LMFDB - Embedded newform 4029.2.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.01259 q^{2} +1.00000 q^{3} +2.05052 q^{4} -0.898800 q^{5} -2.01259 q^{6} -4.86016 q^{7} -0.101684 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.01259 q^{2} +1.00000 q^{3} +2.05052 q^{4} -0.898800 q^{5} -2.01259 q^{6} -4.86016 q^{7} -0.101684 q^{8} +1.00000 q^{9} +1.80892 q^{10} -0.654315 q^{11} +2.05052 q^{12} -4.49075 q^{13} +9.78152 q^{14} -0.898800 q^{15} -3.89640 q^{16} -1.00000 q^{17} -2.01259 q^{18} +4.80111 q^{19} -1.84301 q^{20} -4.86016 q^{21} +1.31687 q^{22} +7.89128 q^{23} -0.101684 q^{24} -4.19216 q^{25} +9.03804 q^{26} +1.00000 q^{27} -9.96588 q^{28} +2.96227 q^{29} +1.80892 q^{30} +6.47848 q^{31} +8.04523 q^{32} -0.654315 q^{33} +2.01259 q^{34} +4.36831 q^{35} +2.05052 q^{36} +9.04823 q^{37} -9.66268 q^{38} -4.49075 q^{39} +0.0913939 q^{40} -11.5827 q^{41} +9.78152 q^{42} +10.4993 q^{43} -1.34169 q^{44} -0.898800 q^{45} -15.8819 q^{46} +3.33634 q^{47} -3.89640 q^{48} +16.6212 q^{49} +8.43710 q^{50} -1.00000 q^{51} -9.20839 q^{52} -4.23511 q^{53} -2.01259 q^{54} +0.588098 q^{55} +0.494202 q^{56} +4.80111 q^{57} -5.96183 q^{58} +5.44568 q^{59} -1.84301 q^{60} -13.4929 q^{61} -13.0385 q^{62} -4.86016 q^{63} -8.39896 q^{64} +4.03628 q^{65} +1.31687 q^{66} -6.76034 q^{67} -2.05052 q^{68} +7.89128 q^{69} -8.79163 q^{70} +4.22221 q^{71} -0.101684 q^{72} +8.74108 q^{73} -18.2104 q^{74} -4.19216 q^{75} +9.84480 q^{76} +3.18008 q^{77} +9.03804 q^{78} +1.00000 q^{79} +3.50208 q^{80} +1.00000 q^{81} +23.3113 q^{82} -17.0860 q^{83} -9.96588 q^{84} +0.898800 q^{85} -21.1309 q^{86} +2.96227 q^{87} +0.0665336 q^{88} +1.07232 q^{89} +1.80892 q^{90} +21.8258 q^{91} +16.1813 q^{92} +6.47848 q^{93} -6.71468 q^{94} -4.31524 q^{95} +8.04523 q^{96} +6.15141 q^{97} -33.4516 q^{98} -0.654315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.01259	−1.42312	−0.711559	−	0.702627i	$-0.752010\pi$
$2$	−2.01259	−1.42312	−0.711559	+	0.702627i	$0.752010\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.05052	1.02526
$5$	−0.898800	−0.401956	−0.200978	−	0.979596i	$-0.564412\pi$
$5$	−0.898800	−0.401956	−0.200978	+	0.979596i	$0.564412\pi$
$6$	−2.01259	−0.821637
$7$	−4.86016	−1.83697	−0.918484	−	0.395458i	$-0.870586\pi$
$7$	−4.86016	−1.83697	−0.918484	+	0.395458i	$0.870586\pi$
$8$	−0.101684	−0.0359508
$9$	1.00000	0.333333
$10$	1.80892	0.572030
$11$	−0.654315	−0.197283	−0.0986417	−	0.995123i	$-0.531450\pi$
$11$	−0.654315	−0.197283	−0.0986417	+	0.995123i	$0.531450\pi$
$12$	2.05052	0.591935
$13$	−4.49075	−1.24551	−0.622755	−	0.782417i	$-0.713987\pi$
$13$	−4.49075	−1.24551	−0.622755	+	0.782417i	$0.713987\pi$
$14$	9.78152	2.61422
$15$	−0.898800	−0.232069
$16$	−3.89640	−0.974100
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.01259	−0.474372
$19$	4.80111	1.10145	0.550726	−	0.834686i	$-0.314351\pi$
$19$	4.80111	1.10145	0.550726	+	0.834686i	$0.314351\pi$
$20$	−1.84301	−0.412110
$21$	−4.86016	−1.06057
$22$	1.31687	0.280757
$23$	7.89128	1.64545	0.822723	−	0.568443i	$-0.192454\pi$
$23$	7.89128	1.64545	0.822723	+	0.568443i	$0.192454\pi$
$24$	−0.101684	−0.0207562
$25$	−4.19216	−0.838432
$26$	9.03804	1.77251
$27$	1.00000	0.192450
$28$	−9.96588	−1.88337
$29$	2.96227	0.550079	0.275040	−	0.961433i	$-0.411309\pi$
$29$	2.96227	0.550079	0.275040	+	0.961433i	$0.411309\pi$
$30$	1.80892	0.330262
$31$	6.47848	1.16357	0.581785	−	0.813343i	$-0.302355\pi$
$31$	6.47848	1.16357	0.581785	+	0.813343i	$0.302355\pi$
$32$	8.04523	1.42221
$33$	−0.654315	−0.113902
$34$	2.01259	0.345157
$35$	4.36831	0.738379
$36$	2.05052	0.341754
$37$	9.04823	1.48752	0.743760	−	0.668447i	$-0.233041\pi$
$37$	9.04823	1.48752	0.743760	+	0.668447i	$0.233041\pi$
$38$	−9.66268	−1.56749
$39$	−4.49075	−0.719095
$40$	0.0913939	0.0144506
$41$	−11.5827	−1.80892	−0.904459	−	0.426560i	$-0.859725\pi$
$41$	−11.5827	−1.80892	−0.904459	+	0.426560i	$0.859725\pi$
$42$	9.78152	1.50932
$43$	10.4993	1.60113	0.800567	−	0.599243i	$-0.204532\pi$
$43$	10.4993	1.60113	0.800567	+	0.599243i	$0.204532\pi$
$44$	−1.34169	−0.202267
$45$	−0.898800	−0.133985
$46$	−15.8819	−2.34166
$47$	3.33634	0.486655	0.243327	−	0.969944i	$-0.421761\pi$
$47$	3.33634	0.486655	0.243327	+	0.969944i	$0.421761\pi$
$48$	−3.89640	−0.562397
$49$	16.6212	2.37445
$50$	8.43710	1.19319
$51$	−1.00000	−0.140028
$52$	−9.20839	−1.27697
$53$	−4.23511	−0.581737	−0.290868	−	0.956763i	$-0.593944\pi$
$53$	−4.23511	−0.581737	−0.290868	+	0.956763i	$0.593944\pi$
$54$	−2.01259	−0.273879
$55$	0.588098	0.0792992
$56$	0.494202	0.0660405
$57$	4.80111	0.635923
$58$	−5.96183	−0.782827
$59$	5.44568	0.708967	0.354484	−	0.935062i	$-0.384657\pi$
$59$	5.44568	0.708967	0.354484	+	0.935062i	$0.384657\pi$
$60$	−1.84301	−0.237932
$61$	−13.4929	−1.72759	−0.863796	−	0.503842i	$-0.831919\pi$
$61$	−13.4929	−1.72759	−0.863796	+	0.503842i	$0.831919\pi$
$62$	−13.0385	−1.65590
$63$	−4.86016	−0.612323
$64$	−8.39896	−1.04987
$65$	4.03628	0.500639
$66$	1.31687	0.162095
$67$	−6.76034	−0.825907	−0.412953	−	0.910752i	$-0.635503\pi$
$67$	−6.76034	−0.825907	−0.412953	+	0.910752i	$0.635503\pi$
$68$	−2.05052	−0.248663
$69$	7.89128	0.949998
$70$	−8.79163	−1.05080
$71$	4.22221	0.501084	0.250542	−	0.968106i	$-0.419391\pi$
$71$	4.22221	0.501084	0.250542	+	0.968106i	$0.419391\pi$
$72$	−0.101684	−0.0119836
$73$	8.74108	1.02307	0.511533	−	0.859263i	$-0.329078\pi$
$73$	8.74108	1.02307	0.511533	+	0.859263i	$0.329078\pi$
$74$	−18.2104	−2.11691
$75$	−4.19216	−0.484069
$76$	9.84480	1.12928
$77$	3.18008	0.362403
$78$	9.03804	1.02336
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	3.50208	0.391545
$81$	1.00000	0.111111
$82$	23.3113	2.57430
$83$	−17.0860	−1.87544	−0.937718	−	0.347398i	$-0.887065\pi$
$83$	−17.0860	−1.87544	−0.937718	+	0.347398i	$0.887065\pi$
$84$	−9.96588	−1.08737
$85$	0.898800	0.0974885
$86$	−21.1309	−2.27860
$87$	2.96227	0.317588
$88$	0.0665336	0.00709250
$89$	1.07232	0.113665	0.0568327	−	0.998384i	$-0.481900\pi$
$89$	1.07232	0.113665	0.0568327	+	0.998384i	$0.481900\pi$
$90$	1.80892	0.190677
$91$	21.8258	2.28796
$92$	16.1813	1.68701
$93$	6.47848	0.671787
$94$	−6.71468	−0.692567
$95$	−4.31524	−0.442734
$96$	8.04523	0.821113
$97$	6.15141	0.624581	0.312290	−	0.949987i	$-0.398904\pi$
$97$	6.15141	0.624581	0.312290	+	0.949987i	$0.398904\pi$
$98$	−33.4516	−3.37912
$99$	−0.654315	−0.0657611
$100$	−8.59612	−0.859612
$101$	−18.4263	−1.83349	−0.916743	−	0.399478i	$-0.869191\pi$
$101$	−18.4263	−1.83349	−0.916743	+	0.399478i	$0.869191\pi$
$102$	2.01259	0.199276
$103$	9.16906	0.903454	0.451727	−	0.892156i	$-0.350808\pi$
$103$	9.16906	0.903454	0.451727	+	0.892156i	$0.350808\pi$
$104$	0.456639	0.0447771
$105$	4.36831	0.426304
$106$	8.52354	0.827880
$107$	1.43670	0.138891	0.0694457	−	0.997586i	$-0.477877\pi$
$107$	1.43670	0.138891	0.0694457	+	0.997586i	$0.477877\pi$
$108$	2.05052	0.197312
$109$	−12.8823	−1.23390	−0.616949	−	0.787003i	$-0.711631\pi$
$109$	−12.8823	−1.23390	−0.616949	+	0.787003i	$0.711631\pi$
$110$	−1.18360	−0.112852
$111$	9.04823	0.858820
$112$	18.9371	1.78939
$113$	−13.2682	−1.24816	−0.624082	−	0.781359i	$-0.714527\pi$
$113$	−13.2682	−1.24816	−0.624082	+	0.781359i	$0.714527\pi$
$114$	−9.66268	−0.904993
$115$	−7.09268	−0.661396
$116$	6.07420	0.563975
$117$	−4.49075	−0.415170
$118$	−10.9599	−1.00894
$119$	4.86016	0.445530
$120$	0.0913939	0.00834308
$121$	−10.5719	−0.961079
$122$	27.1557	2.45857
$123$	−11.5827	−1.04438
$124$	13.2843	1.19296
$125$	8.26191	0.738968
$126$	9.78152	0.871407
$127$	17.0590	1.51374	0.756871	−	0.653565i	$-0.226727\pi$
$127$	17.0590	1.51374	0.756871	+	0.653565i	$0.226727\pi$
$128$	0.813215	0.0718787
$129$	10.4993	0.924415
$130$	−8.12339	−0.712469
$131$	−18.4781	−1.61444	−0.807220	−	0.590250i	$-0.799029\pi$
$131$	−18.4781	−1.61444	−0.807220	+	0.590250i	$0.799029\pi$
$132$	−1.34169	−0.116779
$133$	−23.3342	−2.02333
$134$	13.6058	1.17536
$135$	−0.898800	−0.0773564
$136$	0.101684	0.00871936
$137$	−12.0758	−1.03170	−0.515852	−	0.856678i	$-0.672524\pi$
$137$	−12.0758	−1.03170	−0.515852	+	0.856678i	$0.672524\pi$
$138$	−15.8819	−1.35196
$139$	−21.8033	−1.84933	−0.924667	−	0.380776i	$-0.875657\pi$
$139$	−21.8033	−1.84933	−0.924667	+	0.380776i	$0.875657\pi$
$140$	8.95733	0.757032
$141$	3.33634	0.280970
$142$	−8.49758	−0.713101
$143$	2.93836	0.245718
$144$	−3.89640	−0.324700
$145$	−2.66248	−0.221107
$146$	−17.5922	−1.45594
$147$	16.6212	1.37089
$148$	18.5536	1.52510
$149$	1.97653	0.161924	0.0809619	−	0.996717i	$-0.474201\pi$
$149$	1.97653	0.161924	0.0809619	+	0.996717i	$0.474201\pi$
$150$	8.43710	0.688887
$151$	−13.4121	−1.09146	−0.545732	−	0.837960i	$-0.683748\pi$
$151$	−13.4121	−1.09146	−0.545732	+	0.837960i	$0.683748\pi$
$152$	−0.488198	−0.0395981
$153$	−1.00000	−0.0808452
$154$	−6.40019	−0.515742
$155$	−5.82286	−0.467703
$156$	−9.20839	−0.737261
$157$	−8.16874	−0.651937	−0.325968	−	0.945381i	$-0.605690\pi$
$157$	−8.16874	−0.651937	−0.325968	+	0.945381i	$0.605690\pi$
$158$	−2.01259	−0.160113
$159$	−4.23511	−0.335866
$160$	−7.23105	−0.571665
$161$	−38.3529	−3.02263
$162$	−2.01259	−0.158124
$163$	13.4743	1.05539	0.527696	−	0.849433i	$-0.323056\pi$
$163$	13.4743	1.05539	0.527696	+	0.849433i	$0.323056\pi$
$164$	−23.7507	−1.85462
$165$	0.588098	0.0457834
$166$	34.3872	2.66896
$167$	−12.0195	−0.930098	−0.465049	−	0.885285i	$-0.653963\pi$
$167$	−12.0195	−0.930098	−0.465049	+	0.885285i	$0.653963\pi$
$168$	0.494202	0.0381285
$169$	7.16682	0.551294
$170$	−1.80892	−0.138738
$171$	4.80111	0.367150
$172$	21.5291	1.64158
$173$	7.55485	0.574385	0.287192	−	0.957873i	$-0.407278\pi$
$173$	7.55485	0.574385	0.287192	+	0.957873i	$0.407278\pi$
$174$	−5.96183	−0.451965
$175$	20.3746	1.54017
$176$	2.54947	0.192174
$177$	5.44568	0.409322
$178$	−2.15814	−0.161759
$179$	3.69003	0.275806	0.137903	−	0.990446i	$-0.455964\pi$
$179$	3.69003	0.275806	0.137903	+	0.990446i	$0.455964\pi$
$180$	−1.84301	−0.137370
$181$	7.19426	0.534746	0.267373	−	0.963593i	$-0.413845\pi$
$181$	7.19426	0.534746	0.267373	+	0.963593i	$0.413845\pi$
$182$	−43.9263	−3.25604
$183$	−13.4929	−0.997425
$184$	−0.802420	−0.0591552
$185$	−8.13255	−0.597917
$186$	−13.0385	−0.956032
$187$	0.654315	0.0478483
$188$	6.84124	0.498949
$189$	−4.86016	−0.353525
$190$	8.68482	0.630063
$191$	5.43859	0.393523	0.196761	−	0.980451i	$-0.436958\pi$
$191$	5.43859	0.393523	0.196761	+	0.980451i	$0.436958\pi$
$192$	−8.39896	−0.606143
$193$	9.56698	0.688646	0.344323	−	0.938851i	$-0.388108\pi$
$193$	9.56698	0.688646	0.344323	+	0.938851i	$0.388108\pi$
$194$	−12.3803	−0.888852
$195$	4.03628	0.289044
$196$	34.0821	2.43443
$197$	−4.69684	−0.334636	−0.167318	−	0.985903i	$-0.553511\pi$
$197$	−4.69684	−0.334636	−0.167318	+	0.985903i	$0.553511\pi$
$198$	1.31687	0.0935858
$199$	4.85558	0.344203	0.172101	−	0.985079i	$-0.444944\pi$
$199$	4.85558	0.344203	0.172101	+	0.985079i	$0.444944\pi$
$200$	0.426277	0.0301423
$201$	−6.76034	−0.476837
$202$	37.0846	2.60926
$203$	−14.3971	−1.01048
$204$	−2.05052	−0.143565
$205$	10.4106	0.727105
$206$	−18.4536	−1.28572
$207$	7.89128	0.548482
$208$	17.4977	1.21325
$209$	−3.14144	−0.217298
$210$	−8.79163	−0.606680
$211$	−24.2551	−1.66979	−0.834895	−	0.550409i	$-0.814472\pi$
$211$	−24.2551	−1.66979	−0.834895	+	0.550409i	$0.814472\pi$
$212$	−8.68419	−0.596433
$213$	4.22221	0.289301
$214$	−2.89150	−0.197659
$215$	−9.43680	−0.643585
$216$	−0.101684	−0.00691874
$217$	−31.4865	−2.13744
$218$	25.9267	1.75598
$219$	8.74108	0.590668
$220$	1.20591	0.0813024
$221$	4.49075	0.302080
$222$	−18.2104	−1.22220
$223$	3.33952	0.223631	0.111815	−	0.993729i	$-0.464333\pi$
$223$	3.33952	0.223631	0.111815	+	0.993729i	$0.464333\pi$
$224$	−39.1011	−2.61255
$225$	−4.19216	−0.279477
$226$	26.7034	1.77628
$227$	11.5158	0.764330	0.382165	−	0.924094i	$-0.375179\pi$
$227$	11.5158	0.764330	0.382165	+	0.924094i	$0.375179\pi$
$228$	9.84480	0.651988
$229$	7.66325	0.506402	0.253201	−	0.967414i	$-0.418517\pi$
$229$	7.66325	0.506402	0.253201	+	0.967414i	$0.418517\pi$
$230$	14.2747	0.941244
$231$	3.18008	0.209234
$232$	−0.301216	−0.0197758
$233$	−7.77870	−0.509600	−0.254800	−	0.966994i	$-0.582010\pi$
$233$	−7.77870	−0.509600	−0.254800	+	0.966994i	$0.582010\pi$
$234$	9.03804	0.590835
$235$	−2.99870	−0.195614
$236$	11.1665	0.726877
$237$	1.00000	0.0649570
$238$	−9.78152	−0.634042
$239$	9.52763	0.616291	0.308146	−	0.951339i	$-0.400292\pi$
$239$	9.52763	0.616291	0.308146	+	0.951339i	$0.400292\pi$
$240$	3.50208	0.226059
$241$	−2.33522	−0.150424	−0.0752122	−	0.997168i	$-0.523963\pi$
$241$	−2.33522	−0.150424	−0.0752122	+	0.997168i	$0.523963\pi$
$242$	21.2769	1.36773
$243$	1.00000	0.0641500
$244$	−27.6676	−1.77123
$245$	−14.9391	−0.954424
$246$	23.3113	1.48627
$247$	−21.5606	−1.37187
$248$	−0.658760	−0.0418313
$249$	−17.0860	−1.08278
$250$	−16.6279	−1.05164
$251$	−2.98977	−0.188713	−0.0943564	−	0.995538i	$-0.530079\pi$
$251$	−2.98977	−0.188713	−0.0943564	+	0.995538i	$0.530079\pi$
$252$	−9.96588	−0.627791
$253$	−5.16338	−0.324619
$254$	−34.3328	−2.15423
$255$	0.898800	0.0562850
$256$	15.1612	0.947578
$257$	−21.0062	−1.31033	−0.655166	−	0.755485i	$-0.727401\pi$
$257$	−21.0062	−1.31033	−0.655166	+	0.755485i	$0.727401\pi$
$258$	−21.1309	−1.31555
$259$	−43.9758	−2.73252
$260$	8.27650	0.513287
$261$	2.96227	0.183360
$262$	37.1889	2.29754
$263$	−3.65663	−0.225478	−0.112739	−	0.993625i	$-0.535962\pi$
$263$	−3.65663	−0.225478	−0.112739	+	0.993625i	$0.535962\pi$
$264$	0.0665336	0.00409486
$265$	3.80652	0.233832
$266$	46.9622	2.87944
$267$	1.07232	0.0656248
$268$	−13.8622	−0.846771
$269$	−17.6300	−1.07492	−0.537460	−	0.843289i	$-0.680616\pi$
$269$	−17.6300	−1.07492	−0.537460	+	0.843289i	$0.680616\pi$
$270$	1.80892	0.110087
$271$	14.8509	0.902130	0.451065	−	0.892491i	$-0.351044\pi$
$271$	14.8509	0.902130	0.451065	+	0.892491i	$0.351044\pi$
$272$	3.89640	0.236254
$273$	21.8258	1.32095
$274$	24.3036	1.46823
$275$	2.74299	0.165409
$276$	16.1813	0.973997
$277$	−8.18287	−0.491661	−0.245831	−	0.969313i	$-0.579061\pi$
$277$	−8.18287	−0.491661	−0.245831	+	0.969313i	$0.579061\pi$
$278$	43.8812	2.63182
$279$	6.47848	0.387857
$280$	−0.444189	−0.0265454
$281$	16.6569	0.993666	0.496833	−	0.867846i	$-0.334496\pi$
$281$	16.6569	0.993666	0.496833	+	0.867846i	$0.334496\pi$
$282$	−6.71468	−0.399854
$283$	15.7528	0.936404	0.468202	−	0.883621i	$-0.344902\pi$
$283$	15.7528	0.936404	0.468202	+	0.883621i	$0.344902\pi$
$284$	8.65774	0.513742
$285$	−4.31524	−0.255613
$286$	−5.91373	−0.349686
$287$	56.2939	3.32293
$288$	8.04523	0.474070
$289$	1.00000	0.0588235
$290$	5.35849	0.314662
$291$	6.15141	0.360602
$292$	17.9238	1.04891
$293$	24.0029	1.40227	0.701133	−	0.713030i	$-0.252678\pi$
$293$	24.0029	1.40227	0.701133	+	0.713030i	$0.252678\pi$
$294$	−33.4516	−1.95094
$295$	−4.89458	−0.284973
$296$	−0.920063	−0.0534776
$297$	−0.654315	−0.0379672
$298$	−3.97795	−0.230436
$299$	−35.4377	−2.04942
$300$	−8.59612	−0.496297
$301$	−51.0285	−2.94123
$302$	26.9931	1.55328
$303$	−18.4263	−1.05856
$304$	−18.7071	−1.07292
$305$	12.1274	0.694415
$306$	2.01259	0.115052
$307$	3.13677	0.179025	0.0895124	−	0.995986i	$-0.471469\pi$
$307$	3.13677	0.179025	0.0895124	+	0.995986i	$0.471469\pi$
$308$	6.52082	0.371558
$309$	9.16906	0.521610
$310$	11.7190	0.665597
$311$	−9.47121	−0.537063	−0.268531	−	0.963271i	$-0.586538\pi$
$311$	−9.47121	−0.537063	−0.268531	+	0.963271i	$0.586538\pi$
$312$	0.456639	0.0258521
$313$	−0.627509	−0.0354689	−0.0177345	−	0.999843i	$-0.505645\pi$
$313$	−0.627509	−0.0354689	−0.0177345	+	0.999843i	$0.505645\pi$
$314$	16.4403	0.927782
$315$	4.36831	0.246126
$316$	2.05052	0.115351
$317$	19.9758	1.12195	0.560977	−	0.827832i	$-0.310426\pi$
$317$	19.9758	1.12195	0.560977	+	0.827832i	$0.310426\pi$
$318$	8.52354	0.477977
$319$	−1.93826	−0.108521
$320$	7.54898	0.422001
$321$	1.43670	0.0801890
$322$	77.1887	4.30156
$323$	−4.80111	−0.267141
$324$	2.05052	0.113918
$325$	18.8259	1.04427
$326$	−27.1183	−1.50195
$327$	−12.8823	−0.712391
$328$	1.17778	0.0650322
$329$	−16.2151	−0.893969
$330$	−1.18360	−0.0651551
$331$	−22.0207	−1.21037	−0.605185	−	0.796085i	$-0.706901\pi$
$331$	−22.0207	−1.21037	−0.605185	+	0.796085i	$0.706901\pi$
$332$	−35.0353	−1.92281
$333$	9.04823	0.495840
$334$	24.1904	1.32364
$335$	6.07619	0.331978
$336$	18.9371	1.03310
$337$	31.4199	1.71155	0.855776	−	0.517346i	$-0.173080\pi$
$337$	31.4199	1.71155	0.855776	+	0.517346i	$0.173080\pi$
$338$	−14.4239	−0.784556
$339$	−13.2682	−0.720628
$340$	1.84301	0.0999513
$341$	−4.23897	−0.229553
$342$	−9.66268	−0.522498
$343$	−46.7604	−2.52482
$344$	−1.06762	−0.0575621
$345$	−7.09268	−0.381857
$346$	−15.2048	−0.817416
$347$	22.6481	1.21581	0.607907	−	0.794008i	$-0.292009\pi$
$347$	22.6481	1.21581	0.607907	+	0.794008i	$0.292009\pi$
$348$	6.07420	0.325611
$349$	34.4725	1.84527	0.922636	−	0.385672i	$-0.126030\pi$
$349$	34.4725	1.84527	0.922636	+	0.385672i	$0.126030\pi$
$350$	−41.0057	−2.19185
$351$	−4.49075	−0.239698
$352$	−5.26411	−0.280578
$353$	−0.926493	−0.0493123	−0.0246561	−	0.999696i	$-0.507849\pi$
$353$	−0.926493	−0.0493123	−0.0246561	+	0.999696i	$0.507849\pi$
$354$	−10.9599	−0.582514
$355$	−3.79492	−0.201413
$356$	2.19881	0.116537
$357$	4.86016	0.257227
$358$	−7.42652	−0.392504
$359$	−10.6465	−0.561900	−0.280950	−	0.959722i	$-0.590650\pi$
$359$	−10.6465	−0.561900	−0.280950	+	0.959722i	$0.590650\pi$
$360$	0.0913939	0.00481688
$361$	4.05070	0.213195
$362$	−14.4791	−0.761005
$363$	−10.5719	−0.554879
$364$	44.7542	2.34576
$365$	−7.85649	−0.411227
$366$	27.1557	1.41945
$367$	−30.2864	−1.58094	−0.790470	−	0.612501i	$-0.790164\pi$
$367$	−30.2864	−1.58094	−0.790470	+	0.612501i	$0.790164\pi$
$368$	−30.7476	−1.60283
$369$	−11.5827	−0.602973
$370$	16.3675	0.850905
$371$	20.5833	1.06863
$372$	13.2843	0.688758
$373$	37.9315	1.96402	0.982010	−	0.188828i	$-0.0604687\pi$
$373$	37.9315	1.96402	0.982010	+	0.188828i	$0.0604687\pi$
$374$	−1.31687	−0.0680937
$375$	8.26191	0.426643
$376$	−0.339253	−0.0174956
$377$	−13.3028	−0.685129
$378$	9.78152	0.503107
$379$	−14.8379	−0.762171	−0.381086	−	0.924540i	$-0.624450\pi$
$379$	−14.8379	−0.762171	−0.381086	+	0.924540i	$0.624450\pi$
$380$	−8.84851	−0.453919
$381$	17.0590	0.873959
$382$	−10.9457	−0.560029
$383$	7.92591	0.404995	0.202498	−	0.979283i	$-0.435094\pi$
$383$	7.92591	0.404995	0.202498	+	0.979283i	$0.435094\pi$
$384$	0.813215	0.0414992
$385$	−2.85825	−0.145670
$386$	−19.2544	−0.980024
$387$	10.4993	0.533711
$388$	12.6136	0.640359
$389$	2.12540	0.107762	0.0538811	−	0.998547i	$-0.482841\pi$
$389$	2.12540	0.107762	0.0538811	+	0.998547i	$0.482841\pi$
$390$	−8.12339	−0.411344
$391$	−7.89128	−0.399079
$392$	−1.69011	−0.0853635
$393$	−18.4781	−0.932098
$394$	9.45283	0.476227
$395$	−0.898800	−0.0452235
$396$	−1.34169	−0.0674224
$397$	−19.7811	−0.992784	−0.496392	−	0.868099i	$-0.665342\pi$
$397$	−19.7811	−0.992784	−0.496392	+	0.868099i	$0.665342\pi$
$398$	−9.77229	−0.489841
$399$	−23.3342	−1.16817
$400$	16.3343	0.816716
$401$	−22.9670	−1.14692	−0.573459	−	0.819234i	$-0.694399\pi$
$401$	−22.9670	−1.14692	−0.573459	+	0.819234i	$0.694399\pi$
$402$	13.6058	0.678595
$403$	−29.0932	−1.44924
$404$	−37.7836	−1.87980
$405$	−0.898800	−0.0446617
$406$	28.9755	1.43803
$407$	−5.92039	−0.293463
$408$	0.101684	0.00503413
$409$	−24.4144	−1.20721	−0.603607	−	0.797282i	$-0.706271\pi$
$409$	−24.4144	−1.20721	−0.603607	+	0.797282i	$0.706271\pi$
$410$	−20.9522	−1.03476
$411$	−12.0758	−0.595654
$412$	18.8014	0.926278
$413$	−26.4669	−1.30235
$414$	−15.8819	−0.780554
$415$	15.3569	0.753842
$416$	−36.1291	−1.77137
$417$	−21.8033	−1.06771
$418$	6.32244	0.309241
$419$	−31.8015	−1.55360	−0.776802	−	0.629745i	$-0.783159\pi$
$419$	−31.8015	−1.55360	−0.776802	+	0.629745i	$0.783159\pi$
$420$	8.95733	0.437073
$421$	−32.0241	−1.56076	−0.780378	−	0.625308i	$-0.784974\pi$
$421$	−32.0241	−1.56076	−0.780378	+	0.625308i	$0.784974\pi$
$422$	48.8156	2.37631
$423$	3.33634	0.162218
$424$	0.430644	0.0209139
$425$	4.19216	0.203350
$426$	−8.49758	−0.411709
$427$	65.5778	3.17353
$428$	2.94600	0.142400
$429$	2.93836	0.141866
$430$	18.9924	0.915896
$431$	11.0373	0.531650	0.265825	−	0.964021i	$-0.414356\pi$
$431$	11.0373	0.531650	0.265825	+	0.964021i	$0.414356\pi$
$432$	−3.89640	−0.187466
$433$	−1.26796	−0.0609343	−0.0304671	−	0.999536i	$-0.509699\pi$
$433$	−1.26796	−0.0609343	−0.0304671	+	0.999536i	$0.509699\pi$
$434$	63.3694	3.04183
$435$	−2.66248	−0.127656
$436$	−26.4154	−1.26507
$437$	37.8869	1.81238
$438$	−17.5922	−0.840589
$439$	−8.73734	−0.417011	−0.208505	−	0.978021i	$-0.566860\pi$
$439$	−8.73734	−0.417011	−0.208505	+	0.978021i	$0.566860\pi$
$440$	−0.0598004	−0.00285087
$441$	16.6212	0.791484
$442$	−9.03804	−0.429896
$443$	−17.7790	−0.844706	−0.422353	−	0.906431i	$-0.638796\pi$
$443$	−17.7790	−0.844706	−0.422353	+	0.906431i	$0.638796\pi$
$444$	18.5536	0.880515
$445$	−0.963799	−0.0456885
$446$	−6.72109	−0.318253
$447$	1.97653	0.0934867
$448$	40.8203	1.92858
$449$	−8.41890	−0.397312	−0.198656	−	0.980069i	$-0.563658\pi$
$449$	−8.41890	−0.397312	−0.198656	+	0.980069i	$0.563658\pi$
$450$	8.43710	0.397729
$451$	7.57875	0.356870
$452$	−27.2067	−1.27969
$453$	−13.4121	−0.630157
$454$	−23.1766	−1.08773
$455$	−19.6170	−0.919659
$456$	−0.488198	−0.0228620
$457$	22.7830	1.06574	0.532872	−	0.846196i	$-0.321113\pi$
$457$	22.7830	1.06574	0.532872	+	0.846196i	$0.321113\pi$
$458$	−15.4230	−0.720669
$459$	−1.00000	−0.0466760
$460$	−14.5437	−0.678104
$461$	11.8749	0.553071	0.276535	−	0.961004i	$-0.410814\pi$
$461$	11.8749	0.553071	0.276535	+	0.961004i	$0.410814\pi$
$462$	−6.40019	−0.297764
$463$	−26.3771	−1.22585	−0.612925	−	0.790141i	$-0.710007\pi$
$463$	−26.3771	−1.22585	−0.612925	+	0.790141i	$0.710007\pi$
$464$	−11.5422	−0.535832
$465$	−5.82286	−0.270029
$466$	15.6553	0.725220
$467$	−40.2694	−1.86345	−0.931723	−	0.363169i	$-0.881695\pi$
$467$	−40.2694	−1.86345	−0.931723	+	0.363169i	$0.881695\pi$
$468$	−9.20839	−0.425658
$469$	32.8563	1.51716
$470$	6.03516	0.278381
$471$	−8.16874	−0.376396
$472$	−0.553740	−0.0254880
$473$	−6.86987	−0.315877
$474$	−2.01259	−0.0924414
$475$	−20.1270	−0.923492
$476$	9.96588	0.456785
$477$	−4.23511	−0.193912
$478$	−19.1752	−0.877055
$479$	−20.2964	−0.927365	−0.463683	−	0.886001i	$-0.653472\pi$
$479$	−20.2964	−0.927365	−0.463683	+	0.886001i	$0.653472\pi$
$480$	−7.23105	−0.330051
$481$	−40.6333	−1.85272
$482$	4.69983	0.214072
$483$	−38.3529	−1.74512
$484$	−21.6779	−0.985358
$485$	−5.52889	−0.251054
$486$	−2.01259	−0.0912930
$487$	38.1339	1.72801	0.864007	−	0.503480i	$-0.167947\pi$
$487$	38.1339	1.72801	0.864007	+	0.503480i	$0.167947\pi$
$488$	1.37202	0.0621084
$489$	13.4743	0.609331
$490$	30.0663	1.35826
$491$	−4.02898	−0.181825	−0.0909127	−	0.995859i	$-0.528978\pi$
$491$	−4.02898	−0.181825	−0.0909127	+	0.995859i	$0.528978\pi$
$492$	−23.7507	−1.07076
$493$	−2.96227	−0.133414
$494$	43.3927	1.95233
$495$	0.588098	0.0264331
$496$	−25.2428	−1.13343
$497$	−20.5206	−0.920475
$498$	34.3872	1.54093
$499$	9.08340	0.406629	0.203314	−	0.979114i	$-0.434829\pi$
$499$	9.08340	0.406629	0.203314	+	0.979114i	$0.434829\pi$
$500$	16.9412	0.757636
$501$	−12.0195	−0.536992
$502$	6.01719	0.268560
$503$	−34.7644	−1.55007	−0.775035	−	0.631918i	$-0.782268\pi$
$503$	−34.7644	−1.55007	−0.775035	+	0.631918i	$0.782268\pi$
$504$	0.494202	0.0220135
$505$	16.5616	0.736980
$506$	10.3918	0.461971
$507$	7.16682	0.318290
$508$	34.9799	1.55198
$509$	−31.1352	−1.38004	−0.690022	−	0.723789i	$-0.742399\pi$
$509$	−31.1352	−1.38004	−0.690022	+	0.723789i	$0.742399\pi$
$510$	−1.80892	−0.0801002
$511$	−42.4831	−1.87934
$512$	−32.1398	−1.42039
$513$	4.80111	0.211974
$514$	42.2770	1.86476
$515$	−8.24115	−0.363149
$516$	21.5291	0.947768
$517$	−2.18302	−0.0960089
$518$	88.5054	3.88870
$519$	7.55485	0.331621
$520$	−0.410427	−0.0179984
$521$	9.54166	0.418028	0.209014	−	0.977913i	$-0.432975\pi$
$521$	9.54166	0.418028	0.209014	+	0.977913i	$0.432975\pi$
$522$	−5.96183	−0.260942
$523$	−39.3824	−1.72207	−0.861037	−	0.508543i	$-0.830184\pi$
$523$	−39.3824	−1.72207	−0.861037	+	0.508543i	$0.830184\pi$
$524$	−37.8898	−1.65522
$525$	20.3746	0.889219
$526$	7.35930	0.320881
$527$	−6.47848	−0.282207
$528$	2.54947	0.110952
$529$	39.2723	1.70749
$530$	−7.66096	−0.332771
$531$	5.44568	0.236322
$532$	−47.8473	−2.07444
$533$	52.0151	2.25303
$534$	−2.15814	−0.0933918
$535$	−1.29131	−0.0558282
$536$	0.687420	0.0296920
$537$	3.69003	0.159236
$538$	35.4820	1.52974
$539$	−10.8755	−0.468440
$540$	−1.84301	−0.0793106
$541$	−6.76697	−0.290935	−0.145467	−	0.989363i	$-0.546469\pi$
$541$	−6.76697	−0.290935	−0.145467	+	0.989363i	$0.546469\pi$
$542$	−29.8889	−1.28384
$543$	7.19426	0.308735
$544$	−8.04523	−0.344936
$545$	11.5786	0.495972
$546$	−43.9263	−1.87987
$547$	−35.9171	−1.53570	−0.767852	−	0.640628i	$-0.778674\pi$
$547$	−35.9171	−1.53570	−0.767852	+	0.640628i	$0.778674\pi$
$548$	−24.7617	−1.05777
$549$	−13.4929	−0.575864
$550$	−5.52052	−0.235396
$551$	14.2222	0.605885
$552$	−0.802420	−0.0341532
$553$	−4.86016	−0.206675
$554$	16.4688	0.699691
$555$	−8.13255	−0.345207
$556$	−44.7083	−1.89605
$557$	−18.6235	−0.789101	−0.394551	−	0.918874i	$-0.629100\pi$
$557$	−18.6235	−0.789101	−0.394551	+	0.918874i	$0.629100\pi$
$558$	−13.0385	−0.551965
$559$	−47.1499	−1.99423
$560$	−17.0207	−0.719255
$561$	0.654315	0.0276252
$562$	−33.5235	−1.41410
$563$	−2.34440	−0.0988046	−0.0494023	−	0.998779i	$-0.515732\pi$
$563$	−2.34440	−0.0988046	−0.0494023	+	0.998779i	$0.515732\pi$
$564$	6.84124	0.288068
$565$	11.9254	0.501706
$566$	−31.7039	−1.33261
$567$	−4.86016	−0.204108
$568$	−0.429332	−0.0180144
$569$	−43.6285	−1.82900	−0.914502	−	0.404581i	$-0.867417\pi$
$569$	−43.6285	−1.82900	−0.914502	+	0.404581i	$0.867417\pi$
$570$	8.68482	0.363767
$571$	−14.8448	−0.621238	−0.310619	−	0.950535i	$-0.600536\pi$
$571$	−14.8448	−0.621238	−0.310619	+	0.950535i	$0.600536\pi$
$572$	6.02519	0.251926
$573$	5.43859	0.227200
$574$	−113.297	−4.72891
$575$	−33.0815	−1.37959
$576$	−8.39896	−0.349957
$577$	6.31173	0.262761	0.131380	−	0.991332i	$-0.458059\pi$
$577$	6.31173	0.262761	0.131380	+	0.991332i	$0.458059\pi$
$578$	−2.01259	−0.0837128
$579$	9.56698	0.397590
$580$	−5.45949	−0.226693
$581$	83.0409	3.44512
$582$	−12.3803	−0.513179
$583$	2.77110	0.114767
$584$	−0.888831	−0.0367801
$585$	4.03628	0.166880
$586$	−48.3081	−1.99559
$587$	−20.1064	−0.829880	−0.414940	−	0.909849i	$-0.636197\pi$
$587$	−20.1064	−0.829880	−0.414940	+	0.909849i	$0.636197\pi$
$588$	34.0821	1.40552
$589$	31.1039	1.28162
$590$	9.85078	0.405550
$591$	−4.69684	−0.193202
$592$	−35.2555	−1.44899
$593$	−25.3239	−1.03993	−0.519964	−	0.854188i	$-0.674055\pi$
$593$	−25.3239	−1.03993	−0.519964	+	0.854188i	$0.674055\pi$
$594$	1.31687	0.0540318
$595$	−4.36831	−0.179083
$596$	4.05293	0.166014
$597$	4.85558	0.198726
$598$	71.3217	2.91656
$599$	12.0044	0.490487	0.245243	−	0.969462i	$-0.421132\pi$
$599$	12.0044	0.490487	0.245243	+	0.969462i	$0.421132\pi$
$600$	0.426277	0.0174027
$601$	16.5959	0.676961	0.338481	−	0.940973i	$-0.390087\pi$
$601$	16.5959	0.676961	0.338481	+	0.940973i	$0.390087\pi$
$602$	102.699	4.18572
$603$	−6.76034	−0.275302
$604$	−27.5019	−1.11904
$605$	9.50200	0.386311
$606$	37.0846	1.50646
$607$	−23.7231	−0.962892	−0.481446	−	0.876476i	$-0.659888\pi$
$607$	−23.7231	−0.962892	−0.481446	+	0.876476i	$0.659888\pi$
$608$	38.6261	1.56649
$609$	−14.3971	−0.583399
$610$	−24.4076	−0.988234
$611$	−14.9826	−0.606133
$612$	−2.05052	−0.0828875
$613$	21.6833	0.875778	0.437889	−	0.899029i	$-0.355726\pi$
$613$	21.6833	0.875778	0.437889	+	0.899029i	$0.355726\pi$
$614$	−6.31303	−0.254773
$615$	10.4106	0.419794
$616$	−0.323364	−0.0130287
$617$	−14.8044	−0.596003	−0.298002	−	0.954565i	$-0.596320\pi$
$617$	−14.8044	−0.596003	−0.298002	+	0.954565i	$0.596320\pi$
$618$	−18.4536	−0.742312
$619$	31.8926	1.28187	0.640937	−	0.767594i	$-0.278546\pi$
$619$	31.8926	1.28187	0.640937	+	0.767594i	$0.278546\pi$
$620$	−11.9399	−0.479519
$621$	7.89128	0.316666
$622$	19.0617	0.764303
$623$	−5.21164	−0.208800
$624$	17.4977	0.700471
$625$	13.5350	0.541399
$626$	1.26292	0.0504764
$627$	−3.14144	−0.125457
$628$	−16.7502	−0.668406
$629$	−9.04823	−0.360776
$630$	−8.79163	−0.350267
$631$	−4.58175	−0.182397	−0.0911983	−	0.995833i	$-0.529070\pi$
$631$	−4.58175	−0.182397	−0.0911983	+	0.995833i	$0.529070\pi$
$632$	−0.101684	−0.00404479
$633$	−24.2551	−0.964054
$634$	−40.2032	−1.59667
$635$	−15.3326	−0.608457
$636$	−8.68419	−0.344351
$637$	−74.6414	−2.95740
$638$	3.90092	0.154439
$639$	4.22221	0.167028
$640$	−0.730918	−0.0288921
$641$	33.3581	1.31757	0.658784	−	0.752332i	$-0.271071\pi$
$641$	33.3581	1.31757	0.658784	+	0.752332i	$0.271071\pi$
$642$	−2.89150	−0.114118
$643$	−11.7066	−0.461663	−0.230831	−	0.972994i	$-0.574145\pi$
$643$	−11.7066	−0.461663	−0.230831	+	0.972994i	$0.574145\pi$
$644$	−78.6435	−3.09899
$645$	−9.43680	−0.371574
$646$	9.66268	0.380173
$647$	−44.8349	−1.76264	−0.881321	−	0.472519i	$-0.843345\pi$
$647$	−44.8349	−1.76264	−0.881321	+	0.472519i	$0.843345\pi$
$648$	−0.101684	−0.00399454
$649$	−3.56319	−0.139867
$650$	−37.8889	−1.48613
$651$	−31.4865	−1.23405
$652$	27.6295	1.08205
$653$	24.8983	0.974347	0.487174	−	0.873305i	$-0.338028\pi$
$653$	24.8983	0.974347	0.487174	+	0.873305i	$0.338028\pi$
$654$	25.9267	1.01382
$655$	16.6081	0.648933
$656$	45.1309	1.76207
$657$	8.74108	0.341022
$658$	32.6344	1.27222
$659$	37.2608	1.45148	0.725738	−	0.687972i	$-0.241499\pi$
$659$	37.2608	1.45148	0.725738	+	0.687972i	$0.241499\pi$
$660$	1.20591	0.0469400
$661$	8.43161	0.327951	0.163976	−	0.986464i	$-0.447568\pi$
$661$	8.43161	0.327951	0.163976	+	0.986464i	$0.447568\pi$
$662$	44.3188	1.72250
$663$	4.49075	0.174406
$664$	1.73738	0.0674235
$665$	20.9728	0.813289
$666$	−18.2104	−0.705638
$667$	23.3761	0.905125
$668$	−24.6463	−0.953594
$669$	3.33952	0.129113
$670$	−12.2289	−0.472443
$671$	8.82862	0.340825
$672$	−39.1011	−1.50836
$673$	−23.7559	−0.915724	−0.457862	−	0.889023i	$-0.651385\pi$
$673$	−23.7559	−0.915724	−0.457862	+	0.889023i	$0.651385\pi$
$674$	−63.2355	−2.43574
$675$	−4.19216	−0.161356
$676$	14.6957	0.565221
$677$	36.1686	1.39007	0.695037	−	0.718974i	$-0.255388\pi$
$677$	36.1686	1.39007	0.695037	+	0.718974i	$0.255388\pi$
$678$	26.7034	1.02554
$679$	−29.8968	−1.14734
$680$	−0.0913939	−0.00350480
$681$	11.5158	0.441286
$682$	8.53131	0.326681
$683$	13.5194	0.517306	0.258653	−	0.965970i	$-0.416721\pi$
$683$	13.5194	0.517306	0.258653	+	0.965970i	$0.416721\pi$
$684$	9.84480	0.376425
$685$	10.8537	0.414699
$686$	94.1095	3.59312
$687$	7.66325	0.292371
$688$	−40.9096	−1.55966
$689$	19.0188	0.724559
$690$	14.2747	0.543427
$691$	26.8671	1.02207	0.511037	−	0.859559i	$-0.329262\pi$
$691$	26.8671	1.02207	0.511037	+	0.859559i	$0.329262\pi$
$692$	15.4914	0.588895
$693$	3.18008	0.120801
$694$	−45.5814	−1.73025
$695$	19.5968	0.743350
$696$	−0.301216	−0.0114176
$697$	11.5827	0.438727
$698$	−69.3791	−2.62604
$699$	−7.77870	−0.294217
$700$	41.7785	1.57908
$701$	3.29397	0.124412	0.0622058	−	0.998063i	$-0.480186\pi$
$701$	3.29397	0.124412	0.0622058	+	0.998063i	$0.480186\pi$
$702$	9.03804	0.341119
$703$	43.4416	1.63843
$704$	5.49556	0.207122
$705$	−2.99870	−0.112938
$706$	1.86465	0.0701771
$707$	89.5548	3.36805
$708$	11.1665	0.419663
$709$	−22.9368	−0.861408	−0.430704	−	0.902493i	$-0.641735\pi$
$709$	−22.9368	−0.861408	−0.430704	+	0.902493i	$0.641735\pi$
$710$	7.63762	0.286635
$711$	1.00000	0.0375029
$712$	−0.109038	−0.00408637
$713$	51.1235	1.91459
$714$	−9.78152	−0.366064
$715$	−2.64100	−0.0987679
$716$	7.56649	0.282773
$717$	9.52763	0.355816
$718$	21.4270	0.799650
$719$	−0.204133	−0.00761288	−0.00380644	−	0.999993i	$-0.501212\pi$
$719$	−0.204133	−0.00761288	−0.00380644	+	0.999993i	$0.501212\pi$
$720$	3.50208	0.130515
$721$	−44.5631	−1.65962
$722$	−8.15241	−0.303401
$723$	−2.33522	−0.0868476
$724$	14.7520	0.548254
$725$	−12.4183	−0.461204
$726$	21.2769	0.789658
$727$	23.7450	0.880654	0.440327	−	0.897838i	$-0.354863\pi$
$727$	23.7450	0.880654	0.440327	+	0.897838i	$0.354863\pi$
$728$	−2.21934	−0.0822541
$729$	1.00000	0.0370370
$730$	15.8119	0.585225
$731$	−10.4993	−0.388332
$732$	−27.6676	−1.02262
$733$	−14.4444	−0.533515	−0.266758	−	0.963764i	$-0.585952\pi$
$733$	−14.4444	−0.533515	−0.266758	+	0.963764i	$0.585952\pi$
$734$	60.9542	2.24986
$735$	−14.9391	−0.551037
$736$	63.4871	2.34017
$737$	4.42339	0.162938
$738$	23.3113	0.858101
$739$	23.2817	0.856432	0.428216	−	0.903676i	$-0.359142\pi$
$739$	23.2817	0.856432	0.428216	+	0.903676i	$0.359142\pi$
$740$	−16.6760	−0.613021
$741$	−21.5606	−0.792048
$742$	−41.4258	−1.52079
$743$	47.3923	1.73866	0.869328	−	0.494236i	$-0.164552\pi$
$743$	47.3923	1.73866	0.869328	+	0.494236i	$0.164552\pi$
$744$	−0.658760	−0.0241513
$745$	−1.77651	−0.0650862
$746$	−76.3407	−2.79503
$747$	−17.0860	−0.625145
$748$	1.34169	0.0490570
$749$	−6.98261	−0.255139
$750$	−16.6279	−0.607163
$751$	−21.3879	−0.780457	−0.390228	−	0.920718i	$-0.627604\pi$
$751$	−21.3879	−0.780457	−0.390228	+	0.920718i	$0.627604\pi$
$752$	−12.9997	−0.474050
$753$	−2.98977	−0.108953
$754$	26.7731	0.975018
$755$	12.0548	0.438720
$756$	−9.96588	−0.362455
$757$	4.11896	0.149706	0.0748530	−	0.997195i	$-0.476151\pi$
$757$	4.11896	0.149706	0.0748530	+	0.997195i	$0.476151\pi$
$758$	29.8626	1.08466
$759$	−5.16338	−0.187419
$760$	0.438793	0.0159167
$761$	−10.4069	−0.377251	−0.188625	−	0.982049i	$-0.560403\pi$
$761$	−10.4069	−0.377251	−0.188625	+	0.982049i	$0.560403\pi$
$762$	−34.3328	−1.24375
$763$	62.6099	2.26663
$764$	11.1520	0.403464
$765$	0.898800	0.0324962
$766$	−15.9516	−0.576356
$767$	−24.4552	−0.883025
$768$	15.1612	0.547084
$769$	−1.35947	−0.0490238	−0.0245119	−	0.999700i	$-0.507803\pi$
$769$	−1.35947	−0.0490238	−0.0245119	+	0.999700i	$0.507803\pi$
$770$	5.75249	0.207305
$771$	−21.0062	−0.756521
$772$	19.6173	0.706043
$773$	−42.5291	−1.52967	−0.764833	−	0.644228i	$-0.777179\pi$
$773$	−42.5291	−1.52967	−0.764833	+	0.644228i	$0.777179\pi$
$774$	−21.1309	−0.759534
$775$	−27.1588	−0.975574
$776$	−0.625502	−0.0224542
$777$	−43.9758	−1.57762
$778$	−4.27756	−0.153358
$779$	−55.6100	−1.99244
$780$	8.27650	0.296346
$781$	−2.76265	−0.0988555
$782$	15.8819	0.567936
$783$	2.96227	0.105863
$784$	−64.7627	−2.31295
$785$	7.34207	0.262050
$786$	37.1889	1.32648
$787$	−31.7018	−1.13005	−0.565024	−	0.825075i	$-0.691133\pi$
$787$	−31.7018	−1.13005	−0.565024	+	0.825075i	$0.691133\pi$
$788$	−9.63099	−0.343090
$789$	−3.65663	−0.130180
$790$	1.80892	0.0643584
$791$	64.4854	2.29284
$792$	0.0665336	0.00236417
$793$	60.5933	2.15173
$794$	39.8112	1.41285
$795$	3.80652	0.135003
$796$	9.95648	0.352898
$797$	−28.0219	−0.992588	−0.496294	−	0.868155i	$-0.665306\pi$
$797$	−28.0219	−0.992588	−0.496294	+	0.868155i	$0.665306\pi$
$798$	46.9622	1.66244
$799$	−3.33634	−0.118031
$800$	−33.7269	−1.19242
$801$	1.07232	0.0378885
$802$	46.2232	1.63220
$803$	−5.71942	−0.201834
$804$	−13.8622	−0.488883
$805$	34.4716	1.21496
$806$	58.5528	2.06243
$807$	−17.6300	−0.620605
$808$	1.87367	0.0659153
$809$	7.14119	0.251071	0.125535	−	0.992089i	$-0.459935\pi$
$809$	7.14119	0.251071	0.125535	+	0.992089i	$0.459935\pi$
$810$	1.80892	0.0635589
$811$	25.2837	0.887829	0.443915	−	0.896069i	$-0.353589\pi$
$811$	25.2837	0.887829	0.443915	+	0.896069i	$0.353589\pi$
$812$	−29.5216	−1.03600
$813$	14.8509	0.520845
$814$	11.9153	0.417632
$815$	−12.1107	−0.424221
$816$	3.89640	0.136401
$817$	50.4085	1.76357
$818$	49.1362	1.71801
$819$	21.8258	0.762654
$820$	21.3471	0.745473
$821$	−42.1231	−1.47010	−0.735052	−	0.678010i	$-0.762842\pi$
$821$	−42.1231	−1.47010	−0.735052	+	0.678010i	$0.762842\pi$
$822$	24.3036	0.847686
$823$	−36.9627	−1.28844	−0.644220	−	0.764840i	$-0.722818\pi$
$823$	−36.9627	−1.28844	−0.644220	+	0.764840i	$0.722818\pi$
$824$	−0.932350	−0.0324800
$825$	2.74299	0.0954987
$826$	53.2670	1.85340
$827$	1.45399	0.0505601	0.0252801	−	0.999680i	$-0.491952\pi$
$827$	1.45399	0.0505601	0.0252801	+	0.999680i	$0.491952\pi$
$828$	16.1813	0.562338
$829$	−5.74208	−0.199431	−0.0997154	−	0.995016i	$-0.531793\pi$
$829$	−5.74208	−0.199431	−0.0997154	+	0.995016i	$0.531793\pi$
$830$	−30.9072	−1.07281
$831$	−8.18287	−0.283861
$832$	37.7176	1.30762
$833$	−16.6212	−0.575889
$834$	43.8812	1.51948
$835$	10.8031	0.373858
$836$	−6.44160	−0.222787
$837$	6.47848	0.223929
$838$	64.0034	2.21096
$839$	−44.9237	−1.55094	−0.775470	−	0.631385i	$-0.782487\pi$
$839$	−44.9237	−1.55094	−0.775470	+	0.631385i	$0.782487\pi$
$840$	−0.444189	−0.0153260
$841$	−20.2250	−0.697413
$842$	64.4513	2.22114
$843$	16.6569	0.573693
$844$	−49.7357	−1.71197
$845$	−6.44154	−0.221596
$846$	−6.71468	−0.230856
$847$	51.3810	1.76547
$848$	16.5017	0.566670
$849$	15.7528	0.540633
$850$	−8.43710	−0.289390
$851$	71.4021	2.44763
$852$	8.65774	0.296609
$853$	27.0505	0.926193	0.463097	−	0.886308i	$-0.346738\pi$
$853$	27.0505	0.926193	0.463097	+	0.886308i	$0.346738\pi$
$854$	−131.981	−4.51630
$855$	−4.31524	−0.147578
$856$	−0.146090	−0.00499326
$857$	−12.9217	−0.441396	−0.220698	−	0.975342i	$-0.570833\pi$
$857$	−12.9217	−0.441396	−0.220698	+	0.975342i	$0.570833\pi$
$858$	−5.91373	−0.201891
$859$	35.9087	1.22519	0.612595	−	0.790397i	$-0.290126\pi$
$859$	35.9087	1.22519	0.612595	+	0.790397i	$0.290126\pi$
$860$	−19.3504	−0.659843
$861$	56.2939	1.91849
$862$	−22.2137	−0.756601
$863$	−25.5230	−0.868813	−0.434407	−	0.900717i	$-0.643042\pi$
$863$	−25.5230	−0.868813	−0.434407	+	0.900717i	$0.643042\pi$
$864$	8.04523	0.273704
$865$	−6.79030	−0.230877
$866$	2.55189	0.0867166
$867$	1.00000	0.0339618
$868$	−64.5638	−2.19144
$869$	−0.654315	−0.0221961
$870$	5.35849	0.181670
$871$	30.3590	1.02867
$872$	1.30993	0.0443597
$873$	6.15141	0.208194
$874$	−76.2509	−2.57923
$875$	−40.1542	−1.35746
$876$	17.9238	0.605589
$877$	43.3893	1.46515	0.732576	−	0.680685i	$-0.238318\pi$
$877$	43.3893	1.46515	0.732576	+	0.680685i	$0.238318\pi$
$878$	17.5847	0.593455
$879$	24.0029	0.809599
$880$	−2.29147	−0.0772453
$881$	40.5212	1.36519	0.682597	−	0.730795i	$-0.260851\pi$
$881$	40.5212	1.36519	0.682597	+	0.730795i	$0.260851\pi$
$882$	−33.4516	−1.12637
$883$	−23.9343	−0.805452	−0.402726	−	0.915321i	$-0.631937\pi$
$883$	−23.9343	−0.805452	−0.402726	+	0.915321i	$0.631937\pi$
$884$	9.20839	0.309712
$885$	−4.89458	−0.164529
$886$	35.7819	1.20212
$887$	41.7848	1.40300	0.701498	−	0.712671i	$-0.252515\pi$
$887$	41.7848	1.40300	0.701498	+	0.712671i	$0.252515\pi$
$888$	−0.920063	−0.0308753
$889$	−82.9094	−2.78069
$890$	1.93973	0.0650200
$891$	−0.654315	−0.0219204
$892$	6.84777	0.229280
$893$	16.0181	0.536026
$894$	−3.97795	−0.133043
$895$	−3.31660	−0.110862
$896$	−3.95236	−0.132039
$897$	−35.4377	−1.18323
$898$	16.9438	0.565422
$899$	19.1910	0.640055
$900$	−8.59612	−0.286537
$901$	4.23511	0.141092
$902$	−15.2529	−0.507867
$903$	−51.0285	−1.69812
$904$	1.34916	0.0448725
$905$	−6.46621	−0.214944
$906$	26.9931	0.896787
$907$	−39.7075	−1.31847	−0.659233	−	0.751938i	$-0.729119\pi$
$907$	−39.7075	−1.31847	−0.659233	+	0.751938i	$0.729119\pi$
$908$	23.6134	0.783639
$909$	−18.4263	−0.611162
$910$	39.4810	1.30878
$911$	−25.3982	−0.841480	−0.420740	−	0.907181i	$-0.638230\pi$
$911$	−25.3982	−0.841480	−0.420740	+	0.907181i	$0.638230\pi$
$912$	−18.7071	−0.619453
$913$	11.1796	0.369992
$914$	−45.8528	−1.51668
$915$	12.1274	0.400921
$916$	15.7137	0.519195
$917$	89.8066	2.96568
$918$	2.01259	0.0664254
$919$	−16.6483	−0.549175	−0.274588	−	0.961562i	$-0.588541\pi$
$919$	−16.6483	−0.549175	−0.274588	+	0.961562i	$0.588541\pi$
$920$	0.721215	0.0237777
$921$	3.13677	0.103360
$922$	−23.8994	−0.787084
$923$	−18.9609	−0.624105
$924$	6.52082	0.214519
$925$	−37.9316	−1.24718
$926$	53.0864	1.74453
$927$	9.16906	0.301151
$928$	23.8321	0.782327
$929$	28.1208	0.922612	0.461306	−	0.887241i	$-0.347381\pi$
$929$	28.1208	0.922612	0.461306	+	0.887241i	$0.347381\pi$
$930$	11.7190	0.384282
$931$	79.8001	2.61534
$932$	−15.9504	−0.522473
$933$	−9.47121	−0.310073
$934$	81.0459	2.65190
$935$	−0.588098	−0.0192329
$936$	0.456639	0.0149257
$937$	−20.2681	−0.662131	−0.331065	−	0.943608i	$-0.607408\pi$
$937$	−20.2681	−0.662131	−0.331065	+	0.943608i	$0.607408\pi$
$938$	−66.1263	−2.15910
$939$	−0.627509	−0.0204780
$940$	−6.14890	−0.200555
$941$	52.8704	1.72352	0.861762	−	0.507312i	$-0.169361\pi$
$941$	52.8704	1.72352	0.861762	+	0.507312i	$0.169361\pi$
$942$	16.4403	0.535655
$943$	−91.4026	−2.97648
$944$	−21.2185	−0.690605
$945$	4.36831	0.142101
$946$	13.8262	0.449530
$947$	16.6327	0.540489	0.270244	−	0.962792i	$-0.412895\pi$
$947$	16.6327	0.540489	0.270244	+	0.962792i	$0.412895\pi$
$948$	2.05052	0.0665979
$949$	−39.2540	−1.27424
$950$	40.5075	1.31424
$951$	19.9758	0.647760
$952$	−0.494202	−0.0160172
$953$	−19.0936	−0.618501	−0.309251	−	0.950981i	$-0.600078\pi$
$953$	−19.0936	−0.618501	−0.309251	+	0.950981i	$0.600078\pi$
$954$	8.52354	0.275960
$955$	−4.88820	−0.158179
$956$	19.5366	0.631860
$957$	−1.93826	−0.0626549
$958$	40.8483	1.31975
$959$	58.6902	1.89521
$960$	7.54898	0.243642
$961$	10.9707	0.353895
$962$	81.7782	2.63664
$963$	1.43670	0.0462971
$964$	−4.78842	−0.154224
$965$	−8.59880	−0.276805
$966$	77.1887	2.48350
$967$	17.5240	0.563535	0.281767	−	0.959483i	$-0.409079\pi$
$967$	17.5240	0.563535	0.281767	+	0.959483i	$0.409079\pi$
$968$	1.07499	0.0345516
$969$	−4.80111	−0.154234
$970$	11.1274	0.357279
$971$	−39.7401	−1.27532	−0.637660	−	0.770318i	$-0.720098\pi$
$971$	−39.7401	−1.27532	−0.637660	+	0.770318i	$0.720098\pi$
$972$	2.05052	0.0657706
$973$	105.968	3.39717
$974$	−76.7480	−2.45917
$975$	18.8259	0.602912
$976$	52.5738	1.68285
$977$	−52.6210	−1.68349	−0.841747	−	0.539872i	$-0.818473\pi$
$977$	−52.6210	−1.68349	−0.841747	+	0.539872i	$0.818473\pi$
$978$	−27.1183	−0.867149
$979$	−0.701634	−0.0224243
$980$	−30.6330	−0.978534
$981$	−12.8823	−0.411299
$982$	8.10870	0.258759
$983$	16.0156	0.510818	0.255409	−	0.966833i	$-0.417790\pi$
$983$	16.0156	0.510818	0.255409	+	0.966833i	$0.417790\pi$
$984$	1.17778	0.0375463
$985$	4.22152	0.134509
$986$	5.96183	0.189863
$987$	−16.2151	−0.516133
$988$	−44.2105	−1.40652
$989$	82.8532	2.63458
$990$	−1.18360	−0.0376173
$991$	45.1126	1.43305	0.716525	−	0.697561i	$-0.245731\pi$
$991$	45.1126	1.43305	0.716525	+	0.697561i	$0.245731\pi$
$992$	52.1209	1.65484
$993$	−22.0207	−0.698807
$994$	41.2996	1.30994
$995$	−4.36419	−0.138354
$996$	−35.0353	−1.11014
$997$	−5.44667	−0.172498	−0.0862489	−	0.996274i	$-0.527488\pi$
$997$	−5.44667	−0.172498	−0.0862489	+	0.996274i	$0.527488\pi$
$998$	−18.2812	−0.578680
$999$	9.04823	0.286273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.7	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01259 q^{2} +1.00000 q^{3} +2.05052 q^{4} -0.898800 q^{5} -2.01259 q^{6} -4.86016 q^{7} -0.101684 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.01259 q^{2} +1.00000 q^{3} +2.05052 q^{4} -0.898800 q^{5} -2.01259 q^{6} -4.86016 q^{7} -0.101684 q^{8} +1.00000 q^{9} +1.80892 q^{10} -0.654315 q^{11} +2.05052 q^{12} -4.49075 q^{13} +9.78152 q^{14} -0.898800 q^{15} -3.89640 q^{16} -1.00000 q^{17} -2.01259 q^{18} +4.80111 q^{19} -1.84301 q^{20} -4.86016 q^{21} +1.31687 q^{22} +7.89128 q^{23} -0.101684 q^{24} -4.19216 q^{25} +9.03804 q^{26} +1.00000 q^{27} -9.96588 q^{28} +2.96227 q^{29} +1.80892 q^{30} +6.47848 q^{31} +8.04523 q^{32} -0.654315 q^{33} +2.01259 q^{34} +4.36831 q^{35} +2.05052 q^{36} +9.04823 q^{37} -9.66268 q^{38} -4.49075 q^{39} +0.0913939 q^{40} -11.5827 q^{41} +9.78152 q^{42} +10.4993 q^{43} -1.34169 q^{44} -0.898800 q^{45} -15.8819 q^{46} +3.33634 q^{47} -3.89640 q^{48} +16.6212 q^{49} +8.43710 q^{50} -1.00000 q^{51} -9.20839 q^{52} -4.23511 q^{53} -2.01259 q^{54} +0.588098 q^{55} +0.494202 q^{56} +4.80111 q^{57} -5.96183 q^{58} +5.44568 q^{59} -1.84301 q^{60} -13.4929 q^{61} -13.0385 q^{62} -4.86016 q^{63} -8.39896 q^{64} +4.03628 q^{65} +1.31687 q^{66} -6.76034 q^{67} -2.05052 q^{68} +7.89128 q^{69} -8.79163 q^{70} +4.22221 q^{71} -0.101684 q^{72} +8.74108 q^{73} -18.2104 q^{74} -4.19216 q^{75} +9.84480 q^{76} +3.18008 q^{77} +9.03804 q^{78} +1.00000 q^{79} +3.50208 q^{80} +1.00000 q^{81} +23.3113 q^{82} -17.0860 q^{83} -9.96588 q^{84} +0.898800 q^{85} -21.1309 q^{86} +2.96227 q^{87} +0.0665336 q^{88} +1.07232 q^{89} +1.80892 q^{90} +21.8258 q^{91} +16.1813 q^{92} +6.47848 q^{93} -6.71468 q^{94} -4.31524 q^{95} +8.04523 q^{96} +6.15141 q^{97} -33.4516 q^{98} -0.654315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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