LMFDB - Embedded newform 503.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, 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("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61798 q^{2} +2.76613 q^{3} +0.617860 q^{4} +3.34245 q^{5} +4.47554 q^{6} -5.14301 q^{7} -2.23628 q^{8} +4.65146 q^{9} +O(q^{10})$	\(q+1.61798 q^{2} +2.76613 q^{3} +0.617860 q^{4} +3.34245 q^{5} +4.47554 q^{6} -5.14301 q^{7} -2.23628 q^{8} +4.65146 q^{9} +5.40802 q^{10} -1.82068 q^{11} +1.70908 q^{12} +4.81926 q^{13} -8.32129 q^{14} +9.24565 q^{15} -4.85397 q^{16} -2.57438 q^{17} +7.52597 q^{18} -0.856193 q^{19} +2.06517 q^{20} -14.2262 q^{21} -2.94583 q^{22} +4.83970 q^{23} -6.18582 q^{24} +6.17198 q^{25} +7.79747 q^{26} +4.56816 q^{27} -3.17766 q^{28} +1.45021 q^{29} +14.9593 q^{30} -5.44799 q^{31} -3.38107 q^{32} -5.03625 q^{33} -4.16530 q^{34} -17.1903 q^{35} +2.87395 q^{36} -7.40163 q^{37} -1.38530 q^{38} +13.3307 q^{39} -7.47464 q^{40} -4.34034 q^{41} -23.0177 q^{42} -7.82010 q^{43} -1.12493 q^{44} +15.5473 q^{45} +7.83054 q^{46} +4.92683 q^{47} -13.4267 q^{48} +19.4505 q^{49} +9.98614 q^{50} -7.12107 q^{51} +2.97763 q^{52} -1.60749 q^{53} +7.39119 q^{54} -6.08555 q^{55} +11.5012 q^{56} -2.36834 q^{57} +2.34641 q^{58} +1.63046 q^{59} +5.71251 q^{60} +1.91900 q^{61} -8.81474 q^{62} -23.9225 q^{63} +4.23743 q^{64} +16.1081 q^{65} -8.14855 q^{66} -6.11331 q^{67} -1.59061 q^{68} +13.3872 q^{69} -27.8135 q^{70} +14.4442 q^{71} -10.4020 q^{72} +13.0499 q^{73} -11.9757 q^{74} +17.0725 q^{75} -0.529007 q^{76} +9.36380 q^{77} +21.5688 q^{78} -12.4006 q^{79} -16.2242 q^{80} -1.31829 q^{81} -7.02258 q^{82} +11.2887 q^{83} -8.78981 q^{84} -8.60474 q^{85} -12.6528 q^{86} +4.01146 q^{87} +4.07155 q^{88} +12.6210 q^{89} +25.1552 q^{90} -24.7855 q^{91} +2.99026 q^{92} -15.0698 q^{93} +7.97151 q^{94} -2.86178 q^{95} -9.35248 q^{96} +18.2145 q^{97} +31.4706 q^{98} -8.46885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * 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 $

$2$	1.61798	1.14408	0.572042	−	0.820224i	$-0.306151\pi$
$2$	1.61798	1.14408	0.572042	+	0.820224i	$0.306151\pi$
$3$	2.76613	1.59702	0.798512	−	0.601979i	$-0.205621\pi$
$3$	2.76613	1.59702	0.798512	+	0.601979i	$0.205621\pi$
$4$	0.617860	0.308930
$5$	3.34245	1.49479	0.747395	−	0.664380i	$-0.231304\pi$
$5$	3.34245	1.49479	0.747395	+	0.664380i	$0.231304\pi$
$6$	4.47554	1.82713
$7$	−5.14301	−1.94387	−0.971937	−	0.235239i	$-0.924413\pi$
$7$	−5.14301	−1.94387	−0.971937	+	0.235239i	$0.924413\pi$
$8$	−2.23628	−0.790643
$9$	4.65146	1.55049
$10$	5.40802	1.71017
$11$	−1.82068	−0.548957	−0.274479	−	0.961593i	$-0.588505\pi$
$11$	−1.82068	−0.548957	−0.274479	+	0.961593i	$0.588505\pi$
$12$	1.70908	0.493369
$13$	4.81926	1.33662	0.668312	−	0.743881i	$-0.267017\pi$
$13$	4.81926	1.33662	0.668312	+	0.743881i	$0.267017\pi$
$14$	−8.32129	−2.22396
$15$	9.24565	2.38722
$16$	−4.85397	−1.21349
$17$	−2.57438	−0.624379	−0.312190	−	0.950020i	$-0.601062\pi$
$17$	−2.57438	−0.624379	−0.312190	+	0.950020i	$0.601062\pi$
$18$	7.52597	1.77389
$19$	−0.856193	−0.196424	−0.0982121	−	0.995166i	$-0.531312\pi$
$19$	−0.856193	−0.196424	−0.0982121	+	0.995166i	$0.531312\pi$
$20$	2.06517	0.461785
$21$	−14.2262	−3.10442
$22$	−2.94583	−0.628053
$23$	4.83970	1.00915	0.504574	−	0.863369i	$-0.331650\pi$
$23$	4.83970	1.00915	0.504574	+	0.863369i	$0.331650\pi$
$24$	−6.18582	−1.26268
$25$	6.17198	1.23440
$26$	7.79747	1.52921
$27$	4.56816	0.879142
$28$	−3.17766	−0.600521
$29$	1.45021	0.269297	0.134648	−	0.990893i	$-0.457010\pi$
$29$	1.45021	0.269297	0.134648	+	0.990893i	$0.457010\pi$
$30$	14.9593	2.73118
$31$	−5.44799	−0.978488	−0.489244	−	0.872147i	$-0.662727\pi$
$31$	−5.44799	−0.978488	−0.489244	+	0.872147i	$0.662727\pi$
$32$	−3.38107	−0.597695
$33$	−5.03625	−0.876698
$34$	−4.16530	−0.714343
$35$	−17.1903	−2.90568
$36$	2.87395	0.478992
$37$	−7.40163	−1.21682	−0.608411	−	0.793622i	$-0.708193\pi$
$37$	−7.40163	−1.21682	−0.608411	+	0.793622i	$0.708193\pi$
$38$	−1.38530	−0.224726
$39$	13.3307	2.13462
$40$	−7.47464	−1.18184
$41$	−4.34034	−0.677847	−0.338924	−	0.940814i	$-0.610063\pi$
$41$	−4.34034	−0.677847	−0.338924	+	0.940814i	$0.610063\pi$
$42$	−23.0177	−3.55172
$43$	−7.82010	−1.19255	−0.596277	−	0.802779i	$-0.703354\pi$
$43$	−7.82010	−1.19255	−0.596277	+	0.802779i	$0.703354\pi$
$44$	−1.12493	−0.169589
$45$	15.5473	2.31765
$46$	7.83054	1.15455
$47$	4.92683	0.718652	0.359326	−	0.933212i	$-0.383007\pi$
$47$	4.92683	0.718652	0.359326	+	0.933212i	$0.383007\pi$
$48$	−13.4267	−1.93798
$49$	19.4505	2.77865
$50$	9.98614	1.41225
$51$	−7.12107	−0.997149
$52$	2.97763	0.412923
$53$	−1.60749	−0.220806	−0.110403	−	0.993887i	$-0.535214\pi$
$53$	−1.60749	−0.220806	−0.110403	+	0.993887i	$0.535214\pi$
$54$	7.39119	1.00581
$55$	−6.08555	−0.820575
$56$	11.5012	1.53691
$57$	−2.36834	−0.313694
$58$	2.34641	0.308098
$59$	1.63046	0.212268	0.106134	−	0.994352i	$-0.466153\pi$
$59$	1.63046	0.212268	0.106134	+	0.994352i	$0.466153\pi$
$60$	5.71251	0.737482
$61$	1.91900	0.245702	0.122851	−	0.992425i	$-0.460796\pi$
$61$	1.91900	0.245702	0.122851	+	0.992425i	$0.460796\pi$
$62$	−8.81474	−1.11947
$63$	−23.9225	−3.01395
$64$	4.23743	0.529678
$65$	16.1081	1.99797
$66$	−8.14855	−1.00302
$67$	−6.11331	−0.746860	−0.373430	−	0.927658i	$-0.621818\pi$
$67$	−6.11331	−0.746860	−0.373430	+	0.927658i	$0.621818\pi$
$68$	−1.59061	−0.192889
$69$	13.3872	1.61163
$70$	−27.8135	−3.32435
$71$	14.4442	1.71421	0.857105	−	0.515143i	$-0.172261\pi$
$71$	14.4442	1.71421	0.857105	+	0.515143i	$0.172261\pi$
$72$	−10.4020	−1.22588
$73$	13.0499	1.52738	0.763690	−	0.645583i	$-0.223386\pi$
$73$	13.0499	1.52738	0.763690	+	0.645583i	$0.223386\pi$
$74$	−11.9757	−1.39215
$75$	17.0725	1.97136
$76$	−0.529007	−0.0606813
$77$	9.36380	1.06710
$78$	21.5688	2.44219
$79$	−12.4006	−1.39518	−0.697588	−	0.716499i	$-0.745743\pi$
$79$	−12.4006	−1.39518	−0.697588	+	0.716499i	$0.745743\pi$
$80$	−16.2242	−1.81392
$81$	−1.31829	−0.146476
$82$	−7.02258	−0.775514
$83$	11.2887	1.23909	0.619547	−	0.784960i	$-0.287316\pi$
$83$	11.2887	1.23909	0.619547	+	0.784960i	$0.287316\pi$
$84$	−8.78981	−0.959047
$85$	−8.60474	−0.933315
$86$	−12.6528	−1.36438
$87$	4.01146	0.430073
$88$	4.07155	0.434029
$89$	12.6210	1.33783	0.668914	−	0.743340i	$-0.266759\pi$
$89$	12.6210	1.33783	0.668914	+	0.743340i	$0.266759\pi$
$90$	25.1552	2.65159
$91$	−24.7855	−2.59823
$92$	2.99026	0.311756
$93$	−15.0698	−1.56267
$94$	7.97151	0.822198
$95$	−2.86178	−0.293613
$96$	−9.35248	−0.954534
$97$	18.2145	1.84941	0.924703	−	0.380690i	$-0.124313\pi$
$97$	18.2145	1.84941	0.924703	+	0.380690i	$0.124313\pi$
$98$	31.4706	3.17901
$99$	−8.46885	−0.851151
$100$	3.81342	0.381342
$101$	7.43675	0.739985	0.369992	−	0.929035i	$-0.379360\pi$
$101$	7.43675	0.739985	0.369992	+	0.929035i	$0.379360\pi$
$102$	−11.5217	−1.14082
$103$	−14.1402	−1.39328	−0.696638	−	0.717423i	$-0.745322\pi$
$103$	−14.1402	−1.39328	−0.696638	+	0.717423i	$0.745322\pi$
$104$	−10.7772	−1.05679
$105$	−47.5504	−4.64045
$106$	−2.60089	−0.252621
$107$	−12.3080	−1.18986	−0.594931	−	0.803777i	$-0.702821\pi$
$107$	−12.3080	−1.18986	−0.594931	+	0.803777i	$0.702821\pi$
$108$	2.82248	0.271593
$109$	−15.3717	−1.47234	−0.736170	−	0.676797i	$-0.763368\pi$
$109$	−15.3717	−1.47234	−0.736170	+	0.676797i	$0.763368\pi$
$110$	−9.84630	−0.938808
$111$	−20.4739	−1.94329
$112$	24.9640	2.35888
$113$	6.22010	0.585138	0.292569	−	0.956244i	$-0.405490\pi$
$113$	6.22010	0.585138	0.292569	+	0.956244i	$0.405490\pi$
$114$	−3.83193	−0.358893
$115$	16.1765	1.50846
$116$	0.896025	0.0831938
$117$	22.4166	2.07242
$118$	2.63806	0.242853
$119$	13.2401	1.21372
$120$	−20.6758	−1.88743
$121$	−7.68511	−0.698646
$122$	3.10490	0.281104
$123$	−12.0059	−1.08254
$124$	−3.36609	−0.302284
$125$	3.91727	0.350372
$126$	−38.7062	−3.44822
$127$	20.1860	1.79122	0.895608	−	0.444844i	$-0.146741\pi$
$127$	20.1860	1.79122	0.895608	+	0.444844i	$0.146741\pi$
$128$	13.6182	1.20369
$129$	−21.6314	−1.90454
$130$	26.0627	2.28585
$131$	11.1040	0.970162	0.485081	−	0.874469i	$-0.338790\pi$
$131$	11.1040	0.970162	0.485081	+	0.874469i	$0.338790\pi$
$132$	−3.11169	−0.270838
$133$	4.40341	0.381824
$134$	−9.89122	−0.854471
$135$	15.2688	1.31413
$136$	5.75703	0.493661
$137$	5.78829	0.494527	0.247264	−	0.968948i	$-0.420469\pi$
$137$	5.78829	0.494527	0.247264	+	0.968948i	$0.420469\pi$
$138$	21.6603	1.84384
$139$	8.50615	0.721483	0.360741	−	0.932666i	$-0.382524\pi$
$139$	8.50615	0.721483	0.360741	+	0.932666i	$0.382524\pi$
$140$	−10.6212	−0.897653
$141$	13.6282	1.14770
$142$	23.3704	1.96120
$143$	−8.77436	−0.733749
$144$	−22.5781	−1.88150
$145$	4.84724	0.402542
$146$	21.1145	1.74745
$147$	53.8027	4.43757
$148$	−4.57317	−0.375912
$149$	−11.4346	−0.936758	−0.468379	−	0.883528i	$-0.655162\pi$
$149$	−11.4346	−0.936758	−0.468379	+	0.883528i	$0.655162\pi$
$150$	27.6229	2.25540
$151$	−18.3418	−1.49264	−0.746319	−	0.665588i	$-0.768181\pi$
$151$	−18.3418	−1.49264	−0.746319	+	0.665588i	$0.768181\pi$
$152$	1.91468	0.155301
$153$	−11.9746	−0.968092
$154$	15.1504	1.22086
$155$	−18.2096	−1.46263
$156$	8.23650	0.659448
$157$	−3.75823	−0.299940	−0.149970	−	0.988691i	$-0.547918\pi$
$157$	−3.75823	−0.299940	−0.149970	+	0.988691i	$0.547918\pi$
$158$	−20.0639	−1.59620
$159$	−4.44653	−0.352633
$160$	−11.3011	−0.893428
$161$	−24.8906	−1.96166
$162$	−2.13296	−0.167581
$163$	−2.85236	−0.223414	−0.111707	−	0.993741i	$-0.535632\pi$
$163$	−2.85236	−0.223414	−0.111707	+	0.993741i	$0.535632\pi$
$164$	−2.68172	−0.209407
$165$	−16.8334	−1.31048
$166$	18.2649	1.41763
$167$	−13.6689	−1.05773	−0.528865	−	0.848706i	$-0.677382\pi$
$167$	−13.6689	−1.05773	−0.528865	+	0.848706i	$0.677382\pi$
$168$	31.8137	2.45448
$169$	10.2253	0.786561
$170$	−13.9223	−1.06779
$171$	−3.98255	−0.304553
$172$	−4.83172	−0.368415
$173$	−7.06250	−0.536952	−0.268476	−	0.963286i	$-0.586520\pi$
$173$	−7.06250	−0.536952	−0.268476	+	0.963286i	$0.586520\pi$
$174$	6.49046	0.492040
$175$	−31.7425	−2.39951
$176$	8.83755	0.666155
$177$	4.51007	0.338998
$178$	20.4206	1.53059
$179$	7.83806	0.585844	0.292922	−	0.956136i	$-0.405372\pi$
$179$	7.83806	0.585844	0.292922	+	0.956136i	$0.405372\pi$
$180$	9.60604	0.715992
$181$	11.0153	0.818763	0.409382	−	0.912363i	$-0.365745\pi$
$181$	11.0153	0.818763	0.409382	+	0.912363i	$0.365745\pi$
$182$	−40.1025	−2.97259
$183$	5.30819	0.392392
$184$	−10.8229	−0.797875
$185$	−24.7396	−1.81889
$186$	−24.3827	−1.78783
$187$	4.68714	0.342757
$188$	3.04409	0.222013
$189$	−23.4941	−1.70894
$190$	−4.63031	−0.335918
$191$	11.8267	0.855753	0.427877	−	0.903837i	$-0.359262\pi$
$191$	11.8267	0.855753	0.427877	+	0.903837i	$0.359262\pi$
$192$	11.7213	0.845909
$193$	−2.78330	−0.200346	−0.100173	−	0.994970i	$-0.531940\pi$
$193$	−2.78330	−0.200346	−0.100173	+	0.994970i	$0.531940\pi$
$194$	29.4708	2.11588
$195$	44.5572	3.19081
$196$	12.0177	0.858408
$197$	−22.4227	−1.59755	−0.798777	−	0.601627i	$-0.794519\pi$
$197$	−22.4227	−1.59755	−0.798777	+	0.601627i	$0.794519\pi$
$198$	−13.7024	−0.973789
$199$	16.8238	1.19261	0.596304	−	0.802759i	$-0.296635\pi$
$199$	16.8238	1.19261	0.596304	+	0.802759i	$0.296635\pi$
$200$	−13.8022	−0.975966
$201$	−16.9102	−1.19275
$202$	12.0325	0.846605
$203$	−7.45843	−0.523479
$204$	−4.39982	−0.308049
$205$	−14.5074	−1.01324
$206$	−22.8786	−1.59403
$207$	22.5117	1.56467
$208$	−23.3926	−1.62198
$209$	1.55886	0.107828
$210$	−76.9357	−5.30907
$211$	11.3066	0.778378	0.389189	−	0.921158i	$-0.372755\pi$
$211$	11.3066	0.778378	0.389189	+	0.921158i	$0.372755\pi$
$212$	−0.993205	−0.0682136
$213$	39.9545	2.73763
$214$	−19.9141	−1.36130
$215$	−26.1383	−1.78262
$216$	−10.2157	−0.695087
$217$	28.0191	1.90206
$218$	−24.8711	−1.68448
$219$	36.0978	2.43926
$220$	−3.76002	−0.253500
$221$	−12.4066	−0.834560
$222$	−33.1263	−2.22329
$223$	5.41314	0.362491	0.181245	−	0.983438i	$-0.441987\pi$
$223$	5.41314	0.362491	0.181245	+	0.983438i	$0.441987\pi$
$224$	17.3889	1.16184
$225$	28.7087	1.91391
$226$	10.0640	0.669447
$227$	11.7281	0.778418	0.389209	−	0.921149i	$-0.372748\pi$
$227$	11.7281	0.778418	0.389209	+	0.921149i	$0.372748\pi$
$228$	−1.46330	−0.0969095
$229$	−16.3257	−1.07884	−0.539418	−	0.842038i	$-0.681356\pi$
$229$	−16.3257	−1.07884	−0.539418	+	0.842038i	$0.681356\pi$
$230$	26.1732	1.72581
$231$	25.9015	1.70419
$232$	−3.24306	−0.212917
$233$	2.04582	0.134026	0.0670132	−	0.997752i	$-0.478653\pi$
$233$	2.04582	0.134026	0.0670132	+	0.997752i	$0.478653\pi$
$234$	36.2696	2.37102
$235$	16.4677	1.07423
$236$	1.00740	0.0655760
$237$	−34.3016	−2.22813
$238$	21.4222	1.38859
$239$	−24.1593	−1.56273	−0.781366	−	0.624073i	$-0.785477\pi$
$239$	−24.1593	−1.56273	−0.781366	+	0.624073i	$0.785477\pi$
$240$	−44.8781	−2.89687
$241$	28.8745	1.85997	0.929986	−	0.367594i	$-0.119818\pi$
$241$	28.8745	1.85997	0.929986	+	0.367594i	$0.119818\pi$
$242$	−12.4344	−0.799310
$243$	−17.3510	−1.11307
$244$	1.18567	0.0759048
$245$	65.0125	4.15350
$246$	−19.4254	−1.23852
$247$	−4.12622	−0.262545
$248$	12.1832	0.773634
$249$	31.2259	1.97886
$250$	6.33807	0.400855
$251$	−11.6916	−0.737965	−0.368982	−	0.929436i	$-0.620294\pi$
$251$	−11.6916	−0.737965	−0.368982	+	0.929436i	$0.620294\pi$
$252$	−14.7808	−0.931101
$253$	−8.81157	−0.553979
$254$	32.6605	2.04930
$255$	−23.8018	−1.49053
$256$	13.5592	0.847447
$257$	−7.78832	−0.485822	−0.242911	−	0.970049i	$-0.578102\pi$
$257$	−7.78832	−0.485822	−0.242911	+	0.970049i	$0.578102\pi$
$258$	−34.9992	−2.17895
$259$	38.0667	2.36535
$260$	9.95258	0.617233
$261$	6.74558	0.417541
$262$	17.9661	1.10995
$263$	20.3702	1.25608	0.628040	−	0.778181i	$-0.283857\pi$
$263$	20.3702	1.25608	0.628040	+	0.778181i	$0.283857\pi$
$264$	11.2624	0.693155
$265$	−5.37296	−0.330059
$266$	7.12463	0.436839
$267$	34.9114	2.13654
$268$	−3.77717	−0.230727
$269$	−6.59060	−0.401836	−0.200918	−	0.979608i	$-0.564392\pi$
$269$	−6.59060	−0.401836	−0.200918	+	0.979608i	$0.564392\pi$
$270$	24.7047	1.50348
$271$	−18.7555	−1.13931	−0.569657	−	0.821882i	$-0.692924\pi$
$271$	−18.7555	−1.13931	−0.569657	+	0.821882i	$0.692924\pi$
$272$	12.4960	0.757679
$273$	−68.5599	−4.14943
$274$	9.36534	0.565781
$275$	−11.2372	−0.677630
$276$	8.27143	0.497882
$277$	6.08066	0.365351	0.182676	−	0.983173i	$-0.441524\pi$
$277$	6.08066	0.365351	0.182676	+	0.983173i	$0.441524\pi$
$278$	13.7628	0.825437
$279$	−25.3411	−1.51713
$280$	38.4421	2.29736
$281$	6.66758	0.397755	0.198877	−	0.980024i	$-0.436270\pi$
$281$	6.66758	0.397755	0.198877	+	0.980024i	$0.436270\pi$
$282$	22.0502	1.31307
$283$	23.8875	1.41996	0.709981	−	0.704221i	$-0.248703\pi$
$283$	23.8875	1.41996	0.709981	+	0.704221i	$0.248703\pi$
$284$	8.92448	0.529570
$285$	−7.91606	−0.468907
$286$	−14.1967	−0.839471
$287$	22.3224	1.31765
$288$	−15.7269	−0.926719
$289$	−10.3726	−0.610151
$290$	7.84275	0.460542
$291$	50.3837	2.95355
$292$	8.06303	0.471853
$293$	−12.7722	−0.746162	−0.373081	−	0.927799i	$-0.621699\pi$
$293$	−12.7722	−0.746162	−0.373081	+	0.927799i	$0.621699\pi$
$294$	87.0517	5.07696
$295$	5.44975	0.317296
$296$	16.5521	0.962071
$297$	−8.31717	−0.482611
$298$	−18.5009	−1.07173
$299$	23.3238	1.34885
$300$	10.5484	0.609012
$301$	40.2188	2.31817
$302$	−29.6767	−1.70771
$303$	20.5710	1.18177
$304$	4.15594	0.238359
$305$	6.41415	0.367273
$306$	−19.3747	−1.10758
$307$	−8.37412	−0.477936	−0.238968	−	0.971027i	$-0.576809\pi$
$307$	−8.37412	−0.477936	−0.238968	+	0.971027i	$0.576809\pi$
$308$	5.78552	0.329660
$309$	−39.1136	−2.22510
$310$	−29.4628	−1.67338
$311$	−0.0651489	−0.00369426	−0.00184713	−	0.999998i	$-0.500588\pi$
$311$	−0.0651489	−0.00369426	−0.00184713	+	0.999998i	$0.500588\pi$
$312$	−29.8111	−1.68772
$313$	−8.59812	−0.485994	−0.242997	−	0.970027i	$-0.578131\pi$
$313$	−8.59812	−0.485994	−0.242997	+	0.970027i	$0.578131\pi$
$314$	−6.08075	−0.343156
$315$	−79.9598	−4.50523
$316$	−7.66183	−0.431012
$317$	7.12312	0.400074	0.200037	−	0.979788i	$-0.435894\pi$
$317$	7.12312	0.400074	0.200037	+	0.979788i	$0.435894\pi$
$318$	−7.19440	−0.403442
$319$	−2.64037	−0.147832
$320$	14.1634	0.791757
$321$	−34.0456	−1.90024
$322$	−40.2725	−2.24430
$323$	2.20417	0.122643
$324$	−0.814516	−0.0452509
$325$	29.7444	1.64992
$326$	−4.61506	−0.255605
$327$	−42.5200	−2.35136
$328$	9.70619	0.535935
$329$	−25.3387	−1.39697
$330$	−27.2361	−1.49930
$331$	−23.4158	−1.28705	−0.643525	−	0.765425i	$-0.722529\pi$
$331$	−23.4158	−1.28705	−0.643525	+	0.765425i	$0.722529\pi$
$332$	6.97482	0.382793
$333$	−34.4284	−1.88667
$334$	−22.1160	−1.21013
$335$	−20.4334	−1.11640
$336$	69.0536	3.76718
$337$	−2.19137	−0.119371	−0.0596857	−	0.998217i	$-0.519010\pi$
$337$	−2.19137	−0.119371	−0.0596857	+	0.998217i	$0.519010\pi$
$338$	16.5443	0.899893
$339$	17.2056	0.934480
$340$	−5.31653	−0.288329
$341$	9.91907	0.537148
$342$	−6.44369	−0.348435
$343$	−64.0333	−3.45747
$344$	17.4879	0.942884
$345$	44.7462	2.40905
$346$	−11.4270	−0.614318
$347$	0.721686	0.0387422	0.0193711	−	0.999812i	$-0.493834\pi$
$347$	0.721686	0.0387422	0.0193711	+	0.999812i	$0.493834\pi$
$348$	2.47852	0.132863
$349$	0.698018	0.0373641	0.0186820	−	0.999825i	$-0.494053\pi$
$349$	0.698018	0.0373641	0.0186820	+	0.999825i	$0.494053\pi$
$350$	−51.3588	−2.74524
$351$	22.0151	1.17508
$352$	6.15587	0.328109
$353$	19.8924	1.05876	0.529382	−	0.848383i	$-0.322424\pi$
$353$	19.8924	1.05876	0.529382	+	0.848383i	$0.322424\pi$
$354$	7.29721	0.387842
$355$	48.2790	2.56238
$356$	7.79804	0.413295
$357$	36.6237	1.93833
$358$	12.6818	0.670256
$359$	−30.3994	−1.60442	−0.802209	−	0.597043i	$-0.796342\pi$
$359$	−30.3994	−1.60442	−0.802209	+	0.597043i	$0.796342\pi$
$360$	−34.7680	−1.83243
$361$	−18.2669	−0.961418
$362$	17.8226	0.936734
$363$	−21.2580	−1.11575
$364$	−15.3140	−0.802670
$365$	43.6188	2.28311
$366$	8.58854	0.448930
$367$	−6.90222	−0.360293	−0.180146	−	0.983640i	$-0.557657\pi$
$367$	−6.90222	−0.360293	−0.180146	+	0.983640i	$0.557657\pi$
$368$	−23.4918	−1.22459
$369$	−20.1889	−1.05099
$370$	−40.0282	−2.08097
$371$	8.26735	0.429219
$372$	−9.31104	−0.482755
$373$	13.3045	0.688880	0.344440	−	0.938808i	$-0.388069\pi$
$373$	13.3045	0.688880	0.344440	+	0.938808i	$0.388069\pi$
$374$	7.58370	0.392144
$375$	10.8357	0.559552
$376$	−11.0177	−0.568197
$377$	6.98893	0.359948
$378$	−38.0129	−1.95517
$379$	2.15430	0.110659	0.0553294	−	0.998468i	$-0.482379\pi$
$379$	2.15430	0.110659	0.0553294	+	0.998468i	$0.482379\pi$
$380$	−1.76818	−0.0907058
$381$	55.8370	2.86062
$382$	19.1354	0.979054
$383$	10.4610	0.534530	0.267265	−	0.963623i	$-0.413880\pi$
$383$	10.4610	0.534530	0.267265	+	0.963623i	$0.413880\pi$
$384$	37.6697	1.92233
$385$	31.2980	1.59510
$386$	−4.50333	−0.229213
$387$	−36.3749	−1.84904
$388$	11.2540	0.571337
$389$	6.98896	0.354354	0.177177	−	0.984179i	$-0.443303\pi$
$389$	6.98896	0.354354	0.177177	+	0.984179i	$0.443303\pi$
$390$	72.0927	3.65055
$391$	−12.4592	−0.630091
$392$	−43.4968	−2.19692
$393$	30.7151	1.54937
$394$	−36.2795	−1.82774
$395$	−41.4484	−2.08549
$396$	−5.23256	−0.262946
$397$	2.26523	0.113689	0.0568444	−	0.998383i	$-0.481896\pi$
$397$	2.26523	0.113689	0.0568444	+	0.998383i	$0.481896\pi$
$398$	27.2206	1.36444
$399$	12.1804	0.609782
$400$	−29.9586	−1.49793
$401$	−33.6763	−1.68171	−0.840857	−	0.541258i	$-0.817948\pi$
$401$	−33.6763	−1.68171	−0.840857	+	0.541258i	$0.817948\pi$
$402$	−27.3604	−1.36461
$403$	−26.2553	−1.30787
$404$	4.59487	0.228603
$405$	−4.40630	−0.218951
$406$	−12.0676	−0.598904
$407$	13.4760	0.667983
$408$	15.9247	0.788389
$409$	9.89483	0.489268	0.244634	−	0.969616i	$-0.421332\pi$
$409$	9.89483	0.489268	0.244634	+	0.969616i	$0.421332\pi$
$410$	−23.4726	−1.15923
$411$	16.0112	0.789772
$412$	−8.73667	−0.430425
$413$	−8.38549	−0.412623
$414$	36.4235	1.79012
$415$	37.7319	1.85218
$416$	−16.2943	−0.798893
$417$	23.5291	1.15223
$418$	2.52220	0.123365
$419$	−5.21203	−0.254624	−0.127312	−	0.991863i	$-0.540635\pi$
$419$	−5.21203	−0.254624	−0.127312	+	0.991863i	$0.540635\pi$
$420$	−29.3795	−1.43357
$421$	−2.25491	−0.109898	−0.0549489	−	0.998489i	$-0.517500\pi$
$421$	−2.25491	−0.109898	−0.0549489	+	0.998489i	$0.517500\pi$
$422$	18.2938	0.890531
$423$	22.9170	1.11426
$424$	3.59480	0.174579
$425$	−15.8890	−0.770731
$426$	64.6455	3.13209
$427$	−9.86941	−0.477614
$428$	−7.60464	−0.367584
$429$	−24.2710	−1.17181
$430$	−42.2912	−2.03946
$431$	−26.0038	−1.25256	−0.626280	−	0.779598i	$-0.715423\pi$
$431$	−26.0038	−1.25256	−0.626280	+	0.779598i	$0.715423\pi$
$432$	−22.1737	−1.06683
$433$	−3.46922	−0.166720	−0.0833600	−	0.996519i	$-0.526565\pi$
$433$	−3.46922	−0.166720	−0.0833600	+	0.996519i	$0.526565\pi$
$434$	45.3343	2.17611
$435$	13.4081	0.642869
$436$	−9.49755	−0.454850
$437$	−4.14372	−0.198221
$438$	58.4055	2.79072
$439$	24.5086	1.16973	0.584866	−	0.811130i	$-0.301147\pi$
$439$	24.5086	1.16973	0.584866	+	0.811130i	$0.301147\pi$
$440$	13.6090	0.648782
$441$	90.4735	4.30826
$442$	−20.0737	−0.954807
$443$	−34.7032	−1.64880	−0.824399	−	0.566008i	$-0.808487\pi$
$443$	−34.7032	−1.64880	−0.824399	+	0.566008i	$0.808487\pi$
$444$	−12.6500	−0.600341
$445$	42.1852	1.99977
$446$	8.75835	0.414720
$447$	−31.6295	−1.49603
$448$	−21.7931	−1.02963
$449$	11.0061	0.519408	0.259704	−	0.965688i	$-0.416375\pi$
$449$	11.0061	0.519408	0.259704	+	0.965688i	$0.416375\pi$
$450$	46.4501	2.18968
$451$	7.90239	0.372109
$452$	3.84315	0.180767
$453$	−50.7359	−2.38378
$454$	18.9758	0.890576
$455$	−82.8444	−3.88380
$456$	5.29626	0.248020
$457$	6.25638	0.292661	0.146331	−	0.989236i	$-0.453254\pi$
$457$	6.25638	0.292661	0.146331	+	0.989236i	$0.453254\pi$
$458$	−26.4147	−1.23428
$459$	−11.7602	−0.548918
$460$	9.99479	0.466009
$461$	2.88977	0.134590	0.0672950	−	0.997733i	$-0.478563\pi$
$461$	2.88977	0.134590	0.0672950	+	0.997733i	$0.478563\pi$
$462$	41.9081	1.94974
$463$	−34.9130	−1.62255	−0.811273	−	0.584668i	$-0.801225\pi$
$463$	−34.9130	−1.62255	−0.811273	+	0.584668i	$0.801225\pi$
$464$	−7.03926	−0.326789
$465$	−50.3702	−2.33586
$466$	3.31010	0.153337
$467$	−14.5129	−0.671577	−0.335789	−	0.941937i	$-0.609003\pi$
$467$	−14.5129	−0.671577	−0.335789	+	0.941937i	$0.609003\pi$
$468$	13.8503	0.640232
$469$	31.4408	1.45180
$470$	26.6444	1.22901
$471$	−10.3958	−0.479011
$472$	−3.64617	−0.167828
$473$	14.2379	0.654661
$474$	−55.4994	−2.54917
$475$	−5.28440	−0.242465
$476$	8.18051	0.374953
$477$	−7.47719	−0.342357
$478$	−39.0892	−1.78790
$479$	10.8141	0.494107	0.247054	−	0.969002i	$-0.420538\pi$
$479$	10.8141	0.494107	0.247054	+	0.969002i	$0.420538\pi$
$480$	−31.2602	−1.42683
$481$	−35.6704	−1.62643
$482$	46.7184	2.12797
$483$	−68.8507	−3.13281
$484$	−4.74832	−0.215833
$485$	60.8812	2.76447
$486$	−28.0736	−1.27344
$487$	19.9723	0.905032	0.452516	−	0.891756i	$-0.350527\pi$
$487$	19.9723	0.905032	0.452516	+	0.891756i	$0.350527\pi$
$488$	−4.29140	−0.194263
$489$	−7.88999	−0.356798
$490$	105.189	4.75195
$491$	11.4609	0.517222	0.258611	−	0.965982i	$-0.416735\pi$
$491$	11.4609	0.517222	0.258611	+	0.965982i	$0.416735\pi$
$492$	−7.41798	−0.334429
$493$	−3.73339	−0.168143
$494$	−6.67614	−0.300374
$495$	−28.3067	−1.27229
$496$	26.4444	1.18739
$497$	−74.2866	−3.33221
$498$	50.5229	2.26399
$499$	−6.24711	−0.279659	−0.139830	−	0.990176i	$-0.544655\pi$
$499$	−6.24711	−0.279659	−0.139830	+	0.990176i	$0.544655\pi$
$500$	2.42033	0.108240
$501$	−37.8099	−1.68922
$502$	−18.9167	−0.844294
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	53.4973	2.38296
$505$	24.8570	1.10612
$506$	−14.2569	−0.633798
$507$	28.2845	1.25616
$508$	12.4721	0.553360
$509$	0.769215	0.0340949	0.0170474	−	0.999855i	$-0.494573\pi$
$509$	0.769215	0.0340949	0.0170474	+	0.999855i	$0.494573\pi$
$510$	−38.5109	−1.70529
$511$	−67.1160	−2.96904
$512$	−5.29799	−0.234140
$513$	−3.91122	−0.172685
$514$	−12.6013	−0.555821
$515$	−47.2630	−2.08265
$516$	−13.3652	−0.588369
$517$	−8.97020	−0.394509
$518$	61.5911	2.70616
$519$	−19.5358	−0.857525
$520$	−36.0223	−1.57968
$521$	30.8026	1.34949	0.674744	−	0.738052i	$-0.264254\pi$
$521$	30.8026	1.34949	0.674744	+	0.738052i	$0.264254\pi$
$522$	10.9142	0.477702
$523$	15.2562	0.667105	0.333553	−	0.942731i	$-0.391753\pi$
$523$	15.2562	0.667105	0.333553	+	0.942731i	$0.391753\pi$
$524$	6.86072	0.299712
$525$	−87.8039	−3.83208
$526$	32.9586	1.43706
$527$	14.0252	0.610947
$528$	24.4458	1.06387
$529$	0.422703	0.0183784
$530$	−8.69335	−0.377615
$531$	7.58404	0.329119
$532$	2.72069	0.117957
$533$	−20.9172	−0.906026
$534$	56.4860	2.44439
$535$	−41.1390	−1.77859
$536$	13.6711	0.590500
$537$	21.6811	0.935608
$538$	−10.6635	−0.459734
$539$	−35.4133	−1.52536
$540$	9.43400	0.405975
$541$	−12.2909	−0.528425	−0.264213	−	0.964464i	$-0.585112\pi$
$541$	−12.2909	−0.528425	−0.264213	+	0.964464i	$0.585112\pi$
$542$	−30.3460	−1.30347
$543$	30.4698	1.30758
$544$	8.70418	0.373188
$545$	−51.3791	−2.20084
$546$	−110.929	−4.74730
$547$	27.5682	1.17873	0.589366	−	0.807866i	$-0.299378\pi$
$547$	27.5682	1.17873	0.589366	+	0.807866i	$0.299378\pi$
$548$	3.57635	0.152774
$549$	8.92613	0.380958
$550$	−18.1816	−0.775266
$551$	−1.24166	−0.0528964
$552$	−29.9375	−1.27423
$553$	63.7764	2.71205
$554$	9.83838	0.417993
$555$	−68.4329	−2.90481
$556$	5.25561	0.222888
$557$	−36.1420	−1.53139	−0.765693	−	0.643207i	$-0.777604\pi$
$557$	−36.1420	−1.53139	−0.765693	+	0.643207i	$0.777604\pi$
$558$	−41.0014	−1.73573
$559$	−37.6871	−1.59399
$560$	83.4410	3.52602
$561$	12.9652	0.547392
$562$	10.7880	0.455065
$563$	14.3662	0.605463	0.302731	−	0.953076i	$-0.402101\pi$
$563$	14.3662	0.605463	0.302731	+	0.953076i	$0.402101\pi$
$564$	8.42034	0.354560
$565$	20.7904	0.874658
$566$	38.6494	1.62456
$567$	6.77995	0.284731
$568$	−32.3012	−1.35533
$569$	−13.7567	−0.576711	−0.288356	−	0.957523i	$-0.593109\pi$
$569$	−13.7567	−0.576711	−0.288356	+	0.957523i	$0.593109\pi$
$570$	−12.8080	−0.536469
$571$	28.4069	1.18879	0.594396	−	0.804172i	$-0.297391\pi$
$571$	28.4069	1.18879	0.594396	+	0.804172i	$0.297391\pi$
$572$	−5.42132	−0.226677
$573$	32.7143	1.36666
$574$	36.1172	1.50750
$575$	29.8705	1.24569
$576$	19.7102	0.821259
$577$	−6.39829	−0.266364	−0.133182	−	0.991092i	$-0.542520\pi$
$577$	−6.39829	−0.266364	−0.133182	+	0.991092i	$0.542520\pi$
$578$	−16.7826	−0.698064
$579$	−7.69897	−0.319958
$580$	2.99492	0.124357
$581$	−58.0578	−2.40864
$582$	81.5199	3.37911
$583$	2.92674	0.121213
$584$	−29.1833	−1.20761
$585$	74.9264	3.09783
$586$	−20.6652	−0.853672
$587$	2.90698	0.119984	0.0599920	−	0.998199i	$-0.480892\pi$
$587$	2.90698	0.119984	0.0599920	+	0.998199i	$0.480892\pi$
$588$	33.2425	1.37090
$589$	4.66453	0.192199
$590$	8.81758	0.363014
$591$	−62.0241	−2.55133
$592$	35.9273	1.47660
$593$	−46.5357	−1.91099	−0.955496	−	0.295003i	$-0.904679\pi$
$593$	−46.5357	−1.91099	−0.955496	+	0.295003i	$0.904679\pi$
$594$	−13.4570	−0.552148
$595$	44.2543	1.81425
$596$	−7.06498	−0.289393
$597$	46.5368	1.90462
$598$	37.7374	1.54320
$599$	−12.6605	−0.517292	−0.258646	−	0.965972i	$-0.583276\pi$
$599$	−12.6605	−0.517292	−0.258646	+	0.965972i	$0.583276\pi$
$600$	−38.1788	−1.55864
$601$	23.6897	0.966324	0.483162	−	0.875531i	$-0.339488\pi$
$601$	23.6897	0.966324	0.483162	+	0.875531i	$0.339488\pi$
$602$	65.0733	2.65219
$603$	−28.4358	−1.15800
$604$	−11.3327	−0.461121
$605$	−25.6871	−1.04433
$606$	33.2835	1.35205
$607$	17.8561	0.724755	0.362378	−	0.932031i	$-0.381965\pi$
$607$	17.8561	0.724755	0.362378	+	0.932031i	$0.381965\pi$
$608$	2.89485	0.117402
$609$	−20.6310	−0.836009
$610$	10.3780	0.420191
$611$	23.7437	0.960566
$612$	−7.39865	−0.299073
$613$	−44.0201	−1.77795	−0.888977	−	0.457952i	$-0.848583\pi$
$613$	−44.0201	−1.77795	−0.888977	+	0.457952i	$0.848583\pi$
$614$	−13.5492	−0.546799
$615$	−40.1292	−1.61817
$616$	−20.9400	−0.843698
$617$	29.8501	1.20172	0.600861	−	0.799354i	$-0.294825\pi$
$617$	29.8501	1.20172	0.600861	+	0.799354i	$0.294825\pi$
$618$	−63.2851	−2.54570
$619$	5.22204	0.209892	0.104946	−	0.994478i	$-0.466533\pi$
$619$	5.22204	0.209892	0.104946	+	0.994478i	$0.466533\pi$
$620$	−11.2510	−0.451851
$621$	22.1085	0.887184
$622$	−0.105410	−0.00422654
$623$	−64.9102	−2.60057
$624$	−64.7068	−2.59034
$625$	−17.7666	−0.710664
$626$	−13.9116	−0.556019
$627$	4.31200	0.172205
$628$	−2.32206	−0.0926603
$629$	19.0546	0.759758
$630$	−129.373	−5.15436
$631$	9.43945	0.375778	0.187889	−	0.982190i	$-0.439835\pi$
$631$	9.43945	0.375778	0.187889	+	0.982190i	$0.439835\pi$
$632$	27.7312	1.10309
$633$	31.2755	1.24309
$634$	11.5251	0.457719
$635$	67.4706	2.67749
$636$	−2.74733	−0.108939
$637$	93.7373	3.71401
$638$	−4.27207	−0.169133
$639$	67.1866	2.65786
$640$	45.5182	1.79927
$641$	−6.76513	−0.267206	−0.133603	−	0.991035i	$-0.542655\pi$
$641$	−6.76513	−0.267206	−0.133603	+	0.991035i	$0.542655\pi$
$642$	−55.0851	−2.17403
$643$	−44.0518	−1.73723	−0.868616	−	0.495486i	$-0.834990\pi$
$643$	−44.0518	−1.73723	−0.868616	+	0.495486i	$0.834990\pi$
$644$	−15.3789	−0.606014
$645$	−72.3018	−2.84688
$646$	3.56630	0.140314
$647$	17.7181	0.696570	0.348285	−	0.937389i	$-0.386764\pi$
$647$	17.7181	0.696570	0.348285	+	0.937389i	$0.386764\pi$
$648$	2.94805	0.115810
$649$	−2.96856	−0.116526
$650$	48.1258	1.88765
$651$	77.5043	3.03763
$652$	−1.76236	−0.0690193
$653$	−18.6561	−0.730068	−0.365034	−	0.930994i	$-0.618943\pi$
$653$	−18.6561	−0.730068	−0.365034	+	0.930994i	$0.618943\pi$
$654$	−68.7966	−2.69016
$655$	37.1146	1.45019
$656$	21.0679	0.822562
$657$	60.7013	2.36818
$658$	−40.9976	−1.59825
$659$	−1.43590	−0.0559347	−0.0279674	−	0.999609i	$-0.508903\pi$
$659$	−1.43590	−0.0559347	−0.0279674	+	0.999609i	$0.508903\pi$
$660$	−10.4007	−0.404846
$661$	−25.4440	−0.989656	−0.494828	−	0.868991i	$-0.664769\pi$
$661$	−25.4440	−0.989656	−0.494828	+	0.868991i	$0.664769\pi$
$662$	−37.8863	−1.47249
$663$	−34.3183	−1.33281
$664$	−25.2446	−0.979681
$665$	14.7182	0.570747
$666$	−55.7045	−2.15851
$667$	7.01857	0.271760
$668$	−8.44546	−0.326765
$669$	14.9734	0.578906
$670$	−33.0609	−1.27725
$671$	−3.49389	−0.134880
$672$	48.0999	1.85549
$673$	10.5172	0.405410	0.202705	−	0.979240i	$-0.435027\pi$
$673$	10.5172	0.405410	0.202705	+	0.979240i	$0.435027\pi$
$674$	−3.54559	−0.136571
$675$	28.1945	1.08521
$676$	6.31780	0.242992
$677$	−16.7755	−0.644736	−0.322368	−	0.946614i	$-0.604479\pi$
$677$	−16.7755	−0.644736	−0.322368	+	0.946614i	$0.604479\pi$
$678$	27.8383	1.06912
$679$	−93.6775	−3.59501
$680$	19.2426	0.737919
$681$	32.4413	1.24315
$682$	16.0489	0.614542
$683$	0.210478	0.00805370	0.00402685	−	0.999992i	$-0.498718\pi$
$683$	0.210478	0.00805370	0.00402685	+	0.999992i	$0.498718\pi$
$684$	−2.46066	−0.0940856
$685$	19.3471	0.739214
$686$	−103.605	−3.95564
$687$	−45.1591	−1.72293
$688$	37.9585	1.44715
$689$	−7.74693	−0.295134
$690$	72.3984	2.75616
$691$	5.89948	0.224427	0.112213	−	0.993684i	$-0.464206\pi$
$691$	5.89948	0.224427	0.112213	+	0.993684i	$0.464206\pi$
$692$	−4.36363	−0.165880
$693$	43.5554	1.65453
$694$	1.16767	0.0443243
$695$	28.4314	1.07846
$696$	−8.97072	−0.340034
$697$	11.1737	0.423234
$698$	1.12938	0.0427476
$699$	5.65901	0.214043
$700$	−19.6124	−0.741280
$701$	13.3721	0.505055	0.252528	−	0.967590i	$-0.418738\pi$
$701$	13.3721	0.505055	0.252528	+	0.967590i	$0.418738\pi$
$702$	35.6201	1.34439
$703$	6.33723	0.239013
$704$	−7.71502	−0.290771
$705$	45.5517	1.71558
$706$	32.1855	1.21132
$707$	−38.2473	−1.43844
$708$	2.78659	0.104727
$709$	−16.6820	−0.626507	−0.313254	−	0.949669i	$-0.601419\pi$
$709$	−16.6820	−0.626507	−0.313254	+	0.949669i	$0.601419\pi$
$710$	78.1144	2.93158
$711$	−57.6809	−2.16320
$712$	−28.2241	−1.05774
$713$	−26.3666	−0.987438
$714$	59.2565	2.21762
$715$	−29.3279	−1.09680
$716$	4.84282	0.180985
$717$	−66.8276	−2.49572
$718$	−49.1856	−1.83559
$719$	0.987720	0.0368357	0.0184179	−	0.999830i	$-0.494137\pi$
$719$	0.987720	0.0368357	0.0184179	+	0.999830i	$0.494137\pi$
$720$	−75.4660	−2.81245
$721$	72.7233	2.70836
$722$	−29.5555	−1.09994
$723$	79.8707	2.97042
$724$	6.80593	0.252940
$725$	8.95064	0.332419
$726$	−34.3950	−1.27652
$727$	−4.38063	−0.162469	−0.0812344	−	0.996695i	$-0.525886\pi$
$727$	−4.38063	−0.162469	−0.0812344	+	0.996695i	$0.525886\pi$
$728$	55.4272	2.05427
$729$	−44.0403	−1.63112
$730$	70.5743	2.61207
$731$	20.1319	0.744606
$732$	3.27971	0.121222
$733$	−6.13844	−0.226728	−0.113364	−	0.993553i	$-0.536163\pi$
$733$	−6.13844	−0.226728	−0.113364	+	0.993553i	$0.536163\pi$
$734$	−11.1677	−0.412206
$735$	179.833	6.63324
$736$	−16.3634	−0.603163
$737$	11.1304	0.409994
$738$	−32.6653	−1.20243
$739$	41.2291	1.51664	0.758319	−	0.651884i	$-0.226021\pi$
$739$	41.2291	1.51664	0.758319	+	0.651884i	$0.226021\pi$
$740$	−15.2856	−0.561910
$741$	−11.4137	−0.419291
$742$	13.3764	0.491063
$743$	20.7978	0.762999	0.381499	−	0.924369i	$-0.375408\pi$
$743$	20.7978	0.762999	0.381499	+	0.924369i	$0.375408\pi$
$744$	33.7003	1.23551
$745$	−38.2196	−1.40026
$746$	21.5264	0.788138
$747$	52.5089	1.92120
$748$	2.89599	0.105888
$749$	63.3003	2.31294
$750$	17.5319	0.640175
$751$	8.11865	0.296254	0.148127	−	0.988968i	$-0.452676\pi$
$751$	8.11865	0.296254	0.148127	+	0.988968i	$0.452676\pi$
$752$	−23.9147	−0.872078
$753$	−32.3403	−1.17855
$754$	11.3079	0.411811
$755$	−61.3067	−2.23118
$756$	−14.5160	−0.527943
$757$	41.1146	1.49434	0.747168	−	0.664635i	$-0.231413\pi$
$757$	41.1146	1.49434	0.747168	+	0.664635i	$0.231413\pi$
$758$	3.48561	0.126603
$759$	−24.3739	−0.884717
$760$	6.39974	0.232143
$761$	−17.6088	−0.638320	−0.319160	−	0.947701i	$-0.603401\pi$
$761$	−17.6088	−0.638320	−0.319160	+	0.947701i	$0.603401\pi$
$762$	90.3432	3.27279
$763$	79.0567	2.86205
$764$	7.30727	0.264368
$765$	−40.0246	−1.44709
$766$	16.9256	0.611548
$767$	7.85764	0.283723
$768$	37.5064	1.35339
$769$	5.09307	0.183661	0.0918304	−	0.995775i	$-0.470728\pi$
$769$	5.09307	0.183661	0.0918304	+	0.995775i	$0.470728\pi$
$770$	50.6396	1.82492
$771$	−21.5435	−0.775869
$772$	−1.71969	−0.0618930
$773$	42.2694	1.52032	0.760162	−	0.649734i	$-0.225120\pi$
$773$	42.2694	1.52032	0.760162	+	0.649734i	$0.225120\pi$
$774$	−58.8538	−2.11546
$775$	−33.6249	−1.20784
$776$	−40.7327	−1.46222
$777$	105.297	3.77752
$778$	11.3080	0.405411
$779$	3.71617	0.133146
$780$	27.5301	0.985736
$781$	−26.2983	−0.941027
$782$	−20.1588	−0.720877
$783$	6.62477	0.236750
$784$	−94.4124	−3.37187
$785$	−12.5617	−0.448347
$786$	49.6964	1.77261
$787$	−15.7173	−0.560260	−0.280130	−	0.959962i	$-0.590378\pi$
$787$	−15.7173	−0.560260	−0.280130	+	0.959962i	$0.590378\pi$
$788$	−13.8541	−0.493532
$789$	56.3466	2.00599
$790$	−67.0627	−2.38598
$791$	−31.9900	−1.13743
$792$	18.9387	0.672956
$793$	9.24814	0.328411
$794$	3.66510	0.130070
$795$	−14.8623	−0.527112
$796$	10.3947	0.368432
$797$	−0.501196	−0.0177533	−0.00887664	−	0.999961i	$-0.502826\pi$
$797$	−0.501196	−0.0177533	−0.00887664	+	0.999961i	$0.502826\pi$
$798$	19.7076	0.697643
$799$	−12.6835	−0.448711
$800$	−20.8679	−0.737792
$801$	58.7063	2.07429
$802$	−54.4876	−1.92402
$803$	−23.7598	−0.838466
$804$	−10.4481	−0.368477
$805$	−83.1957	−2.93226
$806$	−42.4805	−1.49631
$807$	−18.2304	−0.641742
$808$	−16.6306	−0.585063
$809$	11.8211	0.415607	0.207803	−	0.978171i	$-0.433369\pi$
$809$	11.8211	0.415607	0.207803	+	0.978171i	$0.433369\pi$
$810$	−7.12931	−0.250498
$811$	−21.5435	−0.756496	−0.378248	−	0.925704i	$-0.623473\pi$
$811$	−21.5435	−0.756496	−0.378248	+	0.925704i	$0.623473\pi$
$812$	−4.60826	−0.161718
$813$	−51.8800	−1.81951
$814$	21.8040	0.764229
$815$	−9.53387	−0.333957
$816$	34.5654	1.21003
$817$	6.69551	0.234246
$818$	16.0096	0.559764
$819$	−115.289	−4.02852
$820$	−8.96352	−0.313020
$821$	26.2671	0.916727	0.458364	−	0.888765i	$-0.348436\pi$
$821$	26.2671	0.916727	0.458364	+	0.888765i	$0.348436\pi$
$822$	25.9057	0.903566
$823$	7.38730	0.257505	0.128753	−	0.991677i	$-0.458903\pi$
$823$	7.38730	0.257505	0.128753	+	0.991677i	$0.458903\pi$
$824$	31.6214	1.10158
$825$	−31.0836	−1.08219
$826$	−13.5676	−0.472076
$827$	−10.3952	−0.361478	−0.180739	−	0.983531i	$-0.557849\pi$
$827$	−10.3952	−0.361478	−0.180739	+	0.983531i	$0.557849\pi$
$828$	13.9091	0.483373
$829$	−37.1713	−1.29101	−0.645507	−	0.763755i	$-0.723354\pi$
$829$	−37.1713	−1.29101	−0.645507	+	0.763755i	$0.723354\pi$
$830$	61.0494	2.11906
$831$	16.8199	0.583475
$832$	20.4213	0.707980
$833$	−50.0731	−1.73493
$834$	38.0696	1.31824
$835$	−45.6876	−1.58108
$836$	0.963156	0.0333114
$837$	−24.8873	−0.860229
$838$	−8.43296	−0.291312
$839$	45.0220	1.55433	0.777166	−	0.629296i	$-0.216657\pi$
$839$	45.0220	1.55433	0.777166	+	0.629296i	$0.216657\pi$
$840$	106.336	3.66894
$841$	−26.8969	−0.927479
$842$	−3.64841	−0.125732
$843$	18.4434	0.635224
$844$	6.98589	0.240464
$845$	34.1776	1.17574
$846$	37.0792	1.27481
$847$	39.5246	1.35808
$848$	7.80272	0.267946
$849$	66.0758	2.26771
$850$	−25.7081	−0.881781
$851$	−35.8217	−1.22795
$852$	24.6863	0.845737
$853$	19.1536	0.655807	0.327904	−	0.944711i	$-0.393658\pi$
$853$	19.1536	0.655807	0.327904	+	0.944711i	$0.393658\pi$
$854$	−15.9685	−0.546431
$855$	−13.3115	−0.455243
$856$	27.5241	0.940756
$857$	16.0317	0.547634	0.273817	−	0.961782i	$-0.411714\pi$
$857$	16.0317	0.547634	0.273817	+	0.961782i	$0.411714\pi$
$858$	−39.2700	−1.34066
$859$	33.6636	1.14859	0.574294	−	0.818649i	$-0.305277\pi$
$859$	33.6636	1.14859	0.574294	+	0.818649i	$0.305277\pi$
$860$	−16.1498	−0.550704
$861$	61.7466	2.10432
$862$	−42.0737	−1.43304
$863$	1.72041	0.0585634	0.0292817	−	0.999571i	$-0.490678\pi$
$863$	1.72041	0.0585634	0.0292817	+	0.999571i	$0.490678\pi$
$864$	−15.4453	−0.525459
$865$	−23.6060	−0.802630
$866$	−5.61313	−0.190742
$867$	−28.6918	−0.974425
$868$	17.3118	0.587602
$869$	22.5776	0.765892
$870$	21.6940	0.735497
$871$	−29.4617	−0.998270
$872$	34.3753	1.16410
$873$	84.7242	2.86748
$874$	−6.70446	−0.226782
$875$	−20.1466	−0.681078
$876$	22.3034	0.753561
$877$	49.4104	1.66847	0.834236	−	0.551408i	$-0.185909\pi$
$877$	49.4104	1.66847	0.834236	+	0.551408i	$0.185909\pi$
$878$	39.6545	1.33827
$879$	−35.3296	−1.19164
$880$	29.5391	0.995762
$881$	7.34287	0.247388	0.123694	−	0.992320i	$-0.460526\pi$
$881$	7.34287	0.247388	0.123694	+	0.992320i	$0.460526\pi$
$882$	146.384	4.92902
$883$	36.8658	1.24063	0.620316	−	0.784352i	$-0.287004\pi$
$883$	36.8658	1.24063	0.620316	+	0.784352i	$0.287004\pi$
$884$	−7.66555	−0.257820
$885$	15.0747	0.506730
$886$	−56.1491	−1.88637
$887$	−58.3877	−1.96047	−0.980233	−	0.197847i	$-0.936605\pi$
$887$	−58.3877	−1.96047	−0.980233	+	0.197847i	$0.936605\pi$
$888$	45.7852	1.53645
$889$	−103.817	−3.48190
$890$	68.2549	2.28791
$891$	2.40018	0.0804091
$892$	3.34456	0.111984
$893$	−4.21832	−0.141161
$894$	−51.1760	−1.71158
$895$	26.1983	0.875714
$896$	−70.0386	−2.33983
$897$	64.5166	2.15415
$898$	17.8076	0.594247
$899$	−7.90071	−0.263503
$900$	17.7380	0.591265
$901$	4.13830	0.137867
$902$	12.7859	0.425724
$903$	111.250	3.70218
$904$	−13.9099	−0.462635
$905$	36.8182	1.22388
$906$	−82.0897	−2.72725
$907$	42.9745	1.42694	0.713472	−	0.700684i	$-0.247122\pi$
$907$	42.9745	1.42694	0.713472	+	0.700684i	$0.247122\pi$
$908$	7.24629	0.240477
$909$	34.5918	1.14734
$910$	−134.041	−4.44340
$911$	−38.0688	−1.26128	−0.630638	−	0.776077i	$-0.717207\pi$
$911$	−38.0688	−1.26128	−0.630638	+	0.776077i	$0.717207\pi$
$912$	11.4958	0.380666
$913$	−20.5531	−0.680209
$914$	10.1227	0.334829
$915$	17.7423	0.586544
$916$	−10.0870	−0.333285
$917$	−57.1080	−1.88587
$918$	−19.0277	−0.628009
$919$	40.0439	1.32093	0.660463	−	0.750858i	$-0.270360\pi$
$919$	40.0439	1.32093	0.660463	+	0.750858i	$0.270360\pi$
$920$	−36.1750	−1.19266
$921$	−23.1639	−0.763276
$922$	4.67559	0.153982
$923$	69.6103	2.29125
$924$	16.0035	0.526476
$925$	−45.6827	−1.50204
$926$	−56.4886	−1.85633
$927$	−65.7727	−2.16026
$928$	−4.90326	−0.160957
$929$	−4.17987	−0.137137	−0.0685686	−	0.997646i	$-0.521843\pi$
$929$	−4.17987	−0.137137	−0.0685686	+	0.997646i	$0.521843\pi$
$930$	−81.4979	−2.67242
$931$	−16.6534	−0.545794
$932$	1.26403	0.0414047
$933$	−0.180210	−0.00589982
$934$	−23.4816	−0.768341
$935$	15.6665	0.512350
$936$	−50.1297	−1.63854
$937$	−3.29637	−0.107688	−0.0538438	−	0.998549i	$-0.517147\pi$
$937$	−3.29637	−0.107688	−0.0538438	+	0.998549i	$0.517147\pi$
$938$	50.8706	1.66099
$939$	−23.7835	−0.776145
$940$	10.1747	0.331863
$941$	−11.5152	−0.375385	−0.187692	−	0.982228i	$-0.560101\pi$
$941$	−11.5152	−0.375385	−0.187692	+	0.982228i	$0.560101\pi$
$942$	−16.8201	−0.548029
$943$	−21.0059	−0.684048
$944$	−7.91422	−0.257586
$945$	−78.5278	−2.55451
$946$	23.0367	0.748987
$947$	−18.1580	−0.590054	−0.295027	−	0.955489i	$-0.595329\pi$
$947$	−18.1580	−0.590054	−0.295027	+	0.955489i	$0.595329\pi$
$948$	−21.1936	−0.688336
$949$	62.8911	2.04153
$950$	−8.55006	−0.277401
$951$	19.7034	0.638928
$952$	−29.6084	−0.959615
$953$	54.1262	1.75332	0.876660	−	0.481110i	$-0.159766\pi$
$953$	54.1262	1.75332	0.876660	+	0.481110i	$0.159766\pi$
$954$	−12.0979	−0.391685
$955$	39.5303	1.27917
$956$	−14.9270	−0.482775
$957$	−7.30360	−0.236092
$958$	17.4969	0.565301
$959$	−29.7692	−0.961299
$960$	39.1777	1.26446
$961$	−1.31943	−0.0425621
$962$	−57.7140	−1.86078
$963$	−57.2503	−1.84487
$964$	17.8404	0.574601
$965$	−9.30305	−0.299476
$966$	−111.399	−3.58420
$967$	33.5152	1.07777	0.538887	−	0.842378i	$-0.318845\pi$
$967$	33.5152	1.07777	0.538887	+	0.842378i	$0.318845\pi$
$968$	17.1860	0.552379
$969$	6.09701	0.195864
$970$	98.5045	3.16279
$971$	−10.1191	−0.324739	−0.162369	−	0.986730i	$-0.551914\pi$
$971$	−10.1191	−0.324739	−0.162369	+	0.986730i	$0.551914\pi$
$972$	−10.7205	−0.343860
$973$	−43.7472	−1.40247
$974$	32.3148	1.03543
$975$	82.2767	2.63496
$976$	−9.31474	−0.298158
$977$	−1.56499	−0.0500685	−0.0250343	−	0.999687i	$-0.507969\pi$
$977$	−1.56499	−0.0500685	−0.0250343	+	0.999687i	$0.507969\pi$
$978$	−12.7658	−0.408207
$979$	−22.9789	−0.734410
$980$	40.1686	1.28314
$981$	−71.5008	−2.28285
$982$	18.5435	0.591745
$983$	−24.3960	−0.778112	−0.389056	−	0.921214i	$-0.627199\pi$
$983$	−24.3960	−0.778112	−0.389056	+	0.921214i	$0.627199\pi$
$984$	26.8486	0.855901
$985$	−74.9469	−2.38801
$986$	−6.04054	−0.192370
$987$	−70.0901	−2.23099
$988$	−2.54943	−0.0811080
$989$	−37.8469	−1.20346
$990$	−45.7997	−1.45561
$991$	−10.8667	−0.345193	−0.172597	−	0.984993i	$-0.555216\pi$
$991$	−10.8667	−0.345193	−0.172597	+	0.984993i	$0.555216\pi$
$992$	18.4201	0.584837
$993$	−64.7712	−2.05545
$994$	−120.194	−3.81233
$995$	56.2327	1.78270
$996$	19.2933	0.611330
$997$	15.7618	0.499182	0.249591	−	0.968351i	$-0.419704\pi$
$997$	15.7618	0.499182	0.249591	+	0.968351i	$0.419704\pi$
$998$	−10.1077	−0.319954
$999$	−33.8118	−1.06976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.18	✓	26
3.2	odd	2		4527.2.a.o.1.9		26
4.3	odd	2		8048.2.a.u.1.5		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.18	✓	26	1.1	even	1	trivial
4527.2.a.o.1.9		26	3.2	odd	2
8048.2.a.u.1.5		26	4.3	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61798 q^{2} +2.76613 q^{3} +0.617860 q^{4} +3.34245 q^{5} +4.47554 q^{6} -5.14301 q^{7} -2.23628 q^{8} +4.65146 q^{9} +O(q^{10})\)	\(q+1.61798 q^{2} +2.76613 q^{3} +0.617860 q^{4} +3.34245 q^{5} +4.47554 q^{6} -5.14301 q^{7} -2.23628 q^{8} +4.65146 q^{9} +5.40802 q^{10} -1.82068 q^{11} +1.70908 q^{12} +4.81926 q^{13} -8.32129 q^{14} +9.24565 q^{15} -4.85397 q^{16} -2.57438 q^{17} +7.52597 q^{18} -0.856193 q^{19} +2.06517 q^{20} -14.2262 q^{21} -2.94583 q^{22} +4.83970 q^{23} -6.18582 q^{24} +6.17198 q^{25} +7.79747 q^{26} +4.56816 q^{27} -3.17766 q^{28} +1.45021 q^{29} +14.9593 q^{30} -5.44799 q^{31} -3.38107 q^{32} -5.03625 q^{33} -4.16530 q^{34} -17.1903 q^{35} +2.87395 q^{36} -7.40163 q^{37} -1.38530 q^{38} +13.3307 q^{39} -7.47464 q^{40} -4.34034 q^{41} -23.0177 q^{42} -7.82010 q^{43} -1.12493 q^{44} +15.5473 q^{45} +7.83054 q^{46} +4.92683 q^{47} -13.4267 q^{48} +19.4505 q^{49} +9.98614 q^{50} -7.12107 q^{51} +2.97763 q^{52} -1.60749 q^{53} +7.39119 q^{54} -6.08555 q^{55} +11.5012 q^{56} -2.36834 q^{57} +2.34641 q^{58} +1.63046 q^{59} +5.71251 q^{60} +1.91900 q^{61} -8.81474 q^{62} -23.9225 q^{63} +4.23743 q^{64} +16.1081 q^{65} -8.14855 q^{66} -6.11331 q^{67} -1.59061 q^{68} +13.3872 q^{69} -27.8135 q^{70} +14.4442 q^{71} -10.4020 q^{72} +13.0499 q^{73} -11.9757 q^{74} +17.0725 q^{75} -0.529007 q^{76} +9.36380 q^{77} +21.5688 q^{78} -12.4006 q^{79} -16.2242 q^{80} -1.31829 q^{81} -7.02258 q^{82} +11.2887 q^{83} -8.78981 q^{84} -8.60474 q^{85} -12.6528 q^{86} +4.01146 q^{87} +4.07155 q^{88} +12.6210 q^{89} +25.1552 q^{90} -24.7855 q^{91} +2.99026 q^{92} -15.0698 q^{93} +7.97151 q^{94} -2.86178 q^{95} -9.35248 q^{96} +18.2145 q^{97} +31.4706 q^{98} -8.46885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

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