.985111i	$0.554997\pi$
$854$	28.8213	0.986245
$855$	0.272981	0.00933576
$856$	5.37302	0.183646
$857$	−1.63988	−0.0560172	−0.0280086	−	0.999608i	$-0.508917\pi$
$857$	−1.63988	−0.0560172	−0.0280086	+	0.999608i	$0.508917\pi$
$858$	3.36011	0.114712
$859$	0.558435	0.0190536	0.00952678	−	0.999955i	$-0.496967\pi$
$859$	0.558435	0.0190536	0.00952678	+	0.999955i	$0.496967\pi$
$860$	−20.4055	−0.695820
$861$	13.2809	0.452613
$862$	−21.4660	−0.731135
$863$	−3.07800	−0.104776	−0.0523882	−	0.998627i	$-0.516683\pi$
$863$	−3.07800	−0.104776	−0.0523882	+	0.998627i	$0.516683\pi$
$864$	−36.2627	−1.23368
$865$	−47.5392	−1.61638
$866$	36.9203	1.25460
$867$	41.6803	1.41554
$868$	−49.7875	−1.68990
$869$	−6.32703	−0.214630
$870$	56.8406	1.92708
$871$	3.21259	0.108855
$872$	−4.60893	−0.156078
$873$	1.10828	0.0375096
$874$	4.00971	0.135630
$875$	20.9600	0.708577
$876$	−50.7100	−1.71333
$877$	−30.0790	−1.01570	−0.507848	−	0.861447i	$-0.669559\pi$
$877$	−30.0790	−1.01570	−0.507848	+	0.861447i	$0.669559\pi$
$878$	−28.8120	−0.972358
$879$	−41.8909	−1.41295
$880$	37.6064	1.26771
$881$	41.9483	1.41328	0.706638	−	0.707576i	$-0.250211\pi$
$881$	41.9483	1.41328	0.706638	+	0.707576i	$0.250211\pi$
$882$	−4.79849	−0.161574
$883$	16.3788	0.551192	0.275596	−	0.961274i	$-0.411125\pi$
$883$	16.3788	0.551192	0.275596	+	0.961274i	$0.411125\pi$
$884$	−3.47970	−0.117035
$885$	73.1288	2.45820
$886$	−48.3162	−1.62321
$887$	7.74076	0.259909	0.129955	−	0.991520i	$-0.458517\pi$
$887$	7.74076	0.259909	0.129955	+	0.991520i	$0.458517\pi$
$888$	−12.7965	−0.429423
$889$	−27.4322	−0.920045
$890$	−0.841050	−0.0281920
$891$	28.7041	0.961623
$892$	−35.2265	−1.17947
$893$	2.02386	0.0677258
$894$	4.02998	0.134783
$895$	17.3671	0.580519
$896$	19.3223	0.645511
$897$	−4.34751	−0.145159
$898$	48.8606	1.63050
$899$	−44.8373	−1.49541
$900$	1.68668	0.0562227
$901$	−75.3282	−2.50955
$902$	−10.5950	−0.352776
$903$	30.0761	1.00087
$904$	2.84726	0.0946986
$905$	9.76973	0.324757
$906$	26.0432	0.865228
$907$	13.7664	0.457104	0.228552	−	0.973532i	$-0.426601\pi$
$907$	13.7664	0.457104	0.228552	+	0.973532i	$0.426601\pi$
$908$	−24.7742	−0.822161
$909$	−4.10579	−0.136180
$910$	6.87773	0.227994
$911$	−1.28075	−0.0424332	−0.0212166	−	0.999775i	$-0.506754\pi$
$911$	−1.28075	−0.0424332	−0.0212166	+	0.999775i	$0.506754\pi$
$912$	−2.42107	−0.0801696
$913$	−50.7090	−1.67822
$914$	26.2961	0.869797
$915$	20.4288	0.675354
$916$	−2.65198	−0.0876237
$917$	7.82137	0.258284
$918$	−58.8732	−1.94310
$919$	−22.2871	−0.735183	−0.367592	−	0.929987i	$-0.619818\pi$
$919$	−22.2871	−0.735183	−0.367592	+	0.929987i	$0.619818\pi$
$920$	−13.1065	−0.432107
$921$	−59.9372	−1.97500
$922$	5.45388	0.179614
$923$	−3.47649	−0.114430
$924$	33.7157	1.10916
$925$	−33.5512	−1.10316
$926$	58.6894	1.92865
$927$	−6.34621	−0.208437
$928$	−42.6323	−1.39947
$929$	−8.86194	−0.290751	−0.145375	−	0.989377i	$-0.546439\pi$
$929$	−8.86194	−0.290751	−0.145375	+	0.989377i	$0.546439\pi$
$930$	−77.6791	−2.54720
$931$	2.20991	0.0724269
$932$	−11.3140	−0.370601
$933$	−14.4326	−0.472502
$934$	42.7166	1.39773
$935$	52.0803	1.70321
$936$	0.0701010	0.00229132
$937$	−44.3016	−1.44727	−0.723635	−	0.690183i	$-0.757530\pi$
$937$	−44.3016	−1.44727	−0.723635	+	0.690183i	$0.757530\pi$
$938$	70.9561	2.31680
$939$	32.1678	1.04976
$940$	32.8826	1.07251
$941$	−23.9783	−0.781669	−0.390834	−	0.920461i	$-0.627813\pi$
$941$	−23.9783	−0.781669	−0.390834	+	0.920461i	$0.627813\pi$
$942$	−2.38935	−0.0778493
$943$	13.7085	0.446410
$944$	−64.3006	−2.09281
$945$	52.8645	1.71968
$946$	−23.9936	−0.780099
$947$	−25.4094	−0.825696	−0.412848	−	0.910800i	$-0.635466\pi$
$947$	−25.4094	−0.825696	−0.412848	+	0.910800i	$0.635466\pi$
$948$	6.61807	0.214945
$949$	−5.52587	−0.179377
$950$	−1.70985	−0.0554750
$951$	−0.616714	−0.0199983
$952$	15.4619	0.501123
$953$	−27.8088	−0.900816	−0.450408	−	0.892823i	$-0.648721\pi$
$953$	−27.8088	−0.900816	−0.450408	+	0.892823i	$0.648721\pi$
$954$	−7.54315	−0.244219
$955$	49.2265	1.59293
$956$	39.2854	1.27058
$957$	30.3635	0.981512
$958$	20.5184	0.662919
$959$	21.9902	0.710102
$960$	−26.6090	−0.858800
$961$	30.2753	0.976623
$962$	6.93126	0.223473
$963$	2.76623	0.0891406
$964$	7.56229	0.243565
$965$	−56.7766	−1.82770
$966$	−96.0229	−3.08949
$967$	2.60412	0.0837430	0.0418715	−	0.999123i	$-0.486668\pi$
$967$	2.60412	0.0837430	0.0418715	+	0.999123i	$0.486668\pi$
$968$	−1.64289	−0.0528045
$969$	−3.35288	−0.107710
$970$	−18.2542	−0.586106
$971$	−7.37146	−0.236561	−0.118281	−	0.992980i	$-0.537738\pi$
$971$	−7.37146	−0.236561	−0.118281	+	0.992980i	$0.537738\pi$
$972$	−5.68777	−0.182435
$973$	−17.9157	−0.574351
$974$	−28.7095	−0.919913
$975$	1.85390	0.0593724
$976$	−17.9626	−0.574968
$977$	−31.6523	−1.01265	−0.506324	−	0.862343i	$-0.668996\pi$
$977$	−31.6523	−1.01265	−0.506324	+	0.862343i	$0.668996\pi$
$978$	−1.11696	−0.0357165
$979$	−0.449278	−0.0143590
$980$	35.9055	1.14696
$981$	−2.37285	−0.0757593
$982$	−33.5237	−1.06978
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	−2.22956	−0.0710759
$985$	−24.9827	−0.796016
$986$	−69.2144	−2.20423
$987$	−48.4665	−1.54271
$988$	0.160475	0.00510539
$989$	31.0444	0.987153
$990$	5.21517	0.165749
$991$	17.2224	0.547088	0.273544	−	0.961860i	$-0.411804\pi$
$991$	17.2224	0.547088	0.273544	+	0.961860i	$0.411804\pi$
$992$	58.2619	1.84982
$993$	−46.6450	−1.48023
$994$	−76.7847	−2.43546
$995$	52.7121	1.67108
$996$	53.0416	1.68069
$997$	16.6043	0.525863	0.262931	−	0.964815i	$-0.415311\pi$
$997$	16.6043	0.525863	0.262931	+	0.964815i	$0.415311\pi$
$998$	7.97030	0.252295
$999$	53.2760	1.68558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.6	✓	28
3.2	odd	2		8847.2.a.b.1.23		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.6	✓	28	1.1	even	1	trivial
8847.2.a.b.1.23		28	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)

\(f(q)\)	\(=\)	\(q-1.91443 q^{2} +1.82487 q^{3} +1.66503 q^{4} +2.84047 q^{5} -3.49358 q^{6} -3.81993 q^{7} +0.641279 q^{8} +0.330154 q^{9} +O(q^{10})\)	\(q-1.91443 q^{2} +1.82487 q^{3} +1.66503 q^{4} +2.84047 q^{5} -3.49358 q^{6} -3.81993 q^{7} +0.641279 q^{8} +0.330154 q^{9} -5.43787 q^{10} -2.90484 q^{11} +3.03846 q^{12} +0.331101 q^{13} +7.31298 q^{14} +5.18349 q^{15} -4.55774 q^{16} -6.31190 q^{17} -0.632056 q^{18} +0.291089 q^{19} +4.72947 q^{20} -6.97088 q^{21} +5.56111 q^{22} -7.19529 q^{23} +1.17025 q^{24} +3.06828 q^{25} -0.633868 q^{26} -4.87212 q^{27} -6.36029 q^{28} -5.72792 q^{29} -9.92342 q^{30} +7.82786 q^{31} +7.44290 q^{32} -5.30096 q^{33} +12.0837 q^{34} -10.8504 q^{35} +0.549716 q^{36} -10.9349 q^{37} -0.557268 q^{38} +0.604216 q^{39} +1.82153 q^{40} -1.90520 q^{41} +13.3452 q^{42} -4.31454 q^{43} -4.83664 q^{44} +0.937794 q^{45} +13.7749 q^{46} +6.95271 q^{47} -8.31728 q^{48} +7.59188 q^{49} -5.87399 q^{50} -11.5184 q^{51} +0.551292 q^{52} +11.9343 q^{53} +9.32732 q^{54} -8.25112 q^{55} -2.44964 q^{56} +0.531200 q^{57} +10.9657 q^{58} +14.1080 q^{59} +8.63066 q^{60} +3.94112 q^{61} -14.9859 q^{62} -1.26117 q^{63} -5.13340 q^{64} +0.940483 q^{65} +10.1483 q^{66} +9.70276 q^{67} -10.5095 q^{68} -13.1305 q^{69} +20.7723 q^{70} -10.4998 q^{71} +0.211721 q^{72} -16.6894 q^{73} +20.9340 q^{74} +5.59921 q^{75} +0.484671 q^{76} +11.0963 q^{77} -1.15673 q^{78} +2.17810 q^{79} -12.9461 q^{80} -9.88146 q^{81} +3.64737 q^{82} +17.4567 q^{83} -11.6067 q^{84} -17.9288 q^{85} +8.25987 q^{86} -10.4527 q^{87} -1.86281 q^{88} +0.154665 q^{89} -1.79534 q^{90} -1.26478 q^{91} -11.9804 q^{92} +14.2848 q^{93} -13.3105 q^{94} +0.826830 q^{95} +13.5823 q^{96} +3.35686 q^{97} -14.5341 q^{98} -0.959046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

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