LMFDB - Embedded newform 4026.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.26825.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + 5x + 5 $ x^4 - 2x^3 - 5x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.68442$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.40047 q^{5} -1.00000 q^{6} +3.20612 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.40047 q^{5} -1.00000 q^{6} +3.20612 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.40047 q^{10} -1.00000 q^{11} -1.00000 q^{12} +5.23775 q^{13} +3.20612 q^{14} -3.40047 q^{15} +1.00000 q^{16} -2.49008 q^{17} +1.00000 q^{18} +2.68442 q^{19} +3.40047 q^{20} -3.20612 q^{21} -1.00000 q^{22} +2.68442 q^{23} -1.00000 q^{24} +6.56319 q^{25} +5.23775 q^{26} -1.00000 q^{27} +3.20612 q^{28} -0.162720 q^{29} -3.40047 q^{30} -3.75945 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.49008 q^{34} +10.9023 q^{35} +1.00000 q^{36} -5.00986 q^{37} +2.68442 q^{38} -5.23775 q^{39} +3.40047 q^{40} +1.12123 q^{41} -3.20612 q^{42} -3.47830 q^{43} -1.00000 q^{44} +3.40047 q^{45} +2.68442 q^{46} +4.35706 q^{47} -1.00000 q^{48} +3.27924 q^{49} +6.56319 q^{50} +2.49008 q^{51} +5.23775 q^{52} +7.89055 q^{53} -1.00000 q^{54} -3.40047 q^{55} +3.20612 q^{56} -2.68442 q^{57} -0.162720 q^{58} +4.89527 q^{59} -3.40047 q^{60} -1.00000 q^{61} -3.75945 q^{62} +3.20612 q^{63} +1.00000 q^{64} +17.8108 q^{65} +1.00000 q^{66} -7.69620 q^{67} -2.49008 q^{68} -2.68442 q^{69} +10.9023 q^{70} -9.45374 q^{71} +1.00000 q^{72} -11.6184 q^{73} -5.00986 q^{74} -6.56319 q^{75} +2.68442 q^{76} -3.20612 q^{77} -5.23775 q^{78} -12.0622 q^{79} +3.40047 q^{80} +1.00000 q^{81} +1.12123 q^{82} -6.00706 q^{83} -3.20612 q^{84} -8.46743 q^{85} -3.47830 q^{86} +0.162720 q^{87} -1.00000 q^{88} -7.57025 q^{89} +3.40047 q^{90} +16.7929 q^{91} +2.68442 q^{92} +3.75945 q^{93} +4.35706 q^{94} +9.12830 q^{95} -1.00000 q^{96} -12.4971 q^{97} +3.27924 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} + 3 q^{10} - 4 q^{11} - 4 q^{12} + 13 q^{13} - 2 q^{14} - 3 q^{15} + 4 q^{16} + 3 q^{17} + 4 q^{18} + 2 q^{19} + 3 q^{20} + 2 q^{21} - 4 q^{22} + 2 q^{23} - 4 q^{24} + 13 q^{25} + 13 q^{26} - 4 q^{27} - 2 q^{28} + 2 q^{29} - 3 q^{30} - q^{31} + 4 q^{32} + 4 q^{33} + 3 q^{34} + q^{35} + 4 q^{36} - 6 q^{37} + 2 q^{38} - 13 q^{39} + 3 q^{40} + 9 q^{41} + 2 q^{42} - 20 q^{43} - 4 q^{44} + 3 q^{45} + 2 q^{46} + 19 q^{47} - 4 q^{48} - 2 q^{49} + 13 q^{50} - 3 q^{51} + 13 q^{52} + 8 q^{53} - 4 q^{54} - 3 q^{55} - 2 q^{56} - 2 q^{57} + 2 q^{58} + 13 q^{59} - 3 q^{60} - 4 q^{61} - q^{62} - 2 q^{63} + 4 q^{64} + 36 q^{65} + 4 q^{66} - 3 q^{67} + 3 q^{68} - 2 q^{69} + q^{70} - q^{71} + 4 q^{72} - 2 q^{73} - 6 q^{74} - 13 q^{75} + 2 q^{76} + 2 q^{77} - 13 q^{78} + 19 q^{79} + 3 q^{80} + 4 q^{81} + 9 q^{82} + 12 q^{83} + 2 q^{84} + 27 q^{85} - 20 q^{86} - 2 q^{87} - 4 q^{88} + 19 q^{89} + 3 q^{90} + q^{91} + 2 q^{92} + q^{93} + 19 q^{94} + 5 q^{95} - 4 q^{96} - q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 + 3 * q^10 - 4 * q^11 - 4 * q^12 + 13 * q^13 - 2 * q^14 - 3 * q^15 + 4 * q^16 + 3 * q^17 + 4 * q^18 + 2 * q^19 + 3 * q^20 + 2 * q^21 - 4 * q^22 + 2 * q^23 - 4 * q^24 + 13 * q^25 + 13 * q^26 - 4 * q^27 - 2 * q^28 + 2 * q^29 - 3 * q^30 - q^31 + 4 * q^32 + 4 * q^33 + 3 * q^34 + q^35 + 4 * q^36 - 6 * q^37 + 2 * q^38 - 13 * q^39 + 3 * q^40 + 9 * q^41 + 2 * q^42 - 20 * q^43 - 4 * q^44 + 3 * q^45 + 2 * q^46 + 19 * q^47 - 4 * q^48 - 2 * q^49 + 13 * q^50 - 3 * q^51 + 13 * q^52 + 8 * q^53 - 4 * q^54 - 3 * q^55 - 2 * q^56 - 2 * q^57 + 2 * q^58 + 13 * q^59 - 3 * q^60 - 4 * q^61 - q^62 - 2 * q^63 + 4 * q^64 + 36 * q^65 + 4 * q^66 - 3 * q^67 + 3 * q^68 - 2 * q^69 + q^70 - q^71 + 4 * q^72 - 2 * q^73 - 6 * q^74 - 13 * q^75 + 2 * q^76 + 2 * q^77 - 13 * q^78 + 19 * q^79 + 3 * q^80 + 4 * q^81 + 9 * q^82 + 12 * q^83 + 2 * q^84 + 27 * q^85 - 20 * q^86 - 2 * q^87 - 4 * q^88 + 19 * q^89 + 3 * q^90 + q^91 + 2 * q^92 + q^93 + 19 * q^94 + 5 * q^95 - 4 * q^96 - q^97 - 2 * q^98 - 4 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.40047	1.52074	0.760368	−	0.649493i	$-0.225019\pi$
$5$	3.40047	1.52074	0.760368	+	0.649493i	$0.225019\pi$
$6$	−1.00000	−0.408248
$7$	3.20612	1.21180	0.605901	−	0.795540i	$-0.292813\pi$
$7$	3.20612	1.21180	0.605901	+	0.795540i	$0.292813\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.40047	1.07532
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	5.23775	1.45269	0.726345	−	0.687330i	$-0.241217\pi$
$13$	5.23775	1.45269	0.726345	+	0.687330i	$0.241217\pi$
$14$	3.20612	0.856873
$15$	−3.40047	−0.877997
$16$	1.00000	0.250000
$17$	−2.49008	−0.603933	−0.301966	−	0.953319i	$-0.597643\pi$
$17$	−2.49008	−0.603933	−0.301966	+	0.953319i	$0.597643\pi$
$18$	1.00000	0.235702
$19$	2.68442	0.615849	0.307924	−	0.951411i	$-0.400366\pi$
$19$	2.68442	0.615849	0.307924	+	0.951411i	$0.400366\pi$
$20$	3.40047	0.760368
$21$	−3.20612	−0.699634
$22$	−1.00000	−0.213201
$23$	2.68442	0.559741	0.279870	−	0.960038i	$-0.409708\pi$
$23$	2.68442	0.559741	0.279870	+	0.960038i	$0.409708\pi$
$24$	−1.00000	−0.204124
$25$	6.56319	1.31264
$26$	5.23775	1.02721
$27$	−1.00000	−0.192450
$28$	3.20612	0.605901
$29$	−0.162720	−0.0302164	−0.0151082	−	0.999886i	$-0.504809\pi$
$29$	−0.162720	−0.0302164	−0.0151082	+	0.999886i	$0.504809\pi$
$30$	−3.40047	−0.620838
$31$	−3.75945	−0.675217	−0.337609	−	0.941287i	$-0.609618\pi$
$31$	−3.75945	−0.675217	−0.337609	+	0.941287i	$0.609618\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−2.49008	−0.427045
$35$	10.9023	1.84283
$36$	1.00000	0.166667
$37$	−5.00986	−0.823616	−0.411808	−	0.911271i	$-0.635103\pi$
$37$	−5.00986	−0.823616	−0.411808	+	0.911271i	$0.635103\pi$
$38$	2.68442	0.435471
$39$	−5.23775	−0.838711
$40$	3.40047	0.537661
$41$	1.12123	0.175107	0.0875536	−	0.996160i	$-0.472095\pi$
$41$	1.12123	0.175107	0.0875536	+	0.996160i	$0.472095\pi$
$42$	−3.20612	−0.494716
$43$	−3.47830	−0.530435	−0.265218	−	0.964189i	$-0.585444\pi$
$43$	−3.47830	−0.530435	−0.265218	+	0.964189i	$0.585444\pi$
$44$	−1.00000	−0.150756
$45$	3.40047	0.506912
$46$	2.68442	0.395797
$47$	4.35706	0.635543	0.317772	−	0.948167i	$-0.397065\pi$
$47$	4.35706	0.635543	0.317772	+	0.948167i	$0.397065\pi$
$48$	−1.00000	−0.144338
$49$	3.27924	0.468462
$50$	6.56319	0.928175
$51$	2.49008	0.348681
$52$	5.23775	0.726345
$53$	7.89055	1.08385	0.541925	−	0.840427i	$-0.317696\pi$
$53$	7.89055	1.08385	0.541925	+	0.840427i	$0.317696\pi$
$54$	−1.00000	−0.136083
$55$	−3.40047	−0.458519
$56$	3.20612	0.428436
$57$	−2.68442	−0.355560
$58$	−0.162720	−0.0213662
$59$	4.89527	0.637309	0.318655	−	0.947871i	$-0.396769\pi$
$59$	4.89527	0.637309	0.318655	+	0.947871i	$0.396769\pi$
$60$	−3.40047	−0.438999
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−3.75945	−0.477451
$63$	3.20612	0.403934
$64$	1.00000	0.125000
$65$	17.8108	2.20916
$66$	1.00000	0.123091
$67$	−7.69620	−0.940241	−0.470120	−	0.882602i	$-0.655790\pi$
$67$	−7.69620	−0.940241	−0.470120	+	0.882602i	$0.655790\pi$
$68$	−2.49008	−0.301966
$69$	−2.68442	−0.323167
$70$	10.9023	1.30308
$71$	−9.45374	−1.12195	−0.560976	−	0.827832i	$-0.689574\pi$
$71$	−9.45374	−1.12195	−0.560976	+	0.827832i	$0.689574\pi$
$72$	1.00000	0.117851
$73$	−11.6184	−1.35983	−0.679914	−	0.733292i	$-0.737983\pi$
$73$	−11.6184	−1.35983	−0.679914	+	0.733292i	$0.737983\pi$
$74$	−5.00986	−0.582385
$75$	−6.56319	−0.757852
$76$	2.68442	0.307924
$77$	−3.20612	−0.365372
$78$	−5.23775	−0.593058
$79$	−12.0622	−1.35711	−0.678554	−	0.734550i	$-0.737393\pi$
$79$	−12.0622	−1.35711	−0.678554	+	0.734550i	$0.737393\pi$
$80$	3.40047	0.380184
$81$	1.00000	0.111111
$82$	1.12123	0.123819
$83$	−6.00706	−0.659361	−0.329680	−	0.944093i	$-0.606941\pi$
$83$	−6.00706	−0.659361	−0.329680	+	0.944093i	$0.606941\pi$
$84$	−3.20612	−0.349817
$85$	−8.46743	−0.918422
$86$	−3.47830	−0.375075
$87$	0.162720	0.0174455
$88$	−1.00000	−0.106600
$89$	−7.57025	−0.802445	−0.401223	−	0.915981i	$-0.631415\pi$
$89$	−7.57025	−0.802445	−0.401223	+	0.915981i	$0.631415\pi$
$90$	3.40047	0.358441
$91$	16.7929	1.76037
$92$	2.68442	0.279870
$93$	3.75945	0.389837
$94$	4.35706	0.449397
$95$	9.12830	0.936543
$96$	−1.00000	−0.102062
$97$	−12.4971	−1.26889	−0.634446	−	0.772967i	$-0.718772\pi$
$97$	−12.4971	−1.26889	−0.634446	+	0.772967i	$0.718772\pi$
$98$	3.27924	0.331253
$99$	−1.00000	−0.100504
$100$	6.56319	0.656319
$101$	12.0552	1.19954	0.599768	−	0.800174i	$-0.295260\pi$
$101$	12.0552	1.19954	0.599768	+	0.800174i	$0.295260\pi$
$102$	2.49008	0.246554
$103$	1.40047	0.137992	0.0689962	−	0.997617i	$-0.478020\pi$
$103$	1.40047	0.137992	0.0689962	+	0.997617i	$0.478020\pi$
$104$	5.23775	0.513603
$105$	−10.9023	−1.06396
$106$	7.89055	0.766398
$107$	−3.89246	−0.376299	−0.188149	−	0.982140i	$-0.560249\pi$
$107$	−3.89246	−0.376299	−0.188149	+	0.982140i	$0.560249\pi$
$108$	−1.00000	−0.0962250
$109$	9.49994	0.909929	0.454965	−	0.890509i	$-0.349652\pi$
$109$	9.49994	0.909929	0.454965	+	0.890509i	$0.349652\pi$
$110$	−3.40047	−0.324222
$111$	5.00986	0.475515
$112$	3.20612	0.302950
$113$	15.9538	1.50081	0.750403	−	0.660980i	$-0.229859\pi$
$113$	15.9538	1.50081	0.750403	+	0.660980i	$0.229859\pi$
$114$	−2.68442	−0.251419
$115$	9.12830	0.851218
$116$	−0.162720	−0.0151082
$117$	5.23775	0.484230
$118$	4.89527	0.450646
$119$	−7.98350	−0.731846
$120$	−3.40047	−0.310419
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−1.12123	−0.101098
$124$	−3.75945	−0.337609
$125$	5.31558	0.475440
$126$	3.20612	0.285624
$127$	−4.10139	−0.363939	−0.181970	−	0.983304i	$-0.558247\pi$
$127$	−4.10139	−0.363939	−0.181970	+	0.983304i	$0.558247\pi$
$128$	1.00000	0.0883883
$129$	3.47830	0.306247
$130$	17.8108	1.56211
$131$	−12.4585	−1.08850	−0.544250	−	0.838923i	$-0.683186\pi$
$131$	−12.4585	−1.08850	−0.544250	+	0.838923i	$0.683186\pi$
$132$	1.00000	0.0870388
$133$	8.60659	0.746286
$134$	−7.69620	−0.664851
$135$	−3.40047	−0.292666
$136$	−2.49008	−0.213522
$137$	−14.9853	−1.28028	−0.640140	−	0.768258i	$-0.721124\pi$
$137$	−14.9853	−1.28028	−0.640140	+	0.768258i	$0.721124\pi$
$138$	−2.68442	−0.228513
$139$	−21.7565	−1.84537	−0.922683	−	0.385561i	$-0.874008\pi$
$139$	−21.7565	−1.84537	−0.922683	+	0.385561i	$0.874008\pi$
$140$	10.9023	0.921415
$141$	−4.35706	−0.366931
$142$	−9.45374	−0.793340
$143$	−5.23775	−0.438003
$144$	1.00000	0.0833333
$145$	−0.553326	−0.0459512
$146$	−11.6184	−0.961543
$147$	−3.27924	−0.270467
$148$	−5.00986	−0.411808
$149$	7.85892	0.643828	0.321914	−	0.946769i	$-0.395674\pi$
$149$	7.85892	0.643828	0.321914	+	0.946769i	$0.395674\pi$
$150$	−6.56319	−0.535882
$151$	0.155658	0.0126672	0.00633362	−	0.999980i	$-0.497984\pi$
$151$	0.155658	0.0126672	0.00633362	+	0.999980i	$0.497984\pi$
$152$	2.68442	0.217735
$153$	−2.49008	−0.201311
$154$	−3.20612	−0.258357
$155$	−12.7839	−1.02683
$156$	−5.23775	−0.419356
$157$	11.6184	0.927247	0.463624	−	0.886032i	$-0.346549\pi$
$157$	11.6184	0.927247	0.463624	+	0.886032i	$0.346549\pi$
$158$	−12.0622	−0.959621
$159$	−7.89055	−0.625761
$160$	3.40047	0.268831
$161$	8.60659	0.678295
$162$	1.00000	0.0785674
$163$	2.49200	0.195188	0.0975941	−	0.995226i	$-0.468885\pi$
$163$	2.49200	0.195188	0.0975941	+	0.995226i	$0.468885\pi$
$164$	1.12123	0.0875536
$165$	3.40047	0.264726
$166$	−6.00706	−0.466238
$167$	14.8707	1.15073	0.575365	−	0.817897i	$-0.304860\pi$
$167$	14.8707	1.15073	0.575365	+	0.817897i	$0.304860\pi$
$168$	−3.20612	−0.247358
$169$	14.4340	1.11031
$170$	−8.46743	−0.649423
$171$	2.68442	0.205283
$172$	−3.47830	−0.265218
$173$	−4.00706	−0.304651	−0.152326	−	0.988330i	$-0.548676\pi$
$173$	−4.00706	−0.304651	−0.152326	+	0.988330i	$0.548676\pi$
$174$	0.162720	0.0123358
$175$	21.0424	1.59066
$176$	−1.00000	−0.0753778
$177$	−4.89527	−0.367951
$178$	−7.57025	−0.567414
$179$	8.53068	0.637613	0.318807	−	0.947820i	$-0.396718\pi$
$179$	8.53068	0.637613	0.318807	+	0.947820i	$0.396718\pi$
$180$	3.40047	0.253456
$181$	1.44667	0.107530	0.0537652	−	0.998554i	$-0.482878\pi$
$181$	1.44667	0.107530	0.0537652	+	0.998554i	$0.482878\pi$
$182$	16.7929	1.24477
$183$	1.00000	0.0739221
$184$	2.68442	0.197898
$185$	−17.0359	−1.25250
$186$	3.75945	0.275656
$187$	2.49008	0.182093
$188$	4.35706	0.317772
$189$	−3.20612	−0.233211
$190$	9.12830	0.662236
$191$	3.33016	0.240962	0.120481	−	0.992716i	$-0.461556\pi$
$191$	3.33016	0.240962	0.120481	+	0.992716i	$0.461556\pi$
$192$	−1.00000	−0.0721688
$193$	7.28395	0.524310	0.262155	−	0.965026i	$-0.415567\pi$
$193$	7.28395	0.524310	0.262155	+	0.965026i	$0.415567\pi$
$194$	−12.4971	−0.897242
$195$	−17.8108	−1.27546
$196$	3.27924	0.234231
$197$	9.92409	0.707062	0.353531	−	0.935423i	$-0.384981\pi$
$197$	9.92409	0.707062	0.353531	+	0.935423i	$0.384981\pi$
$198$	−1.00000	−0.0710669
$199$	9.27644	0.657589	0.328795	−	0.944401i	$-0.393358\pi$
$199$	9.27644	0.657589	0.328795	+	0.944401i	$0.393358\pi$
$200$	6.56319	0.464088
$201$	7.69620	0.542848
$202$	12.0552	0.848200
$203$	−0.521702	−0.0366163
$204$	2.49008	0.174340
$205$	3.81272	0.266292
$206$	1.40047	0.0975753
$207$	2.68442	0.186580
$208$	5.23775	0.363173
$209$	−2.68442	−0.185685
$210$	−10.9023	−0.752332
$211$	−2.41225	−0.166066	−0.0830331	−	0.996547i	$-0.526461\pi$
$211$	−2.41225	−0.166066	−0.0830331	+	0.996547i	$0.526461\pi$
$212$	7.89055	0.541925
$213$	9.45374	0.647759
$214$	−3.89246	−0.266083
$215$	−11.8278	−0.806652
$216$	−1.00000	−0.0680414
$217$	−12.0533	−0.818229
$218$	9.49994	0.643417
$219$	11.6184	0.785097
$220$	−3.40047	−0.229260
$221$	−13.0424	−0.877327
$222$	5.00986	0.336240
$223$	0.914225	0.0612210	0.0306105	−	0.999531i	$-0.490255\pi$
$223$	0.914225	0.0612210	0.0306105	+	0.999531i	$0.490255\pi$
$224$	3.20612	0.214218
$225$	6.56319	0.437546
$226$	15.9538	1.06123
$227$	5.29293	0.351304	0.175652	−	0.984452i	$-0.443797\pi$
$227$	5.29293	0.351304	0.175652	+	0.984452i	$0.443797\pi$
$228$	−2.68442	−0.177780
$229$	−8.03354	−0.530871	−0.265436	−	0.964129i	$-0.585516\pi$
$229$	−8.03354	−0.530871	−0.265436	+	0.964129i	$0.585516\pi$
$230$	9.12830	0.601902
$231$	3.20612	0.210948
$232$	−0.162720	−0.0106831
$233$	14.4320	0.945470	0.472735	−	0.881205i	$-0.343267\pi$
$233$	14.4320	0.945470	0.472735	+	0.881205i	$0.343267\pi$
$234$	5.23775	0.342402
$235$	14.8161	0.966493
$236$	4.89527	0.318655
$237$	12.0622	0.783527
$238$	−7.98350	−0.517494
$239$	−11.8166	−0.764349	−0.382175	−	0.924090i	$-0.624825\pi$
$239$	−11.8166	−0.764349	−0.382175	+	0.924090i	$0.624825\pi$
$240$	−3.40047	−0.219499
$241$	−6.77123	−0.436173	−0.218087	−	0.975929i	$-0.569982\pi$
$241$	−6.77123	−0.436173	−0.218087	+	0.975929i	$0.569982\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	11.1509	0.712407
$246$	−1.12123	−0.0714872
$247$	14.0603	0.894637
$248$	−3.75945	−0.238725
$249$	6.00706	0.380682
$250$	5.31558	0.336187
$251$	−24.9145	−1.57259	−0.786296	−	0.617850i	$-0.788004\pi$
$251$	−24.9145	−1.57259	−0.786296	+	0.617850i	$0.788004\pi$
$252$	3.20612	0.201967
$253$	−2.68442	−0.168768
$254$	−4.10139	−0.257344
$255$	8.46743	0.530251
$256$	1.00000	0.0625000
$257$	7.39049	0.461006	0.230503	−	0.973072i	$-0.425963\pi$
$257$	7.39049	0.461006	0.230503	+	0.973072i	$0.425963\pi$
$258$	3.47830	0.216549
$259$	−16.0622	−0.998059
$260$	17.8108	1.10458
$261$	−0.162720	−0.0100721
$262$	−12.4585	−0.769686
$263$	−21.7249	−1.33962	−0.669808	−	0.742535i	$-0.733623\pi$
$263$	−21.7249	−1.33962	−0.669808	+	0.742535i	$0.733623\pi$
$264$	1.00000	0.0615457
$265$	26.8316	1.64825
$266$	8.60659	0.527704
$267$	7.57025	0.463292
$268$	−7.69620	−0.470120
$269$	1.12123	0.0683628	0.0341814	−	0.999416i	$-0.489118\pi$
$269$	1.12123	0.0683628	0.0341814	+	0.999416i	$0.489118\pi$
$270$	−3.40047	−0.206946
$271$	4.31546	0.262146	0.131073	−	0.991373i	$-0.458158\pi$
$271$	4.31546	0.262146	0.131073	+	0.991373i	$0.458158\pi$
$272$	−2.49008	−0.150983
$273$	−16.7929	−1.01635
$274$	−14.9853	−0.905295
$275$	−6.56319	−0.395775
$276$	−2.68442	−0.161583
$277$	25.4217	1.52744	0.763720	−	0.645548i	$-0.223371\pi$
$277$	25.4217	1.52744	0.763720	+	0.645548i	$0.223371\pi$
$278$	−21.7565	−1.30487
$279$	−3.75945	−0.225072
$280$	10.9023	0.651539
$281$	30.9145	1.84421	0.922103	−	0.386944i	$-0.126469\pi$
$281$	30.9145	1.84421	0.922103	+	0.386944i	$0.126469\pi$
$282$	−4.35706	−0.259459
$283$	7.96323	0.473365	0.236682	−	0.971587i	$-0.423940\pi$
$283$	7.96323	0.473365	0.236682	+	0.971587i	$0.423940\pi$
$284$	−9.45374	−0.560976
$285$	−9.12830	−0.540714
$286$	−5.23775	−0.309715
$287$	3.59481	0.212195
$288$	1.00000	0.0589256
$289$	−10.7995	−0.635265
$290$	−0.553326	−0.0324924
$291$	12.4971	0.732595
$292$	−11.6184	−0.679914
$293$	6.62824	0.387226	0.193613	−	0.981078i	$-0.437979\pi$
$293$	6.62824	0.387226	0.193613	+	0.981078i	$0.437979\pi$
$294$	−3.27924	−0.191249
$295$	16.6462	0.969179
$296$	−5.00986	−0.291192
$297$	1.00000	0.0580259
$298$	7.85892	0.455255
$299$	14.0603	0.813130
$300$	−6.56319	−0.378926
$301$	−11.1519	−0.642782
$302$	0.155658	0.00895709
$303$	−12.0552	−0.692552
$304$	2.68442	0.153962
$305$	−3.40047	−0.194710
$306$	−2.49008	−0.142348
$307$	−27.0240	−1.54234	−0.771170	−	0.636629i	$-0.780328\pi$
$307$	−27.0240	−1.54234	−0.771170	+	0.636629i	$0.780328\pi$
$308$	−3.20612	−0.182686
$309$	−1.40047	−0.0796699
$310$	−12.7839	−0.726076
$311$	23.4127	1.32761	0.663806	−	0.747905i	$-0.268940\pi$
$311$	23.4127	1.32761	0.663806	+	0.747905i	$0.268940\pi$
$312$	−5.23775	−0.296529
$313$	15.5778	0.880508	0.440254	−	0.897873i	$-0.354888\pi$
$313$	15.5778	0.880508	0.440254	+	0.897873i	$0.354888\pi$
$314$	11.6184	0.655663
$315$	10.9023	0.614277
$316$	−12.0622	−0.678554
$317$	12.4820	0.701060	0.350530	−	0.936552i	$-0.386001\pi$
$317$	12.4820	0.701060	0.350530	+	0.936552i	$0.386001\pi$
$318$	−7.89055	−0.442480
$319$	0.162720	0.00911060
$320$	3.40047	0.190092
$321$	3.89246	0.217256
$322$	8.60659	0.479627
$323$	−6.68442	−0.371931
$324$	1.00000	0.0555556
$325$	34.3763	1.90686
$326$	2.49200	0.138019
$327$	−9.49994	−0.525348
$328$	1.12123	0.0619097
$329$	13.9693	0.770152
$330$	3.40047	0.187190
$331$	−10.2009	−0.560690	−0.280345	−	0.959899i	$-0.590449\pi$
$331$	−10.2009	−0.560690	−0.280345	+	0.959899i	$0.590449\pi$
$332$	−6.00706	−0.329680
$333$	−5.00986	−0.274539
$334$	14.8707	0.813689
$335$	−26.1707	−1.42986
$336$	−3.20612	−0.174908
$337$	22.0471	1.20098	0.600492	−	0.799631i	$-0.294972\pi$
$337$	22.0471	1.20098	0.600492	+	0.799631i	$0.294972\pi$
$338$	14.4340	0.785107
$339$	−15.9538	−0.866491
$340$	−8.46743	−0.459211
$341$	3.75945	0.203586
$342$	2.68442	0.145157
$343$	−11.9292	−0.644118
$344$	−3.47830	−0.187537
$345$	−9.12830	−0.491451
$346$	−4.00706	−0.215421
$347$	19.0353	1.02187	0.510935	−	0.859619i	$-0.329299\pi$
$347$	19.0353	1.02187	0.510935	+	0.859619i	$0.329299\pi$
$348$	0.162720	0.00872273
$349$	−27.7717	−1.48658	−0.743291	−	0.668968i	$-0.766736\pi$
$349$	−27.7717	−1.48658	−0.743291	+	0.668968i	$0.766736\pi$
$350$	21.0424	1.12476
$351$	−5.23775	−0.279570
$352$	−1.00000	−0.0533002
$353$	34.8829	1.85663	0.928315	−	0.371795i	$-0.121257\pi$
$353$	34.8829	1.85663	0.928315	+	0.371795i	$0.121257\pi$
$354$	−4.89527	−0.260180
$355$	−32.1471	−1.70619
$356$	−7.57025	−0.401223
$357$	7.98350	0.422532
$358$	8.53068	0.450861
$359$	−27.3051	−1.44111	−0.720555	−	0.693398i	$-0.756113\pi$
$359$	−27.3051	−1.44111	−0.720555	+	0.693398i	$0.756113\pi$
$360$	3.40047	0.179220
$361$	−11.7939	−0.620730
$362$	1.44667	0.0760355
$363$	−1.00000	−0.0524864
$364$	16.7929	0.880186
$365$	−39.5079	−2.06794
$366$	1.00000	0.0522708
$367$	18.4033	0.960643	0.480321	−	0.877093i	$-0.340520\pi$
$367$	18.4033	0.960643	0.480321	+	0.877093i	$0.340520\pi$
$368$	2.68442	0.139935
$369$	1.12123	0.0583691
$370$	−17.0359	−0.885654
$371$	25.2981	1.31341
$372$	3.75945	0.194918
$373$	9.44430	0.489007	0.244504	−	0.969648i	$-0.421375\pi$
$373$	9.44430	0.489007	0.244504	+	0.969648i	$0.421375\pi$
$374$	2.49008	0.128759
$375$	−5.31558	−0.274495
$376$	4.35706	0.224698
$377$	−0.852289	−0.0438951
$378$	−3.20612	−0.164905
$379$	26.7900	1.37611	0.688054	−	0.725660i	$-0.258465\pi$
$379$	26.7900	1.37611	0.688054	+	0.725660i	$0.258465\pi$
$380$	9.12830	0.468272
$381$	4.10139	0.210121
$382$	3.33016	0.170386
$383$	−22.5731	−1.15343	−0.576715	−	0.816946i	$-0.695666\pi$
$383$	−22.5731	−1.15343	−0.576715	+	0.816946i	$0.695666\pi$
$384$	−1.00000	−0.0510310
$385$	−10.9023	−0.555634
$386$	7.28395	0.370743
$387$	−3.47830	−0.176812
$388$	−12.4971	−0.634446
$389$	−27.1806	−1.37811	−0.689055	−	0.724709i	$-0.741974\pi$
$389$	−27.1806	−1.37811	−0.689055	+	0.724709i	$0.741974\pi$
$390$	−17.8108	−0.901885
$391$	−6.68442	−0.338046
$392$	3.27924	0.165626
$393$	12.4585	0.628446
$394$	9.92409	0.499968
$395$	−41.0173	−2.06380
$396$	−1.00000	−0.0502519
$397$	−10.7990	−0.541987	−0.270994	−	0.962581i	$-0.587352\pi$
$397$	−10.7990	−0.541987	−0.270994	+	0.962581i	$0.587352\pi$
$398$	9.27644	0.464986
$399$	−8.60659	−0.430869
$400$	6.56319	0.328159
$401$	8.74152	0.436531	0.218265	−	0.975889i	$-0.429960\pi$
$401$	8.74152	0.436531	0.218265	+	0.975889i	$0.429960\pi$
$402$	7.69620	0.383852
$403$	−19.6911	−0.980881
$404$	12.0552	0.599768
$405$	3.40047	0.168971
$406$	−0.521702	−0.0258916
$407$	5.00986	0.248330
$408$	2.49008	0.123277
$409$	−6.73577	−0.333063	−0.166531	−	0.986036i	$-0.553257\pi$
$409$	−6.73577	−0.333063	−0.166531	+	0.986036i	$0.553257\pi$
$410$	3.81272	0.188297
$411$	14.9853	0.739170
$412$	1.40047	0.0689962
$413$	15.6948	0.772292
$414$	2.68442	0.131932
$415$	−20.4268	−1.00271
$416$	5.23775	0.256802
$417$	21.7565	1.06542
$418$	−2.68442	−0.131299
$419$	33.3348	1.62851	0.814257	−	0.580505i	$-0.197145\pi$
$419$	33.3348	1.62851	0.814257	+	0.580505i	$0.197145\pi$
$420$	−10.9023	−0.531979
$421$	14.8778	0.725098	0.362549	−	0.931965i	$-0.381907\pi$
$421$	14.8778	0.725098	0.362549	+	0.931965i	$0.381907\pi$
$422$	−2.41225	−0.117426
$423$	4.35706	0.211848
$424$	7.89055	0.383199
$425$	−16.3429	−0.792745
$426$	9.45374	0.458035
$427$	−3.20612	−0.155155
$428$	−3.89246	−0.188149
$429$	5.23775	0.252881
$430$	−11.8278	−0.570389
$431$	−10.0920	−0.486112	−0.243056	−	0.970012i	$-0.578150\pi$
$431$	−10.0920	−0.486112	−0.243056	+	0.970012i	$0.578150\pi$
$432$	−1.00000	−0.0481125
$433$	18.1826	0.873800	0.436900	−	0.899510i	$-0.356076\pi$
$433$	18.1826	0.873800	0.436900	+	0.899510i	$0.356076\pi$
$434$	−12.0533	−0.578575
$435$	0.553326	0.0265299
$436$	9.49994	0.454965
$437$	7.20612	0.344716
$438$	11.6184	0.555147
$439$	−13.7462	−0.656072	−0.328036	−	0.944665i	$-0.606387\pi$
$439$	−13.7462	−0.656072	−0.328036	+	0.944665i	$0.606387\pi$
$440$	−3.40047	−0.162111
$441$	3.27924	0.156154
$442$	−13.0424	−0.620364
$443$	11.3378	0.538674	0.269337	−	0.963046i	$-0.413196\pi$
$443$	11.3378	0.538674	0.269337	+	0.963046i	$0.413196\pi$
$444$	5.00986	0.237758
$445$	−25.7424	−1.22031
$446$	0.914225	0.0432898
$447$	−7.85892	−0.371714
$448$	3.20612	0.151475
$449$	−24.6543	−1.16351	−0.581753	−	0.813365i	$-0.697633\pi$
$449$	−24.6543	−1.16351	−0.581753	+	0.813365i	$0.697633\pi$
$450$	6.56319	0.309392
$451$	−1.12123	−0.0527968
$452$	15.9538	0.750403
$453$	−0.155658	−0.00731344
$454$	5.29293	0.248410
$455$	57.1037	2.67706
$456$	−2.68442	−0.125710
$457$	−15.8424	−0.741077	−0.370539	−	0.928817i	$-0.620827\pi$
$457$	−15.8424	−0.741077	−0.370539	+	0.928817i	$0.620827\pi$
$458$	−8.03354	−0.375383
$459$	2.49008	0.116227
$460$	9.12830	0.425609
$461$	20.6453	0.961547	0.480773	−	0.876845i	$-0.340356\pi$
$461$	20.6453	0.961547	0.480773	+	0.876845i	$0.340356\pi$
$462$	3.20612	0.149162
$463$	−26.8452	−1.24760	−0.623802	−	0.781583i	$-0.714413\pi$
$463$	−26.8452	−1.24760	−0.623802	+	0.781583i	$0.714413\pi$
$464$	−0.162720	−0.00755411
$465$	12.7839	0.592839
$466$	14.4320	0.668548
$467$	3.83436	0.177433	0.0887166	−	0.996057i	$-0.471723\pi$
$467$	3.83436	0.177433	0.0887166	+	0.996057i	$0.471723\pi$
$468$	5.23775	0.242115
$469$	−24.6750	−1.13939
$470$	14.8161	0.683414
$471$	−11.6184	−0.535346
$472$	4.89527	0.225323
$473$	3.47830	0.159932
$474$	12.0622	0.554037
$475$	17.6184	0.808386
$476$	−7.98350	−0.365923
$477$	7.89055	0.361283
$478$	−11.8166	−0.540477
$479$	13.9538	0.637565	0.318783	−	0.947828i	$-0.396726\pi$
$479$	13.9538	0.637565	0.318783	+	0.947828i	$0.396726\pi$
$480$	−3.40047	−0.155209
$481$	−26.2404	−1.19646
$482$	−6.77123	−0.308421
$483$	−8.60659	−0.391614
$484$	1.00000	0.0454545
$485$	−42.4961	−1.92965
$486$	−1.00000	−0.0453609
$487$	−10.0071	−0.453463	−0.226732	−	0.973957i	$-0.572804\pi$
$487$	−10.0071	−0.453463	−0.226732	+	0.973957i	$0.572804\pi$
$488$	−1.00000	−0.0452679
$489$	−2.49200	−0.112692
$490$	11.1509	0.503748
$491$	22.1377	0.999061	0.499530	−	0.866296i	$-0.333506\pi$
$491$	22.1377	0.999061	0.499530	+	0.866296i	$0.333506\pi$
$492$	−1.12123	−0.0505491
$493$	0.405187	0.0182487
$494$	14.0603	0.632604
$495$	−3.40047	−0.152840
$496$	−3.75945	−0.168804
$497$	−30.3099	−1.35958
$498$	6.00706	0.269183
$499$	15.8433	0.709245	0.354623	−	0.935009i	$-0.384609\pi$
$499$	15.8433	0.709245	0.354623	+	0.935009i	$0.384609\pi$
$500$	5.31558	0.237720
$501$	−14.8707	−0.664374
$502$	−24.9145	−1.11199
$503$	4.50658	0.200938	0.100469	−	0.994940i	$-0.467966\pi$
$503$	4.50658	0.200938	0.100469	+	0.994940i	$0.467966\pi$
$504$	3.20612	0.142812
$505$	40.9933	1.82418
$506$	−2.68442	−0.119337
$507$	−14.4340	−0.641037
$508$	−4.10139	−0.181970
$509$	−21.3533	−0.946467	−0.473233	−	0.880937i	$-0.656913\pi$
$509$	−21.3533	−0.946467	−0.473233	+	0.880937i	$0.656913\pi$
$510$	8.46743	0.374944
$511$	−37.2500	−1.64784
$512$	1.00000	0.0441942
$513$	−2.68442	−0.118520
$514$	7.39049	0.325981
$515$	4.76225	0.209850
$516$	3.47830	0.153124
$517$	−4.35706	−0.191623
$518$	−16.0622	−0.705735
$519$	4.00706	0.175891
$520$	17.8108	0.781055
$521$	−18.9145	−0.828661	−0.414330	−	0.910127i	$-0.635984\pi$
$521$	−18.9145	−0.828661	−0.414330	+	0.910127i	$0.635984\pi$
$522$	−0.162720	−0.00712208
$523$	−3.60479	−0.157627	−0.0788133	−	0.996889i	$-0.525113\pi$
$523$	−3.60479	−0.157627	−0.0788133	+	0.996889i	$0.525113\pi$
$524$	−12.4585	−0.544250
$525$	−21.0424	−0.918366
$526$	−21.7249	−0.947251
$527$	9.36133	0.407786
$528$	1.00000	0.0435194
$529$	−15.7939	−0.686690
$530$	26.8316	1.16549
$531$	4.89527	0.212436
$532$	8.60659	0.373143
$533$	5.87274	0.254376
$534$	7.57025	0.327597
$535$	−13.2362	−0.572251
$536$	−7.69620	−0.332425
$537$	−8.53068	−0.368126
$538$	1.12123	0.0483398
$539$	−3.27924	−0.141247
$540$	−3.40047	−0.146333
$541$	−0.438727	−0.0188624	−0.00943118	−	0.999956i	$-0.503002\pi$
$541$	−0.438727	−0.0188624	−0.00943118	+	0.999956i	$0.503002\pi$
$542$	4.31546	0.185365
$543$	−1.44667	−0.0620827
$544$	−2.49008	−0.106761
$545$	32.3043	1.38376
$546$	−16.7929	−0.718669
$547$	7.71885	0.330034	0.165017	−	0.986291i	$-0.447232\pi$
$547$	7.71885	0.330034	0.165017	+	0.986291i	$0.447232\pi$
$548$	−14.9853	−0.640140
$549$	−1.00000	−0.0426790
$550$	−6.56319	−0.279855
$551$	−0.436811	−0.0186088
$552$	−2.68442	−0.114257
$553$	−38.6731	−1.64455
$554$	25.4217	1.08006
$555$	17.0359	0.723133
$556$	−21.7565	−0.922683
$557$	−37.3849	−1.58405	−0.792024	−	0.610490i	$-0.790973\pi$
$557$	−37.3849	−1.58405	−0.792024	+	0.610490i	$0.790973\pi$
$558$	−3.75945	−0.159150
$559$	−18.2184	−0.770558
$560$	10.9023	0.460707
$561$	−2.49008	−0.105131
$562$	30.9145	1.30405
$563$	10.6071	0.447038	0.223519	−	0.974700i	$-0.428246\pi$
$563$	10.6071	0.447038	0.223519	+	0.974700i	$0.428246\pi$
$564$	−4.35706	−0.183466
$565$	54.2504	2.28233
$566$	7.96323	0.334720
$567$	3.20612	0.134645
$568$	−9.45374	−0.396670
$569$	14.4736	0.606764	0.303382	−	0.952869i	$-0.401884\pi$
$569$	14.4736	0.606764	0.303382	+	0.952869i	$0.401884\pi$
$570$	−9.12830	−0.382342
$571$	6.38063	0.267021	0.133510	−	0.991047i	$-0.457375\pi$
$571$	6.38063	0.267021	0.133510	+	0.991047i	$0.457375\pi$
$572$	−5.23775	−0.219001
$573$	−3.33016	−0.139119
$574$	3.59481	0.150045
$575$	17.6184	0.734737
$576$	1.00000	0.0416667
$577$	24.9607	1.03913	0.519565	−	0.854431i	$-0.326094\pi$
$577$	24.9607	1.03913	0.519565	+	0.854431i	$0.326094\pi$
$578$	−10.7995	−0.449200
$579$	−7.28395	−0.302711
$580$	−0.553326	−0.0229756
$581$	−19.2594	−0.799014
$582$	12.4971	0.518023
$583$	−7.89055	−0.326793
$584$	−11.6184	−0.480772
$585$	17.8108	0.736386
$586$	6.62824	0.273810
$587$	−33.9528	−1.40138	−0.700691	−	0.713465i	$-0.747125\pi$
$587$	−33.9528	−1.40138	−0.700691	+	0.713465i	$0.747125\pi$
$588$	−3.27924	−0.135233
$589$	−10.0920	−0.415832
$590$	16.6462	0.685313
$591$	−9.92409	−0.408222
$592$	−5.00986	−0.205904
$593$	−11.5792	−0.475502	−0.237751	−	0.971326i	$-0.576410\pi$
$593$	−11.5792	−0.475502	−0.237751	+	0.971326i	$0.576410\pi$
$594$	1.00000	0.0410305
$595$	−27.1477	−1.11295
$596$	7.85892	0.321914
$597$	−9.27644	−0.379659
$598$	14.0603	0.574970
$599$	33.7074	1.37725	0.688624	−	0.725119i	$-0.258215\pi$
$599$	33.7074	1.37725	0.688624	+	0.725119i	$0.258215\pi$
$600$	−6.56319	−0.267941
$601$	39.2222	1.59991	0.799953	−	0.600063i	$-0.204858\pi$
$601$	39.2222	1.59991	0.799953	+	0.600063i	$0.204858\pi$
$602$	−11.1519	−0.454516
$603$	−7.69620	−0.313414
$604$	0.155658	0.00633362
$605$	3.40047	0.138249
$606$	−12.0552	−0.489708
$607$	−31.1380	−1.26385	−0.631927	−	0.775028i	$-0.717736\pi$
$607$	−31.1380	−1.26385	−0.631927	+	0.775028i	$0.717736\pi$
$608$	2.68442	0.108868
$609$	0.521702	0.0211404
$610$	−3.40047	−0.137681
$611$	22.8212	0.923247
$612$	−2.49008	−0.100655
$613$	−20.9807	−0.847403	−0.423701	−	0.905802i	$-0.639269\pi$
$613$	−20.9807	−0.847403	−0.423701	+	0.905802i	$0.639269\pi$
$614$	−27.0240	−1.09060
$615$	−3.81272	−0.153744
$616$	−3.20612	−0.129178
$617$	−13.3326	−0.536751	−0.268376	−	0.963314i	$-0.586487\pi$
$617$	−13.3326	−0.536751	−0.268376	+	0.963314i	$0.586487\pi$
$618$	−1.40047	−0.0563351
$619$	−14.4618	−0.581270	−0.290635	−	0.956834i	$-0.593867\pi$
$619$	−14.4618	−0.581270	−0.290635	+	0.956834i	$0.593867\pi$
$620$	−12.7839	−0.513414
$621$	−2.68442	−0.107722
$622$	23.4127	0.938763
$623$	−24.2712	−0.972404
$624$	−5.23775	−0.209678
$625$	−14.7405	−0.589620
$626$	15.5778	0.622613
$627$	2.68442	0.107206
$628$	11.6184	0.463624
$629$	12.4750	0.497409
$630$	10.9023	0.434359
$631$	−25.3414	−1.00882	−0.504412	−	0.863463i	$-0.668291\pi$
$631$	−25.3414	−1.00882	−0.504412	+	0.863463i	$0.668291\pi$
$632$	−12.0622	−0.479810
$633$	2.41225	0.0958783
$634$	12.4820	0.495724
$635$	−13.9466	−0.553456
$636$	−7.89055	−0.312881
$637$	17.1758	0.680530
$638$	0.162720	0.00644217
$639$	−9.45374	−0.373984
$640$	3.40047	0.134415
$641$	−32.0236	−1.26485	−0.632427	−	0.774620i	$-0.717941\pi$
$641$	−32.0236	−1.26485	−0.632427	+	0.774620i	$0.717941\pi$
$642$	3.89246	0.153623
$643$	−0.327902	−0.0129312	−0.00646560	−	0.999979i	$-0.502058\pi$
$643$	−0.327902	−0.0129312	−0.00646560	+	0.999979i	$0.502058\pi$
$644$	8.60659	0.339147
$645$	11.8278	0.465721
$646$	−6.68442	−0.262995
$647$	24.1763	0.950468	0.475234	−	0.879859i	$-0.342363\pi$
$647$	24.1763	0.950468	0.475234	+	0.879859i	$0.342363\pi$
$648$	1.00000	0.0392837
$649$	−4.89527	−0.192156
$650$	34.3763	1.34835
$651$	12.0533	0.472405
$652$	2.49200	0.0975941
$653$	16.3109	0.638293	0.319147	−	0.947705i	$-0.396604\pi$
$653$	16.3109	0.638293	0.319147	+	0.947705i	$0.396604\pi$
$654$	−9.49994	−0.371477
$655$	−42.3646	−1.65532
$656$	1.12123	0.0437768
$657$	−11.6184	−0.453276
$658$	13.9693	0.544580
$659$	19.8585	0.773576	0.386788	−	0.922169i	$-0.373585\pi$
$659$	19.8585	0.773576	0.386788	+	0.922169i	$0.373585\pi$
$660$	3.40047	0.132363
$661$	−43.6731	−1.69869	−0.849343	−	0.527841i	$-0.823002\pi$
$661$	−43.6731	−1.69869	−0.849343	+	0.527841i	$0.823002\pi$
$662$	−10.2009	−0.396468
$663$	13.0424	0.506525
$664$	−6.00706	−0.233119
$665$	29.2665	1.13490
$666$	−5.00986	−0.194128
$667$	−0.436811	−0.0169134
$668$	14.8707	0.575365
$669$	−0.914225	−0.0353460
$670$	−26.1707	−1.01106
$671$	1.00000	0.0386046
$672$	−3.20612	−0.123679
$673$	−5.50615	−0.212246	−0.106123	−	0.994353i	$-0.533844\pi$
$673$	−5.50615	−0.212246	−0.106123	+	0.994353i	$0.533844\pi$
$674$	22.0471	0.849223
$675$	−6.56319	−0.252617
$676$	14.4340	0.555154
$677$	−3.18540	−0.122425	−0.0612124	−	0.998125i	$-0.519497\pi$
$677$	−3.18540	−0.122425	−0.0612124	+	0.998125i	$0.519497\pi$
$678$	−15.9538	−0.612702
$679$	−40.0674	−1.53765
$680$	−8.46743	−0.324711
$681$	−5.29293	−0.202826
$682$	3.75945	0.143957
$683$	−41.3868	−1.58362	−0.791811	−	0.610766i	$-0.790862\pi$
$683$	−41.3868	−1.58362	−0.791811	+	0.610766i	$0.790862\pi$
$684$	2.68442	0.102641
$685$	−50.9571	−1.94697
$686$	−11.9292	−0.455460
$687$	8.03354	0.306499
$688$	−3.47830	−0.132609
$689$	41.3287	1.57450
$690$	−9.12830	−0.347508
$691$	−33.9781	−1.29259	−0.646294	−	0.763088i	$-0.723682\pi$
$691$	−33.9781	−1.29259	−0.646294	+	0.763088i	$0.723682\pi$
$692$	−4.00706	−0.152326
$693$	−3.20612	−0.121791
$694$	19.0353	0.722572
$695$	−73.9824	−2.80631
$696$	0.162720	0.00616790
$697$	−2.79196	−0.105753
$698$	−27.7717	−1.05117
$699$	−14.4320	−0.545867
$700$	21.0424	0.795328
$701$	−18.0241	−0.680761	−0.340381	−	0.940288i	$-0.610556\pi$
$701$	−18.0241	−0.680761	−0.340381	+	0.940288i	$0.610556\pi$
$702$	−5.23775	−0.197686
$703$	−13.4486	−0.507223
$704$	−1.00000	−0.0376889
$705$	−14.8161	−0.558005
$706$	34.8829	1.31284
$707$	38.6504	1.45360
$708$	−4.89527	−0.183975
$709$	25.9406	0.974219	0.487110	−	0.873341i	$-0.338051\pi$
$709$	25.9406	0.974219	0.487110	+	0.873341i	$0.338051\pi$
$710$	−32.1471	−1.20646
$711$	−12.0622	−0.452370
$712$	−7.57025	−0.283707
$713$	−10.0920	−0.377947
$714$	7.98350	0.298775
$715$	−17.8108	−0.666086
$716$	8.53068	0.318807
$717$	11.8166	0.441297
$718$	−27.3051	−1.01902
$719$	5.18394	0.193328	0.0966641	−	0.995317i	$-0.469183\pi$
$719$	5.18394	0.193328	0.0966641	+	0.995317i	$0.469183\pi$
$720$	3.40047	0.126728
$721$	4.49008	0.167219
$722$	−11.7939	−0.438923
$723$	6.77123	0.251825
$724$	1.44667	0.0537652
$725$	−1.06797	−0.0396632
$726$	−1.00000	−0.0371135
$727$	−49.9669	−1.85317	−0.926585	−	0.376085i	$-0.877270\pi$
$727$	−49.9669	−1.85317	−0.926585	+	0.376085i	$0.877270\pi$
$728$	16.7929	0.622385
$729$	1.00000	0.0370370
$730$	−39.5079	−1.46225
$731$	8.66123	0.320347
$732$	1.00000	0.0369611
$733$	11.3414	0.418903	0.209451	−	0.977819i	$-0.432832\pi$
$733$	11.3414	0.418903	0.209451	+	0.977819i	$0.432832\pi$
$734$	18.4033	0.679277
$735$	−11.1509	−0.411309
$736$	2.68442	0.0989491
$737$	7.69620	0.283493
$738$	1.12123	0.0412732
$739$	−21.2575	−0.781969	−0.390984	−	0.920397i	$-0.627865\pi$
$739$	−21.2575	−0.781969	−0.390984	+	0.920397i	$0.627865\pi$
$740$	−17.0359	−0.626252
$741$	−14.0603	−0.516519
$742$	25.2981	0.928722
$743$	−10.9528	−0.401818	−0.200909	−	0.979610i	$-0.564390\pi$
$743$	−10.9528	−0.401818	−0.200909	+	0.979610i	$0.564390\pi$
$744$	3.75945	0.137828
$745$	26.7240	0.979093
$746$	9.44430	0.345780
$747$	−6.00706	−0.219787
$748$	2.49008	0.0910463
$749$	−12.4797	−0.455999
$750$	−5.31558	−0.194097
$751$	−17.2410	−0.629132	−0.314566	−	0.949236i	$-0.601859\pi$
$751$	−17.2410	−0.629132	−0.314566	+	0.949236i	$0.601859\pi$
$752$	4.35706	0.158886
$753$	24.9145	0.907936
$754$	−0.852289	−0.0310385
$755$	0.529309	0.0192635
$756$	−3.20612	−0.116606
$757$	−18.0900	−0.657494	−0.328747	−	0.944418i	$-0.606626\pi$
$757$	−18.0900	−0.657494	−0.328747	+	0.944418i	$0.606626\pi$
$758$	26.7900	0.973055
$759$	2.68442	0.0974384
$760$	9.12830	0.331118
$761$	1.17833	0.0427146	0.0213573	−	0.999772i	$-0.493201\pi$
$761$	1.17833	0.0427146	0.0213573	+	0.999772i	$0.493201\pi$
$762$	4.10139	0.148578
$763$	30.4580	1.10265
$764$	3.33016	0.120481
$765$	−8.46743	−0.306141
$766$	−22.5731	−0.815598
$767$	25.6402	0.925813
$768$	−1.00000	−0.0360844
$769$	−34.6891	−1.25092	−0.625461	−	0.780256i	$-0.715089\pi$
$769$	−34.6891	−1.25092	−0.625461	+	0.780256i	$0.715089\pi$
$770$	−10.9023	−0.392893
$771$	−7.39049	−0.266162
$772$	7.28395	0.262155
$773$	−23.1612	−0.833052	−0.416526	−	0.909124i	$-0.636752\pi$
$773$	−23.1612	−0.833052	−0.416526	+	0.909124i	$0.636752\pi$
$774$	−3.47830	−0.125025
$775$	−24.6740	−0.886316
$776$	−12.4971	−0.448621
$777$	16.0622	0.576230
$778$	−27.1806	−0.974470
$779$	3.00986	0.107840
$780$	−17.8108	−0.637729
$781$	9.45374	0.338281
$782$	−6.68442	−0.239034
$783$	0.162720	0.00581516
$784$	3.27924	0.117116
$785$	39.5079	1.41010
$786$	12.4585	0.444378
$787$	−7.57585	−0.270050	−0.135025	−	0.990842i	$-0.543111\pi$
$787$	−7.57585	−0.270050	−0.135025	+	0.990842i	$0.543111\pi$
$788$	9.92409	0.353531
$789$	21.7249	0.773427
$790$	−41.0173	−1.45933
$791$	51.1499	1.81868
$792$	−1.00000	−0.0355335
$793$	−5.23775	−0.185998
$794$	−10.7990	−0.383243
$795$	−26.8316	−0.951617
$796$	9.27644	0.328795
$797$	9.87450	0.349773	0.174886	−	0.984589i	$-0.444044\pi$
$797$	9.87450	0.349773	0.174886	+	0.984589i	$0.444044\pi$
$798$	−8.60659	−0.304670
$799$	−10.8494	−0.383825
$800$	6.56319	0.232044
$801$	−7.57025	−0.267482
$802$	8.74152	0.308674
$803$	11.6184	0.410004
$804$	7.69620	0.271424
$805$	29.2665	1.03151
$806$	−19.6911	−0.693588
$807$	−1.12123	−0.0394693
$808$	12.0552	0.424100
$809$	48.9746	1.72185	0.860927	−	0.508729i	$-0.169884\pi$
$809$	48.9746	1.72185	0.860927	+	0.508729i	$0.169884\pi$
$810$	3.40047	0.119480
$811$	−18.3325	−0.643741	−0.321871	−	0.946784i	$-0.604312\pi$
$811$	−18.3325	−0.643741	−0.321871	+	0.946784i	$0.604312\pi$
$812$	−0.521702	−0.0183082
$813$	−4.31546	−0.151350
$814$	5.00986	0.175596
$815$	8.47395	0.296830
$816$	2.49008	0.0871702
$817$	−9.33722	−0.326668
$818$	−6.73577	−0.235511
$819$	16.7929	0.586791
$820$	3.81272	0.133146
$821$	−54.6146	−1.90606	−0.953031	−	0.302873i	$-0.902054\pi$
$821$	−54.6146	−1.90606	−0.953031	+	0.302873i	$0.902054\pi$
$822$	14.9853	0.522672
$823$	1.92486	0.0670963	0.0335481	−	0.999437i	$-0.489319\pi$
$823$	1.92486	0.0670963	0.0335481	+	0.999437i	$0.489319\pi$
$824$	1.40047	0.0487876
$825$	6.56319	0.228501
$826$	15.6948	0.546093
$827$	11.9178	0.414422	0.207211	−	0.978296i	$-0.433561\pi$
$827$	11.9178	0.414422	0.207211	+	0.978296i	$0.433561\pi$
$828$	2.68442	0.0932901
$829$	52.4442	1.82146	0.910731	−	0.413000i	$-0.135519\pi$
$829$	52.4442	1.82146	0.910731	+	0.413000i	$0.135519\pi$
$830$	−20.4268	−0.709026
$831$	−25.4217	−0.881868
$832$	5.23775	0.181586
$833$	−8.16555	−0.282920
$834$	21.7565	0.753367
$835$	50.5674	1.74996
$836$	−2.68442	−0.0928427
$837$	3.75945	0.129946
$838$	33.3348	1.15153
$839$	−4.87362	−0.168256	−0.0841280	−	0.996455i	$-0.526810\pi$
$839$	−4.87362	−0.168256	−0.0841280	+	0.996455i	$0.526810\pi$
$840$	−10.9023	−0.376166
$841$	−28.9735	−0.999087
$842$	14.8778	0.512722
$843$	−30.9145	−1.06475
$844$	−2.41225	−0.0830331
$845$	49.0824	1.68849
$846$	4.35706	0.149799
$847$	3.20612	0.110164
$848$	7.89055	0.270963
$849$	−7.96323	−0.273297
$850$	−16.3429	−0.560555
$851$	−13.4486	−0.461012
$852$	9.45374	0.323880
$853$	−25.0711	−0.858418	−0.429209	−	0.903205i	$-0.641208\pi$
$853$	−25.0711	−0.858418	−0.429209	+	0.903205i	$0.641208\pi$
$854$	−3.20612	−0.109711
$855$	9.12830	0.312181
$856$	−3.89246	−0.133042
$857$	−16.9732	−0.579793	−0.289896	−	0.957058i	$-0.593621\pi$
$857$	−16.9732	−0.579793	−0.289896	+	0.957058i	$0.593621\pi$
$858$	5.23775	0.178814
$859$	21.7998	0.743800	0.371900	−	0.928273i	$-0.378706\pi$
$859$	21.7998	0.743800	0.371900	+	0.928273i	$0.378706\pi$
$860$	−11.8278	−0.403326
$861$	−3.59481	−0.122511
$862$	−10.0920	−0.343733
$863$	−18.9468	−0.644955	−0.322478	−	0.946577i	$-0.604516\pi$
$863$	−18.9468	−0.644955	−0.322478	+	0.946577i	$0.604516\pi$
$864$	−1.00000	−0.0340207
$865$	−13.6259	−0.463294
$866$	18.1826	0.617870
$867$	10.7995	0.366771
$868$	−12.0533	−0.409115
$869$	12.0622	0.409184
$870$	0.553326	0.0187595
$871$	−40.3108	−1.36588
$872$	9.49994	0.321709
$873$	−12.4971	−0.422964
$874$	7.20612	0.243751
$875$	17.0424	0.576138
$876$	11.6184	0.392548
$877$	12.7022	0.428924	0.214462	−	0.976732i	$-0.431200\pi$
$877$	12.7022	0.428924	0.214462	+	0.976732i	$0.431200\pi$
$878$	−13.7462	−0.463913
$879$	−6.62824	−0.223565
$880$	−3.40047	−0.114630
$881$	−1.90513	−0.0641854	−0.0320927	−	0.999485i	$-0.510217\pi$
$881$	−1.90513	−0.0641854	−0.0320927	+	0.999485i	$0.510217\pi$
$882$	3.27924	0.110418
$883$	−45.3515	−1.52620	−0.763100	−	0.646281i	$-0.776323\pi$
$883$	−45.3515	−1.52620	−0.763100	+	0.646281i	$0.776323\pi$
$884$	−13.0424	−0.438664
$885$	−16.6462	−0.559556
$886$	11.3378	0.380900
$887$	19.5471	0.656326	0.328163	−	0.944621i	$-0.393570\pi$
$887$	19.5471	0.656326	0.328163	+	0.944621i	$0.393570\pi$
$888$	5.00986	0.168120
$889$	−13.1496	−0.441022
$890$	−25.7424	−0.862887
$891$	−1.00000	−0.0335013
$892$	0.914225	0.0306105
$893$	11.6962	0.391399
$894$	−7.85892	−0.262842
$895$	29.0083	0.969641
$896$	3.20612	0.107109
$897$	−14.0603	−0.469461
$898$	−24.6543	−0.822723
$899$	0.611740	0.0204027
$900$	6.56319	0.218773
$901$	−19.6481	−0.654572
$902$	−1.12123	−0.0373330
$903$	11.1519	0.371111
$904$	15.9538	0.530615
$905$	4.91937	0.163525
$906$	−0.155658	−0.00517138
$907$	44.7234	1.48502	0.742508	−	0.669837i	$-0.233636\pi$
$907$	44.7234	1.48502	0.742508	+	0.669837i	$0.233636\pi$
$908$	5.29293	0.175652
$909$	12.0552	0.399845
$910$	57.1037	1.89297
$911$	−19.4253	−0.643590	−0.321795	−	0.946809i	$-0.604286\pi$
$911$	−19.4253	−0.643590	−0.321795	+	0.946809i	$0.604286\pi$
$912$	−2.68442	−0.0888901
$913$	6.00706	0.198805
$914$	−15.8424	−0.524021
$915$	3.40047	0.112416
$916$	−8.03354	−0.265436
$917$	−39.9434	−1.31905
$918$	2.49008	0.0821848
$919$	17.2335	0.568481	0.284241	−	0.958753i	$-0.408259\pi$
$919$	17.2335	0.568481	0.284241	+	0.958753i	$0.408259\pi$
$920$	9.12830	0.300951
$921$	27.0240	0.890471
$922$	20.6453	0.679916
$923$	−49.5163	−1.62985
$924$	3.20612	0.105474
$925$	−32.8807	−1.08111
$926$	−26.8452	−0.882189
$927$	1.40047	0.0459974
$928$	−0.162720	−0.00534156
$929$	−7.69943	−0.252610	−0.126305	−	0.991991i	$-0.540312\pi$
$929$	−7.69943	−0.252610	−0.126305	+	0.991991i	$0.540312\pi$
$930$	12.7839	0.419200
$931$	8.80285	0.288502
$932$	14.4320	0.472735
$933$	−23.4127	−0.766497
$934$	3.83436	0.125464
$935$	8.46743	0.276915
$936$	5.23775	0.171201
$937$	−16.5339	−0.540139	−0.270070	−	0.962841i	$-0.587047\pi$
$937$	−16.5339	−0.540139	−0.270070	+	0.962841i	$0.587047\pi$
$938$	−24.6750	−0.805667
$939$	−15.5778	−0.508361
$940$	14.8161	0.483247
$941$	23.4844	0.765568	0.382784	−	0.923838i	$-0.374965\pi$
$941$	23.4844	0.765568	0.382784	+	0.923838i	$0.374965\pi$
$942$	−11.6184	−0.378547
$943$	3.00986	0.0980146
$944$	4.89527	0.159327
$945$	−10.9023	−0.354653
$946$	3.47830	0.113089
$947$	−1.36985	−0.0445140	−0.0222570	−	0.999752i	$-0.507085\pi$
$947$	−1.36985	−0.0445140	−0.0222570	+	0.999752i	$0.507085\pi$
$948$	12.0622	0.391764
$949$	−60.8541	−1.97541
$950$	17.6184	0.571616
$951$	−12.4820	−0.404757
$952$	−7.98350	−0.258747
$953$	29.4179	0.952939	0.476469	−	0.879191i	$-0.341916\pi$
$953$	29.4179	0.952939	0.476469	+	0.879191i	$0.341916\pi$
$954$	7.89055	0.255466
$955$	11.3241	0.366439
$956$	−11.8166	−0.382175
$957$	−0.162720	−0.00526001
$958$	13.9538	0.450827
$959$	−48.0447	−1.55145
$960$	−3.40047	−0.109750
$961$	−16.8665	−0.544082
$962$	−26.2404	−0.846025
$963$	−3.89246	−0.125433
$964$	−6.77123	−0.218087
$965$	24.7689	0.797338
$966$	−8.60659	−0.276913
$967$	15.9241	0.512084	0.256042	−	0.966666i	$-0.417581\pi$
$967$	15.9241	0.512084	0.256042	+	0.966666i	$0.417581\pi$
$968$	1.00000	0.0321412
$969$	6.68442	0.214735
$970$	−42.4961	−1.36447
$971$	−38.4227	−1.23304	−0.616521	−	0.787338i	$-0.711459\pi$
$971$	−38.4227	−1.23304	−0.616521	+	0.787338i	$0.711459\pi$
$972$	−1.00000	−0.0320750
$973$	−69.7542	−2.23622
$974$	−10.0071	−0.320647
$975$	−34.3763	−1.10092
$976$	−1.00000	−0.0320092
$977$	−28.6229	−0.915726	−0.457863	−	0.889023i	$-0.651385\pi$
$977$	−28.6229	−0.915726	−0.457863	+	0.889023i	$0.651385\pi$
$978$	−2.49200	−0.0796852
$979$	7.57025	0.241946
$980$	11.1509	0.356204
$981$	9.49994	0.303310
$982$	22.1377	0.706443
$983$	−46.0149	−1.46765	−0.733824	−	0.679340i	$-0.762266\pi$
$983$	−46.0149	−1.46765	−0.733824	+	0.679340i	$0.762266\pi$
$984$	−1.12123	−0.0357436
$985$	33.7466	1.07525
$986$	0.405187	0.0129038
$987$	−13.9693	−0.444647
$988$	14.0603	0.447319
$989$	−9.33722	−0.296906
$990$	−3.40047	−0.108074
$991$	19.0913	0.606455	0.303227	−	0.952918i	$-0.401936\pi$
$991$	19.0913	0.606455	0.303227	+	0.952918i	$0.401936\pi$
$992$	−3.75945	−0.119363
$993$	10.2009	0.323715
$994$	−30.3099	−0.961370
$995$	31.5442	1.00002
$996$	6.00706	0.190341
$997$	48.9612	1.55062	0.775308	−	0.631583i	$-0.217594\pi$
$997$	48.9612	1.55062	0.775308	+	0.631583i	$0.217594\pi$
$998$	15.8433	0.501512
$999$	5.00986	0.158505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.s.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.s.1.3	✓	4	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.40047 q^{5} -1.00000 q^{6} +3.20612 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.40047 q^{5} -1.00000 q^{6} +3.20612 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.40047 q^{10} -1.00000 q^{11} -1.00000 q^{12} +5.23775 q^{13} +3.20612 q^{14} -3.40047 q^{15} +1.00000 q^{16} -2.49008 q^{17} +1.00000 q^{18} +2.68442 q^{19} +3.40047 q^{20} -3.20612 q^{21} -1.00000 q^{22} +2.68442 q^{23} -1.00000 q^{24} +6.56319 q^{25} +5.23775 q^{26} -1.00000 q^{27} +3.20612 q^{28} -0.162720 q^{29} -3.40047 q^{30} -3.75945 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.49008 q^{34} +10.9023 q^{35} +1.00000 q^{36} -5.00986 q^{37} +2.68442 q^{38} -5.23775 q^{39} +3.40047 q^{40} +1.12123 q^{41} -3.20612 q^{42} -3.47830 q^{43} -1.00000 q^{44} +3.40047 q^{45} +2.68442 q^{46} +4.35706 q^{47} -1.00000 q^{48} +3.27924 q^{49} +6.56319 q^{50} +2.49008 q^{51} +5.23775 q^{52} +7.89055 q^{53} -1.00000 q^{54} -3.40047 q^{55} +3.20612 q^{56} -2.68442 q^{57} -0.162720 q^{58} +4.89527 q^{59} -3.40047 q^{60} -1.00000 q^{61} -3.75945 q^{62} +3.20612 q^{63} +1.00000 q^{64} +17.8108 q^{65} +1.00000 q^{66} -7.69620 q^{67} -2.49008 q^{68} -2.68442 q^{69} +10.9023 q^{70} -9.45374 q^{71} +1.00000 q^{72} -11.6184 q^{73} -5.00986 q^{74} -6.56319 q^{75} +2.68442 q^{76} -3.20612 q^{77} -5.23775 q^{78} -12.0622 q^{79} +3.40047 q^{80} +1.00000 q^{81} +1.12123 q^{82} -6.00706 q^{83} -3.20612 q^{84} -8.46743 q^{85} -3.47830 q^{86} +0.162720 q^{87} -1.00000 q^{88} -7.57025 q^{89} +3.40047 q^{90} +16.7929 q^{91} +2.68442 q^{92} +3.75945 q^{93} +4.35706 q^{94} +9.12830 q^{95} -1.00000 q^{96} -12.4971 q^{97} +3.27924 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} + 3 q^{10} - 4 q^{11} - 4 q^{12} + 13 q^{13} - 2 q^{14} - 3 q^{15} + 4 q^{16} + 3 q^{17} + 4 q^{18} + 2 q^{19} + 3 q^{20} + 2 q^{21} - 4 q^{22} + 2 q^{23} - 4 q^{24} + 13 q^{25} + 13 q^{26} - 4 q^{27} - 2 q^{28} + 2 q^{29} - 3 q^{30} - q^{31} + 4 q^{32} + 4 q^{33} + 3 q^{34} + q^{35} + 4 q^{36} - 6 q^{37} + 2 q^{38} - 13 q^{39} + 3 q^{40} + 9 q^{41} + 2 q^{42} - 20 q^{43} - 4 q^{44} + 3 q^{45} + 2 q^{46} + 19 q^{47} - 4 q^{48} - 2 q^{49} + 13 q^{50} - 3 q^{51} + 13 q^{52} + 8 q^{53} - 4 q^{54} - 3 q^{55} - 2 q^{56} - 2 q^{57} + 2 q^{58} + 13 q^{59} - 3 q^{60} - 4 q^{61} - q^{62} - 2 q^{63} + 4 q^{64} + 36 q^{65} + 4 q^{66} - 3 q^{67} + 3 q^{68} - 2 q^{69} + q^{70} - q^{71} + 4 q^{72} - 2 q^{73} - 6 q^{74} - 13 q^{75} + 2 q^{76} + 2 q^{77} - 13 q^{78} + 19 q^{79} + 3 q^{80} + 4 q^{81} + 9 q^{82} + 12 q^{83} + 2 q^{84} + 27 q^{85} - 20 q^{86} - 2 q^{87} - 4 q^{88} + 19 q^{89} + 3 q^{90} + q^{91} + 2 q^{92} + q^{93} + 19 q^{94} + 5 q^{95} - 4 q^{96} - q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 + 3 * q^10 - 4 * q^11 - 4 * q^12 + 13 * q^13 - 2 * q^14 - 3 * q^15 + 4 * q^16 + 3 * q^17 + 4 * q^18 + 2 * q^19 + 3 * q^20 + 2 * q^21 - 4 * q^22 + 2 * q^23 - 4 * q^24 + 13 * q^25 + 13 * q^26 - 4 * q^27 - 2 * q^28 + 2 * q^29 - 3 * q^30 - q^31 + 4 * q^32 + 4 * q^33 + 3 * q^34 + q^35 + 4 * q^36 - 6 * q^37 + 2 * q^38 - 13 * q^39 + 3 * q^40 + 9 * q^41 + 2 * q^42 - 20 * q^43 - 4 * q^44 + 3 * q^45 + 2 * q^46 + 19 * q^47 - 4 * q^48 - 2 * q^49 + 13 * q^50 - 3 * q^51 + 13 * q^52 + 8 * q^53 - 4 * q^54 - 3 * q^55 - 2 * q^56 - 2 * q^57 + 2 * q^58 + 13 * q^59 - 3 * q^60 - 4 * q^61 - q^62 - 2 * q^63 + 4 * q^64 + 36 * q^65 + 4 * q^66 - 3 * q^67 + 3 * q^68 - 2 * q^69 + q^70 - q^71 + 4 * q^72 - 2 * q^73 - 6 * q^74 - 13 * q^75 + 2 * q^76 + 2 * q^77 - 13 * q^78 + 19 * q^79 + 3 * q^80 + 4 * q^81 + 9 * q^82 + 12 * q^83 + 2 * q^84 + 27 * q^85 - 20 * q^86 - 2 * q^87 - 4 * q^88 + 19 * q^89 + 3 * q^90 + q^91 + 2 * q^92 + q^93 + 19 * q^94 + 5 * q^95 - 4 * q^96 - q^97 - 2 * q^98 - 4 * q^99

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