LMFDB - Embedded newform 4029.2.a.i.1.6

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:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-1.76780 q^{2} -1.00000 q^{3} +1.12513 q^{4} +2.69545 q^{5} +1.76780 q^{6} -0.714180 q^{7} +1.54660 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.76780 q^{2} -1.00000 q^{3} +1.12513 q^{4} +2.69545 q^{5} +1.76780 q^{6} -0.714180 q^{7} +1.54660 q^{8} +1.00000 q^{9} -4.76502 q^{10} -1.68005 q^{11} -1.12513 q^{12} +2.54130 q^{13} +1.26253 q^{14} -2.69545 q^{15} -4.98434 q^{16} +1.00000 q^{17} -1.76780 q^{18} +6.37137 q^{19} +3.03273 q^{20} +0.714180 q^{21} +2.96999 q^{22} +3.24204 q^{23} -1.54660 q^{24} +2.26544 q^{25} -4.49252 q^{26} -1.00000 q^{27} -0.803547 q^{28} +3.15620 q^{29} +4.76502 q^{30} +2.83015 q^{31} +5.71815 q^{32} +1.68005 q^{33} -1.76780 q^{34} -1.92504 q^{35} +1.12513 q^{36} -8.46556 q^{37} -11.2633 q^{38} -2.54130 q^{39} +4.16877 q^{40} -8.96930 q^{41} -1.26253 q^{42} +6.33262 q^{43} -1.89027 q^{44} +2.69545 q^{45} -5.73128 q^{46} +3.77416 q^{47} +4.98434 q^{48} -6.48995 q^{49} -4.00485 q^{50} -1.00000 q^{51} +2.85930 q^{52} +9.52417 q^{53} +1.76780 q^{54} -4.52848 q^{55} -1.10455 q^{56} -6.37137 q^{57} -5.57954 q^{58} +5.83142 q^{59} -3.03273 q^{60} +5.40120 q^{61} -5.00315 q^{62} -0.714180 q^{63} -0.139881 q^{64} +6.84995 q^{65} -2.96999 q^{66} -5.80636 q^{67} +1.12513 q^{68} -3.24204 q^{69} +3.40309 q^{70} +15.8573 q^{71} +1.54660 q^{72} +12.3154 q^{73} +14.9655 q^{74} -2.26544 q^{75} +7.16862 q^{76} +1.19986 q^{77} +4.49252 q^{78} -1.00000 q^{79} -13.4350 q^{80} +1.00000 q^{81} +15.8560 q^{82} +1.57980 q^{83} +0.803547 q^{84} +2.69545 q^{85} -11.1948 q^{86} -3.15620 q^{87} -2.59835 q^{88} +1.99678 q^{89} -4.76502 q^{90} -1.81495 q^{91} +3.64772 q^{92} -2.83015 q^{93} -6.67197 q^{94} +17.1737 q^{95} -5.71815 q^{96} -3.32352 q^{97} +11.4730 q^{98} -1.68005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * 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 $

$2$	−1.76780	−1.25003	−0.625013	−	0.780614i	$-0.714906\pi$
$2$	−1.76780	−1.25003	−0.625013	+	0.780614i	$0.714906\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.12513	0.562566
$5$	2.69545	1.20544	0.602720	−	0.797953i	$-0.294083\pi$
$5$	2.69545	1.20544	0.602720	+	0.797953i	$0.294083\pi$
$6$	1.76780	0.721703
$7$	−0.714180	−0.269935	−0.134967	−	0.990850i	$-0.543093\pi$
$7$	−0.714180	−0.269935	−0.134967	+	0.990850i	$0.543093\pi$
$8$	1.54660	0.546804
$9$	1.00000	0.333333
$10$	−4.76502	−1.50683
$11$	−1.68005	−0.506553	−0.253277	−	0.967394i	$-0.581508\pi$
$11$	−1.68005	−0.506553	−0.253277	+	0.967394i	$0.581508\pi$
$12$	−1.12513	−0.324797
$13$	2.54130	0.704830	0.352415	−	0.935844i	$-0.385360\pi$
$13$	2.54130	0.704830	0.352415	+	0.935844i	$0.385360\pi$
$14$	1.26253	0.337426
$15$	−2.69545	−0.695961
$16$	−4.98434	−1.24609
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.76780	−0.416675
$19$	6.37137	1.46169	0.730846	−	0.682543i	$-0.239126\pi$
$19$	6.37137	1.46169	0.730846	+	0.682543i	$0.239126\pi$
$20$	3.03273	0.678140
$21$	0.714180	0.155847
$22$	2.96999	0.633205
$23$	3.24204	0.676011	0.338006	−	0.941144i	$-0.390248\pi$
$23$	3.24204	0.676011	0.338006	+	0.941144i	$0.390248\pi$
$24$	−1.54660	−0.315698
$25$	2.26544	0.453087
$26$	−4.49252	−0.881057
$27$	−1.00000	−0.192450
$28$	−0.803547	−0.151856
$29$	3.15620	0.586091	0.293045	−	0.956099i	$-0.405331\pi$
$29$	3.15620	0.586091	0.293045	+	0.956099i	$0.405331\pi$
$30$	4.76502	0.869970
$31$	2.83015	0.508310	0.254155	−	0.967163i	$-0.418203\pi$
$31$	2.83015	0.508310	0.254155	+	0.967163i	$0.418203\pi$
$32$	5.71815	1.01084
$33$	1.68005	0.292459
$34$	−1.76780	−0.303176
$35$	−1.92504	−0.325390
$36$	1.12513	0.187522
$37$	−8.46556	−1.39173	−0.695865	−	0.718173i	$-0.744979\pi$
$37$	−8.46556	−1.39173	−0.695865	+	0.718173i	$0.744979\pi$
$38$	−11.2633	−1.82715
$39$	−2.54130	−0.406934
$40$	4.16877	0.659140
$41$	−8.96930	−1.40077	−0.700384	−	0.713766i	$-0.746988\pi$
$41$	−8.96930	−1.40077	−0.700384	+	0.713766i	$0.746988\pi$
$42$	−1.26253	−0.194813
$43$	6.33262	0.965715	0.482858	−	0.875699i	$-0.339599\pi$
$43$	6.33262	0.965715	0.482858	+	0.875699i	$0.339599\pi$
$44$	−1.89027	−0.284969
$45$	2.69545	0.401814
$46$	−5.73128	−0.845032
$47$	3.77416	0.550517	0.275259	−	0.961370i	$-0.411237\pi$
$47$	3.77416	0.550517	0.275259	+	0.961370i	$0.411237\pi$
$48$	4.98434	0.719428
$49$	−6.48995	−0.927135
$50$	−4.00485	−0.566371
$51$	−1.00000	−0.140028
$52$	2.85930	0.396513
$53$	9.52417	1.30825	0.654123	−	0.756388i	$-0.273038\pi$
$53$	9.52417	1.30825	0.654123	+	0.756388i	$0.273038\pi$
$54$	1.76780	0.240568
$55$	−4.52848	−0.610620
$56$	−1.10455	−0.147602
$57$	−6.37137	−0.843908
$58$	−5.57954	−0.732629
$59$	5.83142	0.759187	0.379593	−	0.925153i	$-0.376064\pi$
$59$	5.83142	0.759187	0.379593	+	0.925153i	$0.376064\pi$
$60$	−3.03273	−0.391524
$61$	5.40120	0.691553	0.345777	−	0.938317i	$-0.387615\pi$
$61$	5.40120	0.691553	0.345777	+	0.938317i	$0.387615\pi$
$62$	−5.00315	−0.635401
$63$	−0.714180	−0.0899783
$64$	−0.139881	−0.0174852
$65$	6.84995	0.849631
$66$	−2.96999	−0.365581
$67$	−5.80636	−0.709359	−0.354680	−	0.934988i	$-0.615410\pi$
$67$	−5.80636	−0.709359	−0.354680	+	0.934988i	$0.615410\pi$
$68$	1.12513	0.136442
$69$	−3.24204	−0.390295
$70$	3.40309	0.406746
$71$	15.8573	1.88191	0.940956	−	0.338529i	$-0.109929\pi$
$71$	15.8573	1.88191	0.940956	+	0.338529i	$0.109929\pi$
$72$	1.54660	0.182268
$73$	12.3154	1.44141	0.720704	−	0.693243i	$-0.243819\pi$
$73$	12.3154	1.44141	0.720704	+	0.693243i	$0.243819\pi$
$74$	14.9655	1.73970
$75$	−2.26544	−0.261590
$76$	7.16862	0.822298
$77$	1.19986	0.136736
$78$	4.49252	0.508678
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−13.4350	−1.50208
$81$	1.00000	0.111111
$82$	15.8560	1.75100
$83$	1.57980	0.173405	0.0867026	−	0.996234i	$-0.472367\pi$
$83$	1.57980	0.173405	0.0867026	+	0.996234i	$0.472367\pi$
$84$	0.803547	0.0876741
$85$	2.69545	0.292362
$86$	−11.1948	−1.20717
$87$	−3.15620	−0.338380
$88$	−2.59835	−0.276986
$89$	1.99678	0.211659	0.105829	−	0.994384i	$-0.466250\pi$
$89$	1.99678	0.211659	0.105829	+	0.994384i	$0.466250\pi$
$90$	−4.76502	−0.502277
$91$	−1.81495	−0.190258
$92$	3.64772	0.380301
$93$	−2.83015	−0.293473
$94$	−6.67197	−0.688161
$95$	17.1737	1.76198
$96$	−5.71815	−0.583606
$97$	−3.32352	−0.337453	−0.168726	−	0.985663i	$-0.553965\pi$
$97$	−3.32352	−0.337453	−0.168726	+	0.985663i	$0.553965\pi$
$98$	11.4730	1.15894
$99$	−1.68005	−0.168851
$100$	2.54891	0.254891
$101$	−15.9192	−1.58402	−0.792012	−	0.610506i	$-0.790966\pi$
$101$	−15.9192	−1.58402	−0.792012	+	0.610506i	$0.790966\pi$
$102$	1.76780	0.175039
$103$	3.75083	0.369581	0.184790	−	0.982778i	$-0.440839\pi$
$103$	3.75083	0.369581	0.184790	+	0.982778i	$0.440839\pi$
$104$	3.93037	0.385404
$105$	1.92504	0.187864
$106$	−16.8369	−1.63534
$107$	−11.8326	−1.14390	−0.571948	−	0.820290i	$-0.693812\pi$
$107$	−11.8326	−1.14390	−0.571948	+	0.820290i	$0.693812\pi$
$108$	−1.12513	−0.108266
$109$	15.0557	1.44207	0.721035	−	0.692899i	$-0.243667\pi$
$109$	15.0557	1.44207	0.721035	+	0.692899i	$0.243667\pi$
$110$	8.00546	0.763291
$111$	8.46556	0.803515
$112$	3.55972	0.336362
$113$	−8.36643	−0.787047	−0.393524	−	0.919314i	$-0.628744\pi$
$113$	−8.36643	−0.787047	−0.393524	+	0.919314i	$0.628744\pi$
$114$	11.2633	1.05491
$115$	8.73873	0.814891
$116$	3.55114	0.329715
$117$	2.54130	0.234943
$118$	−10.3088	−0.949003
$119$	−0.714180	−0.0654688
$120$	−4.16877	−0.380555
$121$	−8.17744	−0.743404
$122$	−9.54827	−0.864460
$123$	8.96930	0.808734
$124$	3.18429	0.285958
$125$	−7.37087	−0.659271
$126$	1.26253	0.112475
$127$	−7.50954	−0.666364	−0.333182	−	0.942863i	$-0.608122\pi$
$127$	−7.50954	−0.666364	−0.333182	+	0.942863i	$0.608122\pi$
$128$	−11.1890	−0.988978
$129$	−6.33262	−0.557556
$130$	−12.1094	−1.06206
$131$	−11.7090	−1.02302	−0.511508	−	0.859278i	$-0.670913\pi$
$131$	−11.7090	−1.02302	−0.511508	+	0.859278i	$0.670913\pi$
$132$	1.89027	0.164527
$133$	−4.55030	−0.394561
$134$	10.2645	0.886718
$135$	−2.69545	−0.231987
$136$	1.54660	0.132620
$137$	−10.0486	−0.858510	−0.429255	−	0.903183i	$-0.641224\pi$
$137$	−10.0486	−0.858510	−0.429255	+	0.903183i	$0.641224\pi$
$138$	5.73128	0.487879
$139$	1.93127	0.163808	0.0819039	−	0.996640i	$-0.473900\pi$
$139$	1.93127	0.163808	0.0819039	+	0.996640i	$0.473900\pi$
$140$	−2.16592	−0.183053
$141$	−3.77416	−0.317841
$142$	−28.0325	−2.35244
$143$	−4.26951	−0.357034
$144$	−4.98434	−0.415362
$145$	8.50736	0.706498
$146$	−21.7712	−1.80180
$147$	6.48995	0.535282
$148$	−9.52487	−0.782939
$149$	−6.85831	−0.561855	−0.280928	−	0.959729i	$-0.590642\pi$
$149$	−6.85831	−0.561855	−0.280928	+	0.959729i	$0.590642\pi$
$150$	4.00485	0.326994
$151$	5.46470	0.444711	0.222355	−	0.974966i	$-0.428625\pi$
$151$	5.46470	0.444711	0.222355	+	0.974966i	$0.428625\pi$
$152$	9.85393	0.799259
$153$	1.00000	0.0808452
$154$	−2.12111	−0.170924
$155$	7.62852	0.612738
$156$	−2.85930	−0.228927
$157$	9.26726	0.739608	0.369804	−	0.929110i	$-0.379425\pi$
$157$	9.26726	0.739608	0.369804	+	0.929110i	$0.379425\pi$
$158$	1.76780	0.140639
$159$	−9.52417	−0.755316
$160$	15.4130	1.21850
$161$	−2.31540	−0.182479
$162$	−1.76780	−0.138892
$163$	15.5793	1.22027	0.610134	−	0.792299i	$-0.291116\pi$
$163$	15.5793	1.22027	0.610134	+	0.792299i	$0.291116\pi$
$164$	−10.0916	−0.788024
$165$	4.52848	0.352542
$166$	−2.79277	−0.216761
$167$	−15.9793	−1.23652	−0.618258	−	0.785975i	$-0.712161\pi$
$167$	−15.9793	−1.23652	−0.618258	+	0.785975i	$0.712161\pi$
$168$	1.10455	0.0852178
$169$	−6.54178	−0.503214
$170$	−4.76502	−0.365461
$171$	6.37137	0.487231
$172$	7.12503	0.543278
$173$	−11.4450	−0.870149	−0.435074	−	0.900394i	$-0.643278\pi$
$173$	−11.4450	−0.870149	−0.435074	+	0.900394i	$0.643278\pi$
$174$	5.57954	0.422984
$175$	−1.61793	−0.122304
$176$	8.37393	0.631209
$177$	−5.83142	−0.438317
$178$	−3.52992	−0.264579
$179$	−22.0538	−1.64838	−0.824189	−	0.566314i	$-0.808369\pi$
$179$	−22.0538	−1.64838	−0.824189	+	0.566314i	$0.808369\pi$
$180$	3.03273	0.226047
$181$	14.5681	1.08284	0.541420	−	0.840752i	$-0.317887\pi$
$181$	14.5681	1.08284	0.541420	+	0.840752i	$0.317887\pi$
$182$	3.20847	0.237828
$183$	−5.40120	−0.399268
$184$	5.01412	0.369646
$185$	−22.8185	−1.67765
$186$	5.00315	0.366849
$187$	−1.68005	−0.122857
$188$	4.24642	0.309702
$189$	0.714180	0.0519490
$190$	−30.3597	−2.20252
$191$	3.39488	0.245645	0.122822	−	0.992429i	$-0.460805\pi$
$191$	3.39488	0.245645	0.122822	+	0.992429i	$0.460805\pi$
$192$	0.139881	0.0100951
$193$	18.1663	1.30764	0.653819	−	0.756651i	$-0.273166\pi$
$193$	18.1663	1.30764	0.653819	+	0.756651i	$0.273166\pi$
$194$	5.87534	0.421825
$195$	−6.84995	−0.490535
$196$	−7.30204	−0.521574
$197$	10.2200	0.728145	0.364072	−	0.931371i	$-0.381386\pi$
$197$	10.2200	0.728145	0.364072	+	0.931371i	$0.381386\pi$
$198$	2.96999	0.211068
$199$	21.1932	1.50234	0.751172	−	0.660107i	$-0.229489\pi$
$199$	21.1932	1.50234	0.751172	+	0.660107i	$0.229489\pi$
$200$	3.50371	0.247750
$201$	5.80636	0.409549
$202$	28.1421	1.98007
$203$	−2.25409	−0.158206
$204$	−1.12513	−0.0787750
$205$	−24.1763	−1.68854
$206$	−6.63074	−0.461985
$207$	3.24204	0.225337
$208$	−12.6667	−0.878279
$209$	−10.7042	−0.740425
$210$	−3.40309	−0.234835
$211$	5.41749	0.372955	0.186478	−	0.982459i	$-0.440293\pi$
$211$	5.41749	0.372955	0.186478	+	0.982459i	$0.440293\pi$
$212$	10.7159	0.735974
$213$	−15.8573	−1.08652
$214$	20.9177	1.42990
$215$	17.0692	1.16411
$216$	−1.54660	−0.105233
$217$	−2.02124	−0.137211
$218$	−26.6154	−1.80263
$219$	−12.3154	−0.832197
$220$	−5.09513	−0.343514
$221$	2.54130	0.170946
$222$	−14.9655	−1.00442
$223$	24.5921	1.64681	0.823404	−	0.567455i	$-0.192072\pi$
$223$	24.5921	1.64681	0.823404	+	0.567455i	$0.192072\pi$
$224$	−4.08379	−0.272860
$225$	2.26544	0.151029
$226$	14.7902	0.983830
$227$	−12.3859	−0.822082	−0.411041	−	0.911617i	$-0.634835\pi$
$227$	−12.3859	−0.822082	−0.411041	+	0.911617i	$0.634835\pi$
$228$	−7.16862	−0.474754
$229$	−8.98675	−0.593861	−0.296930	−	0.954899i	$-0.595963\pi$
$229$	−8.98675	−0.593861	−0.296930	+	0.954899i	$0.595963\pi$
$230$	−15.4484	−1.01864
$231$	−1.19986	−0.0789448
$232$	4.88136	0.320477
$233$	9.00970	0.590245	0.295123	−	0.955459i	$-0.404640\pi$
$233$	9.00970	0.590245	0.295123	+	0.955459i	$0.404640\pi$
$234$	−4.49252	−0.293686
$235$	10.1730	0.663616
$236$	6.56112	0.427092
$237$	1.00000	0.0649570
$238$	1.26253	0.0818377
$239$	−5.09059	−0.329283	−0.164641	−	0.986353i	$-0.552647\pi$
$239$	−5.09059	−0.329283	−0.164641	+	0.986353i	$0.552647\pi$
$240$	13.4350	0.867228
$241$	10.0702	0.648681	0.324341	−	0.945940i	$-0.394858\pi$
$241$	10.0702	0.648681	0.324341	+	0.945940i	$0.394858\pi$
$242$	14.4561	0.929274
$243$	−1.00000	−0.0641500
$244$	6.07706	0.389044
$245$	−17.4933	−1.11761
$246$	−15.8560	−1.01094
$247$	16.1916	1.03024
$248$	4.37710	0.277946
$249$	−1.57980	−0.100116
$250$	13.0303	0.824106
$251$	12.4660	0.786849	0.393425	−	0.919357i	$-0.371290\pi$
$251$	12.4660	0.786849	0.393425	+	0.919357i	$0.371290\pi$
$252$	−0.803547	−0.0506187
$253$	−5.44677	−0.342436
$254$	13.2754	0.832972
$255$	−2.69545	−0.168795
$256$	20.0597	1.25373
$257$	−15.4988	−0.966786	−0.483393	−	0.875403i	$-0.660596\pi$
$257$	−15.4988	−0.966786	−0.483393	+	0.875403i	$0.660596\pi$
$258$	11.1948	0.696959
$259$	6.04594	0.375676
$260$	7.70709	0.477973
$261$	3.15620	0.195364
$262$	20.6991	1.27880
$263$	5.80727	0.358091	0.179046	−	0.983841i	$-0.442699\pi$
$263$	5.80727	0.358091	0.179046	+	0.983841i	$0.442699\pi$
$264$	2.59835	0.159918
$265$	25.6719	1.57701
$266$	8.04405	0.493212
$267$	−1.99678	−0.122201
$268$	−6.53291	−0.399061
$269$	31.3656	1.91240	0.956198	−	0.292719i	$-0.0945601\pi$
$269$	31.3656	1.91240	0.956198	+	0.292719i	$0.0945601\pi$
$270$	4.76502	0.289990
$271$	−0.200805	−0.0121980	−0.00609901	−	0.999981i	$-0.501941\pi$
$271$	−0.200805	−0.0121980	−0.00609901	+	0.999981i	$0.501941\pi$
$272$	−4.98434	−0.302220
$273$	1.81495	0.109846
$274$	17.7640	1.07316
$275$	−3.80604	−0.229513
$276$	−3.64772	−0.219567
$277$	−23.6442	−1.42064	−0.710322	−	0.703877i	$-0.751451\pi$
$277$	−23.6442	−1.42064	−0.710322	+	0.703877i	$0.751451\pi$
$278$	−3.41410	−0.204764
$279$	2.83015	0.169437
$280$	−2.97725	−0.177925
$281$	3.03492	0.181048	0.0905242	−	0.995894i	$-0.471146\pi$
$281$	3.03492	0.181048	0.0905242	+	0.995894i	$0.471146\pi$
$282$	6.67197	0.397310
$283$	19.4023	1.15335	0.576675	−	0.816974i	$-0.304350\pi$
$283$	19.4023	1.15335	0.576675	+	0.816974i	$0.304350\pi$
$284$	17.8415	1.05870
$285$	−17.1737	−1.01728
$286$	7.54765	0.446302
$287$	6.40569	0.378116
$288$	5.71815	0.336945
$289$	1.00000	0.0588235
$290$	−15.0393	−0.883141
$291$	3.32352	0.194828
$292$	13.8564	0.810886
$293$	8.79053	0.513548	0.256774	−	0.966471i	$-0.417340\pi$
$293$	8.79053	0.513548	0.256774	+	0.966471i	$0.417340\pi$
$294$	−11.4730	−0.669116
$295$	15.7183	0.915155
$296$	−13.0928	−0.761004
$297$	1.68005	0.0974862
$298$	12.1242	0.702334
$299$	8.23899	0.476473
$300$	−2.54891	−0.147162
$301$	−4.52263	−0.260680
$302$	−9.66051	−0.555900
$303$	15.9192	0.914537
$304$	−31.7571	−1.82139
$305$	14.5587	0.833626
$306$	−1.76780	−0.101059
$307$	−12.6037	−0.719331	−0.359666	−	0.933081i	$-0.617109\pi$
$307$	−12.6037	−0.719331	−0.359666	+	0.933081i	$0.617109\pi$
$308$	1.35000	0.0769232
$309$	−3.75083	−0.213377
$310$	−13.4857	−0.765938
$311$	25.7635	1.46091	0.730457	−	0.682959i	$-0.239307\pi$
$311$	25.7635	1.46091	0.730457	+	0.682959i	$0.239307\pi$
$312$	−3.93037	−0.222513
$313$	−18.4286	−1.04165	−0.520824	−	0.853664i	$-0.674375\pi$
$313$	−18.4286	−1.04165	−0.520824	+	0.853664i	$0.674375\pi$
$314$	−16.3827	−0.924529
$315$	−1.92504	−0.108463
$316$	−1.12513	−0.0632936
$317$	2.04053	0.114608	0.0573038	−	0.998357i	$-0.481750\pi$
$317$	2.04053	0.114608	0.0573038	+	0.998357i	$0.481750\pi$
$318$	16.8369	0.944165
$319$	−5.30256	−0.296886
$320$	−0.377042	−0.0210773
$321$	11.8326	0.660429
$322$	4.09317	0.228103
$323$	6.37137	0.354512
$324$	1.12513	0.0625073
$325$	5.75716	0.319350
$326$	−27.5412	−1.52537
$327$	−15.0557	−0.832579
$328$	−13.8719	−0.765946
$329$	−2.69543	−0.148604
$330$	−8.00546	−0.440686
$331$	1.75229	0.0963148	0.0481574	−	0.998840i	$-0.484665\pi$
$331$	1.75229	0.0963148	0.0481574	+	0.998840i	$0.484665\pi$
$332$	1.77748	0.0975518
$333$	−8.46556	−0.463910
$334$	28.2483	1.54568
$335$	−15.6507	−0.855091
$336$	−3.55972	−0.194199
$337$	14.1546	0.771052	0.385526	−	0.922697i	$-0.374020\pi$
$337$	14.1546	0.771052	0.385526	+	0.922697i	$0.374020\pi$
$338$	11.5646	0.629031
$339$	8.36643	0.454402
$340$	3.03273	0.164473
$341$	−4.75479	−0.257486
$342$	−11.2633	−0.609051
$343$	9.63425	0.520201
$344$	9.79400	0.528057
$345$	−8.73873	−0.470478
$346$	20.2326	1.08771
$347$	−7.29874	−0.391817	−0.195908	−	0.980622i	$-0.562766\pi$
$347$	−7.29874	−0.391817	−0.195908	+	0.980622i	$0.562766\pi$
$348$	−3.55114	−0.190361
$349$	−5.13075	−0.274643	−0.137321	−	0.990527i	$-0.543849\pi$
$349$	−5.13075	−0.274643	−0.137321	+	0.990527i	$0.543849\pi$
$350$	2.86018	0.152883
$351$	−2.54130	−0.135645
$352$	−9.60676	−0.512042
$353$	−8.05082	−0.428502	−0.214251	−	0.976779i	$-0.568731\pi$
$353$	−8.05082	−0.428502	−0.214251	+	0.976779i	$0.568731\pi$
$354$	10.3088	0.547907
$355$	42.7424	2.26853
$356$	2.24664	0.119072
$357$	0.714180	0.0377984
$358$	38.9868	2.06052
$359$	13.9040	0.733826	0.366913	−	0.930255i	$-0.380415\pi$
$359$	13.9040	0.733826	0.366913	+	0.930255i	$0.380415\pi$
$360$	4.16877	0.219713
$361$	21.5943	1.13654
$362$	−25.7536	−1.35358
$363$	8.17744	0.429204
$364$	−2.04205	−0.107033
$365$	33.1955	1.73753
$366$	9.54827	0.499096
$367$	25.8055	1.34704	0.673518	−	0.739171i	$-0.264783\pi$
$367$	25.8055	1.34704	0.673518	+	0.739171i	$0.264783\pi$
$368$	−16.1594	−0.842368
$369$	−8.96930	−0.466923
$370$	40.3386	2.09710
$371$	−6.80198	−0.353141
$372$	−3.18429	−0.165098
$373$	−14.2096	−0.735748	−0.367874	−	0.929876i	$-0.619914\pi$
$373$	−14.2096	−0.735748	−0.367874	+	0.929876i	$0.619914\pi$
$374$	2.96999	0.153575
$375$	7.37087	0.380630
$376$	5.83709	0.301025
$377$	8.02085	0.413095
$378$	−1.26253	−0.0649376
$379$	6.12108	0.314419	0.157209	−	0.987565i	$-0.449750\pi$
$379$	6.12108	0.314419	0.157209	+	0.987565i	$0.449750\pi$
$380$	19.3226	0.991231
$381$	7.50954	0.384725
$382$	−6.00148	−0.307062
$383$	28.7401	1.46855	0.734274	−	0.678853i	$-0.237523\pi$
$383$	28.7401	1.46855	0.734274	+	0.678853i	$0.237523\pi$
$384$	11.1890	0.570987
$385$	3.23415	0.164828
$386$	−32.1144	−1.63458
$387$	6.33262	0.321905
$388$	−3.73940	−0.189839
$389$	28.9589	1.46828	0.734138	−	0.679000i	$-0.237586\pi$
$389$	28.9589	1.46828	0.734138	+	0.679000i	$0.237586\pi$
$390$	12.1094	0.613181
$391$	3.24204	0.163957
$392$	−10.0373	−0.506962
$393$	11.7090	0.590639
$394$	−18.0670	−0.910200
$395$	−2.69545	−0.135623
$396$	−1.89027	−0.0949898
$397$	10.3049	0.517189	0.258595	−	0.965986i	$-0.416741\pi$
$397$	10.3049	0.517189	0.258595	+	0.965986i	$0.416741\pi$
$398$	−37.4654	−1.87797
$399$	4.55030	0.227800
$400$	−11.2917	−0.564585
$401$	−21.9400	−1.09563	−0.547815	−	0.836600i	$-0.684540\pi$
$401$	−21.9400	−1.09563	−0.547815	+	0.836600i	$0.684540\pi$
$402$	−10.2645	−0.511947
$403$	7.19227	0.358273
$404$	−17.9112	−0.891117
$405$	2.69545	0.133938
$406$	3.98479	0.197762
$407$	14.2225	0.704985
$408$	−1.54660	−0.0765679
$409$	8.75846	0.433078	0.216539	−	0.976274i	$-0.430523\pi$
$409$	8.75846	0.433078	0.216539	+	0.976274i	$0.430523\pi$
$410$	42.7389	2.11072
$411$	10.0486	0.495661
$412$	4.22018	0.207913
$413$	−4.16469	−0.204931
$414$	−5.73128	−0.281677
$415$	4.25826	0.209030
$416$	14.5315	0.712467
$417$	−1.93127	−0.0945745
$418$	18.9229	0.925550
$419$	16.7054	0.816114	0.408057	−	0.912957i	$-0.366207\pi$
$419$	16.7054	0.816114	0.408057	+	0.912957i	$0.366207\pi$
$420$	2.16592	0.105686
$421$	−0.279750	−0.0136342	−0.00681709	−	0.999977i	$-0.502170\pi$
$421$	−0.279750	−0.0136342	−0.00681709	+	0.999977i	$0.502170\pi$
$422$	−9.57706	−0.466204
$423$	3.77416	0.183506
$424$	14.7301	0.715355
$425$	2.26544	0.109890
$426$	28.0325	1.35818
$427$	−3.85743	−0.186674
$428$	−13.3132	−0.643517
$429$	4.26951	0.206134
$430$	−30.1751	−1.45517
$431$	5.00898	0.241274	0.120637	−	0.992697i	$-0.461506\pi$
$431$	5.00898	0.241274	0.120637	+	0.992697i	$0.461506\pi$
$432$	4.98434	0.239809
$433$	−27.0761	−1.30119	−0.650596	−	0.759424i	$-0.725481\pi$
$433$	−27.0761	−1.30119	−0.650596	+	0.759424i	$0.725481\pi$
$434$	3.57315	0.171517
$435$	−8.50736	−0.407897
$436$	16.9396	0.811259
$437$	20.6562	0.988120
$438$	21.7712	1.04027
$439$	22.9025	1.09308	0.546538	−	0.837435i	$-0.315946\pi$
$439$	22.9025	1.09308	0.546538	+	0.837435i	$0.315946\pi$
$440$	−7.00373	−0.333890
$441$	−6.48995	−0.309045
$442$	−4.49252	−0.213688
$443$	−18.6609	−0.886604	−0.443302	−	0.896372i	$-0.646193\pi$
$443$	−18.6609	−0.886604	−0.443302	+	0.896372i	$0.646193\pi$
$444$	9.52487	0.452030
$445$	5.38222	0.255142
$446$	−43.4740	−2.05855
$447$	6.85831	0.324387
$448$	0.0999004	0.00471985
$449$	41.7245	1.96910	0.984550	−	0.175105i	$-0.0560266\pi$
$449$	41.7245	1.96910	0.984550	+	0.175105i	$0.0560266\pi$
$450$	−4.00485	−0.188790
$451$	15.0688	0.709564
$452$	−9.41333	−0.442766
$453$	−5.46470	−0.256754
$454$	21.8959	1.02762
$455$	−4.89210	−0.229345
$456$	−9.85393	−0.461453
$457$	−17.0129	−0.795831	−0.397915	−	0.917422i	$-0.630266\pi$
$457$	−17.0129	−0.795831	−0.397915	+	0.917422i	$0.630266\pi$
$458$	15.8868	0.742342
$459$	−1.00000	−0.0466760
$460$	9.83223	0.458430
$461$	−39.8612	−1.85652	−0.928260	−	0.371931i	$-0.878696\pi$
$461$	−39.8612	−1.85652	−0.928260	+	0.371931i	$0.878696\pi$
$462$	2.12111	0.0986830
$463$	29.5097	1.37143	0.685715	−	0.727870i	$-0.259490\pi$
$463$	29.5097	1.37143	0.685715	+	0.727870i	$0.259490\pi$
$464$	−15.7316	−0.730319
$465$	−7.62852	−0.353764
$466$	−15.9274	−0.737822
$467$	−23.5570	−1.09009	−0.545044	−	0.838407i	$-0.683487\pi$
$467$	−23.5570	−1.09009	−0.545044	+	0.838407i	$0.683487\pi$
$468$	2.85930	0.132171
$469$	4.14679	0.191481
$470$	−17.9839	−0.829537
$471$	−9.26726	−0.427013
$472$	9.01886	0.415127
$473$	−10.6391	−0.489186
$474$	−1.76780	−0.0811979
$475$	14.4339	0.662274
$476$	−0.803547	−0.0368305
$477$	9.52417	0.436082
$478$	8.99917	0.411612
$479$	−4.07548	−0.186213	−0.0931067	−	0.995656i	$-0.529680\pi$
$479$	−4.07548	−0.186213	−0.0931067	+	0.995656i	$0.529680\pi$
$480$	−15.4130	−0.703502
$481$	−21.5135	−0.980933
$482$	−17.8022	−0.810868
$483$	2.31540	0.105354
$484$	−9.20070	−0.418213
$485$	−8.95838	−0.406779
$486$	1.76780	0.0801892
$487$	−11.3606	−0.514799	−0.257400	−	0.966305i	$-0.582866\pi$
$487$	−11.3606	−0.514799	−0.257400	+	0.966305i	$0.582866\pi$
$488$	8.35348	0.378144
$489$	−15.5793	−0.704522
$490$	30.9247	1.39704
$491$	33.7699	1.52401	0.762007	−	0.647569i	$-0.224214\pi$
$491$	33.7699	1.52401	0.762007	+	0.647569i	$0.224214\pi$
$492$	10.0916	0.454966
$493$	3.15620	0.142148
$494$	−28.6235	−1.28783
$495$	−4.52848	−0.203540
$496$	−14.1064	−0.633398
$497$	−11.3250	−0.507993
$498$	2.79277	0.125147
$499$	16.6871	0.747018	0.373509	−	0.927627i	$-0.378154\pi$
$499$	16.6871	0.747018	0.373509	+	0.927627i	$0.378154\pi$
$500$	−8.29320	−0.370883
$501$	15.9793	0.713903
$502$	−22.0375	−0.983582
$503$	−10.2459	−0.456843	−0.228421	−	0.973562i	$-0.573356\pi$
$503$	−10.2459	−0.456843	−0.228421	+	0.973562i	$0.573356\pi$
$504$	−1.10455	−0.0492005
$505$	−42.9095	−1.90945
$506$	9.62883	0.428054
$507$	6.54178	0.290531
$508$	−8.44922	−0.374873
$509$	1.24526	0.0551953	0.0275977	−	0.999619i	$-0.491214\pi$
$509$	1.24526	0.0551953	0.0275977	+	0.999619i	$0.491214\pi$
$510$	4.76502	0.210999
$511$	−8.79541	−0.389086
$512$	−13.0837	−0.578222
$513$	−6.37137	−0.281303
$514$	27.3988	1.20851
$515$	10.1102	0.445507
$516$	−7.12503	−0.313662
$517$	−6.34076	−0.278866
$518$	−10.6880	−0.469605
$519$	11.4450	0.502381
$520$	10.5941	0.464582
$521$	7.06743	0.309630	0.154815	−	0.987943i	$-0.450522\pi$
$521$	7.06743	0.309630	0.154815	+	0.987943i	$0.450522\pi$
$522$	−5.57954	−0.244210
$523$	27.6291	1.20813	0.604067	−	0.796933i	$-0.293546\pi$
$523$	27.6291	1.20813	0.604067	+	0.796933i	$0.293546\pi$
$524$	−13.1741	−0.575514
$525$	1.61793	0.0706122
$526$	−10.2661	−0.447624
$527$	2.83015	0.123283
$528$	−8.37393	−0.364429
$529$	−12.4892	−0.543009
$530$	−45.3829	−1.97131
$531$	5.83142	0.253062
$532$	−5.11969	−0.221967
$533$	−22.7937	−0.987304
$534$	3.52992	0.152755
$535$	−31.8940	−1.37890
$536$	−8.98009	−0.387881
$537$	22.0538	0.951692
$538$	−55.4483	−2.39055
$539$	10.9034	0.469643
$540$	−3.03273	−0.130508
$541$	21.8028	0.937374	0.468687	−	0.883364i	$-0.344727\pi$
$541$	21.8028	0.937374	0.468687	+	0.883364i	$0.344727\pi$
$542$	0.354984	0.0152479
$543$	−14.5681	−0.625178
$544$	5.71815	0.245164
$545$	40.5817	1.73833
$546$	−3.20847	−0.137310
$547$	17.5496	0.750366	0.375183	−	0.926951i	$-0.377580\pi$
$547$	17.5496	0.750366	0.375183	+	0.926951i	$0.377580\pi$
$548$	−11.3060	−0.482968
$549$	5.40120	0.230518
$550$	6.72833	0.286897
$551$	20.1093	0.856684
$552$	−5.01412	−0.213415
$553$	0.714180	0.0303700
$554$	41.7984	1.77584
$555$	22.8185	0.968590
$556$	2.17293	0.0921526
$557$	−1.34741	−0.0570914	−0.0285457	−	0.999592i	$-0.509088\pi$
$557$	−1.34741	−0.0570914	−0.0285457	+	0.999592i	$0.509088\pi$
$558$	−5.00315	−0.211800
$559$	16.0931	0.680665
$560$	9.59503	0.405464
$561$	1.68005	0.0709316
$562$	−5.36515	−0.226315
$563$	31.9439	1.34627	0.673137	−	0.739518i	$-0.264946\pi$
$563$	31.9439	1.34627	0.673137	+	0.739518i	$0.264946\pi$
$564$	−4.24642	−0.178807
$565$	−22.5513	−0.948739
$566$	−34.2995	−1.44172
$567$	−0.714180	−0.0299928
$568$	24.5248	1.02904
$569$	−4.59193	−0.192504	−0.0962518	−	0.995357i	$-0.530685\pi$
$569$	−4.59193	−0.192504	−0.0962518	+	0.995357i	$0.530685\pi$
$570$	30.3597	1.27163
$571$	27.6948	1.15899	0.579496	−	0.814975i	$-0.303249\pi$
$571$	27.6948	1.15899	0.579496	+	0.814975i	$0.303249\pi$
$572$	−4.80376	−0.200855
$573$	−3.39488	−0.141823
$574$	−11.3240	−0.472655
$575$	7.34462	0.306292
$576$	−0.139881	−0.00582838
$577$	−25.1961	−1.04893	−0.524464	−	0.851432i	$-0.675734\pi$
$577$	−25.1961	−1.04893	−0.524464	+	0.851432i	$0.675734\pi$
$578$	−1.76780	−0.0735310
$579$	−18.1663	−0.754965
$580$	9.57190	0.397451
$581$	−1.12826	−0.0468081
$582$	−5.87534	−0.243541
$583$	−16.0011	−0.662696
$584$	19.0469	0.788168
$585$	6.84995	0.283210
$586$	−15.5399	−0.641949
$587$	−4.23210	−0.174677	−0.0873387	−	0.996179i	$-0.527836\pi$
$587$	−4.23210	−0.174677	−0.0873387	+	0.996179i	$0.527836\pi$
$588$	7.30204	0.301131
$589$	18.0319	0.742993
$590$	−27.7869	−1.14397
$591$	−10.2200	−0.420395
$592$	42.1953	1.73421
$593$	−7.63759	−0.313638	−0.156819	−	0.987627i	$-0.550124\pi$
$593$	−7.63759	−0.313638	−0.156819	+	0.987627i	$0.550124\pi$
$594$	−2.96999	−0.121860
$595$	−1.92504	−0.0789187
$596$	−7.71651	−0.316080
$597$	−21.1932	−0.867378
$598$	−14.5649	−0.595604
$599$	8.56463	0.349941	0.174971	−	0.984574i	$-0.444017\pi$
$599$	8.56463	0.349941	0.174971	+	0.984574i	$0.444017\pi$
$600$	−3.50371	−0.143039
$601$	26.8257	1.09424	0.547121	−	0.837054i	$-0.315724\pi$
$601$	26.8257	1.09424	0.547121	+	0.837054i	$0.315724\pi$
$602$	7.99512	0.325857
$603$	−5.80636	−0.236453
$604$	6.14850	0.250179
$605$	−22.0419	−0.896129
$606$	−28.1421	−1.14319
$607$	1.84810	0.0750122	0.0375061	−	0.999296i	$-0.488059\pi$
$607$	1.84810	0.0750122	0.0375061	+	0.999296i	$0.488059\pi$
$608$	36.4324	1.47753
$609$	2.25409	0.0913405
$610$	−25.7369	−1.04205
$611$	9.59127	0.388021
$612$	1.12513	0.0454807
$613$	24.8265	1.00273	0.501366	−	0.865235i	$-0.332831\pi$
$613$	24.8265	1.00273	0.501366	+	0.865235i	$0.332831\pi$
$614$	22.2809	0.899183
$615$	24.1763	0.974881
$616$	1.85569	0.0747680
$617$	5.17783	0.208451	0.104226	−	0.994554i	$-0.466764\pi$
$617$	5.17783	0.208451	0.104226	+	0.994554i	$0.466764\pi$
$618$	6.63074	0.266727
$619$	3.83152	0.154002	0.0770010	−	0.997031i	$-0.475466\pi$
$619$	3.83152	0.154002	0.0770010	+	0.997031i	$0.475466\pi$
$620$	8.58309	0.344705
$621$	−3.24204	−0.130098
$622$	−45.5448	−1.82618
$623$	−1.42606	−0.0571340
$624$	12.6667	0.507075
$625$	−31.1950	−1.24780
$626$	32.5782	1.30209
$627$	10.7042	0.427484
$628$	10.4269	0.416078
$629$	−8.46556	−0.337544
$630$	3.40309	0.135582
$631$	−24.5059	−0.975565	−0.487782	−	0.872965i	$-0.662194\pi$
$631$	−24.5059	−0.975565	−0.487782	+	0.872965i	$0.662194\pi$
$632$	−1.54660	−0.0615203
$633$	−5.41749	−0.215326
$634$	−3.60726	−0.143263
$635$	−20.2416	−0.803262
$636$	−10.7159	−0.424915
$637$	−16.4929	−0.653473
$638$	9.37388	0.371116
$639$	15.8573	0.627304
$640$	−30.1594	−1.19215
$641$	41.7267	1.64810	0.824052	−	0.566514i	$-0.191708\pi$
$641$	41.7267	1.64810	0.824052	+	0.566514i	$0.191708\pi$
$642$	−20.9177	−0.825554
$643$	−31.1495	−1.22842	−0.614209	−	0.789143i	$-0.710525\pi$
$643$	−31.1495	−1.22842	−0.614209	+	0.789143i	$0.710525\pi$
$644$	−2.60513	−0.102656
$645$	−17.0692	−0.672100
$646$	−11.2633	−0.443150
$647$	30.7936	1.21062	0.605310	−	0.795990i	$-0.293049\pi$
$647$	30.7936	1.21062	0.605310	+	0.795990i	$0.293049\pi$
$648$	1.54660	0.0607560
$649$	−9.79707	−0.384569
$650$	−10.1775	−0.399195
$651$	2.02124	0.0792186
$652$	17.5288	0.686481
$653$	−15.3190	−0.599478	−0.299739	−	0.954021i	$-0.596900\pi$
$653$	−15.3190	−0.599478	−0.299739	+	0.954021i	$0.596900\pi$
$654$	26.6154	1.04075
$655$	−31.5609	−1.23319
$656$	44.7060	1.74548
$657$	12.3154	0.480469
$658$	4.76499	0.185759
$659$	−37.8371	−1.47392	−0.736961	−	0.675935i	$-0.763740\pi$
$659$	−37.8371	−1.47392	−0.736961	+	0.675935i	$0.763740\pi$
$660$	5.09513	0.198328
$661$	−28.4095	−1.10500	−0.552501	−	0.833512i	$-0.686326\pi$
$661$	−28.4095	−1.10500	−0.552501	+	0.833512i	$0.686326\pi$
$662$	−3.09771	−0.120396
$663$	−2.54130	−0.0986960
$664$	2.44331	0.0948187
$665$	−12.2651	−0.475620
$666$	14.9655	0.579900
$667$	10.2325	0.396204
$668$	−17.9788	−0.695622
$669$	−24.5921	−0.950785
$670$	27.6674	1.06889
$671$	−9.07428	−0.350309
$672$	4.08379	0.157536
$673$	30.0105	1.15682	0.578410	−	0.815747i	$-0.303674\pi$
$673$	30.0105	1.15682	0.578410	+	0.815747i	$0.303674\pi$
$674$	−25.0226	−0.963835
$675$	−2.26544	−0.0871966
$676$	−7.36037	−0.283091
$677$	−26.8459	−1.03177	−0.515885	−	0.856658i	$-0.672537\pi$
$677$	−26.8459	−1.03177	−0.515885	+	0.856658i	$0.672537\pi$
$678$	−14.7902	−0.568015
$679$	2.37359	0.0910902
$680$	4.16877	0.159865
$681$	12.3859	0.474629
$682$	8.40553	0.321865
$683$	−28.7258	−1.09916	−0.549580	−	0.835441i	$-0.685212\pi$
$683$	−28.7258	−1.09916	−0.549580	+	0.835441i	$0.685212\pi$
$684$	7.16862	0.274099
$685$	−27.0855	−1.03488
$686$	−17.0315	−0.650265
$687$	8.98675	0.342866
$688$	−31.5639	−1.20336
$689$	24.2038	0.922091
$690$	15.4484	0.588109
$691$	30.6598	1.16636	0.583178	−	0.812345i	$-0.301809\pi$
$691$	30.6598	1.16636	0.583178	+	0.812345i	$0.301809\pi$
$692$	−12.8772	−0.489516
$693$	1.19986	0.0455788
$694$	12.9027	0.489781
$695$	5.20562	0.197461
$696$	−4.88136	−0.185028
$697$	−8.96930	−0.339736
$698$	9.07016	0.343310
$699$	−9.00970	−0.340778
$700$	−1.82038	−0.0688040
$701$	33.2606	1.25623	0.628117	−	0.778119i	$-0.283826\pi$
$701$	33.2606	1.25623	0.628117	+	0.778119i	$0.283826\pi$
$702$	4.49252	0.169559
$703$	−53.9372	−2.03428
$704$	0.235007	0.00885716
$705$	−10.1730	−0.383139
$706$	14.2323	0.535638
$707$	11.3692	0.427583
$708$	−6.56112	−0.246582
$709$	−48.5032	−1.82158	−0.910789	−	0.412873i	$-0.864525\pi$
$709$	−48.5032	−1.82158	−0.910789	+	0.412873i	$0.864525\pi$
$710$	−75.5603	−2.83573
$711$	−1.00000	−0.0375029
$712$	3.08822	0.115736
$713$	9.17545	0.343623
$714$	−1.26253	−0.0472490
$715$	−11.5082	−0.430383
$716$	−24.8134	−0.927321
$717$	5.09059	0.190112
$718$	−24.5796	−0.917302
$719$	−24.3973	−0.909868	−0.454934	−	0.890525i	$-0.650337\pi$
$719$	−24.3973	−0.909868	−0.454934	+	0.890525i	$0.650337\pi$
$720$	−13.4350	−0.500694
$721$	−2.67877	−0.0997627
$722$	−38.1745	−1.42071
$723$	−10.0702	−0.374516
$724$	16.3910	0.609168
$725$	7.15016	0.265550
$726$	−14.4561	−0.536517
$727$	−5.47878	−0.203197	−0.101598	−	0.994826i	$-0.532396\pi$
$727$	−5.47878	−0.203197	−0.101598	+	0.994826i	$0.532396\pi$
$728$	−2.80699	−0.104034
$729$	1.00000	0.0370370
$730$	−58.6831	−2.17196
$731$	6.33262	0.234220
$732$	−6.07706	−0.224615
$733$	29.8642	1.10306	0.551529	−	0.834156i	$-0.314045\pi$
$733$	29.8642	1.10306	0.551529	+	0.834156i	$0.314045\pi$
$734$	−45.6190	−1.68383
$735$	17.4933	0.645250
$736$	18.5384	0.683336
$737$	9.75495	0.359328
$738$	15.8560	0.583666
$739$	38.9061	1.43118	0.715591	−	0.698519i	$-0.246157\pi$
$739$	38.9061	1.43118	0.715591	+	0.698519i	$0.246157\pi$
$740$	−25.6738	−0.943787
$741$	−16.1916	−0.594812
$742$	12.0246	0.441436
$743$	−10.2914	−0.377554	−0.188777	−	0.982020i	$-0.560452\pi$
$743$	−10.2914	−0.377554	−0.188777	+	0.982020i	$0.560452\pi$
$744$	−4.37710	−0.160472
$745$	−18.4862	−0.677283
$746$	25.1199	0.919704
$747$	1.57980	0.0578017
$748$	−1.89027	−0.0691153
$749$	8.45058	0.308778
$750$	−13.0303	−0.475798
$751$	19.8136	0.723008	0.361504	−	0.932371i	$-0.382263\pi$
$751$	19.8136	0.723008	0.361504	+	0.932371i	$0.382263\pi$
$752$	−18.8117	−0.685991
$753$	−12.4660	−0.454288
$754$	−14.1793	−0.516379
$755$	14.7298	0.536072
$756$	0.803547	0.0292247
$757$	32.6321	1.18603	0.593017	−	0.805190i	$-0.297937\pi$
$757$	32.6321	1.18603	0.593017	+	0.805190i	$0.297937\pi$
$758$	−10.8209	−0.393032
$759$	5.44677	0.197705
$760$	26.5608	0.963460
$761$	−41.6567	−1.51006	−0.755028	−	0.655693i	$-0.772377\pi$
$761$	−41.6567	−1.51006	−0.755028	+	0.655693i	$0.772377\pi$
$762$	−13.2754	−0.480917
$763$	−10.7524	−0.389265
$764$	3.81968	0.138191
$765$	2.69545	0.0974541
$766$	−50.8068	−1.83572
$767$	14.8194	0.535098
$768$	−20.0597	−0.723844
$769$	3.35352	0.120931	0.0604655	−	0.998170i	$-0.480741\pi$
$769$	3.35352	0.120931	0.0604655	+	0.998170i	$0.480741\pi$
$770$	−5.71734	−0.206039
$771$	15.4988	0.558174
$772$	20.4394	0.735632
$773$	−47.3974	−1.70477	−0.852384	−	0.522917i	$-0.824844\pi$
$773$	−47.3974	−1.70477	−0.852384	+	0.522917i	$0.824844\pi$
$774$	−11.1948	−0.402390
$775$	6.41153	0.230309
$776$	−5.14015	−0.184521
$777$	−6.04594	−0.216897
$778$	−51.1937	−1.83538
$779$	−57.1467	−2.04749
$780$	−7.70709	−0.275958
$781$	−26.6410	−0.953289
$782$	−5.73128	−0.204950
$783$	−3.15620	−0.112793
$784$	32.3481	1.15529
$785$	24.9794	0.891553
$786$	−20.6991	−0.738314
$787$	5.16616	0.184154	0.0920769	−	0.995752i	$-0.470649\pi$
$787$	5.16616	0.184154	0.0920769	+	0.995752i	$0.470649\pi$
$788$	11.4988	0.409629
$789$	−5.80727	−0.206744
$790$	4.76502	0.169532
$791$	5.97514	0.212451
$792$	−2.59835	−0.0923285
$793$	13.7261	0.487428
$794$	−18.2171	−0.646500
$795$	−25.6719	−0.910489
$796$	23.8451	0.845167
$797$	−20.8300	−0.737837	−0.368918	−	0.929462i	$-0.620272\pi$
$797$	−20.8300	−0.737837	−0.368918	+	0.929462i	$0.620272\pi$
$798$	−8.04405	−0.284756
$799$	3.77416	0.133520
$800$	12.9541	0.457996
$801$	1.99678	0.0705529
$802$	38.7856	1.36957
$803$	−20.6904	−0.730150
$804$	6.53291	0.230398
$805$	−6.24103	−0.219967
$806$	−12.7145	−0.447850
$807$	−31.3656	−1.10412
$808$	−24.6206	−0.866151
$809$	27.5050	0.967023	0.483512	−	0.875338i	$-0.339361\pi$
$809$	27.5050	0.967023	0.483512	+	0.875338i	$0.339361\pi$
$810$	−4.76502	−0.167426
$811$	−19.1305	−0.671763	−0.335882	−	0.941904i	$-0.609034\pi$
$811$	−19.1305	−0.671763	−0.335882	+	0.941904i	$0.609034\pi$
$812$	−2.53615	−0.0890014
$813$	0.200805	0.00704253
$814$	−25.1427	−0.881250
$815$	41.9933	1.47096
$816$	4.98434	0.174487
$817$	40.3474	1.41158
$818$	−15.4832	−0.541359
$819$	−1.81495	−0.0634194
$820$	−27.2015	−0.949917
$821$	22.3436	0.779798	0.389899	−	0.920858i	$-0.372510\pi$
$821$	22.3436	0.779798	0.389899	+	0.920858i	$0.372510\pi$
$822$	−17.7640	−0.619589
$823$	12.3508	0.430523	0.215261	−	0.976556i	$-0.430940\pi$
$823$	12.3508	0.430523	0.215261	+	0.976556i	$0.430940\pi$
$824$	5.80103	0.202088
$825$	3.80604	0.132509
$826$	7.36235	0.256169
$827$	−39.8278	−1.38495	−0.692474	−	0.721443i	$-0.743479\pi$
$827$	−39.8278	−1.38495	−0.692474	+	0.721443i	$0.743479\pi$
$828$	3.64772	0.126767
$829$	14.9077	0.517766	0.258883	−	0.965909i	$-0.416646\pi$
$829$	14.9077	0.517766	0.258883	+	0.965909i	$0.416646\pi$
$830$	−7.52777	−0.261293
$831$	23.6442	0.820209
$832$	−0.355480	−0.0123241
$833$	−6.48995	−0.224863
$834$	3.41410	0.118221
$835$	−43.0714	−1.49055
$836$	−12.0436	−0.416538
$837$	−2.83015	−0.0978244
$838$	−29.5319	−1.02016
$839$	50.4651	1.74225	0.871124	−	0.491063i	$-0.163391\pi$
$839$	50.4651	1.74225	0.871124	+	0.491063i	$0.163391\pi$
$840$	2.97725	0.102725
$841$	−19.0384	−0.656497
$842$	0.494543	0.0170431
$843$	−3.03492	−0.104528
$844$	6.09539	0.209812
$845$	−17.6330	−0.606595
$846$	−6.67197	−0.229387
$847$	5.84017	0.200671
$848$	−47.4717	−1.63019
$849$	−19.4023	−0.665887
$850$	−4.00485	−0.137365
$851$	−27.4456	−0.940825
$852$	−17.8415	−0.611240
$853$	8.95619	0.306654	0.153327	−	0.988176i	$-0.451001\pi$
$853$	8.95619	0.306654	0.153327	+	0.988176i	$0.451001\pi$
$854$	6.81919	0.233348
$855$	17.1737	0.587328
$856$	−18.3002	−0.625488
$857$	−8.87077	−0.303020	−0.151510	−	0.988456i	$-0.548414\pi$
$857$	−8.87077	−0.303020	−0.151510	+	0.988456i	$0.548414\pi$
$858$	−7.54765	−0.257673
$859$	−46.7887	−1.59641	−0.798205	−	0.602386i	$-0.794217\pi$
$859$	−46.7887	−1.59641	−0.798205	+	0.602386i	$0.794217\pi$
$860$	19.2051	0.654890
$861$	−6.40569	−0.218305
$862$	−8.85490	−0.301599
$863$	0.995812	0.0338978	0.0169489	−	0.999856i	$-0.494605\pi$
$863$	0.995812	0.0338978	0.0169489	+	0.999856i	$0.494605\pi$
$864$	−5.71815	−0.194535
$865$	−30.8494	−1.04891
$866$	47.8652	1.62653
$867$	−1.00000	−0.0339618
$868$	−2.27416	−0.0771900
$869$	1.68005	0.0569917
$870$	15.0393	0.509882
$871$	−14.7557	−0.499978
$872$	23.2850	0.788530
$873$	−3.32352	−0.112484
$874$	−36.5161	−1.23518
$875$	5.26413	0.177960
$876$	−13.8564	−0.468165
$877$	27.3490	0.923509	0.461754	−	0.887008i	$-0.347220\pi$
$877$	27.3490	0.923509	0.461754	+	0.887008i	$0.347220\pi$
$878$	−40.4871	−1.36637
$879$	−8.79053	−0.296497
$880$	22.5715	0.760885
$881$	30.5713	1.02997	0.514986	−	0.857199i	$-0.327797\pi$
$881$	30.5713	1.02997	0.514986	+	0.857199i	$0.327797\pi$
$882$	11.4730	0.386314
$883$	−1.01350	−0.0341070	−0.0170535	−	0.999855i	$-0.505429\pi$
$883$	−1.01350	−0.0341070	−0.0170535	+	0.999855i	$0.505429\pi$
$884$	2.85930	0.0961686
$885$	−15.7183	−0.528365
$886$	32.9888	1.10828
$887$	−40.1843	−1.34926	−0.674629	−	0.738157i	$-0.735696\pi$
$887$	−40.1843	−1.34926	−0.674629	+	0.738157i	$0.735696\pi$
$888$	13.0928	0.439366
$889$	5.36317	0.179875
$890$	−9.51472	−0.318934
$891$	−1.68005	−0.0562837
$892$	27.6693	0.926438
$893$	24.0465	0.804686
$894$	−12.1242	−0.405492
$895$	−59.4449	−1.98702
$896$	7.99097	0.266960
$897$	−8.23899	−0.275092
$898$	−73.7607	−2.46143
$899$	8.93251	0.297916
$900$	2.54891	0.0849637
$901$	9.52417	0.317296
$902$	−26.6388	−0.886974
$903$	4.52263	0.150504
$904$	−12.9395	−0.430361
$905$	39.2676	1.30530
$906$	9.66051	0.320949
$907$	17.3015	0.574487	0.287243	−	0.957858i	$-0.407261\pi$
$907$	17.3015	0.574487	0.287243	+	0.957858i	$0.407261\pi$
$908$	−13.9358	−0.462475
$909$	−15.9192	−0.528008
$910$	8.64827	0.286687
$911$	41.0449	1.35988	0.679939	−	0.733269i	$-0.262006\pi$
$911$	41.0449	1.35988	0.679939	+	0.733269i	$0.262006\pi$
$912$	31.7571	1.05158
$913$	−2.65413	−0.0878390
$914$	30.0755	0.994809
$915$	−14.5587	−0.481294
$916$	−10.1113	−0.334086
$917$	8.36231	0.276148
$918$	1.76780	0.0583462
$919$	48.7119	1.60686	0.803429	−	0.595401i	$-0.203007\pi$
$919$	48.7119	1.60686	0.803429	+	0.595401i	$0.203007\pi$
$920$	13.5153	0.445586
$921$	12.6037	0.415306
$922$	70.4668	2.32070
$923$	40.2981	1.32643
$924$	−1.35000	−0.0444116
$925$	−19.1782	−0.630575
$926$	−52.1673	−1.71432
$927$	3.75083	0.123194
$928$	18.0476	0.592441
$929$	−13.5572	−0.444797	−0.222399	−	0.974956i	$-0.571389\pi$
$929$	−13.5572	−0.444797	−0.222399	+	0.974956i	$0.571389\pi$
$930$	13.4857	0.442215
$931$	−41.3498	−1.35519
$932$	10.1371	0.332052
$933$	−25.7635	−0.843459
$934$	41.6442	1.36264
$935$	−4.52848	−0.148097
$936$	3.93037	0.128468
$937$	25.5692	0.835311	0.417655	−	0.908606i	$-0.362852\pi$
$937$	25.5692	0.835311	0.417655	+	0.908606i	$0.362852\pi$
$938$	−7.33070	−0.239356
$939$	18.4286	0.601396
$940$	11.4460	0.373327
$941$	47.5649	1.55057	0.775286	−	0.631610i	$-0.217606\pi$
$941$	47.5649	1.55057	0.775286	+	0.631610i	$0.217606\pi$
$942$	16.3827	0.533777
$943$	−29.0788	−0.946935
$944$	−29.0658	−0.946012
$945$	1.92504	0.0626214
$946$	18.8078	0.611496
$947$	29.5591	0.960541	0.480271	−	0.877120i	$-0.340538\pi$
$947$	29.5591	0.960541	0.480271	+	0.877120i	$0.340538\pi$
$948$	1.12513	0.0365426
$949$	31.2971	1.01595
$950$	−25.5163	−0.827859
$951$	−2.04053	−0.0661688
$952$	−1.10455	−0.0357986
$953$	−16.7758	−0.543420	−0.271710	−	0.962379i	$-0.587589\pi$
$953$	−16.7758	−0.543420	−0.271710	+	0.962379i	$0.587589\pi$
$954$	−16.8369	−0.545114
$955$	9.15071	0.296110
$956$	−5.72758	−0.185243
$957$	5.30256	0.171407
$958$	7.20465	0.232772
$959$	7.17651	0.231742
$960$	0.377042	0.0121690
$961$	−22.9902	−0.741621
$962$	38.0317	1.22619
$963$	−11.8326	−0.381299
$964$	11.3303	0.364926
$965$	48.9662	1.57628
$966$	−4.09317	−0.131696
$967$	8.87532	0.285411	0.142706	−	0.989765i	$-0.454420\pi$
$967$	8.87532	0.285411	0.142706	+	0.989765i	$0.454420\pi$
$968$	−12.6472	−0.406496
$969$	−6.37137	−0.204678
$970$	15.8367	0.508485
$971$	−3.19891	−0.102658	−0.0513290	−	0.998682i	$-0.516346\pi$
$971$	−3.19891	−0.102658	−0.0513290	+	0.998682i	$0.516346\pi$
$972$	−1.12513	−0.0360886
$973$	−1.37927	−0.0442174
$974$	20.0834	0.643513
$975$	−5.75716	−0.184377
$976$	−26.9214	−0.861734
$977$	−34.8094	−1.11365	−0.556826	−	0.830629i	$-0.687981\pi$
$977$	−34.8094	−1.11365	−0.556826	+	0.830629i	$0.687981\pi$
$978$	27.5412	0.880671
$979$	−3.35469	−0.107216
$980$	−19.6823	−0.628727
$981$	15.0557	0.480690
$982$	−59.6986	−1.90506
$983$	−1.65742	−0.0528635	−0.0264317	−	0.999651i	$-0.508414\pi$
$983$	−1.65742	−0.0528635	−0.0264317	+	0.999651i	$0.508414\pi$
$984$	13.8719	0.442219
$985$	27.5475	0.877736
$986$	−5.57954	−0.177689
$987$	2.69543	0.0857964
$988$	18.2176	0.579580
$989$	20.5306	0.652834
$990$	8.00546	0.254430
$991$	−6.48029	−0.205853	−0.102927	−	0.994689i	$-0.532821\pi$
$991$	−6.48029	−0.205853	−0.102927	+	0.994689i	$0.532821\pi$
$992$	16.1832	0.513818
$993$	−1.75229	−0.0556074
$994$	20.0203	0.635005
$995$	57.1251	1.81099
$996$	−1.77748	−0.0563216
$997$	−33.7496	−1.06886	−0.534431	−	0.845212i	$-0.679474\pi$
$997$	−33.7496	−1.06886	−0.534431	+	0.845212i	$0.679474\pi$
$998$	−29.4996	−0.933792
$999$	8.46556	0.267838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.6	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.76780 q^{2} -1.00000 q^{3} +1.12513 q^{4} +2.69545 q^{5} +1.76780 q^{6} -0.714180 q^{7} +1.54660 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.76780 q^{2} -1.00000 q^{3} +1.12513 q^{4} +2.69545 q^{5} +1.76780 q^{6} -0.714180 q^{7} +1.54660 q^{8} +1.00000 q^{9} -4.76502 q^{10} -1.68005 q^{11} -1.12513 q^{12} +2.54130 q^{13} +1.26253 q^{14} -2.69545 q^{15} -4.98434 q^{16} +1.00000 q^{17} -1.76780 q^{18} +6.37137 q^{19} +3.03273 q^{20} +0.714180 q^{21} +2.96999 q^{22} +3.24204 q^{23} -1.54660 q^{24} +2.26544 q^{25} -4.49252 q^{26} -1.00000 q^{27} -0.803547 q^{28} +3.15620 q^{29} +4.76502 q^{30} +2.83015 q^{31} +5.71815 q^{32} +1.68005 q^{33} -1.76780 q^{34} -1.92504 q^{35} +1.12513 q^{36} -8.46556 q^{37} -11.2633 q^{38} -2.54130 q^{39} +4.16877 q^{40} -8.96930 q^{41} -1.26253 q^{42} +6.33262 q^{43} -1.89027 q^{44} +2.69545 q^{45} -5.73128 q^{46} +3.77416 q^{47} +4.98434 q^{48} -6.48995 q^{49} -4.00485 q^{50} -1.00000 q^{51} +2.85930 q^{52} +9.52417 q^{53} +1.76780 q^{54} -4.52848 q^{55} -1.10455 q^{56} -6.37137 q^{57} -5.57954 q^{58} +5.83142 q^{59} -3.03273 q^{60} +5.40120 q^{61} -5.00315 q^{62} -0.714180 q^{63} -0.139881 q^{64} +6.84995 q^{65} -2.96999 q^{66} -5.80636 q^{67} +1.12513 q^{68} -3.24204 q^{69} +3.40309 q^{70} +15.8573 q^{71} +1.54660 q^{72} +12.3154 q^{73} +14.9655 q^{74} -2.26544 q^{75} +7.16862 q^{76} +1.19986 q^{77} +4.49252 q^{78} -1.00000 q^{79} -13.4350 q^{80} +1.00000 q^{81} +15.8560 q^{82} +1.57980 q^{83} +0.803547 q^{84} +2.69545 q^{85} -11.1948 q^{86} -3.15620 q^{87} -2.59835 q^{88} +1.99678 q^{89} -4.76502 q^{90} -1.81495 q^{91} +3.64772 q^{92} -2.83015 q^{93} -6.67197 q^{94} +17.1737 q^{95} -5.71815 q^{96} -3.32352 q^{97} +11.4730 q^{98} -1.68005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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