LMFDB - Embedded newform 4026.2.a.y.1.6

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:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 $ x^7 - 2x^6 - 21x^5 + 39x^4 + 89x^3 - 100x^2 - 96x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.76251$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.76251 q^{5} +1.00000 q^{6} +1.52396 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.76251 q^{5} +1.00000 q^{6} +1.52396 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.76251 q^{10} -1.00000 q^{11} -1.00000 q^{12} +2.12261 q^{13} -1.52396 q^{14} -1.76251 q^{15} +1.00000 q^{16} -6.67146 q^{17} -1.00000 q^{18} -1.90825 q^{19} +1.76251 q^{20} -1.52396 q^{21} +1.00000 q^{22} +4.54885 q^{23} +1.00000 q^{24} -1.89358 q^{25} -2.12261 q^{26} -1.00000 q^{27} +1.52396 q^{28} -1.93378 q^{29} +1.76251 q^{30} +4.61977 q^{31} -1.00000 q^{32} +1.00000 q^{33} +6.67146 q^{34} +2.68599 q^{35} +1.00000 q^{36} +3.74417 q^{37} +1.90825 q^{38} -2.12261 q^{39} -1.76251 q^{40} -9.44243 q^{41} +1.52396 q^{42} -9.84107 q^{43} -1.00000 q^{44} +1.76251 q^{45} -4.54885 q^{46} -0.480325 q^{47} -1.00000 q^{48} -4.67753 q^{49} +1.89358 q^{50} +6.67146 q^{51} +2.12261 q^{52} -9.07010 q^{53} +1.00000 q^{54} -1.76251 q^{55} -1.52396 q^{56} +1.90825 q^{57} +1.93378 q^{58} -8.55460 q^{59} -1.76251 q^{60} -1.00000 q^{61} -4.61977 q^{62} +1.52396 q^{63} +1.00000 q^{64} +3.74111 q^{65} -1.00000 q^{66} -7.60797 q^{67} -6.67146 q^{68} -4.54885 q^{69} -2.68599 q^{70} -5.44444 q^{71} -1.00000 q^{72} -1.75277 q^{73} -3.74417 q^{74} +1.89358 q^{75} -1.90825 q^{76} -1.52396 q^{77} +2.12261 q^{78} +5.33711 q^{79} +1.76251 q^{80} +1.00000 q^{81} +9.44243 q^{82} -9.98107 q^{83} -1.52396 q^{84} -11.7585 q^{85} +9.84107 q^{86} +1.93378 q^{87} +1.00000 q^{88} +11.7585 q^{89} -1.76251 q^{90} +3.23478 q^{91} +4.54885 q^{92} -4.61977 q^{93} +0.480325 q^{94} -3.36330 q^{95} +1.00000 q^{96} +11.8624 q^{97} +4.67753 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * 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
$5$	1.76251	0.788216	0.394108	−	0.919064i	$-0.371054\pi$
$5$	1.76251	0.788216	0.394108	+	0.919064i	$0.371054\pi$
$6$	1.00000	0.408248
$7$	1.52396	0.576004	0.288002	−	0.957630i	$-0.407009\pi$
$7$	1.52396	0.576004	0.288002	+	0.957630i	$0.407009\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.76251	−0.557353
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	2.12261	0.588706	0.294353	−	0.955697i	$-0.404896\pi$
$13$	2.12261	0.588706	0.294353	+	0.955697i	$0.404896\pi$
$14$	−1.52396	−0.407297
$15$	−1.76251	−0.455077
$16$	1.00000	0.250000
$17$	−6.67146	−1.61807	−0.809034	−	0.587762i	$-0.800009\pi$
$17$	−6.67146	−1.61807	−0.809034	+	0.587762i	$0.800009\pi$
$18$	−1.00000	−0.235702
$19$	−1.90825	−0.437783	−0.218892	−	0.975749i	$-0.570244\pi$
$19$	−1.90825	−0.437783	−0.218892	+	0.975749i	$0.570244\pi$
$20$	1.76251	0.394108
$21$	−1.52396	−0.332556
$22$	1.00000	0.213201
$23$	4.54885	0.948501	0.474251	−	0.880390i	$-0.342719\pi$
$23$	4.54885	0.948501	0.474251	+	0.880390i	$0.342719\pi$
$24$	1.00000	0.204124
$25$	−1.89358	−0.378715
$26$	−2.12261	−0.416278
$27$	−1.00000	−0.192450
$28$	1.52396	0.288002
$29$	−1.93378	−0.359094	−0.179547	−	0.983749i	$-0.557463\pi$
$29$	−1.93378	−0.359094	−0.179547	+	0.983749i	$0.557463\pi$
$30$	1.76251	0.321788
$31$	4.61977	0.829736	0.414868	−	0.909882i	$-0.363828\pi$
$31$	4.61977	0.829736	0.414868	+	0.909882i	$0.363828\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	6.67146	1.14415
$35$	2.68599	0.454016
$36$	1.00000	0.166667
$37$	3.74417	0.615537	0.307769	−	0.951461i	$-0.400418\pi$
$37$	3.74417	0.615537	0.307769	+	0.951461i	$0.400418\pi$
$38$	1.90825	0.309559
$39$	−2.12261	−0.339890
$40$	−1.76251	−0.278677
$41$	−9.44243	−1.47466	−0.737330	−	0.675533i	$-0.763914\pi$
$41$	−9.44243	−1.47466	−0.737330	+	0.675533i	$0.763914\pi$
$42$	1.52396	0.235153
$43$	−9.84107	−1.50075	−0.750374	−	0.661013i	$-0.770127\pi$
$43$	−9.84107	−1.50075	−0.750374	+	0.661013i	$0.770127\pi$
$44$	−1.00000	−0.150756
$45$	1.76251	0.262739
$46$	−4.54885	−0.670692
$47$	−0.480325	−0.0700626	−0.0350313	−	0.999386i	$-0.511153\pi$
$47$	−0.480325	−0.0700626	−0.0350313	+	0.999386i	$0.511153\pi$
$48$	−1.00000	−0.144338
$49$	−4.67753	−0.668219
$50$	1.89358	0.267792
$51$	6.67146	0.934192
$52$	2.12261	0.294353
$53$	−9.07010	−1.24587	−0.622937	−	0.782272i	$-0.714061\pi$
$53$	−9.07010	−1.24587	−0.622937	+	0.782272i	$0.714061\pi$
$54$	1.00000	0.136083
$55$	−1.76251	−0.237656
$56$	−1.52396	−0.203648
$57$	1.90825	0.252754
$58$	1.93378	0.253918
$59$	−8.55460	−1.11371	−0.556857	−	0.830608i	$-0.687993\pi$
$59$	−8.55460	−1.11371	−0.556857	+	0.830608i	$0.687993\pi$
$60$	−1.76251	−0.227538
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−4.61977	−0.586712
$63$	1.52396	0.192001
$64$	1.00000	0.125000
$65$	3.74111	0.464028
$66$	−1.00000	−0.123091
$67$	−7.60797	−0.929462	−0.464731	−	0.885452i	$-0.653849\pi$
$67$	−7.60797	−0.929462	−0.464731	+	0.885452i	$0.653849\pi$
$68$	−6.67146	−0.809034
$69$	−4.54885	−0.547617
$70$	−2.68599	−0.321038
$71$	−5.44444	−0.646136	−0.323068	−	0.946376i	$-0.604714\pi$
$71$	−5.44444	−0.646136	−0.323068	+	0.946376i	$0.604714\pi$
$72$	−1.00000	−0.117851
$73$	−1.75277	−0.205146	−0.102573	−	0.994725i	$-0.532708\pi$
$73$	−1.75277	−0.205146	−0.102573	+	0.994725i	$0.532708\pi$
$74$	−3.74417	−0.435250
$75$	1.89358	0.218651
$76$	−1.90825	−0.218892
$77$	−1.52396	−0.173672
$78$	2.12261	0.240338
$79$	5.33711	0.600472	0.300236	−	0.953865i	$-0.402935\pi$
$79$	5.33711	0.600472	0.300236	+	0.953865i	$0.402935\pi$
$80$	1.76251	0.197054
$81$	1.00000	0.111111
$82$	9.44243	1.04274
$83$	−9.98107	−1.09556	−0.547782	−	0.836621i	$-0.684528\pi$
$83$	−9.98107	−1.09556	−0.547782	+	0.836621i	$0.684528\pi$
$84$	−1.52396	−0.166278
$85$	−11.7585	−1.27539
$86$	9.84107	1.06119
$87$	1.93378	0.207323
$88$	1.00000	0.106600
$89$	11.7585	1.24640	0.623199	−	0.782064i	$-0.285833\pi$
$89$	11.7585	1.24640	0.623199	+	0.782064i	$0.285833\pi$
$90$	−1.76251	−0.185784
$91$	3.23478	0.339097
$92$	4.54885	0.474251
$93$	−4.61977	−0.479048
$94$	0.480325	0.0495417
$95$	−3.36330	−0.345068
$96$	1.00000	0.102062
$97$	11.8624	1.20444	0.602221	−	0.798329i	$-0.294283\pi$
$97$	11.8624	1.20444	0.602221	+	0.798329i	$0.294283\pi$
$98$	4.67753	0.472502
$99$	−1.00000	−0.100504
$100$	−1.89358	−0.189358
$101$	13.2193	1.31537	0.657684	−	0.753294i	$-0.271536\pi$
$101$	13.2193	1.31537	0.657684	+	0.753294i	$0.271536\pi$
$102$	−6.67146	−0.660573
$103$	6.87515	0.677429	0.338715	−	0.940889i	$-0.390008\pi$
$103$	6.87515	0.677429	0.338715	+	0.940889i	$0.390008\pi$
$104$	−2.12261	−0.208139
$105$	−2.68599	−0.262126
$106$	9.07010	0.880966
$107$	2.98953	0.289009	0.144504	−	0.989504i	$-0.453841\pi$
$107$	2.98953	0.289009	0.144504	+	0.989504i	$0.453841\pi$
$108$	−1.00000	−0.0962250
$109$	−7.45010	−0.713590	−0.356795	−	0.934183i	$-0.616131\pi$
$109$	−7.45010	−0.713590	−0.356795	+	0.934183i	$0.616131\pi$
$110$	1.76251	0.168048
$111$	−3.74417	−0.355381
$112$	1.52396	0.144001
$113$	5.84411	0.549767	0.274884	−	0.961477i	$-0.411361\pi$
$113$	5.84411	0.549767	0.274884	+	0.961477i	$0.411361\pi$
$114$	−1.90825	−0.178724
$115$	8.01738	0.747624
$116$	−1.93378	−0.179547
$117$	2.12261	0.196235
$118$	8.55460	0.787515
$119$	−10.1671	−0.932014
$120$	1.76251	0.160894
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	9.44243	0.851395
$124$	4.61977	0.414868
$125$	−12.1500	−1.08673
$126$	−1.52396	−0.135766
$127$	−10.6117	−0.941639	−0.470820	−	0.882230i	$-0.656042\pi$
$127$	−10.6117	−0.941639	−0.470820	+	0.882230i	$0.656042\pi$
$128$	−1.00000	−0.0883883
$129$	9.84107	0.866458
$130$	−3.74111	−0.328117
$131$	−17.4503	−1.52464	−0.762318	−	0.647203i	$-0.775939\pi$
$131$	−17.4503	−1.52464	−0.762318	+	0.647203i	$0.775939\pi$
$132$	1.00000	0.0870388
$133$	−2.90811	−0.252165
$134$	7.60797	0.657229
$135$	−1.76251	−0.151692
$136$	6.67146	0.572073
$137$	12.7073	1.08566	0.542828	−	0.839844i	$-0.317354\pi$
$137$	12.7073	1.08566	0.542828	+	0.839844i	$0.317354\pi$
$138$	4.54885	0.387224
$139$	14.9258	1.26599	0.632994	−	0.774157i	$-0.281826\pi$
$139$	14.9258	1.26599	0.632994	+	0.774157i	$0.281826\pi$
$140$	2.68599	0.227008
$141$	0.480325	0.0404506
$142$	5.44444	0.456887
$143$	−2.12261	−0.177502
$144$	1.00000	0.0833333
$145$	−3.40830	−0.283044
$146$	1.75277	0.145060
$147$	4.67753	0.385796
$148$	3.74417	0.307769
$149$	−4.83902	−0.396428	−0.198214	−	0.980159i	$-0.563514\pi$
$149$	−4.83902	−0.396428	−0.198214	+	0.980159i	$0.563514\pi$
$150$	−1.89358	−0.154610
$151$	−11.5385	−0.938987	−0.469493	−	0.882936i	$-0.655563\pi$
$151$	−11.5385	−0.938987	−0.469493	+	0.882936i	$0.655563\pi$
$152$	1.90825	0.154780
$153$	−6.67146	−0.539356
$154$	1.52396	0.122805
$155$	8.14237	0.654011
$156$	−2.12261	−0.169945
$157$	3.26153	0.260299	0.130149	−	0.991494i	$-0.458454\pi$
$157$	3.26153	0.260299	0.130149	+	0.991494i	$0.458454\pi$
$158$	−5.33711	−0.424598
$159$	9.07010	0.719306
$160$	−1.76251	−0.139338
$161$	6.93229	0.546341
$162$	−1.00000	−0.0785674
$163$	22.1516	1.73505	0.867523	−	0.497398i	$-0.165711\pi$
$163$	22.1516	1.73505	0.867523	+	0.497398i	$0.165711\pi$
$164$	−9.44243	−0.737330
$165$	1.76251	0.137211
$166$	9.98107	0.774681
$167$	−21.6805	−1.67769	−0.838843	−	0.544373i	$-0.816768\pi$
$167$	−21.6805	−1.67769	−0.838843	+	0.544373i	$0.816768\pi$
$168$	1.52396	0.117576
$169$	−8.49453	−0.653425
$170$	11.7585	0.901835
$171$	−1.90825	−0.145928
$172$	−9.84107	−0.750374
$173$	12.0984	0.919826	0.459913	−	0.887964i	$-0.347881\pi$
$173$	12.0984	0.919826	0.459913	+	0.887964i	$0.347881\pi$
$174$	−1.93378	−0.146599
$175$	−2.88574	−0.218142
$176$	−1.00000	−0.0753778
$177$	8.55460	0.643003
$178$	−11.7585	−0.881336
$179$	−2.41556	−0.180548	−0.0902738	−	0.995917i	$-0.528774\pi$
$179$	−2.41556	−0.180548	−0.0902738	+	0.995917i	$0.528774\pi$
$180$	1.76251	0.131369
$181$	−10.0525	−0.747199	−0.373600	−	0.927590i	$-0.621877\pi$
$181$	−10.0525	−0.747199	−0.373600	+	0.927590i	$0.621877\pi$
$182$	−3.23478	−0.239778
$183$	1.00000	0.0739221
$184$	−4.54885	−0.335346
$185$	6.59911	0.485176
$186$	4.61977	0.338738
$187$	6.67146	0.487866
$188$	−0.480325	−0.0350313
$189$	−1.52396	−0.110852
$190$	3.36330	0.244000
$191$	−21.3332	−1.54362	−0.771808	−	0.635856i	$-0.780647\pi$
$191$	−21.3332	−1.54362	−0.771808	+	0.635856i	$0.780647\pi$
$192$	−1.00000	−0.0721688
$193$	12.7280	0.916185	0.458092	−	0.888905i	$-0.348533\pi$
$193$	12.7280	0.916185	0.458092	+	0.888905i	$0.348533\pi$
$194$	−11.8624	−0.851669
$195$	−3.74111	−0.267906
$196$	−4.67753	−0.334110
$197$	11.6865	0.832630	0.416315	−	0.909220i	$-0.363321\pi$
$197$	11.6865	0.832630	0.416315	+	0.909220i	$0.363321\pi$
$198$	1.00000	0.0710669
$199$	−14.9220	−1.05780	−0.528898	−	0.848686i	$-0.677395\pi$
$199$	−14.9220	−1.05780	−0.528898	+	0.848686i	$0.677395\pi$
$200$	1.89358	0.133896
$201$	7.60797	0.536625
$202$	−13.2193	−0.930106
$203$	−2.94701	−0.206840
$204$	6.67146	0.467096
$205$	−16.6423	−1.16235
$206$	−6.87515	−0.479015
$207$	4.54885	0.316167
$208$	2.12261	0.147176
$209$	1.90825	0.131997
$210$	2.68599	0.185351
$211$	−12.8257	−0.882956	−0.441478	−	0.897272i	$-0.645546\pi$
$211$	−12.8257	−0.882956	−0.441478	+	0.897272i	$0.645546\pi$
$212$	−9.07010	−0.622937
$213$	5.44444	0.373047
$214$	−2.98953	−0.204360
$215$	−17.3449	−1.18291
$216$	1.00000	0.0680414
$217$	7.04037	0.477931
$218$	7.45010	0.504585
$219$	1.75277	0.118441
$220$	−1.76251	−0.118828
$221$	−14.1609	−0.952566
$222$	3.74417	0.251292
$223$	−16.5087	−1.10550	−0.552752	−	0.833346i	$-0.686422\pi$
$223$	−16.5087	−1.10550	−0.552752	+	0.833346i	$0.686422\pi$
$224$	−1.52396	−0.101824
$225$	−1.89358	−0.126238
$226$	−5.84411	−0.388744
$227$	−11.7919	−0.782658	−0.391329	−	0.920251i	$-0.627985\pi$
$227$	−11.7919	−0.782658	−0.391329	+	0.920251i	$0.627985\pi$
$228$	1.90825	0.126377
$229$	3.73426	0.246767	0.123383	−	0.992359i	$-0.460626\pi$
$229$	3.73426	0.246767	0.123383	+	0.992359i	$0.460626\pi$
$230$	−8.01738	−0.528650
$231$	1.52396	0.100269
$232$	1.93378	0.126959
$233$	4.55083	0.298135	0.149068	−	0.988827i	$-0.452373\pi$
$233$	4.55083	0.298135	0.149068	+	0.988827i	$0.452373\pi$
$234$	−2.12261	−0.138759
$235$	−0.846575	−0.0552245
$236$	−8.55460	−0.556857
$237$	−5.33711	−0.346683
$238$	10.1671	0.659033
$239$	−1.50302	−0.0972220	−0.0486110	−	0.998818i	$-0.515479\pi$
$239$	−1.50302	−0.0972220	−0.0486110	+	0.998818i	$0.515479\pi$
$240$	−1.76251	−0.113769
$241$	23.7844	1.53209	0.766043	−	0.642789i	$-0.222223\pi$
$241$	23.7844	1.53209	0.766043	+	0.642789i	$0.222223\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−8.24418	−0.526701
$246$	−9.44243	−0.602027
$247$	−4.05047	−0.257726
$248$	−4.61977	−0.293356
$249$	9.98107	0.632525
$250$	12.1500	0.768431
$251$	−5.66788	−0.357754	−0.178877	−	0.983871i	$-0.557246\pi$
$251$	−5.66788	−0.357754	−0.178877	+	0.983871i	$0.557246\pi$
$252$	1.52396	0.0960007
$253$	−4.54885	−0.285984
$254$	10.6117	0.665839
$255$	11.7585	0.736345
$256$	1.00000	0.0625000
$257$	3.86279	0.240954	0.120477	−	0.992716i	$-0.461558\pi$
$257$	3.86279	0.240954	0.120477	+	0.992716i	$0.461558\pi$
$258$	−9.84107	−0.612678
$259$	5.70597	0.354552
$260$	3.74111	0.232014
$261$	−1.93378	−0.119698
$262$	17.4503	1.07808
$263$	−8.46401	−0.521913	−0.260957	−	0.965351i	$-0.584038\pi$
$263$	−8.46401	−0.521913	−0.260957	+	0.965351i	$0.584038\pi$
$264$	−1.00000	−0.0615457
$265$	−15.9861	−0.982018
$266$	2.90811	0.178308
$267$	−11.7585	−0.719608
$268$	−7.60797	−0.464731
$269$	16.6550	1.01547	0.507737	−	0.861512i	$-0.330482\pi$
$269$	16.6550	1.01547	0.507737	+	0.861512i	$0.330482\pi$
$270$	1.76251	0.107263
$271$	13.4995	0.820033	0.410017	−	0.912078i	$-0.365523\pi$
$271$	13.4995	0.820033	0.410017	+	0.912078i	$0.365523\pi$
$272$	−6.67146	−0.404517
$273$	−3.23478	−0.195778
$274$	−12.7073	−0.767675
$275$	1.89358	0.114187
$276$	−4.54885	−0.273809
$277$	25.3096	1.52071	0.760353	−	0.649510i	$-0.225026\pi$
$277$	25.3096	1.52071	0.760353	+	0.649510i	$0.225026\pi$
$278$	−14.9258	−0.895189
$279$	4.61977	0.276579
$280$	−2.68599	−0.160519
$281$	4.93263	0.294256	0.147128	−	0.989117i	$-0.452997\pi$
$281$	4.93263	0.294256	0.147128	+	0.989117i	$0.452997\pi$
$282$	−0.480325	−0.0286029
$283$	−12.1149	−0.720156	−0.360078	−	0.932922i	$-0.617250\pi$
$283$	−12.1149	−0.720156	−0.360078	+	0.932922i	$0.617250\pi$
$284$	−5.44444	−0.323068
$285$	3.36330	0.199225
$286$	2.12261	0.125513
$287$	−14.3899	−0.849410
$288$	−1.00000	−0.0589256
$289$	27.5084	1.61814
$290$	3.40830	0.200142
$291$	−11.8624	−0.695385
$292$	−1.75277	−0.102573
$293$	−26.9803	−1.57621	−0.788104	−	0.615542i	$-0.788937\pi$
$293$	−26.9803	−1.57621	−0.788104	+	0.615542i	$0.788937\pi$
$294$	−4.67753	−0.272799
$295$	−15.0775	−0.877847
$296$	−3.74417	−0.217625
$297$	1.00000	0.0580259
$298$	4.83902	0.280317
$299$	9.65544	0.558388
$300$	1.89358	0.109326
$301$	−14.9974	−0.864438
$302$	11.5385	0.663964
$303$	−13.2193	−0.759428
$304$	−1.90825	−0.109446
$305$	−1.76251	−0.100921
$306$	6.67146	0.381382
$307$	24.9049	1.42140	0.710700	−	0.703496i	$-0.248379\pi$
$307$	24.9049	1.42140	0.710700	+	0.703496i	$0.248379\pi$
$308$	−1.52396	−0.0868359
$309$	−6.87515	−0.391114
$310$	−8.14237	−0.462456
$311$	12.8864	0.730720	0.365360	−	0.930866i	$-0.380946\pi$
$311$	12.8864	0.730720	0.365360	+	0.930866i	$0.380946\pi$
$312$	2.12261	0.120169
$313$	−13.1222	−0.741710	−0.370855	−	0.928691i	$-0.620935\pi$
$313$	−13.1222	−0.741710	−0.370855	+	0.928691i	$0.620935\pi$
$314$	−3.26153	−0.184059
$315$	2.68599	0.151339
$316$	5.33711	0.300236
$317$	−11.7823	−0.661762	−0.330881	−	0.943672i	$-0.607346\pi$
$317$	−11.7823	−0.661762	−0.330881	+	0.943672i	$0.607346\pi$
$318$	−9.07010	−0.508626
$319$	1.93378	0.108271
$320$	1.76251	0.0985270
$321$	−2.98953	−0.166859
$322$	−6.93229	−0.386321
$323$	12.7308	0.708363
$324$	1.00000	0.0555556
$325$	−4.01932	−0.222952
$326$	−22.1516	−1.22686
$327$	7.45010	0.411992
$328$	9.44243	0.521371
$329$	−0.731998	−0.0403563
$330$	−1.76251	−0.0970227
$331$	−8.80568	−0.484004	−0.242002	−	0.970276i	$-0.577804\pi$
$331$	−8.80568	−0.484004	−0.242002	+	0.970276i	$0.577804\pi$
$332$	−9.98107	−0.547782
$333$	3.74417	0.205179
$334$	21.6805	1.18630
$335$	−13.4091	−0.732617
$336$	−1.52396	−0.0831391
$337$	−17.8368	−0.971634	−0.485817	−	0.874061i	$-0.661478\pi$
$337$	−17.8368	−0.971634	−0.485817	+	0.874061i	$0.661478\pi$
$338$	8.49453	0.462041
$339$	−5.84411	−0.317408
$340$	−11.7585	−0.637693
$341$	−4.61977	−0.250175
$342$	1.90825	0.103186
$343$	−17.7961	−0.960901
$344$	9.84107	0.530595
$345$	−8.01738	−0.431641
$346$	−12.0984	−0.650415
$347$	−34.2795	−1.84022	−0.920110	−	0.391659i	$-0.871901\pi$
$347$	−34.2795	−1.84022	−0.920110	+	0.391659i	$0.871901\pi$
$348$	1.93378	0.103661
$349$	23.2961	1.24701	0.623506	−	0.781819i	$-0.285708\pi$
$349$	23.2961	1.24701	0.623506	+	0.781819i	$0.285708\pi$
$350$	2.88574	0.154249
$351$	−2.12261	−0.113297
$352$	1.00000	0.0533002
$353$	−18.7503	−0.997979	−0.498989	−	0.866608i	$-0.666295\pi$
$353$	−18.7503	−0.997979	−0.498989	+	0.866608i	$0.666295\pi$
$354$	−8.55460	−0.454672
$355$	−9.59585	−0.509295
$356$	11.7585	0.623199
$357$	10.1671	0.538098
$358$	2.41556	0.127666
$359$	−10.3804	−0.547858	−0.273929	−	0.961750i	$-0.588323\pi$
$359$	−10.3804	−0.547858	−0.273929	+	0.961750i	$0.588323\pi$
$360$	−1.76251	−0.0928922
$361$	−15.3586	−0.808346
$362$	10.0525	0.528350
$363$	−1.00000	−0.0524864
$364$	3.23478	0.169549
$365$	−3.08927	−0.161700
$366$	−1.00000	−0.0522708
$367$	−12.2538	−0.639644	−0.319822	−	0.947478i	$-0.603623\pi$
$367$	−12.2538	−0.639644	−0.319822	+	0.947478i	$0.603623\pi$
$368$	4.54885	0.237125
$369$	−9.44243	−0.491553
$370$	−6.59911	−0.343071
$371$	−13.8225	−0.717629
$372$	−4.61977	−0.239524
$373$	−9.04809	−0.468493	−0.234246	−	0.972177i	$-0.575262\pi$
$373$	−9.04809	−0.468493	−0.234246	+	0.972177i	$0.575262\pi$
$374$	−6.67146	−0.344973
$375$	12.1500	0.627421
$376$	0.480325	0.0247709
$377$	−4.10466	−0.211401
$378$	1.52396	0.0783843
$379$	5.80920	0.298398	0.149199	−	0.988807i	$-0.452330\pi$
$379$	5.80920	0.298398	0.149199	+	0.988807i	$0.452330\pi$
$380$	−3.36330	−0.172534
$381$	10.6117	0.543656
$382$	21.3332	1.09150
$383$	−30.2024	−1.54327	−0.771634	−	0.636066i	$-0.780560\pi$
$383$	−30.2024	−1.54327	−0.771634	+	0.636066i	$0.780560\pi$
$384$	1.00000	0.0510310
$385$	−2.68599	−0.136891
$386$	−12.7280	−0.647840
$387$	−9.84107	−0.500250
$388$	11.8624	0.602221
$389$	0.453003	0.0229682	0.0114841	−	0.999934i	$-0.496344\pi$
$389$	0.453003	0.0229682	0.0114841	+	0.999934i	$0.496344\pi$
$390$	3.74111	0.189438
$391$	−30.3475	−1.53474
$392$	4.67753	0.236251
$393$	17.4503	0.880249
$394$	−11.6865	−0.588758
$395$	9.40669	0.473302
$396$	−1.00000	−0.0502519
$397$	−6.08259	−0.305276	−0.152638	−	0.988282i	$-0.548777\pi$
$397$	−6.08259	−0.305276	−0.152638	+	0.988282i	$0.548777\pi$
$398$	14.9220	0.747974
$399$	2.90811	0.145587
$400$	−1.89358	−0.0946788
$401$	−16.9591	−0.846898	−0.423449	−	0.905920i	$-0.639181\pi$
$401$	−16.9591	−0.846898	−0.423449	+	0.905920i	$0.639181\pi$
$402$	−7.60797	−0.379451
$403$	9.80598	0.488470
$404$	13.2193	0.657684
$405$	1.76251	0.0875796
$406$	2.94701	0.146258
$407$	−3.74417	−0.185591
$408$	−6.67146	−0.330287
$409$	7.48907	0.370310	0.185155	−	0.982709i	$-0.440721\pi$
$409$	7.48907	0.370310	0.185155	+	0.982709i	$0.440721\pi$
$410$	16.6423	0.821906
$411$	−12.7073	−0.626804
$412$	6.87515	0.338715
$413$	−13.0369	−0.641504
$414$	−4.54885	−0.223564
$415$	−17.5917	−0.863542
$416$	−2.12261	−0.104070
$417$	−14.9258	−0.730919
$418$	−1.90825	−0.0933357
$419$	−15.9779	−0.780570	−0.390285	−	0.920694i	$-0.627624\pi$
$419$	−15.9779	−0.780570	−0.390285	+	0.920694i	$0.627624\pi$
$420$	−2.68599	−0.131063
$421$	32.4789	1.58292	0.791461	−	0.611219i	$-0.209321\pi$
$421$	32.4789	1.58292	0.791461	+	0.611219i	$0.209321\pi$
$422$	12.8257	0.624344
$423$	−0.480325	−0.0233542
$424$	9.07010	0.440483
$425$	12.6329	0.612787
$426$	−5.44444	−0.263784
$427$	−1.52396	−0.0737498
$428$	2.98953	0.144504
$429$	2.12261	0.102481
$430$	17.3449	0.836447
$431$	−4.75109	−0.228852	−0.114426	−	0.993432i	$-0.536503\pi$
$431$	−4.75109	−0.228852	−0.114426	+	0.993432i	$0.536503\pi$
$432$	−1.00000	−0.0481125
$433$	−9.86957	−0.474301	−0.237151	−	0.971473i	$-0.576213\pi$
$433$	−9.86957	−0.474301	−0.237151	+	0.971473i	$0.576213\pi$
$434$	−7.04037	−0.337949
$435$	3.40830	0.163415
$436$	−7.45010	−0.356795
$437$	−8.68036	−0.415238
$438$	−1.75277	−0.0837507
$439$	−40.8858	−1.95137	−0.975687	−	0.219169i	$-0.929666\pi$
$439$	−40.8858	−1.95137	−0.975687	+	0.219169i	$0.929666\pi$
$440$	1.76251	0.0840241
$441$	−4.67753	−0.222740
$442$	14.1609	0.673566
$443$	31.4389	1.49371	0.746855	−	0.664987i	$-0.231563\pi$
$443$	31.4389	1.49371	0.746855	+	0.664987i	$0.231563\pi$
$444$	−3.74417	−0.177690
$445$	20.7244	0.982430
$446$	16.5087	0.781709
$447$	4.83902	0.228878
$448$	1.52396	0.0720005
$449$	−8.17497	−0.385801	−0.192900	−	0.981218i	$-0.561789\pi$
$449$	−8.17497	−0.385801	−0.192900	+	0.981218i	$0.561789\pi$
$450$	1.89358	0.0892640
$451$	9.44243	0.444627
$452$	5.84411	0.274884
$453$	11.5385	0.542124
$454$	11.7919	0.553423
$455$	5.70132	0.267282
$456$	−1.90825	−0.0893621
$457$	28.8764	1.35078	0.675389	−	0.737461i	$-0.263976\pi$
$457$	28.8764	1.35078	0.675389	+	0.737461i	$0.263976\pi$
$458$	−3.73426	−0.174490
$459$	6.67146	0.311397
$460$	8.01738	0.373812
$461$	−37.5723	−1.74992	−0.874959	−	0.484197i	$-0.839112\pi$
$461$	−37.5723	−1.74992	−0.874959	+	0.484197i	$0.839112\pi$
$462$	−1.52396	−0.0709012
$463$	4.36174	0.202707	0.101354	−	0.994850i	$-0.467683\pi$
$463$	4.36174	0.202707	0.101354	+	0.994850i	$0.467683\pi$
$464$	−1.93378	−0.0897734
$465$	−8.14237	−0.377594
$466$	−4.55083	−0.210813
$467$	0.522021	0.0241562	0.0120781	−	0.999927i	$-0.496155\pi$
$467$	0.522021	0.0241562	0.0120781	+	0.999927i	$0.496155\pi$
$468$	2.12261	0.0981177
$469$	−11.5943	−0.535374
$470$	0.846575	0.0390496
$471$	−3.26153	−0.150284
$472$	8.55460	0.393757
$473$	9.84107	0.452493
$474$	5.33711	0.245142
$475$	3.61342	0.165795
$476$	−10.1671	−0.466007
$477$	−9.07010	−0.415291
$478$	1.50302	0.0687464
$479$	−18.7610	−0.857211	−0.428606	−	0.903492i	$-0.640995\pi$
$479$	−18.7610	−0.857211	−0.428606	+	0.903492i	$0.640995\pi$
$480$	1.76251	0.0804470
$481$	7.94740	0.362370
$482$	−23.7844	−1.08335
$483$	−6.93229	−0.315430
$484$	1.00000	0.0454545
$485$	20.9075	0.949361
$486$	1.00000	0.0453609
$487$	32.9767	1.49432	0.747158	−	0.664646i	$-0.231418\pi$
$487$	32.9767	1.49432	0.747158	+	0.664646i	$0.231418\pi$
$488$	1.00000	0.0452679
$489$	−22.1516	−1.00173
$490$	8.24418	0.372434
$491$	−34.0590	−1.53706	−0.768530	−	0.639813i	$-0.779012\pi$
$491$	−34.0590	−1.53706	−0.768530	+	0.639813i	$0.779012\pi$
$492$	9.44243	0.425698
$493$	12.9011	0.581038
$494$	4.05047	0.182239
$495$	−1.76251	−0.0792187
$496$	4.61977	0.207434
$497$	−8.29713	−0.372177
$498$	−9.98107	−0.447262
$499$	−33.0223	−1.47828	−0.739140	−	0.673551i	$-0.764768\pi$
$499$	−33.0223	−1.47828	−0.739140	+	0.673551i	$0.764768\pi$
$500$	−12.1500	−0.543363
$501$	21.6805	0.968613
$502$	5.66788	0.252970
$503$	27.6846	1.23440	0.617198	−	0.786808i	$-0.288268\pi$
$503$	27.6846	1.23440	0.617198	+	0.786808i	$0.288268\pi$
$504$	−1.52396	−0.0678828
$505$	23.2991	1.03679
$506$	4.54885	0.202221
$507$	8.49453	0.377255
$508$	−10.6117	−0.470820
$509$	6.60504	0.292763	0.146382	−	0.989228i	$-0.453237\pi$
$509$	6.60504	0.292763	0.146382	+	0.989228i	$0.453237\pi$
$510$	−11.7585	−0.520675
$511$	−2.67116	−0.118165
$512$	−1.00000	−0.0441942
$513$	1.90825	0.0842514
$514$	−3.86279	−0.170380
$515$	12.1175	0.533961
$516$	9.84107	0.433229
$517$	0.480325	0.0211247
$518$	−5.70597	−0.250706
$519$	−12.0984	−0.531062
$520$	−3.74111	−0.164059
$521$	−42.0695	−1.84310	−0.921550	−	0.388260i	$-0.873076\pi$
$521$	−42.0695	−1.84310	−0.921550	+	0.388260i	$0.873076\pi$
$522$	1.93378	0.0846392
$523$	−18.2707	−0.798923	−0.399461	−	0.916750i	$-0.630803\pi$
$523$	−18.2707	−0.798923	−0.399461	+	0.916750i	$0.630803\pi$
$524$	−17.4503	−0.762318
$525$	2.88574	0.125944
$526$	8.46401	0.369048
$527$	−30.8206	−1.34257
$528$	1.00000	0.0435194
$529$	−2.30794	−0.100345
$530$	15.9861	0.694392
$531$	−8.55460	−0.371238
$532$	−2.90811	−0.126082
$533$	−20.0426	−0.868141
$534$	11.7585	0.508839
$535$	5.26906	0.227801
$536$	7.60797	0.328614
$537$	2.41556	0.104239
$538$	−16.6550	−0.718048
$539$	4.67753	0.201476
$540$	−1.76251	−0.0758461
$541$	−9.69222	−0.416701	−0.208351	−	0.978054i	$-0.566810\pi$
$541$	−9.69222	−0.416701	−0.208351	+	0.978054i	$0.566810\pi$
$542$	−13.4995	−0.579851
$543$	10.0525	0.431396
$544$	6.67146	0.286037
$545$	−13.1308	−0.562464
$546$	3.23478	0.138436
$547$	39.1085	1.67216	0.836080	−	0.548608i	$-0.184842\pi$
$547$	39.1085	1.67216	0.836080	+	0.548608i	$0.184842\pi$
$548$	12.7073	0.542828
$549$	−1.00000	−0.0426790
$550$	−1.89358	−0.0807423
$551$	3.69014	0.157205
$552$	4.54885	0.193612
$553$	8.13357	0.345874
$554$	−25.3096	−1.07530
$555$	−6.59911	−0.280117
$556$	14.9258	0.632994
$557$	9.94668	0.421454	0.210727	−	0.977545i	$-0.432417\pi$
$557$	9.94668	0.421454	0.210727	+	0.977545i	$0.432417\pi$
$558$	−4.61977	−0.195571
$559$	−20.8887	−0.883500
$560$	2.68599	0.113504
$561$	−6.67146	−0.281669
$562$	−4.93263	−0.208070
$563$	−14.4667	−0.609699	−0.304849	−	0.952401i	$-0.598606\pi$
$563$	−14.4667	−0.609699	−0.304849	+	0.952401i	$0.598606\pi$
$564$	0.480325	0.0202253
$565$	10.3003	0.433336
$566$	12.1149	0.509227
$567$	1.52396	0.0640005
$568$	5.44444	0.228444
$569$	−27.1080	−1.13643	−0.568213	−	0.822882i	$-0.692365\pi$
$569$	−27.1080	−1.13643	−0.568213	+	0.822882i	$0.692365\pi$
$570$	−3.36330	−0.140873
$571$	25.4551	1.06526	0.532631	−	0.846347i	$-0.321203\pi$
$571$	25.4551	1.06526	0.532631	+	0.846347i	$0.321203\pi$
$572$	−2.12261	−0.0887508
$573$	21.3332	0.891207
$574$	14.3899	0.600624
$575$	−8.61360	−0.359212
$576$	1.00000	0.0416667
$577$	−24.0457	−1.00103	−0.500517	−	0.865727i	$-0.666857\pi$
$577$	−24.0457	−1.00103	−0.500517	+	0.865727i	$0.666857\pi$
$578$	−27.5084	−1.14420
$579$	−12.7280	−0.528959
$580$	−3.40830	−0.141522
$581$	−15.2108	−0.631050
$582$	11.8624	0.491711
$583$	9.07010	0.375645
$584$	1.75277	0.0725302
$585$	3.74111	0.154676
$586$	26.9803	1.11455
$587$	−2.22012	−0.0916343	−0.0458172	−	0.998950i	$-0.514589\pi$
$587$	−2.22012	−0.0916343	−0.0458172	+	0.998950i	$0.514589\pi$
$588$	4.67753	0.192898
$589$	−8.81569	−0.363244
$590$	15.0775	0.620732
$591$	−11.6865	−0.480719
$592$	3.74417	0.153884
$593$	13.6248	0.559504	0.279752	−	0.960072i	$-0.409748\pi$
$593$	13.6248	0.559504	0.279752	+	0.960072i	$0.409748\pi$
$594$	−1.00000	−0.0410305
$595$	−17.9195	−0.734628
$596$	−4.83902	−0.198214
$597$	14.9220	0.610719
$598$	−9.65544	−0.394840
$599$	15.6517	0.639513	0.319756	−	0.947500i	$-0.396399\pi$
$599$	15.6517	0.639513	0.319756	+	0.947500i	$0.396399\pi$
$600$	−1.89358	−0.0773049
$601$	36.2796	1.47988	0.739938	−	0.672675i	$-0.234855\pi$
$601$	36.2796	1.47988	0.739938	+	0.672675i	$0.234855\pi$
$602$	14.9974	0.611250
$603$	−7.60797	−0.309821
$604$	−11.5385	−0.469493
$605$	1.76251	0.0716560
$606$	13.2193	0.536997
$607$	22.4582	0.911551	0.455775	−	0.890095i	$-0.349362\pi$
$607$	22.4582	0.911551	0.455775	+	0.890095i	$0.349362\pi$
$608$	1.90825	0.0773899
$609$	2.94701	0.119419
$610$	1.76251	0.0713617
$611$	−1.01954	−0.0412463
$612$	−6.67146	−0.269678
$613$	−31.1980	−1.26007	−0.630037	−	0.776565i	$-0.716960\pi$
$613$	−31.1980	−1.26007	−0.630037	+	0.776565i	$0.716960\pi$
$614$	−24.9049	−1.00508
$615$	16.6423	0.671083
$616$	1.52396	0.0614023
$617$	12.9759	0.522388	0.261194	−	0.965286i	$-0.415884\pi$
$617$	12.9759	0.522388	0.261194	+	0.965286i	$0.415884\pi$
$618$	6.87515	0.276559
$619$	9.09423	0.365528	0.182764	−	0.983157i	$-0.441496\pi$
$619$	9.09423	0.365528	0.182764	+	0.983157i	$0.441496\pi$
$620$	8.14237	0.327006
$621$	−4.54885	−0.182539
$622$	−12.8864	−0.516697
$623$	17.9195	0.717930
$624$	−2.12261	−0.0849724
$625$	−11.9465	−0.477860
$626$	13.1222	0.524468
$627$	−1.90825	−0.0762083
$628$	3.26153	0.130149
$629$	−24.9791	−0.995980
$630$	−2.68599	−0.107013
$631$	−20.6523	−0.822155	−0.411077	−	0.911600i	$-0.634847\pi$
$631$	−20.6523	−0.822155	−0.411077	+	0.911600i	$0.634847\pi$
$632$	−5.33711	−0.212299
$633$	12.8257	0.509775
$634$	11.7823	0.467937
$635$	−18.7032	−0.742215
$636$	9.07010	0.359653
$637$	−9.92858	−0.393385
$638$	−1.93378	−0.0765591
$639$	−5.44444	−0.215379
$640$	−1.76251	−0.0696691
$641$	47.1733	1.86323	0.931616	−	0.363445i	$-0.118399\pi$
$641$	47.1733	1.86323	0.931616	+	0.363445i	$0.118399\pi$
$642$	2.98953	0.117987
$643$	46.9574	1.85182	0.925909	−	0.377746i	$-0.123301\pi$
$643$	46.9574	1.85182	0.925909	+	0.377746i	$0.123301\pi$
$644$	6.93229	0.273170
$645$	17.3449	0.682956
$646$	−12.7308	−0.500888
$647$	40.7869	1.60350	0.801749	−	0.597660i	$-0.203903\pi$
$647$	40.7869	1.60350	0.801749	+	0.597660i	$0.203903\pi$
$648$	−1.00000	−0.0392837
$649$	8.55460	0.335797
$650$	4.01932	0.157651
$651$	−7.04037	−0.275934
$652$	22.1516	0.867523
$653$	45.8466	1.79411	0.897057	−	0.441914i	$-0.145700\pi$
$653$	45.8466	1.79411	0.897057	+	0.441914i	$0.145700\pi$
$654$	−7.45010	−0.291322
$655$	−30.7562	−1.20174
$656$	−9.44243	−0.368665
$657$	−1.75277	−0.0683821
$658$	0.731998	0.0285362
$659$	−0.823726	−0.0320878	−0.0160439	−	0.999871i	$-0.505107\pi$
$659$	−0.823726	−0.0320878	−0.0160439	+	0.999871i	$0.505107\pi$
$660$	1.76251	0.0686054
$661$	−30.4334	−1.18372	−0.591861	−	0.806040i	$-0.701607\pi$
$661$	−30.4334	−1.18372	−0.591861	+	0.806040i	$0.701607\pi$
$662$	8.80568	0.342242
$663$	14.1609	0.549964
$664$	9.98107	0.387341
$665$	−5.12556	−0.198761
$666$	−3.74417	−0.145083
$667$	−8.79648	−0.340601
$668$	−21.6805	−0.838843
$669$	16.5087	0.638263
$670$	13.4091	0.518038
$671$	1.00000	0.0386046
$672$	1.52396	0.0587882
$673$	33.7921	1.30259	0.651296	−	0.758824i	$-0.274226\pi$
$673$	33.7921	1.30259	0.651296	+	0.758824i	$0.274226\pi$
$674$	17.8368	0.687049
$675$	1.89358	0.0728838
$676$	−8.49453	−0.326713
$677$	−34.6752	−1.33268	−0.666338	−	0.745650i	$-0.732139\pi$
$677$	−34.6752	−1.33268	−0.666338	+	0.745650i	$0.732139\pi$
$678$	5.84411	0.224442
$679$	18.0778	0.693764
$680$	11.7585	0.450917
$681$	11.7919	0.451868
$682$	4.61977	0.176900
$683$	1.86987	0.0715487	0.0357743	−	0.999360i	$-0.488610\pi$
$683$	1.86987	0.0715487	0.0357743	+	0.999360i	$0.488610\pi$
$684$	−1.90825	−0.0729639
$685$	22.3966	0.855732
$686$	17.7961	0.679460
$687$	−3.73426	−0.142471
$688$	−9.84107	−0.375187
$689$	−19.2523	−0.733454
$690$	8.01738	0.305216
$691$	−6.07845	−0.231235	−0.115617	−	0.993294i	$-0.536885\pi$
$691$	−6.07845	−0.231235	−0.115617	+	0.993294i	$0.536885\pi$
$692$	12.0984	0.459913
$693$	−1.52396	−0.0578906
$694$	34.2795	1.30123
$695$	26.3068	0.997873
$696$	−1.93378	−0.0732997
$697$	62.9948	2.38610
$698$	−23.2961	−0.881770
$699$	−4.55083	−0.172128
$700$	−2.88574	−0.109071
$701$	−6.05557	−0.228716	−0.114358	−	0.993440i	$-0.536481\pi$
$701$	−6.05557	−0.228716	−0.114358	+	0.993440i	$0.536481\pi$
$702$	2.12261	0.0801127
$703$	−7.14481	−0.269472
$704$	−1.00000	−0.0376889
$705$	0.846575	0.0318839
$706$	18.7503	0.705677
$707$	20.1457	0.757658
$708$	8.55460	0.321502
$709$	1.23383	0.0463374	0.0231687	−	0.999732i	$-0.492625\pi$
$709$	1.23383	0.0463374	0.0231687	+	0.999732i	$0.492625\pi$
$710$	9.59585	0.360126
$711$	5.33711	0.200157
$712$	−11.7585	−0.440668
$713$	21.0147	0.787006
$714$	−10.1671	−0.380493
$715$	−3.74111	−0.139910
$716$	−2.41556	−0.0902738
$717$	1.50302	0.0561312
$718$	10.3804	0.387394
$719$	53.2537	1.98603	0.993015	−	0.117990i	$-0.0376452\pi$
$719$	53.2537	1.98603	0.993015	+	0.117990i	$0.0376452\pi$
$720$	1.76251	0.0656847
$721$	10.4775	0.390202
$722$	15.3586	0.571587
$723$	−23.7844	−0.884551
$724$	−10.0525	−0.373600
$725$	3.66176	0.135994
$726$	1.00000	0.0371135
$727$	33.6512	1.24805	0.624027	−	0.781403i	$-0.285496\pi$
$727$	33.6512	1.24805	0.624027	+	0.781403i	$0.285496\pi$
$728$	−3.23478	−0.119889
$729$	1.00000	0.0370370
$730$	3.08927	0.114339
$731$	65.6543	2.42831
$732$	1.00000	0.0369611
$733$	−4.22708	−0.156131	−0.0780653	−	0.996948i	$-0.524874\pi$
$733$	−4.22708	−0.156131	−0.0780653	+	0.996948i	$0.524874\pi$
$734$	12.2538	0.452296
$735$	8.24418	0.304091
$736$	−4.54885	−0.167673
$737$	7.60797	0.280243
$738$	9.44243	0.347581
$739$	−0.832455	−0.0306224	−0.0153112	−	0.999883i	$-0.504874\pi$
$739$	−0.832455	−0.0306224	−0.0153112	+	0.999883i	$0.504874\pi$
$740$	6.59911	0.242588
$741$	4.05047	0.148798
$742$	13.8225	0.507440
$743$	−11.1808	−0.410184	−0.205092	−	0.978743i	$-0.565749\pi$
$743$	−11.1808	−0.410184	−0.205092	+	0.978743i	$0.565749\pi$
$744$	4.61977	0.169369
$745$	−8.52879	−0.312471
$746$	9.04809	0.331274
$747$	−9.98107	−0.365188
$748$	6.67146	0.243933
$749$	4.55594	0.166470
$750$	−12.1500	−0.443654
$751$	4.76650	0.173932	0.0869660	−	0.996211i	$-0.472283\pi$
$751$	4.76650	0.173932	0.0869660	+	0.996211i	$0.472283\pi$
$752$	−0.480325	−0.0175156
$753$	5.66788	0.206549
$754$	4.10466	0.149483
$755$	−20.3366	−0.740125
$756$	−1.52396	−0.0554260
$757$	3.06038	0.111232	0.0556158	−	0.998452i	$-0.482288\pi$
$757$	3.06038	0.111232	0.0556158	+	0.998452i	$0.482288\pi$
$758$	−5.80920	−0.211000
$759$	4.54885	0.165113
$760$	3.36330	0.122000
$761$	20.6917	0.750074	0.375037	−	0.927010i	$-0.377630\pi$
$761$	20.6917	0.750074	0.375037	+	0.927010i	$0.377630\pi$
$762$	−10.6117	−0.384423
$763$	−11.3537	−0.411031
$764$	−21.3332	−0.771808
$765$	−11.7585	−0.425129
$766$	30.2024	1.09126
$767$	−18.1581	−0.655650
$768$	−1.00000	−0.0360844
$769$	−40.8662	−1.47367	−0.736836	−	0.676071i	$-0.763681\pi$
$769$	−40.8662	−1.47367	−0.736836	+	0.676071i	$0.763681\pi$
$770$	2.68599	0.0967965
$771$	−3.86279	−0.139115
$772$	12.7280	0.458092
$773$	35.0129	1.25933	0.629663	−	0.776868i	$-0.283193\pi$
$773$	35.0129	1.25933	0.629663	+	0.776868i	$0.283193\pi$
$774$	9.84107	0.353730
$775$	−8.74789	−0.314234
$776$	−11.8624	−0.425835
$777$	−5.70597	−0.204701
$778$	−0.453003	−0.0162409
$779$	18.0185	0.645581
$780$	−3.74111	−0.133953
$781$	5.44444	0.194817
$782$	30.3475	1.08522
$783$	1.93378	0.0691076
$784$	−4.67753	−0.167055
$785$	5.74847	0.205172
$786$	−17.4503	−0.622430
$787$	−17.3713	−0.619221	−0.309611	−	0.950863i	$-0.600199\pi$
$787$	−17.3713	−0.619221	−0.309611	+	0.950863i	$0.600199\pi$
$788$	11.6865	0.416315
$789$	8.46401	0.301327
$790$	−9.40669	−0.334675
$791$	8.90621	0.316668
$792$	1.00000	0.0355335
$793$	−2.12261	−0.0753761
$794$	6.08259	0.215863
$795$	15.9861	0.566969
$796$	−14.9220	−0.528898
$797$	−18.4515	−0.653585	−0.326792	−	0.945096i	$-0.605968\pi$
$797$	−18.4515	−0.653585	−0.326792	+	0.945096i	$0.605968\pi$
$798$	−2.90811	−0.102946
$799$	3.20447	0.113366
$800$	1.89358	0.0669480
$801$	11.7585	0.415466
$802$	16.9591	0.598847
$803$	1.75277	0.0618540
$804$	7.60797	0.268312
$805$	12.2182	0.430635
$806$	−9.80598	−0.345401
$807$	−16.6550	−0.586284
$808$	−13.2193	−0.465053
$809$	7.19261	0.252879	0.126439	−	0.991974i	$-0.459645\pi$
$809$	7.19261	0.252879	0.126439	+	0.991974i	$0.459645\pi$
$810$	−1.76251	−0.0619281
$811$	−7.76603	−0.272702	−0.136351	−	0.990661i	$-0.543538\pi$
$811$	−7.76603	−0.272702	−0.136351	+	0.990661i	$0.543538\pi$
$812$	−2.94701	−0.103420
$813$	−13.4995	−0.473446
$814$	3.74417	0.131233
$815$	39.0423	1.36759
$816$	6.67146	0.233548
$817$	18.7792	0.657003
$818$	−7.48907	−0.261849
$819$	3.23478	0.113032
$820$	−16.6423	−0.581175
$821$	−30.9529	−1.08026	−0.540132	−	0.841580i	$-0.681626\pi$
$821$	−30.9529	−1.08026	−0.540132	+	0.841580i	$0.681626\pi$
$822$	12.7073	0.443217
$823$	15.6242	0.544626	0.272313	−	0.962209i	$-0.412211\pi$
$823$	15.6242	0.544626	0.272313	+	0.962209i	$0.412211\pi$
$824$	−6.87515	−0.239507
$825$	−1.89358	−0.0659258
$826$	13.0369	0.453612
$827$	−7.30859	−0.254145	−0.127072	−	0.991893i	$-0.540558\pi$
$827$	−7.30859	−0.254145	−0.127072	+	0.991893i	$0.540558\pi$
$828$	4.54885	0.158084
$829$	7.50290	0.260586	0.130293	−	0.991476i	$-0.458408\pi$
$829$	7.50290	0.260586	0.130293	+	0.991476i	$0.458408\pi$
$830$	17.5917	0.610616
$831$	−25.3096	−0.877980
$832$	2.12261	0.0735882
$833$	31.2060	1.08122
$834$	14.9258	0.516838
$835$	−38.2120	−1.32238
$836$	1.90825	0.0659983
$837$	−4.61977	−0.159683
$838$	15.9779	0.551946
$839$	−19.4835	−0.672644	−0.336322	−	0.941747i	$-0.609183\pi$
$839$	−19.4835	−0.672644	−0.336322	+	0.941747i	$0.609183\pi$
$840$	2.68599	0.0926756
$841$	−25.2605	−0.871052
$842$	−32.4789	−1.11930
$843$	−4.93263	−0.169889
$844$	−12.8257	−0.441478
$845$	−14.9716	−0.515040
$846$	0.480325	0.0165139
$847$	1.52396	0.0523640
$848$	−9.07010	−0.311469
$849$	12.1149	0.415782
$850$	−12.6329	−0.433306
$851$	17.0317	0.583838
$852$	5.44444	0.186523
$853$	−32.9687	−1.12883	−0.564414	−	0.825492i	$-0.690898\pi$
$853$	−32.9687	−1.12883	−0.564414	+	0.825492i	$0.690898\pi$
$854$	1.52396	0.0521490
$855$	−3.36330	−0.115023
$856$	−2.98953	−0.102180
$857$	35.2770	1.20504	0.602520	−	0.798104i	$-0.294164\pi$
$857$	35.2770	1.20504	0.602520	+	0.798104i	$0.294164\pi$
$858$	−2.12261	−0.0724647
$859$	−37.5520	−1.28126	−0.640630	−	0.767850i	$-0.721327\pi$
$859$	−37.5520	−1.28126	−0.640630	+	0.767850i	$0.721327\pi$
$860$	−17.3449	−0.591457
$861$	14.3899	0.490407
$862$	4.75109	0.161823
$863$	8.11079	0.276094	0.138047	−	0.990426i	$-0.455917\pi$
$863$	8.11079	0.276094	0.138047	+	0.990426i	$0.455917\pi$
$864$	1.00000	0.0340207
$865$	21.3235	0.725022
$866$	9.86957	0.335382
$867$	−27.5084	−0.934234
$868$	7.04037	0.238966
$869$	−5.33711	−0.181049
$870$	−3.40830	−0.115552
$871$	−16.1488	−0.547180
$872$	7.45010	0.252292
$873$	11.8624	0.401481
$874$	8.68036	0.293618
$875$	−18.5161	−0.625959
$876$	1.75277	0.0592207
$877$	−14.6282	−0.493958	−0.246979	−	0.969021i	$-0.579438\pi$
$877$	−14.6282	−0.493958	−0.246979	+	0.969021i	$0.579438\pi$
$878$	40.8858	1.37983
$879$	26.9803	0.910024
$880$	−1.76251	−0.0594140
$881$	37.0253	1.24742	0.623708	−	0.781658i	$-0.285626\pi$
$881$	37.0253	1.24742	0.623708	+	0.781658i	$0.285626\pi$
$882$	4.67753	0.157501
$883$	−16.5108	−0.555631	−0.277816	−	0.960634i	$-0.589610\pi$
$883$	−16.5108	−0.555631	−0.277816	+	0.960634i	$0.589610\pi$
$884$	−14.1609	−0.476283
$885$	15.0775	0.506825
$886$	−31.4389	−1.05621
$887$	42.3755	1.42283	0.711416	−	0.702772i	$-0.248054\pi$
$887$	42.3755	1.42283	0.711416	+	0.702772i	$0.248054\pi$
$888$	3.74417	0.125646
$889$	−16.1719	−0.542388
$890$	−20.7244	−0.694683
$891$	−1.00000	−0.0335013
$892$	−16.5087	−0.552752
$893$	0.916581	0.0306722
$894$	−4.83902	−0.161841
$895$	−4.25744	−0.142311
$896$	−1.52396	−0.0509121
$897$	−9.65544	−0.322386
$898$	8.17497	0.272802
$899$	−8.93362	−0.297953
$900$	−1.89358	−0.0631192
$901$	60.5108	2.01591
$902$	−9.44243	−0.314398
$903$	14.9974	0.499083
$904$	−5.84411	−0.194372
$905$	−17.7176	−0.588955
$906$	−11.5385	−0.383340
$907$	39.0702	1.29731	0.648653	−	0.761085i	$-0.275333\pi$
$907$	39.0702	1.29731	0.648653	+	0.761085i	$0.275333\pi$
$908$	−11.7919	−0.391329
$909$	13.2193	0.438456
$910$	−5.70132	−0.188997
$911$	−19.1874	−0.635708	−0.317854	−	0.948140i	$-0.602962\pi$
$911$	−19.1874	−0.635708	−0.317854	+	0.948140i	$0.602962\pi$
$912$	1.90825	0.0631885
$913$	9.98107	0.330325
$914$	−28.8764	−0.955145
$915$	1.76251	0.0582666
$916$	3.73426	0.123383
$917$	−26.5936	−0.878197
$918$	−6.67146	−0.220191
$919$	−38.0658	−1.25567	−0.627837	−	0.778345i	$-0.716059\pi$
$919$	−38.0658	−1.25567	−0.627837	+	0.778345i	$0.716059\pi$
$920$	−8.01738	−0.264325
$921$	−24.9049	−0.820645
$922$	37.5723	1.23738
$923$	−11.5564	−0.380384
$924$	1.52396	0.0501347
$925$	−7.08986	−0.233113
$926$	−4.36174	−0.143336
$927$	6.87515	0.225810
$928$	1.93378	0.0634794
$929$	−9.50947	−0.311995	−0.155998	−	0.987757i	$-0.549859\pi$
$929$	−9.50947	−0.311995	−0.155998	+	0.987757i	$0.549859\pi$
$930$	8.14237	0.266999
$931$	8.92591	0.292535
$932$	4.55083	0.149068
$933$	−12.8864	−0.421881
$934$	−0.522021	−0.0170810
$935$	11.7585	0.384544
$936$	−2.12261	−0.0693797
$937$	−54.8579	−1.79213	−0.896064	−	0.443924i	$-0.853586\pi$
$937$	−54.8579	−1.79213	−0.896064	+	0.443924i	$0.853586\pi$
$938$	11.5943	0.378567
$939$	13.1222	0.428226
$940$	−0.846575	−0.0276122
$941$	10.9018	0.355387	0.177694	−	0.984086i	$-0.443136\pi$
$941$	10.9018	0.355387	0.177694	+	0.984086i	$0.443136\pi$
$942$	3.26153	0.106267
$943$	−42.9522	−1.39872
$944$	−8.55460	−0.278428
$945$	−2.68599	−0.0873754
$946$	−9.84107	−0.319961
$947$	−6.08828	−0.197843	−0.0989213	−	0.995095i	$-0.531539\pi$
$947$	−6.08828	−0.197843	−0.0989213	+	0.995095i	$0.531539\pi$
$948$	−5.33711	−0.173341
$949$	−3.72045	−0.120771
$950$	−3.61342	−0.117235
$951$	11.7823	0.382069
$952$	10.1671	0.329517
$953$	39.4535	1.27803	0.639013	−	0.769196i	$-0.279343\pi$
$953$	39.4535	1.27803	0.639013	+	0.769196i	$0.279343\pi$
$954$	9.07010	0.293655
$955$	−37.5999	−1.21670
$956$	−1.50302	−0.0486110
$957$	−1.93378	−0.0625102
$958$	18.7610	0.606140
$959$	19.3654	0.625342
$960$	−1.76251	−0.0568846
$961$	−9.65769	−0.311538
$962$	−7.94740	−0.256235
$963$	2.98953	0.0963362
$964$	23.7844	0.766043
$965$	22.4332	0.722152
$966$	6.93229	0.223043
$967$	36.5306	1.17474	0.587372	−	0.809317i	$-0.300162\pi$
$967$	36.5306	1.17474	0.587372	+	0.809317i	$0.300162\pi$
$968$	−1.00000	−0.0321412
$969$	−12.7308	−0.408973
$970$	−20.9075	−0.671299
$971$	9.37774	0.300946	0.150473	−	0.988614i	$-0.451920\pi$
$971$	9.37774	0.300946	0.150473	+	0.988614i	$0.451920\pi$
$972$	−1.00000	−0.0320750
$973$	22.7464	0.729215
$974$	−32.9767	−1.05664
$975$	4.01932	0.128721
$976$	−1.00000	−0.0320092
$977$	1.91821	0.0613691	0.0306845	−	0.999529i	$-0.490231\pi$
$977$	1.91821	0.0613691	0.0306845	+	0.999529i	$0.490231\pi$
$978$	22.1516	0.708329
$979$	−11.7585	−0.375803
$980$	−8.24418	−0.263351
$981$	−7.45010	−0.237863
$982$	34.0590	1.08687
$983$	23.5313	0.750533	0.375266	−	0.926917i	$-0.377551\pi$
$983$	23.5313	0.750533	0.375266	+	0.926917i	$0.377551\pi$
$984$	−9.44243	−0.301014
$985$	20.5975	0.656292
$986$	−12.9011	−0.410856
$987$	0.731998	0.0232997
$988$	−4.05047	−0.128863
$989$	−44.7656	−1.42346
$990$	1.76251	0.0560161
$991$	32.5271	1.03326	0.516629	−	0.856210i	$-0.327187\pi$
$991$	32.5271	1.03326	0.516629	+	0.856210i	$0.327187\pi$
$992$	−4.61977	−0.146678
$993$	8.80568	0.279440
$994$	8.29713	0.263169
$995$	−26.3002	−0.833772
$996$	9.98107	0.316262
$997$	31.5861	1.00034	0.500170	−	0.865927i	$-0.333271\pi$
$997$	31.5861	1.00034	0.500170	+	0.865927i	$0.333271\pi$
$998$	33.0223	1.04530
$999$	−3.74417	−0.118460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.y.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.y.1.6	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.76251 q^{5} +1.00000 q^{6} +1.52396 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.76251 q^{5} +1.00000 q^{6} +1.52396 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.76251 q^{10} -1.00000 q^{11} -1.00000 q^{12} +2.12261 q^{13} -1.52396 q^{14} -1.76251 q^{15} +1.00000 q^{16} -6.67146 q^{17} -1.00000 q^{18} -1.90825 q^{19} +1.76251 q^{20} -1.52396 q^{21} +1.00000 q^{22} +4.54885 q^{23} +1.00000 q^{24} -1.89358 q^{25} -2.12261 q^{26} -1.00000 q^{27} +1.52396 q^{28} -1.93378 q^{29} +1.76251 q^{30} +4.61977 q^{31} -1.00000 q^{32} +1.00000 q^{33} +6.67146 q^{34} +2.68599 q^{35} +1.00000 q^{36} +3.74417 q^{37} +1.90825 q^{38} -2.12261 q^{39} -1.76251 q^{40} -9.44243 q^{41} +1.52396 q^{42} -9.84107 q^{43} -1.00000 q^{44} +1.76251 q^{45} -4.54885 q^{46} -0.480325 q^{47} -1.00000 q^{48} -4.67753 q^{49} +1.89358 q^{50} +6.67146 q^{51} +2.12261 q^{52} -9.07010 q^{53} +1.00000 q^{54} -1.76251 q^{55} -1.52396 q^{56} +1.90825 q^{57} +1.93378 q^{58} -8.55460 q^{59} -1.76251 q^{60} -1.00000 q^{61} -4.61977 q^{62} +1.52396 q^{63} +1.00000 q^{64} +3.74111 q^{65} -1.00000 q^{66} -7.60797 q^{67} -6.67146 q^{68} -4.54885 q^{69} -2.68599 q^{70} -5.44444 q^{71} -1.00000 q^{72} -1.75277 q^{73} -3.74417 q^{74} +1.89358 q^{75} -1.90825 q^{76} -1.52396 q^{77} +2.12261 q^{78} +5.33711 q^{79} +1.76251 q^{80} +1.00000 q^{81} +9.44243 q^{82} -9.98107 q^{83} -1.52396 q^{84} -11.7585 q^{85} +9.84107 q^{86} +1.93378 q^{87} +1.00000 q^{88} +11.7585 q^{89} -1.76251 q^{90} +3.23478 q^{91} +4.54885 q^{92} -4.61977 q^{93} +0.480325 q^{94} -3.36330 q^{95} +1.00000 q^{96} +11.8624 q^{97} +4.67753 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * q^99

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