LMFDB - Embedded newform 4017.2.a.l.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.310907 q^{2} +1.00000 q^{3} -1.90334 q^{4} +2.19968 q^{5} +0.310907 q^{6} -3.79510 q^{7} -1.21358 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.310907 q^{2} +1.00000 q^{3} -1.90334 q^{4} +2.19968 q^{5} +0.310907 q^{6} -3.79510 q^{7} -1.21358 q^{8} +1.00000 q^{9} +0.683896 q^{10} +4.23606 q^{11} -1.90334 q^{12} -1.00000 q^{13} -1.17992 q^{14} +2.19968 q^{15} +3.42936 q^{16} -4.06758 q^{17} +0.310907 q^{18} +6.04510 q^{19} -4.18673 q^{20} -3.79510 q^{21} +1.31702 q^{22} +3.95771 q^{23} -1.21358 q^{24} -0.161416 q^{25} -0.310907 q^{26} +1.00000 q^{27} +7.22335 q^{28} -4.42795 q^{29} +0.683896 q^{30} -9.06185 q^{31} +3.49336 q^{32} +4.23606 q^{33} -1.26464 q^{34} -8.34800 q^{35} -1.90334 q^{36} +9.85117 q^{37} +1.87947 q^{38} -1.00000 q^{39} -2.66948 q^{40} +8.31092 q^{41} -1.17992 q^{42} -8.29186 q^{43} -8.06265 q^{44} +2.19968 q^{45} +1.23048 q^{46} +7.23660 q^{47} +3.42936 q^{48} +7.40279 q^{49} -0.0501855 q^{50} -4.06758 q^{51} +1.90334 q^{52} +11.3698 q^{53} +0.310907 q^{54} +9.31797 q^{55} +4.60564 q^{56} +6.04510 q^{57} -1.37668 q^{58} -6.01950 q^{59} -4.18673 q^{60} -6.82227 q^{61} -2.81739 q^{62} -3.79510 q^{63} -5.77262 q^{64} -2.19968 q^{65} +1.31702 q^{66} +1.93049 q^{67} +7.74197 q^{68} +3.95771 q^{69} -2.59545 q^{70} +13.0856 q^{71} -1.21358 q^{72} -6.80696 q^{73} +3.06280 q^{74} -0.161416 q^{75} -11.5059 q^{76} -16.0763 q^{77} -0.310907 q^{78} -11.7216 q^{79} +7.54350 q^{80} +1.00000 q^{81} +2.58392 q^{82} +16.1520 q^{83} +7.22335 q^{84} -8.94736 q^{85} -2.57800 q^{86} -4.42795 q^{87} -5.14078 q^{88} +7.75363 q^{89} +0.683896 q^{90} +3.79510 q^{91} -7.53285 q^{92} -9.06185 q^{93} +2.24991 q^{94} +13.2973 q^{95} +3.49336 q^{96} +10.3889 q^{97} +2.30158 q^{98} +4.23606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	0.310907	0.219845	0.109922	−	0.993940i	$-0.464940\pi$
$2$	0.310907	0.219845	0.109922	+	0.993940i	$0.464940\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90334	−0.951668
$5$	2.19968	0.983726	0.491863	−	0.870673i	$-0.336316\pi$
$5$	2.19968	0.983726	0.491863	+	0.870673i	$0.336316\pi$
$6$	0.310907	0.126927
$7$	−3.79510	−1.43441	−0.717207	−	0.696861i	$-0.754580\pi$
$7$	−3.79510	−1.43441	−0.717207	+	0.696861i	$0.754580\pi$
$8$	−1.21358	−0.429064
$9$	1.00000	0.333333
$10$	0.683896	0.216267
$11$	4.23606	1.27722	0.638610	−	0.769530i	$-0.279510\pi$
$11$	4.23606	1.27722	0.638610	+	0.769530i	$0.279510\pi$
$12$	−1.90334	−0.549446
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.17992	−0.315348
$15$	2.19968	0.567954
$16$	3.42936	0.857341
$17$	−4.06758	−0.986532	−0.493266	−	0.869878i	$-0.664197\pi$
$17$	−4.06758	−0.986532	−0.493266	+	0.869878i	$0.664197\pi$
$18$	0.310907	0.0732815
$19$	6.04510	1.38684	0.693421	−	0.720533i	$-0.256103\pi$
$19$	6.04510	1.38684	0.693421	+	0.720533i	$0.256103\pi$
$20$	−4.18673	−0.936181
$21$	−3.79510	−0.828159
$22$	1.31702	0.280790
$23$	3.95771	0.825239	0.412619	−	0.910904i	$-0.364614\pi$
$23$	3.95771	0.825239	0.412619	+	0.910904i	$0.364614\pi$
$24$	−1.21358	−0.247720
$25$	−0.161416	−0.0322833
$26$	−0.310907	−0.0609739
$27$	1.00000	0.192450
$28$	7.22335	1.36509
$29$	−4.42795	−0.822250	−0.411125	−	0.911579i	$-0.634864\pi$
$29$	−4.42795	−0.822250	−0.411125	+	0.911579i	$0.634864\pi$
$30$	0.683896	0.124862
$31$	−9.06185	−1.62756	−0.813778	−	0.581176i	$-0.802593\pi$
$31$	−9.06185	−1.62756	−0.813778	+	0.581176i	$0.802593\pi$
$32$	3.49336	0.617545
$33$	4.23606	0.737403
$34$	−1.26464	−0.216884
$35$	−8.34800	−1.41107
$36$	−1.90334	−0.317223
$37$	9.85117	1.61952	0.809761	−	0.586760i	$-0.199597\pi$
$37$	9.85117	1.61952	0.809761	+	0.586760i	$0.199597\pi$
$38$	1.87947	0.304890
$39$	−1.00000	−0.160128
$40$	−2.66948	−0.422081
$41$	8.31092	1.29795	0.648974	−	0.760811i	$-0.275199\pi$
$41$	8.31092	1.29795	0.648974	+	0.760811i	$0.275199\pi$
$42$	−1.17992	−0.182066
$43$	−8.29186	−1.26450	−0.632248	−	0.774766i	$-0.717868\pi$
$43$	−8.29186	−1.26450	−0.632248	+	0.774766i	$0.717868\pi$
$44$	−8.06265	−1.21549
$45$	2.19968	0.327909
$46$	1.23048	0.181424
$47$	7.23660	1.05557	0.527784	−	0.849379i	$-0.323023\pi$
$47$	7.23660	1.05557	0.527784	+	0.849379i	$0.323023\pi$
$48$	3.42936	0.494986
$49$	7.40279	1.05754
$50$	−0.0501855	−0.00709731
$51$	−4.06758	−0.569575
$52$	1.90334	0.263945
$53$	11.3698	1.56176	0.780882	−	0.624679i	$-0.214770\pi$
$53$	11.3698	1.56176	0.780882	+	0.624679i	$0.214770\pi$
$54$	0.310907	0.0423091
$55$	9.31797	1.25643
$56$	4.60564	0.615455
$57$	6.04510	0.800693
$58$	−1.37668	−0.180767
$59$	−6.01950	−0.783673	−0.391836	−	0.920035i	$-0.628160\pi$
$59$	−6.01950	−0.783673	−0.391836	+	0.920035i	$0.628160\pi$
$60$	−4.18673	−0.540504
$61$	−6.82227	−0.873502	−0.436751	−	0.899582i	$-0.643871\pi$
$61$	−6.82227	−0.873502	−0.436751	+	0.899582i	$0.643871\pi$
$62$	−2.81739	−0.357809
$63$	−3.79510	−0.478138
$64$	−5.77262	−0.721577
$65$	−2.19968	−0.272836
$66$	1.31702	0.162114
$67$	1.93049	0.235846	0.117923	−	0.993023i	$-0.462376\pi$
$67$	1.93049	0.235846	0.117923	+	0.993023i	$0.462376\pi$
$68$	7.74197	0.938852
$69$	3.95771	0.476452
$70$	−2.59545	−0.310216
$71$	13.0856	1.55298	0.776489	−	0.630131i	$-0.216999\pi$
$71$	13.0856	1.55298	0.776489	+	0.630131i	$0.216999\pi$
$72$	−1.21358	−0.143021
$73$	−6.80696	−0.796695	−0.398347	−	0.917235i	$-0.630416\pi$
$73$	−6.80696	−0.796695	−0.398347	+	0.917235i	$0.630416\pi$
$74$	3.06280	0.356043
$75$	−0.161416	−0.0186388
$76$	−11.5059	−1.31981
$77$	−16.0763	−1.83206
$78$	−0.310907	−0.0352033
$79$	−11.7216	−1.31878	−0.659389	−	0.751802i	$-0.729185\pi$
$79$	−11.7216	−1.31878	−0.659389	+	0.751802i	$0.729185\pi$
$80$	7.54350	0.843389
$81$	1.00000	0.111111
$82$	2.58392	0.285347
$83$	16.1520	1.77291	0.886455	−	0.462814i	$-0.153160\pi$
$83$	16.1520	1.77291	0.886455	+	0.462814i	$0.153160\pi$
$84$	7.22335	0.788133
$85$	−8.94736	−0.970477
$86$	−2.57800	−0.277993
$87$	−4.42795	−0.474726
$88$	−5.14078	−0.548009
$89$	7.75363	0.821883	0.410942	−	0.911662i	$-0.365200\pi$
$89$	7.75363	0.821883	0.410942	+	0.911662i	$0.365200\pi$
$90$	0.683896	0.0720889
$91$	3.79510	0.397835
$92$	−7.53285	−0.785354
$93$	−9.06185	−0.939670
$94$	2.24991	0.232061
$95$	13.2973	1.36427
$96$	3.49336	0.356540
$97$	10.3889	1.05484	0.527418	−	0.849606i	$-0.323160\pi$
$97$	10.3889	1.05484	0.527418	+	0.849606i	$0.323160\pi$
$98$	2.30158	0.232495
$99$	4.23606	0.425740
$100$	0.307230	0.0307230
$101$	13.3529	1.32866	0.664332	−	0.747437i	$-0.268716\pi$
$101$	13.3529	1.32866	0.664332	+	0.747437i	$0.268716\pi$
$102$	−1.26464	−0.125218
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.21358	0.119001
$105$	−8.34800	−0.814681
$106$	3.53495	0.343345
$107$	8.79575	0.850318	0.425159	−	0.905119i	$-0.360218\pi$
$107$	8.79575	0.850318	0.425159	+	0.905119i	$0.360218\pi$
$108$	−1.90334	−0.183149
$109$	7.98098	0.764439	0.382219	−	0.924072i	$-0.375160\pi$
$109$	7.98098	0.764439	0.382219	+	0.924072i	$0.375160\pi$
$110$	2.89702	0.276220
$111$	9.85117	0.935032
$112$	−13.0148	−1.22978
$113$	−3.51934	−0.331072	−0.165536	−	0.986204i	$-0.552935\pi$
$113$	−3.51934	−0.331072	−0.165536	+	0.986204i	$0.552935\pi$
$114$	1.87947	0.176028
$115$	8.70568	0.811809
$116$	8.42789	0.782510
$117$	−1.00000	−0.0924500
$118$	−1.87151	−0.172286
$119$	15.4369	1.41509
$120$	−2.66948	−0.243689
$121$	6.94421	0.631291
$122$	−2.12109	−0.192035
$123$	8.31092	0.749370
$124$	17.2477	1.54889
$125$	−11.3535	−1.01548
$126$	−1.17992	−0.105116
$127$	15.5330	1.37833	0.689167	−	0.724602i	$-0.257977\pi$
$127$	15.5330	1.37833	0.689167	+	0.724602i	$0.257977\pi$
$128$	−8.78148	−0.776180
$129$	−8.29186	−0.730058
$130$	−0.683896	−0.0599816
$131$	21.7829	1.90318	0.951591	−	0.307366i	$-0.0994476\pi$
$131$	21.7829	1.90318	0.951591	+	0.307366i	$0.0994476\pi$
$132$	−8.06265	−0.701764
$133$	−22.9418	−1.98930
$134$	0.600202	0.0518495
$135$	2.19968	0.189318
$136$	4.93631	0.423285
$137$	11.2054	0.957342	0.478671	−	0.877994i	$-0.341119\pi$
$137$	11.2054	0.957342	0.478671	+	0.877994i	$0.341119\pi$
$138$	1.23048	0.104745
$139$	−16.7834	−1.42355	−0.711775	−	0.702408i	$-0.752108\pi$
$139$	−16.7834	−1.42355	−0.711775	+	0.702408i	$0.752108\pi$
$140$	15.8891	1.34287
$141$	7.23660	0.609432
$142$	4.06841	0.341414
$143$	−4.23606	−0.354237
$144$	3.42936	0.285780
$145$	−9.74007	−0.808869
$146$	−2.11633	−0.175149
$147$	7.40279	0.610571
$148$	−18.7501	−1.54125
$149$	0.228761	0.0187408	0.00937042	−	0.999956i	$-0.497017\pi$
$149$	0.228761	0.0187408	0.00937042	+	0.999956i	$0.497017\pi$
$150$	−0.0501855	−0.00409763
$151$	17.5821	1.43081	0.715405	−	0.698710i	$-0.246242\pi$
$151$	17.5821	1.43081	0.715405	+	0.698710i	$0.246242\pi$
$152$	−7.33619	−0.595043
$153$	−4.06758	−0.328844
$154$	−4.99823	−0.402769
$155$	−19.9331	−1.60107
$156$	1.90334	0.152389
$157$	11.0855	0.884718	0.442359	−	0.896838i	$-0.354142\pi$
$157$	11.0855	0.884718	0.442359	+	0.896838i	$0.354142\pi$
$158$	−3.64432	−0.289926
$159$	11.3698	0.901684
$160$	7.68428	0.607495
$161$	−15.0199	−1.18373
$162$	0.310907	0.0244272
$163$	−15.7655	−1.23485	−0.617425	−	0.786630i	$-0.711824\pi$
$163$	−15.7655	−1.23485	−0.617425	+	0.786630i	$0.711824\pi$
$164$	−15.8185	−1.23522
$165$	9.31797	0.725403
$166$	5.02177	0.389765
$167$	16.9002	1.30778	0.653888	−	0.756591i	$-0.273137\pi$
$167$	16.9002	1.30778	0.653888	+	0.756591i	$0.273137\pi$
$168$	4.60564	0.355333
$169$	1.00000	0.0769231
$170$	−2.78180	−0.213354
$171$	6.04510	0.462281
$172$	15.7822	1.20338
$173$	1.53771	0.116910	0.0584548	−	0.998290i	$-0.481383\pi$
$173$	1.53771	0.116910	0.0584548	+	0.998290i	$0.481383\pi$
$174$	−1.37668	−0.104366
$175$	0.612592	0.0463076
$176$	14.5270	1.09501
$177$	−6.01950	−0.452454
$178$	2.41066	0.180687
$179$	2.08899	0.156138	0.0780692	−	0.996948i	$-0.475124\pi$
$179$	2.08899	0.156138	0.0780692	+	0.996948i	$0.475124\pi$
$180$	−4.18673	−0.312060
$181$	10.0968	0.750487	0.375243	−	0.926926i	$-0.377559\pi$
$181$	10.0968	0.750487	0.375243	+	0.926926i	$0.377559\pi$
$182$	1.17992	0.0874618
$183$	−6.82227	−0.504317
$184$	−4.80298	−0.354080
$185$	21.6694	1.59317
$186$	−2.81739	−0.206581
$187$	−17.2305	−1.26002
$188$	−13.7737	−1.00455
$189$	−3.79510	−0.276053
$190$	4.13422	0.299928
$191$	−8.02894	−0.580953	−0.290477	−	0.956882i	$-0.593814\pi$
$191$	−8.02894	−0.580953	−0.290477	+	0.956882i	$0.593814\pi$
$192$	−5.77262	−0.416603
$193$	−25.1036	−1.80700	−0.903499	−	0.428590i	$-0.859010\pi$
$193$	−25.1036	−1.80700	−0.903499	+	0.428590i	$0.859010\pi$
$194$	3.22999	0.231900
$195$	−2.19968	−0.157522
$196$	−14.0900	−1.00643
$197$	18.7136	1.33329	0.666646	−	0.745374i	$-0.267729\pi$
$197$	18.7136	1.33329	0.666646	+	0.745374i	$0.267729\pi$
$198$	1.31702	0.0935966
$199$	13.2261	0.937573	0.468786	−	0.883312i	$-0.344691\pi$
$199$	13.2261	0.937573	0.468786	+	0.883312i	$0.344691\pi$
$200$	0.195891	0.0138516
$201$	1.93049	0.136166
$202$	4.15152	0.292100
$203$	16.8045	1.17945
$204$	7.74197	0.542046
$205$	18.2813	1.27682
$206$	−0.310907	−0.0216619
$207$	3.95771	0.275080
$208$	−3.42936	−0.237784
$209$	25.6074	1.77130
$210$	−2.59545	−0.179103
$211$	−16.0981	−1.10824	−0.554121	−	0.832436i	$-0.686945\pi$
$211$	−16.0981	−1.10824	−0.554121	+	0.832436i	$0.686945\pi$
$212$	−21.6406	−1.48628
$213$	13.0856	0.896612
$214$	2.73466	0.186938
$215$	−18.2394	−1.24392
$216$	−1.21358	−0.0825733
$217$	34.3906	2.33459
$218$	2.48134	0.168058
$219$	−6.80696	−0.459972
$220$	−17.7352	−1.19571
$221$	4.06758	0.273615
$222$	3.06280	0.205562
$223$	22.0756	1.47829	0.739147	−	0.673544i	$-0.235229\pi$
$223$	22.0756	1.47829	0.739147	+	0.673544i	$0.235229\pi$
$224$	−13.2577	−0.885815
$225$	−0.161416	−0.0107611
$226$	−1.09419	−0.0727844
$227$	−12.4015	−0.823119	−0.411559	−	0.911383i	$-0.635016\pi$
$227$	−12.4015	−0.823119	−0.411559	+	0.911383i	$0.635016\pi$
$228$	−11.5059	−0.761995
$229$	−7.44256	−0.491818	−0.245909	−	0.969293i	$-0.579086\pi$
$229$	−7.44256	−0.491818	−0.245909	+	0.969293i	$0.579086\pi$
$230$	2.70666	0.178472
$231$	−16.0763	−1.05774
$232$	5.37365	0.352798
$233$	−4.53505	−0.297101	−0.148551	−	0.988905i	$-0.547461\pi$
$233$	−4.53505	−0.297101	−0.148551	+	0.988905i	$0.547461\pi$
$234$	−0.310907	−0.0203246
$235$	15.9182	1.03839
$236$	11.4571	0.745797
$237$	−11.7216	−0.761397
$238$	4.79943	0.311101
$239$	−3.09618	−0.200275	−0.100138	−	0.994974i	$-0.531928\pi$
$239$	−3.09618	−0.200275	−0.100138	+	0.994974i	$0.531928\pi$
$240$	7.54350	0.486931
$241$	10.6701	0.687323	0.343662	−	0.939094i	$-0.388333\pi$
$241$	10.6701	0.687323	0.343662	+	0.939094i	$0.388333\pi$
$242$	2.15900	0.138786
$243$	1.00000	0.0641500
$244$	12.9851	0.831285
$245$	16.2837	1.04033
$246$	2.58392	0.164745
$247$	−6.04510	−0.384641
$248$	10.9972	0.698325
$249$	16.1520	1.02359
$250$	−3.52987	−0.223249
$251$	8.78351	0.554410	0.277205	−	0.960811i	$-0.410592\pi$
$251$	8.78351	0.554410	0.277205	+	0.960811i	$0.410592\pi$
$252$	7.22335	0.455029
$253$	16.7651	1.05401
$254$	4.82933	0.303019
$255$	−8.94736	−0.560305
$256$	8.81501	0.550938
$257$	−30.2233	−1.88527	−0.942637	−	0.333818i	$-0.891663\pi$
$257$	−30.2233	−1.88527	−0.942637	+	0.333818i	$0.891663\pi$
$258$	−2.57800	−0.160499
$259$	−37.3862	−2.32306
$260$	4.18673	0.259650
$261$	−4.42795	−0.274083
$262$	6.77247	0.418404
$263$	−2.44855	−0.150984	−0.0754920	−	0.997146i	$-0.524053\pi$
$263$	−2.44855	−0.150984	−0.0754920	+	0.997146i	$0.524053\pi$
$264$	−5.14078	−0.316393
$265$	25.0099	1.53635
$266$	−7.13276	−0.437338
$267$	7.75363	0.474514
$268$	−3.67436	−0.224447
$269$	−21.9216	−1.33658	−0.668291	−	0.743900i	$-0.732974\pi$
$269$	−21.9216	−1.33658	−0.668291	+	0.743900i	$0.732974\pi$
$270$	0.683896	0.0416206
$271$	−31.1309	−1.89107	−0.945534	−	0.325524i	$-0.894459\pi$
$271$	−31.1309	−1.89107	−0.945534	+	0.325524i	$0.894459\pi$
$272$	−13.9492	−0.845795
$273$	3.79510	0.229690
$274$	3.48384	0.210466
$275$	−0.683770	−0.0412329
$276$	−7.53285	−0.453424
$277$	−12.2702	−0.737244	−0.368622	−	0.929579i	$-0.620170\pi$
$277$	−12.2702	−0.737244	−0.368622	+	0.929579i	$0.620170\pi$
$278$	−5.21808	−0.312960
$279$	−9.06185	−0.542519
$280$	10.1309	0.605439
$281$	28.6861	1.71127	0.855634	−	0.517581i	$-0.173167\pi$
$281$	28.6861	1.71127	0.855634	+	0.517581i	$0.173167\pi$
$282$	2.24991	0.133980
$283$	1.42576	0.0847525	0.0423763	−	0.999102i	$-0.486507\pi$
$283$	1.42576	0.0847525	0.0423763	+	0.999102i	$0.486507\pi$
$284$	−24.9063	−1.47792
$285$	13.2973	0.787663
$286$	−1.31702	−0.0778771
$287$	−31.5408	−1.86179
$288$	3.49336	0.205848
$289$	−0.454820	−0.0267541
$290$	−3.02826	−0.177825
$291$	10.3889	0.609010
$292$	12.9559	0.758189
$293$	−6.21727	−0.363217	−0.181608	−	0.983371i	$-0.558130\pi$
$293$	−6.21727	−0.363217	−0.181608	+	0.983371i	$0.558130\pi$
$294$	2.30158	0.134231
$295$	−13.2410	−0.770919
$296$	−11.9551	−0.694878
$297$	4.23606	0.245801
$298$	0.0711234	0.00412007
$299$	−3.95771	−0.228880
$300$	0.307230	0.0177379
$301$	31.4684	1.81381
$302$	5.46640	0.314556
$303$	13.3529	0.767105
$304$	20.7309	1.18900
$305$	−15.0068	−0.859287
$306$	−1.26464	−0.0722946
$307$	−19.9138	−1.13654	−0.568270	−	0.822842i	$-0.692387\pi$
$307$	−19.9138	−1.13654	−0.568270	+	0.822842i	$0.692387\pi$
$308$	30.5986	1.74351
$309$	−1.00000	−0.0568880
$310$	−6.19736	−0.351986
$311$	−12.4991	−0.708757	−0.354379	−	0.935102i	$-0.615308\pi$
$311$	−12.4991	−0.708757	−0.354379	+	0.935102i	$0.615308\pi$
$312$	1.21358	0.0687052
$313$	−10.2432	−0.578980	−0.289490	−	0.957181i	$-0.593486\pi$
$313$	−10.2432	−0.578980	−0.289490	+	0.957181i	$0.593486\pi$
$314$	3.44656	0.194500
$315$	−8.34800	−0.470356
$316$	22.3101	1.25504
$317$	7.78199	0.437080	0.218540	−	0.975828i	$-0.429871\pi$
$317$	7.78199	0.437080	0.218540	+	0.975828i	$0.429871\pi$
$318$	3.53495	0.198230
$319$	−18.7571	−1.05019
$320$	−12.6979	−0.709834
$321$	8.79575	0.490931
$322$	−4.66979	−0.260237
$323$	−24.5889	−1.36816
$324$	−1.90334	−0.105741
$325$	0.161416	0.00895377
$326$	−4.90161	−0.271475
$327$	7.98098	0.441349
$328$	−10.0859	−0.556902
$329$	−27.4636	−1.51412
$330$	2.89702	0.159476
$331$	−16.9483	−0.931565	−0.465782	−	0.884899i	$-0.654227\pi$
$331$	−16.9483	−0.931565	−0.465782	+	0.884899i	$0.654227\pi$
$332$	−30.7427	−1.68722
$333$	9.85117	0.539841
$334$	5.25439	0.287508
$335$	4.24645	0.232008
$336$	−13.0148	−0.710015
$337$	12.0861	0.658373	0.329187	−	0.944265i	$-0.393225\pi$
$337$	12.0861	0.658373	0.329187	+	0.944265i	$0.393225\pi$
$338$	0.310907	0.0169111
$339$	−3.51934	−0.191145
$340$	17.0298	0.923573
$341$	−38.3865	−2.07875
$342$	1.87947	0.101630
$343$	−1.52861	−0.0825373
$344$	10.0628	0.542550
$345$	8.70568	0.468698
$346$	0.478084	0.0257020
$347$	24.0765	1.29250	0.646248	−	0.763128i	$-0.276337\pi$
$347$	24.0765	1.29250	0.646248	+	0.763128i	$0.276337\pi$
$348$	8.42789	0.451782
$349$	−9.93275	−0.531688	−0.265844	−	0.964016i	$-0.585651\pi$
$349$	−9.93275	−0.531688	−0.265844	+	0.964016i	$0.585651\pi$
$350$	0.190459	0.0101805
$351$	−1.00000	−0.0533761
$352$	14.7981	0.788742
$353$	−10.6650	−0.567638	−0.283819	−	0.958878i	$-0.591602\pi$
$353$	−10.6650	−0.567638	−0.283819	+	0.958878i	$0.591602\pi$
$354$	−1.87151	−0.0994695
$355$	28.7841	1.52770
$356$	−14.7578	−0.782160
$357$	15.4369	0.817005
$358$	0.649482	0.0343262
$359$	−4.89739	−0.258475	−0.129237	−	0.991614i	$-0.541253\pi$
$359$	−4.89739	−0.258475	−0.129237	+	0.991614i	$0.541253\pi$
$360$	−2.66948	−0.140694
$361$	17.5433	0.923330
$362$	3.13916	0.164990
$363$	6.94421	0.364476
$364$	−7.22335	−0.378607
$365$	−14.9731	−0.783729
$366$	−2.12109	−0.110871
$367$	22.6027	1.17985	0.589926	−	0.807458i	$-0.299157\pi$
$367$	22.6027	1.17985	0.589926	+	0.807458i	$0.299157\pi$
$368$	13.5724	0.707511
$369$	8.31092	0.432649
$370$	6.73717	0.350249
$371$	−43.1496	−2.24021
$372$	17.2477	0.894254
$373$	24.3946	1.26311	0.631554	−	0.775332i	$-0.282418\pi$
$373$	24.3946	1.26311	0.631554	+	0.775332i	$0.282418\pi$
$374$	−5.35709	−0.277008
$375$	−11.3535	−0.586290
$376$	−8.78216	−0.452906
$377$	4.42795	0.228051
$378$	−1.17992	−0.0606887
$379$	33.7426	1.73324	0.866621	−	0.498967i	$-0.166287\pi$
$379$	33.7426	1.73324	0.866621	+	0.498967i	$0.166287\pi$
$380$	−25.3092	−1.29833
$381$	15.5330	0.795782
$382$	−2.49625	−0.127719
$383$	23.5390	1.20279	0.601394	−	0.798953i	$-0.294612\pi$
$383$	23.5390	1.20279	0.601394	+	0.798953i	$0.294612\pi$
$384$	−8.78148	−0.448128
$385$	−35.3626	−1.80225
$386$	−7.80489	−0.397259
$387$	−8.29186	−0.421499
$388$	−19.7736	−1.00385
$389$	−10.5373	−0.534264	−0.267132	−	0.963660i	$-0.586076\pi$
$389$	−10.5373	−0.534264	−0.267132	+	0.963660i	$0.586076\pi$
$390$	−0.683896	−0.0346304
$391$	−16.0983	−0.814125
$392$	−8.98384	−0.453752
$393$	21.7829	1.09880
$394$	5.81821	0.293117
$395$	−25.7836	−1.29732
$396$	−8.06265	−0.405163
$397$	−7.19528	−0.361121	−0.180560	−	0.983564i	$-0.557791\pi$
$397$	−7.19528	−0.361121	−0.180560	+	0.983564i	$0.557791\pi$
$398$	4.11209	0.206120
$399$	−22.9418	−1.14853
$400$	−0.553556	−0.0276778
$401$	−13.4932	−0.673816	−0.336908	−	0.941538i	$-0.609381\pi$
$401$	−13.4932	−0.673816	−0.336908	+	0.941538i	$0.609381\pi$
$402$	0.600202	0.0299353
$403$	9.06185	0.451403
$404$	−25.4151	−1.26445
$405$	2.19968	0.109303
$406$	5.22465	0.259295
$407$	41.7301	2.06849
$408$	4.93631	0.244384
$409$	−14.3420	−0.709165	−0.354583	−	0.935025i	$-0.615377\pi$
$409$	−14.3420	−0.709165	−0.354583	+	0.935025i	$0.615377\pi$
$410$	5.68380	0.280703
$411$	11.2054	0.552721
$412$	1.90334	0.0937707
$413$	22.8446	1.12411
$414$	1.23048	0.0604748
$415$	35.5292	1.74406
$416$	−3.49336	−0.171276
$417$	−16.7834	−0.821887
$418$	7.96153	0.389411
$419$	10.8232	0.528748	0.264374	−	0.964420i	$-0.414835\pi$
$419$	10.8232	0.528748	0.264374	+	0.964420i	$0.414835\pi$
$420$	15.8891	0.775306
$421$	7.48881	0.364982	0.182491	−	0.983208i	$-0.441584\pi$
$421$	7.48881	0.364982	0.182491	+	0.983208i	$0.441584\pi$
$422$	−5.00503	−0.243641
$423$	7.23660	0.351856
$424$	−13.7981	−0.670096
$425$	0.656574	0.0318485
$426$	4.06841	0.197115
$427$	25.8912	1.25296
$428$	−16.7413	−0.809220
$429$	−4.23606	−0.204519
$430$	−5.67077	−0.273469
$431$	16.2990	0.785095	0.392548	−	0.919732i	$-0.371594\pi$
$431$	16.2990	0.785095	0.392548	+	0.919732i	$0.371594\pi$
$432$	3.42936	0.164995
$433$	−8.08492	−0.388537	−0.194268	−	0.980948i	$-0.562233\pi$
$433$	−8.08492	−0.388537	−0.194268	+	0.980948i	$0.562233\pi$
$434$	10.6923	0.513246
$435$	−9.74007	−0.467001
$436$	−15.1905	−0.727492
$437$	23.9247	1.14448
$438$	−2.11633	−0.101122
$439$	−11.3703	−0.542674	−0.271337	−	0.962484i	$-0.587466\pi$
$439$	−11.3703	−0.542674	−0.271337	+	0.962484i	$0.587466\pi$
$440$	−11.3081	−0.539090
$441$	7.40279	0.352514
$442$	1.26464	0.0601527
$443$	33.1567	1.57532	0.787660	−	0.616110i	$-0.211292\pi$
$443$	33.1567	1.57532	0.787660	+	0.616110i	$0.211292\pi$
$444$	−18.7501	−0.889840
$445$	17.0555	0.808508
$446$	6.86347	0.324995
$447$	0.228761	0.0108200
$448$	21.9077	1.03504
$449$	−6.68135	−0.315312	−0.157656	−	0.987494i	$-0.550394\pi$
$449$	−6.68135	−0.315312	−0.157656	+	0.987494i	$0.550394\pi$
$450$	−0.0501855	−0.00236577
$451$	35.2056	1.65776
$452$	6.69850	0.315071
$453$	17.5821	0.826079
$454$	−3.85572	−0.180958
$455$	8.34800	0.391360
$456$	−7.33619	−0.343548
$457$	−31.6532	−1.48067	−0.740337	−	0.672235i	$-0.765334\pi$
$457$	−31.6532	−1.48067	−0.740337	+	0.672235i	$0.765334\pi$
$458$	−2.31395	−0.108124
$459$	−4.06758	−0.189858
$460$	−16.5698	−0.772573
$461$	3.36071	0.156524	0.0782618	−	0.996933i	$-0.475063\pi$
$461$	3.36071	0.156524	0.0782618	+	0.996933i	$0.475063\pi$
$462$	−4.99823	−0.232539
$463$	−19.3355	−0.898599	−0.449300	−	0.893381i	$-0.648326\pi$
$463$	−19.3355	−0.898599	−0.449300	+	0.893381i	$0.648326\pi$
$464$	−15.1851	−0.704949
$465$	−19.9331	−0.924378
$466$	−1.40998	−0.0653160
$467$	−25.6186	−1.18549	−0.592744	−	0.805391i	$-0.701956\pi$
$467$	−25.6186	−1.18549	−0.592744	+	0.805391i	$0.701956\pi$
$468$	1.90334	0.0879818
$469$	−7.32638	−0.338301
$470$	4.94908	0.228284
$471$	11.0855	0.510792
$472$	7.30512	0.336246
$473$	−35.1248	−1.61504
$474$	−3.64432	−0.167389
$475$	−0.975779	−0.0447718
$476$	−29.3815	−1.34670
$477$	11.3698	0.520588
$478$	−0.962625	−0.0440294
$479$	−20.8328	−0.951874	−0.475937	−	0.879479i	$-0.657891\pi$
$479$	−20.8328	−0.951874	−0.475937	+	0.879479i	$0.657891\pi$
$480$	7.68428	0.350738
$481$	−9.85117	−0.449175
$482$	3.31742	0.151104
$483$	−15.0199	−0.683429
$484$	−13.2172	−0.600780
$485$	22.8523	1.03767
$486$	0.310907	0.0141030
$487$	−3.28652	−0.148926	−0.0744631	−	0.997224i	$-0.523724\pi$
$487$	−3.28652	−0.148926	−0.0744631	+	0.997224i	$0.523724\pi$
$488$	8.27934	0.374788
$489$	−15.7655	−0.712941
$490$	5.06273	0.228711
$491$	−10.6011	−0.478419	−0.239209	−	0.970968i	$-0.576888\pi$
$491$	−10.6011	−0.478419	−0.239209	+	0.970968i	$0.576888\pi$
$492$	−15.8185	−0.713152
$493$	18.0110	0.811176
$494$	−1.87947	−0.0845612
$495$	9.31797	0.418812
$496$	−31.0764	−1.39537
$497$	−49.6612	−2.22761
$498$	5.02177	0.225031
$499$	−2.16915	−0.0971046	−0.0485523	−	0.998821i	$-0.515461\pi$
$499$	−2.16915	−0.0971046	−0.0485523	+	0.998821i	$0.515461\pi$
$500$	21.6094	0.966404
$501$	16.9002	0.755045
$502$	2.73086	0.121884
$503$	21.8832	0.975722	0.487861	−	0.872921i	$-0.337777\pi$
$503$	21.8832	0.975722	0.487861	+	0.872921i	$0.337777\pi$
$504$	4.60564	0.205152
$505$	29.3721	1.30704
$506$	5.21238	0.231719
$507$	1.00000	0.0444116
$508$	−29.5646	−1.31172
$509$	15.2683	0.676757	0.338379	−	0.941010i	$-0.390122\pi$
$509$	15.2683	0.676757	0.338379	+	0.941010i	$0.390122\pi$
$510$	−2.78180	−0.123180
$511$	25.8331	1.14279
$512$	20.3036	0.897301
$513$	6.04510	0.266898
$514$	−9.39663	−0.414467
$515$	−2.19968	−0.0969294
$516$	15.7822	0.694773
$517$	30.6547	1.34819
$518$	−11.6236	−0.510713
$519$	1.53771	0.0674978
$520$	2.66948	0.117064
$521$	17.8336	0.781305	0.390653	−	0.920538i	$-0.372249\pi$
$521$	17.8336	0.781305	0.390653	+	0.920538i	$0.372249\pi$
$522$	−1.37668	−0.0602558
$523$	−45.3741	−1.98407	−0.992036	−	0.125953i	$-0.959801\pi$
$523$	−45.3741	−1.98407	−0.992036	+	0.125953i	$0.959801\pi$
$524$	−41.4602	−1.81120
$525$	0.612592	0.0267357
$526$	−0.761271	−0.0331930
$527$	36.8598	1.60564
$528$	14.5270	0.632206
$529$	−7.33656	−0.318981
$530$	7.77576	0.337758
$531$	−6.01950	−0.261224
$532$	43.6659	1.89316
$533$	−8.31092	−0.359986
$534$	2.41066	0.104319
$535$	19.3478	0.836480
$536$	−2.34279	−0.101193
$537$	2.08899	0.0901466
$538$	−6.81558	−0.293840
$539$	31.3586	1.35071
$540$	−4.18673	−0.180168
$541$	−23.0781	−0.992207	−0.496103	−	0.868263i	$-0.665236\pi$
$541$	−23.0781	−0.992207	−0.496103	+	0.868263i	$0.665236\pi$
$542$	−9.67882	−0.415741
$543$	10.0968	0.433294
$544$	−14.2095	−0.609228
$545$	17.5556	0.751998
$546$	1.17992	0.0504961
$547$	13.9048	0.594525	0.297262	−	0.954796i	$-0.403926\pi$
$547$	13.9048	0.594525	0.297262	+	0.954796i	$0.403926\pi$
$548$	−21.3276	−0.911072
$549$	−6.82227	−0.291167
$550$	−0.212589	−0.00906482
$551$	−26.7674	−1.14033
$552$	−4.80298	−0.204428
$553$	44.4845	1.89167
$554$	−3.81489	−0.162079
$555$	21.6694	0.919815
$556$	31.9445	1.35475
$557$	−3.29389	−0.139567	−0.0697834	−	0.997562i	$-0.522231\pi$
$557$	−3.29389	−0.139567	−0.0697834	+	0.997562i	$0.522231\pi$
$558$	−2.81739	−0.119270
$559$	8.29186	0.350708
$560$	−28.6283	−1.20977
$561$	−17.2305	−0.727472
$562$	8.91871	0.376213
$563$	1.10467	0.0465563	0.0232781	−	0.999729i	$-0.492590\pi$
$563$	1.10467	0.0465563	0.0232781	+	0.999729i	$0.492590\pi$
$564$	−13.7737	−0.579977
$565$	−7.74142	−0.325684
$566$	0.443279	0.0186324
$567$	−3.79510	−0.159379
$568$	−15.8804	−0.666326
$569$	−42.7753	−1.79323	−0.896616	−	0.442808i	$-0.853982\pi$
$569$	−42.7753	−1.79323	−0.896616	+	0.442808i	$0.853982\pi$
$570$	4.13422	0.173163
$571$	22.6585	0.948229	0.474114	−	0.880463i	$-0.342768\pi$
$571$	22.6585	0.948229	0.474114	+	0.880463i	$0.342768\pi$
$572$	8.06265	0.337116
$573$	−8.02894	−0.335414
$574$	−9.80625	−0.409305
$575$	−0.638839	−0.0266414
$576$	−5.77262	−0.240526
$577$	26.1303	1.08782	0.543908	−	0.839145i	$-0.316944\pi$
$577$	26.1303	1.08782	0.543908	+	0.839145i	$0.316944\pi$
$578$	−0.141407	−0.00588175
$579$	−25.1036	−1.04327
$580$	18.5386	0.769775
$581$	−61.2984	−2.54309
$582$	3.22999	0.133888
$583$	48.1632	1.99472
$584$	8.26076	0.341833
$585$	−2.19968	−0.0909455
$586$	−1.93299	−0.0798512
$587$	8.53543	0.352295	0.176147	−	0.984364i	$-0.443636\pi$
$587$	8.53543	0.352295	0.176147	+	0.984364i	$0.443636\pi$
$588$	−14.0900	−0.581062
$589$	−54.7798	−2.25716
$590$	−4.11671	−0.169482
$591$	18.7136	0.769777
$592$	33.7832	1.38848
$593$	16.4899	0.677160	0.338580	−	0.940938i	$-0.390053\pi$
$593$	16.4899	0.677160	0.338580	+	0.940938i	$0.390053\pi$
$594$	1.31702	0.0540380
$595$	33.9561	1.39207
$596$	−0.435409	−0.0178351
$597$	13.2261	0.541308
$598$	−1.23048	−0.0503180
$599$	−14.2210	−0.581053	−0.290526	−	0.956867i	$-0.593830\pi$
$599$	−14.2210	−0.581053	−0.290526	+	0.956867i	$0.593830\pi$
$600$	0.195891	0.00799722
$601$	−11.5191	−0.469872	−0.234936	−	0.972011i	$-0.575488\pi$
$601$	−11.5191	−0.469872	−0.234936	+	0.972011i	$0.575488\pi$
$602$	9.78376	0.398756
$603$	1.93049	0.0786154
$604$	−33.4646	−1.36166
$605$	15.2750	0.621018
$606$	4.15152	0.168644
$607$	1.00400	0.0407509	0.0203755	−	0.999792i	$-0.493514\pi$
$607$	1.00400	0.0407509	0.0203755	+	0.999792i	$0.493514\pi$
$608$	21.1177	0.856438
$609$	16.8045	0.680954
$610$	−4.66572	−0.188910
$611$	−7.23660	−0.292762
$612$	7.74197	0.312951
$613$	−33.3349	−1.34638	−0.673192	−	0.739468i	$-0.735077\pi$
$613$	−33.3349	−1.34638	−0.673192	+	0.739468i	$0.735077\pi$
$614$	−6.19134	−0.249862
$615$	18.2813	0.737175
$616$	19.5098	0.786071
$617$	32.1162	1.29295	0.646474	−	0.762936i	$-0.276243\pi$
$617$	32.1162	1.29295	0.646474	+	0.762936i	$0.276243\pi$
$618$	−0.310907	−0.0125065
$619$	−13.6831	−0.549969	−0.274985	−	0.961449i	$-0.588673\pi$
$619$	−13.6831	−0.549969	−0.274985	+	0.961449i	$0.588673\pi$
$620$	37.9395	1.52369
$621$	3.95771	0.158817
$622$	−3.88605	−0.155816
$623$	−29.4258	−1.17892
$624$	−3.42936	−0.137284
$625$	−24.1669	−0.966674
$626$	−3.18468	−0.127286
$627$	25.6074	1.02266
$628$	−21.0994	−0.841958
$629$	−40.0704	−1.59771
$630$	−2.59545	−0.103405
$631$	−9.38851	−0.373751	−0.186875	−	0.982384i	$-0.559836\pi$
$631$	−9.38851	−0.373751	−0.186875	+	0.982384i	$0.559836\pi$
$632$	14.2250	0.565840
$633$	−16.0981	−0.639844
$634$	2.41948	0.0960897
$635$	34.1677	1.35590
$636$	−21.6406	−0.858105
$637$	−7.40279	−0.293309
$638$	−5.83171	−0.230880
$639$	13.0856	0.517659
$640$	−19.3164	−0.763549
$641$	2.20746	0.0871896	0.0435948	−	0.999049i	$-0.486119\pi$
$641$	2.20746	0.0871896	0.0435948	+	0.999049i	$0.486119\pi$
$642$	2.73466	0.107929
$643$	15.6660	0.617808	0.308904	−	0.951093i	$-0.400038\pi$
$643$	15.6660	0.617808	0.308904	+	0.951093i	$0.400038\pi$
$644$	28.5879	1.12652
$645$	−18.2394	−0.718177
$646$	−7.64487	−0.300783
$647$	11.4512	0.450194	0.225097	−	0.974336i	$-0.427730\pi$
$647$	11.4512	0.450194	0.225097	+	0.974336i	$0.427730\pi$
$648$	−1.21358	−0.0476737
$649$	−25.4990	−1.00092
$650$	0.0501855	0.00196844
$651$	34.3906	1.34787
$652$	30.0071	1.17517
$653$	−21.5564	−0.843568	−0.421784	−	0.906696i	$-0.638596\pi$
$653$	−21.5564	−0.843568	−0.421784	+	0.906696i	$0.638596\pi$
$654$	2.48134	0.0970282
$655$	47.9154	1.87221
$656$	28.5012	1.11278
$657$	−6.80696	−0.265565
$658$	−8.53864	−0.332871
$659$	16.7631	0.652998	0.326499	−	0.945198i	$-0.394131\pi$
$659$	16.7631	0.652998	0.326499	+	0.945198i	$0.394131\pi$
$660$	−17.7352	−0.690343
$661$	−22.7601	−0.885265	−0.442632	−	0.896703i	$-0.645955\pi$
$661$	−22.7601	−0.885265	−0.442632	+	0.896703i	$0.645955\pi$
$662$	−5.26936	−0.204799
$663$	4.06758	0.157972
$664$	−19.6017	−0.760692
$665$	−50.4645	−1.95693
$666$	3.06280	0.118681
$667$	−17.5245	−0.678553
$668$	−32.1668	−1.24457
$669$	22.0756	0.853493
$670$	1.32025	0.0510057
$671$	−28.8996	−1.11565
$672$	−13.2577	−0.511426
$673$	−44.0198	−1.69684	−0.848419	−	0.529325i	$-0.822445\pi$
$673$	−44.0198	−1.69684	−0.848419	+	0.529325i	$0.822445\pi$
$674$	3.75766	0.144740
$675$	−0.161416	−0.00621292
$676$	−1.90334	−0.0732053
$677$	−37.2555	−1.43185	−0.715923	−	0.698179i	$-0.753994\pi$
$677$	−37.2555	−1.43185	−0.715923	+	0.698179i	$0.753994\pi$
$678$	−1.09419	−0.0420221
$679$	−39.4270	−1.51307
$680$	10.8583	0.416397
$681$	−12.4015	−0.475228
$682$	−11.9346	−0.457001
$683$	50.2043	1.92102	0.960508	−	0.278254i	$-0.0897555\pi$
$683$	50.2043	1.92102	0.960508	+	0.278254i	$0.0897555\pi$
$684$	−11.5059	−0.439938
$685$	24.6483	0.941762
$686$	−0.475256	−0.0181454
$687$	−7.44256	−0.283951
$688$	−28.4358	−1.08411
$689$	−11.3698	−0.433155
$690$	2.70666	0.103041
$691$	−44.8617	−1.70662	−0.853310	−	0.521405i	$-0.825408\pi$
$691$	−44.8617	−1.70662	−0.853310	+	0.521405i	$0.825408\pi$
$692$	−2.92677	−0.111259
$693$	−16.0763	−0.610687
$694$	7.48556	0.284148
$695$	−36.9181	−1.40038
$696$	5.37365	0.203688
$697$	−33.8053	−1.28047
$698$	−3.08816	−0.116889
$699$	−4.53505	−0.171531
$700$	−1.16597	−0.0440695
$701$	25.2772	0.954708	0.477354	−	0.878711i	$-0.341596\pi$
$701$	25.2772	0.954708	0.477354	+	0.878711i	$0.341596\pi$
$702$	−0.310907	−0.0117344
$703$	59.5513	2.24602
$704$	−24.4532	−0.921613
$705$	15.9182	0.599514
$706$	−3.31581	−0.124792
$707$	−50.6756	−1.90585
$708$	11.4571	0.430586
$709$	15.4012	0.578405	0.289203	−	0.957268i	$-0.406610\pi$
$709$	15.4012	0.578405	0.289203	+	0.957268i	$0.406610\pi$
$710$	8.94920	0.335857
$711$	−11.7216	−0.439593
$712$	−9.40961	−0.352640
$713$	−35.8641	−1.34312
$714$	4.79943	0.179614
$715$	−9.31797	−0.348472
$716$	−3.97605	−0.148592
$717$	−3.09618	−0.115629
$718$	−1.52263	−0.0568242
$719$	−28.1712	−1.05061	−0.525304	−	0.850914i	$-0.676049\pi$
$719$	−28.1712	−1.05061	−0.525304	+	0.850914i	$0.676049\pi$
$720$	7.54350	0.281130
$721$	3.79510	0.141337
$722$	5.45433	0.202989
$723$	10.6701	0.396826
$724$	−19.2175	−0.714214
$725$	0.714745	0.0265449
$726$	2.15900	0.0801281
$727$	−1.53632	−0.0569789	−0.0284894	−	0.999594i	$-0.509070\pi$
$727$	−1.53632	−0.0569789	−0.0284894	+	0.999594i	$0.509070\pi$
$728$	−4.60564	−0.170696
$729$	1.00000	0.0370370
$730$	−4.65525	−0.172299
$731$	33.7278	1.24747
$732$	12.9851	0.479942
$733$	8.83485	0.326323	0.163161	−	0.986599i	$-0.447831\pi$
$733$	8.83485	0.326323	0.163161	+	0.986599i	$0.447831\pi$
$734$	7.02734	0.259384
$735$	16.2837	0.600635
$736$	13.8257	0.509623
$737$	8.17765	0.301228
$738$	2.58392	0.0951156
$739$	−5.19076	−0.190945	−0.0954726	−	0.995432i	$-0.530436\pi$
$739$	−5.19076	−0.190945	−0.0954726	+	0.995432i	$0.530436\pi$
$740$	−41.2442	−1.51617
$741$	−6.04510	−0.222072
$742$	−13.4155	−0.492499
$743$	−20.7948	−0.762886	−0.381443	−	0.924392i	$-0.624573\pi$
$743$	−20.7948	−0.762886	−0.381443	+	0.924392i	$0.624573\pi$
$744$	10.9972	0.403178
$745$	0.503201	0.0184358
$746$	7.58447	0.277687
$747$	16.1520	0.590970
$748$	32.7954	1.19912
$749$	−33.3808	−1.21971
$750$	−3.52987	−0.128893
$751$	39.5093	1.44172	0.720858	−	0.693083i	$-0.243748\pi$
$751$	39.5093	1.44172	0.720858	+	0.693083i	$0.243748\pi$
$752$	24.8170	0.904981
$753$	8.78351	0.320089
$754$	1.37668	0.0501358
$755$	38.6749	1.40752
$756$	7.22335	0.262711
$757$	43.7796	1.59120	0.795598	−	0.605824i	$-0.207157\pi$
$757$	43.7796	1.59120	0.795598	+	0.605824i	$0.207157\pi$
$758$	10.4908	0.381044
$759$	16.7651	0.608534
$760$	−16.1373	−0.585360
$761$	−12.3930	−0.449246	−0.224623	−	0.974446i	$-0.572115\pi$
$761$	−12.3930	−0.449246	−0.224623	+	0.974446i	$0.572115\pi$
$762$	4.82933	0.174948
$763$	−30.2886	−1.09652
$764$	15.2818	0.552875
$765$	−8.94736	−0.323492
$766$	7.31845	0.264426
$767$	6.01950	0.217352
$768$	8.81501	0.318084
$769$	2.29110	0.0826192	0.0413096	−	0.999146i	$-0.486847\pi$
$769$	2.29110	0.0826192	0.0413096	+	0.999146i	$0.486847\pi$
$770$	−10.9945	−0.396214
$771$	−30.2233	−1.08846
$772$	47.7806	1.71966
$773$	−11.8405	−0.425873	−0.212937	−	0.977066i	$-0.568303\pi$
$773$	−11.8405	−0.425873	−0.212937	+	0.977066i	$0.568303\pi$
$774$	−2.57800	−0.0926643
$775$	1.46273	0.0525429
$776$	−12.6078	−0.452592
$777$	−37.3862	−1.34122
$778$	−3.27613	−0.117455
$779$	50.2404	1.80005
$780$	4.18673	0.149909
$781$	55.4315	1.98349
$782$	−5.00507	−0.178981
$783$	−4.42795	−0.158242
$784$	25.3868	0.906673
$785$	24.3845	0.870320
$786$	6.77247	0.241566
$787$	−15.7238	−0.560491	−0.280246	−	0.959928i	$-0.590416\pi$
$787$	−15.7238	−0.560491	−0.280246	+	0.959928i	$0.590416\pi$
$788$	−35.6184	−1.26885
$789$	−2.44855	−0.0871706
$790$	−8.01632	−0.285208
$791$	13.3563	0.474894
$792$	−5.14078	−0.182670
$793$	6.82227	0.242266
$794$	−2.23706	−0.0793904
$795$	25.0099	0.887010
$796$	−25.1737	−0.892258
$797$	28.3387	1.00381	0.501903	−	0.864924i	$-0.332633\pi$
$797$	28.3387	1.00381	0.501903	+	0.864924i	$0.332633\pi$
$798$	−7.13276	−0.252497
$799$	−29.4354	−1.04135
$800$	−0.563887	−0.0199364
$801$	7.75363	0.273961
$802$	−4.19512	−0.148135
$803$	−28.8347	−1.01755
$804$	−3.67436	−0.129585
$805$	−33.0389	−1.16447
$806$	2.81739	0.0992384
$807$	−21.9216	−0.771676
$808$	−16.2048	−0.570082
$809$	3.34673	0.117665	0.0588324	−	0.998268i	$-0.481262\pi$
$809$	3.34673	0.117665	0.0588324	+	0.998268i	$0.481262\pi$
$810$	0.683896	0.0240296
$811$	1.94129	0.0681679	0.0340839	−	0.999419i	$-0.489149\pi$
$811$	1.94129	0.0681679	0.0340839	+	0.999419i	$0.489149\pi$
$812$	−31.9847	−1.12244
$813$	−31.1309	−1.09181
$814$	12.9742	0.454745
$815$	−34.6791	−1.21475
$816$	−13.9492	−0.488320
$817$	−50.1252	−1.75366
$818$	−4.45902	−0.155906
$819$	3.79510	0.132612
$820$	−34.7956	−1.21511
$821$	0.889343	0.0310383	0.0155191	−	0.999880i	$-0.495060\pi$
$821$	0.889343	0.0310383	0.0155191	+	0.999880i	$0.495060\pi$
$822$	3.48384	0.121513
$823$	43.7740	1.52586	0.762932	−	0.646478i	$-0.223759\pi$
$823$	43.7740	1.52586	0.762932	+	0.646478i	$0.223759\pi$
$824$	1.21358	0.0422769
$825$	−0.683770	−0.0238058
$826$	7.10256	0.247130
$827$	30.3164	1.05420	0.527102	−	0.849802i	$-0.323279\pi$
$827$	30.3164	1.05420	0.527102	+	0.849802i	$0.323279\pi$
$828$	−7.53285	−0.261785
$829$	31.4995	1.09402	0.547011	−	0.837125i	$-0.315766\pi$
$829$	31.4995	1.09402	0.547011	+	0.837125i	$0.315766\pi$
$830$	11.0463	0.383422
$831$	−12.2702	−0.425648
$832$	5.77262	0.200129
$833$	−30.1114	−1.04330
$834$	−5.21808	−0.180687
$835$	37.1750	1.28649
$836$	−48.7395	−1.68569
$837$	−9.06185	−0.313223
$838$	3.36501	0.116242
$839$	36.9621	1.27607	0.638037	−	0.770006i	$-0.279747\pi$
$839$	36.9621	1.27607	0.638037	+	0.770006i	$0.279747\pi$
$840$	10.1309	0.349550
$841$	−9.39323	−0.323904
$842$	2.32832	0.0802393
$843$	28.6861	0.988001
$844$	30.6402	1.05468
$845$	2.19968	0.0756712
$846$	2.24991	0.0773536
$847$	−26.3540	−0.905533
$848$	38.9912	1.33896
$849$	1.42576	0.0489319
$850$	0.204134	0.00700172
$851$	38.9880	1.33649
$852$	−24.9063	−0.853277
$853$	−29.0971	−0.996266	−0.498133	−	0.867101i	$-0.665981\pi$
$853$	−29.0971	−0.996266	−0.498133	+	0.867101i	$0.665981\pi$
$854$	8.04976	0.275457
$855$	13.2973	0.454757
$856$	−10.6743	−0.364840
$857$	−19.0210	−0.649745	−0.324873	−	0.945758i	$-0.605321\pi$
$857$	−19.0210	−0.649745	−0.324873	+	0.945758i	$0.605321\pi$
$858$	−1.31702	−0.0449624
$859$	−9.34473	−0.318838	−0.159419	−	0.987211i	$-0.550962\pi$
$859$	−9.34473	−0.318838	−0.159419	+	0.987211i	$0.550962\pi$
$860$	34.7158	1.18380
$861$	−31.5408	−1.07491
$862$	5.06748	0.172599
$863$	−20.8005	−0.708059	−0.354029	−	0.935234i	$-0.615189\pi$
$863$	−20.8005	−0.708059	−0.354029	+	0.935234i	$0.615189\pi$
$864$	3.49336	0.118847
$865$	3.38246	0.115007
$866$	−2.51366	−0.0854177
$867$	−0.454820	−0.0154465
$868$	−65.4569	−2.22175
$869$	−49.6532	−1.68437
$870$	−3.02826	−0.102668
$871$	−1.93049	−0.0654120
$872$	−9.68552	−0.327993
$873$	10.3889	0.351612
$874$	7.43837	0.251607
$875$	43.0875	1.45662
$876$	12.9559	0.437741
$877$	−40.0180	−1.35131	−0.675656	−	0.737217i	$-0.736140\pi$
$877$	−40.0180	−1.35131	−0.675656	+	0.737217i	$0.736140\pi$
$878$	−3.53511	−0.119304
$879$	−6.21727	−0.209703
$880$	31.9547	1.07719
$881$	−36.7785	−1.23910	−0.619550	−	0.784957i	$-0.712685\pi$
$881$	−36.7785	−1.23910	−0.619550	+	0.784957i	$0.712685\pi$
$882$	2.30158	0.0774982
$883$	−2.92267	−0.0983558	−0.0491779	−	0.998790i	$-0.515660\pi$
$883$	−2.92267	−0.0983558	−0.0491779	+	0.998790i	$0.515660\pi$
$884$	−7.74197	−0.260391
$885$	−13.2410	−0.445090
$886$	10.3086	0.346326
$887$	−43.1702	−1.44951	−0.724756	−	0.689006i	$-0.758048\pi$
$887$	−43.1702	−1.44951	−0.724756	+	0.689006i	$0.758048\pi$
$888$	−11.9551	−0.401188
$889$	−58.9495	−1.97710
$890$	5.30267	0.177746
$891$	4.23606	0.141913
$892$	−42.0174	−1.40685
$893$	43.7460	1.46390
$894$	0.0711234	0.00237872
$895$	4.59511	0.153597
$896$	33.3266	1.11336
$897$	−3.95771	−0.132144
$898$	−2.07728	−0.0693197
$899$	40.1254	1.33826
$900$	0.307230	0.0102410
$901$	−46.2476	−1.54073
$902$	10.9457	0.364451
$903$	31.4684	1.04720
$904$	4.27099	0.142051
$905$	22.2096	0.738273
$906$	5.46640	0.181609
$907$	−19.8930	−0.660536	−0.330268	−	0.943887i	$-0.607139\pi$
$907$	−19.8930	−0.660536	−0.330268	+	0.943887i	$0.607139\pi$
$908$	23.6043	0.783336
$909$	13.3529	0.442888
$910$	2.59545	0.0860384
$911$	−50.4146	−1.67031	−0.835156	−	0.550014i	$-0.814623\pi$
$911$	−50.4146	−1.67031	−0.835156	+	0.550014i	$0.814623\pi$
$912$	20.7309	0.686467
$913$	68.4208	2.26440
$914$	−9.84121	−0.325518
$915$	−15.0068	−0.496110
$916$	14.1657	0.468048
$917$	−82.6684	−2.72995
$918$	−1.26464	−0.0417393
$919$	−34.3470	−1.13300	−0.566501	−	0.824061i	$-0.691703\pi$
$919$	−34.3470	−1.13300	−0.566501	+	0.824061i	$0.691703\pi$
$920$	−10.5650	−0.348318
$921$	−19.9138	−0.656182
$922$	1.04487	0.0344109
$923$	−13.0856	−0.430718
$924$	30.5986	1.00662
$925$	−1.59014	−0.0522835
$926$	−6.01156	−0.197552
$927$	−1.00000	−0.0328443
$928$	−15.4685	−0.507777
$929$	−42.3596	−1.38977	−0.694887	−	0.719119i	$-0.744546\pi$
$929$	−42.3596	−1.38977	−0.694887	+	0.719119i	$0.744546\pi$
$930$	−6.19736	−0.203219
$931$	44.7506	1.46664
$932$	8.63173	0.282742
$933$	−12.4991	−0.409201
$934$	−7.96501	−0.260623
$935$	−37.9016	−1.23951
$936$	1.21358	0.0396670
$937$	−53.8279	−1.75848	−0.879241	−	0.476378i	$-0.841949\pi$
$937$	−53.8279	−1.75848	−0.879241	+	0.476378i	$0.841949\pi$
$938$	−2.27783	−0.0743736
$939$	−10.2432	−0.334274
$940$	−30.2977	−0.988202
$941$	−23.1623	−0.755068	−0.377534	−	0.925996i	$-0.623228\pi$
$941$	−23.1623	−0.755068	−0.377534	+	0.925996i	$0.623228\pi$
$942$	3.44656	0.112295
$943$	32.8922	1.07112
$944$	−20.6431	−0.671875
$945$	−8.34800	−0.271560
$946$	−10.9206	−0.355058
$947$	18.4401	0.599223	0.299612	−	0.954061i	$-0.403143\pi$
$947$	18.4401	0.599223	0.299612	+	0.954061i	$0.403143\pi$
$948$	22.3101	0.724597
$949$	6.80696	0.220963
$950$	−0.303377	−0.00984284
$951$	7.78199	0.252348
$952$	−18.7338	−0.607166
$953$	−19.0068	−0.615690	−0.307845	−	0.951437i	$-0.599608\pi$
$953$	−19.0068	−0.615690	−0.307845	+	0.951437i	$0.599608\pi$
$954$	3.53495	0.114448
$955$	−17.6611	−0.571499
$956$	5.89307	0.190596
$957$	−18.7571	−0.606330
$958$	−6.47706	−0.209264
$959$	−42.5256	−1.37322
$960$	−12.6979	−0.409823
$961$	51.1171	1.64894
$962$	−3.06280	−0.0987486
$963$	8.79575	0.283439
$964$	−20.3088	−0.654104
$965$	−55.2199	−1.77759
$966$	−4.66979	−0.150248
$967$	−4.57915	−0.147256	−0.0736278	−	0.997286i	$-0.523458\pi$
$967$	−4.57915	−0.147256	−0.0736278	+	0.997286i	$0.523458\pi$
$968$	−8.42732	−0.270864
$969$	−24.5889	−0.789910
$970$	7.10494	0.228126
$971$	−11.9350	−0.383011	−0.191506	−	0.981492i	$-0.561337\pi$
$971$	−11.9350	−0.383011	−0.191506	+	0.981492i	$0.561337\pi$
$972$	−1.90334	−0.0610496
$973$	63.6947	2.04196
$974$	−1.02180	−0.0327406
$975$	0.161416	0.00516946
$976$	−23.3961	−0.748889
$977$	−52.1230	−1.66756	−0.833781	−	0.552095i	$-0.813829\pi$
$977$	−52.1230	−1.66756	−0.833781	+	0.552095i	$0.813829\pi$
$978$	−4.90161	−0.156736
$979$	32.8448	1.04973
$980$	−30.9935	−0.990049
$981$	7.98098	0.254813
$982$	−3.29594	−0.105178
$983$	54.3789	1.73442	0.867208	−	0.497945i	$-0.165912\pi$
$983$	54.3789	1.73442	0.867208	+	0.497945i	$0.165912\pi$
$984$	−10.0859	−0.321528
$985$	41.1640	1.31159
$986$	5.59976	0.178333
$987$	−27.4636	−0.874177
$988$	11.5059	0.366050
$989$	−32.8168	−1.04351
$990$	2.89702	0.0920734
$991$	38.9118	1.23607	0.618037	−	0.786149i	$-0.287928\pi$
$991$	38.9118	1.23607	0.618037	+	0.786149i	$0.287928\pi$
$992$	−31.6563	−1.00509
$993$	−16.9483	−0.537839
$994$	−15.4400	−0.489728
$995$	29.0931	0.922315
$996$	−30.7427	−0.974119
$997$	21.3760	0.676984	0.338492	−	0.940969i	$-0.390083\pi$
$997$	21.3760	0.676984	0.338492	+	0.940969i	$0.390083\pi$
$998$	−0.674405	−0.0213479
$999$	9.85117	0.311677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.17	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.17	✓	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.310907 q^{2} +1.00000 q^{3} -1.90334 q^{4} +2.19968 q^{5} +0.310907 q^{6} -3.79510 q^{7} -1.21358 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.310907 q^{2} +1.00000 q^{3} -1.90334 q^{4} +2.19968 q^{5} +0.310907 q^{6} -3.79510 q^{7} -1.21358 q^{8} +1.00000 q^{9} +0.683896 q^{10} +4.23606 q^{11} -1.90334 q^{12} -1.00000 q^{13} -1.17992 q^{14} +2.19968 q^{15} +3.42936 q^{16} -4.06758 q^{17} +0.310907 q^{18} +6.04510 q^{19} -4.18673 q^{20} -3.79510 q^{21} +1.31702 q^{22} +3.95771 q^{23} -1.21358 q^{24} -0.161416 q^{25} -0.310907 q^{26} +1.00000 q^{27} +7.22335 q^{28} -4.42795 q^{29} +0.683896 q^{30} -9.06185 q^{31} +3.49336 q^{32} +4.23606 q^{33} -1.26464 q^{34} -8.34800 q^{35} -1.90334 q^{36} +9.85117 q^{37} +1.87947 q^{38} -1.00000 q^{39} -2.66948 q^{40} +8.31092 q^{41} -1.17992 q^{42} -8.29186 q^{43} -8.06265 q^{44} +2.19968 q^{45} +1.23048 q^{46} +7.23660 q^{47} +3.42936 q^{48} +7.40279 q^{49} -0.0501855 q^{50} -4.06758 q^{51} +1.90334 q^{52} +11.3698 q^{53} +0.310907 q^{54} +9.31797 q^{55} +4.60564 q^{56} +6.04510 q^{57} -1.37668 q^{58} -6.01950 q^{59} -4.18673 q^{60} -6.82227 q^{61} -2.81739 q^{62} -3.79510 q^{63} -5.77262 q^{64} -2.19968 q^{65} +1.31702 q^{66} +1.93049 q^{67} +7.74197 q^{68} +3.95771 q^{69} -2.59545 q^{70} +13.0856 q^{71} -1.21358 q^{72} -6.80696 q^{73} +3.06280 q^{74} -0.161416 q^{75} -11.5059 q^{76} -16.0763 q^{77} -0.310907 q^{78} -11.7216 q^{79} +7.54350 q^{80} +1.00000 q^{81} +2.58392 q^{82} +16.1520 q^{83} +7.22335 q^{84} -8.94736 q^{85} -2.57800 q^{86} -4.42795 q^{87} -5.14078 q^{88} +7.75363 q^{89} +0.683896 q^{90} +3.79510 q^{91} -7.53285 q^{92} -9.06185 q^{93} +2.24991 q^{94} +13.2973 q^{95} +3.49336 q^{96} +10.3889 q^{97} +2.30158 q^{98} +4.23606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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