LMFDB - Embedded newform 2890.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2890,2,Mod(1,2890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2890.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2890 = 2 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2890.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:	$23.0767661842$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	2890.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -3.41421 q^{7} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -3.41421 q^{7} +1.00000 q^{8} -2.82843 q^{9} +1.00000 q^{10} +1.41421 q^{11} +0.414214 q^{12} -1.00000 q^{13} -3.41421 q^{14} +0.414214 q^{15} +1.00000 q^{16} -2.82843 q^{18} -0.414214 q^{19} +1.00000 q^{20} -1.41421 q^{21} +1.41421 q^{22} -8.82843 q^{23} +0.414214 q^{24} +1.00000 q^{25} -1.00000 q^{26} -2.41421 q^{27} -3.41421 q^{28} -4.17157 q^{29} +0.414214 q^{30} -3.24264 q^{31} +1.00000 q^{32} +0.585786 q^{33} -3.41421 q^{35} -2.82843 q^{36} +6.24264 q^{37} -0.414214 q^{38} -0.414214 q^{39} +1.00000 q^{40} -6.58579 q^{41} -1.41421 q^{42} +1.75736 q^{43} +1.41421 q^{44} -2.82843 q^{45} -8.82843 q^{46} +5.24264 q^{47} +0.414214 q^{48} +4.65685 q^{49} +1.00000 q^{50} -1.00000 q^{52} -13.4853 q^{53} -2.41421 q^{54} +1.41421 q^{55} -3.41421 q^{56} -0.171573 q^{57} -4.17157 q^{58} +8.89949 q^{59} +0.414214 q^{60} -13.8284 q^{61} -3.24264 q^{62} +9.65685 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.585786 q^{66} +3.17157 q^{67} -3.65685 q^{69} -3.41421 q^{70} -13.7279 q^{71} -2.82843 q^{72} +2.17157 q^{73} +6.24264 q^{74} +0.414214 q^{75} -0.414214 q^{76} -4.82843 q^{77} -0.414214 q^{78} -0.343146 q^{79} +1.00000 q^{80} +7.48528 q^{81} -6.58579 q^{82} +9.89949 q^{83} -1.41421 q^{84} +1.75736 q^{86} -1.72792 q^{87} +1.41421 q^{88} -3.34315 q^{89} -2.82843 q^{90} +3.41421 q^{91} -8.82843 q^{92} -1.34315 q^{93} +5.24264 q^{94} -0.414214 q^{95} +0.414214 q^{96} -8.31371 q^{97} +4.65685 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{10} - 2 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{20} - 12 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 4 q^{28} - 14 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} + 4 q^{33} - 4 q^{35} + 4 q^{37} + 2 q^{38} + 2 q^{39} + 2 q^{40} - 16 q^{41} + 12 q^{43} - 12 q^{46} + 2 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} - 2 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{56} - 6 q^{57} - 14 q^{58} - 2 q^{59} - 2 q^{60} - 22 q^{61} + 2 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 4 q^{66} + 12 q^{67} + 4 q^{69} - 4 q^{70} - 2 q^{71} + 10 q^{73} + 4 q^{74} - 2 q^{75} + 2 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 2 q^{80} - 2 q^{81} - 16 q^{82} + 12 q^{86} + 22 q^{87} - 18 q^{89} + 4 q^{91} - 12 q^{92} - 14 q^{93} + 2 q^{94} + 2 q^{95} - 2 q^{96} + 6 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 2 * q^10 - 2 * q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^20 - 12 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 4 * q^28 - 14 * q^29 - 2 * q^30 + 2 * q^31 + 2 * q^32 + 4 * q^33 - 4 * q^35 + 4 * q^37 + 2 * q^38 + 2 * q^39 + 2 * q^40 - 16 * q^41 + 12 * q^43 - 12 * q^46 + 2 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 - 2 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^56 - 6 * q^57 - 14 * q^58 - 2 * q^59 - 2 * q^60 - 22 * q^61 + 2 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^65 + 4 * q^66 + 12 * q^67 + 4 * q^69 - 4 * q^70 - 2 * q^71 + 10 * q^73 + 4 * q^74 - 2 * q^75 + 2 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 2 * q^80 - 2 * q^81 - 16 * q^82 + 12 * q^86 + 22 * q^87 - 18 * q^89 + 4 * q^91 - 12 * q^92 - 14 * q^93 + 2 * q^94 + 2 * q^95 - 2 * q^96 + 6 * q^97 - 2 * q^98 - 8 * 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
$3$	0.414214	0.239146	0.119573	−	0.992825i	$-0.461847\pi$
$3$	0.414214	0.239146	0.119573	+	0.992825i	$0.461847\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.414214	0.169102
$7$	−3.41421	−1.29045	−0.645226	−	0.763992i	$-0.723237\pi$
$7$	−3.41421	−1.29045	−0.645226	+	0.763992i	$0.723237\pi$
$8$	1.00000	0.353553
$9$	−2.82843	−0.942809
$10$	1.00000	0.316228
$11$	1.41421	0.426401	0.213201	−	0.977008i	$-0.431611\pi$
$11$	1.41421	0.426401	0.213201	+	0.977008i	$0.431611\pi$
$12$	0.414214	0.119573
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−3.41421	−0.912487
$15$	0.414214	0.106949
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−2.82843	−0.666667
$19$	−0.414214	−0.0950271	−0.0475136	−	0.998871i	$-0.515130\pi$
$19$	−0.414214	−0.0950271	−0.0475136	+	0.998871i	$0.515130\pi$
$20$	1.00000	0.223607
$21$	−1.41421	−0.308607
$22$	1.41421	0.301511
$23$	−8.82843	−1.84085	−0.920427	−	0.390914i	$-0.872159\pi$
$23$	−8.82843	−1.84085	−0.920427	+	0.390914i	$0.872159\pi$
$24$	0.414214	0.0845510
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−2.41421	−0.464616
$28$	−3.41421	−0.645226
$29$	−4.17157	−0.774642	−0.387321	−	0.921945i	$-0.626599\pi$
$29$	−4.17157	−0.774642	−0.387321	+	0.921945i	$0.626599\pi$
$30$	0.414214	0.0756247
$31$	−3.24264	−0.582395	−0.291198	−	0.956663i	$-0.594054\pi$
$31$	−3.24264	−0.582395	−0.291198	+	0.956663i	$0.594054\pi$
$32$	1.00000	0.176777
$33$	0.585786	0.101972
$34$	0	0
$35$	−3.41421	−0.577107
$36$	−2.82843	−0.471405
$37$	6.24264	1.02628	0.513142	−	0.858304i	$-0.328481\pi$
$37$	6.24264	1.02628	0.513142	+	0.858304i	$0.328481\pi$
$38$	−0.414214	−0.0671943
$39$	−0.414214	−0.0663273
$40$	1.00000	0.158114
$41$	−6.58579	−1.02853	−0.514264	−	0.857632i	$-0.671935\pi$
$41$	−6.58579	−1.02853	−0.514264	+	0.857632i	$0.671935\pi$
$42$	−1.41421	−0.218218
$43$	1.75736	0.267995	0.133997	−	0.990982i	$-0.457219\pi$
$43$	1.75736	0.267995	0.133997	+	0.990982i	$0.457219\pi$
$44$	1.41421	0.213201
$45$	−2.82843	−0.421637
$46$	−8.82843	−1.30168
$47$	5.24264	0.764718	0.382359	−	0.924014i	$-0.375112\pi$
$47$	5.24264	0.764718	0.382359	+	0.924014i	$0.375112\pi$
$48$	0.414214	0.0597866
$49$	4.65685	0.665265
$50$	1.00000	0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−13.4853	−1.85235	−0.926173	−	0.377099i	$-0.876922\pi$
$53$	−13.4853	−1.85235	−0.926173	+	0.377099i	$0.876922\pi$
$54$	−2.41421	−0.328533
$55$	1.41421	0.190693
$56$	−3.41421	−0.456243
$57$	−0.171573	−0.0227254
$58$	−4.17157	−0.547754
$59$	8.89949	1.15862	0.579308	−	0.815109i	$-0.303323\pi$
$59$	8.89949	1.15862	0.579308	+	0.815109i	$0.303323\pi$
$60$	0.414214	0.0534747
$61$	−13.8284	−1.77055	−0.885274	−	0.465069i	$-0.846029\pi$
$61$	−13.8284	−1.77055	−0.885274	+	0.465069i	$0.846029\pi$
$62$	−3.24264	−0.411816
$63$	9.65685	1.21665
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	0.585786	0.0721053
$67$	3.17157	0.387469	0.193735	−	0.981054i	$-0.437940\pi$
$67$	3.17157	0.387469	0.193735	+	0.981054i	$0.437940\pi$
$68$	0	0
$69$	−3.65685	−0.440234
$70$	−3.41421	−0.408077
$71$	−13.7279	−1.62920	−0.814602	−	0.580020i	$-0.803045\pi$
$71$	−13.7279	−1.62920	−0.814602	+	0.580020i	$0.803045\pi$
$72$	−2.82843	−0.333333
$73$	2.17157	0.254163	0.127082	−	0.991892i	$-0.459439\pi$
$73$	2.17157	0.254163	0.127082	+	0.991892i	$0.459439\pi$
$74$	6.24264	0.725692
$75$	0.414214	0.0478293
$76$	−0.414214	−0.0475136
$77$	−4.82843	−0.550250
$78$	−0.414214	−0.0469005
$79$	−0.343146	−0.0386069	−0.0193035	−	0.999814i	$-0.506145\pi$
$79$	−0.343146	−0.0386069	−0.0193035	+	0.999814i	$0.506145\pi$
$80$	1.00000	0.111803
$81$	7.48528	0.831698
$82$	−6.58579	−0.727278
$83$	9.89949	1.08661	0.543305	−	0.839535i	$-0.317173\pi$
$83$	9.89949	1.08661	0.543305	+	0.839535i	$0.317173\pi$
$84$	−1.41421	−0.154303
$85$	0	0
$86$	1.75736	0.189501
$87$	−1.72792	−0.185253
$88$	1.41421	0.150756
$89$	−3.34315	−0.354373	−0.177186	−	0.984177i	$-0.556700\pi$
$89$	−3.34315	−0.354373	−0.177186	+	0.984177i	$0.556700\pi$
$90$	−2.82843	−0.298142
$91$	3.41421	0.357907
$92$	−8.82843	−0.920427
$93$	−1.34315	−0.139278
$94$	5.24264	0.540737
$95$	−0.414214	−0.0424974
$96$	0.414214	0.0422755
$97$	−8.31371	−0.844129	−0.422065	−	0.906566i	$-0.638694\pi$
$97$	−8.31371	−0.844129	−0.422065	+	0.906566i	$0.638694\pi$
$98$	4.65685	0.470413
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	−15.6569	−1.55792	−0.778958	−	0.627077i	$-0.784251\pi$
$101$	−15.6569	−1.55792	−0.778958	+	0.627077i	$0.784251\pi$
$102$	0	0
$103$	−13.6569	−1.34565	−0.672825	−	0.739802i	$-0.734919\pi$
$103$	−13.6569	−1.34565	−0.672825	+	0.739802i	$0.734919\pi$
$104$	−1.00000	−0.0980581
$105$	−1.41421	−0.138013
$106$	−13.4853	−1.30981
$107$	4.48528	0.433609	0.216804	−	0.976215i	$-0.430437\pi$
$107$	4.48528	0.433609	0.216804	+	0.976215i	$0.430437\pi$
$108$	−2.41421	−0.232308
$109$	−6.17157	−0.591129	−0.295565	−	0.955323i	$-0.595508\pi$
$109$	−6.17157	−0.591129	−0.295565	+	0.955323i	$0.595508\pi$
$110$	1.41421	0.134840
$111$	2.58579	0.245432
$112$	−3.41421	−0.322613
$113$	13.4853	1.26859	0.634294	−	0.773092i	$-0.281291\pi$
$113$	13.4853	1.26859	0.634294	+	0.773092i	$0.281291\pi$
$114$	−0.171573	−0.0160693
$115$	−8.82843	−0.823255
$116$	−4.17157	−0.387321
$117$	2.82843	0.261488
$118$	8.89949	0.819265
$119$	0	0
$120$	0.414214	0.0378124
$121$	−9.00000	−0.818182
$122$	−13.8284	−1.25197
$123$	−2.72792	−0.245968
$124$	−3.24264	−0.291198
$125$	1.00000	0.0894427
$126$	9.65685	0.860301
$127$	17.7279	1.57310	0.786549	−	0.617527i	$-0.211866\pi$
$127$	17.7279	1.57310	0.786549	+	0.617527i	$0.211866\pi$
$128$	1.00000	0.0883883
$129$	0.727922	0.0640900
$130$	−1.00000	−0.0877058
$131$	0.100505	0.00878117	0.00439058	−	0.999990i	$-0.498602\pi$
$131$	0.100505	0.00878117	0.00439058	+	0.999990i	$0.498602\pi$
$132$	0.585786	0.0509862
$133$	1.41421	0.122628
$134$	3.17157	0.273982
$135$	−2.41421	−0.207782
$136$	0	0
$137$	8.72792	0.745677	0.372838	−	0.927896i	$-0.378385\pi$
$137$	8.72792	0.745677	0.372838	+	0.927896i	$0.378385\pi$
$138$	−3.65685	−0.311292
$139$	15.0711	1.27831	0.639156	−	0.769077i	$-0.279284\pi$
$139$	15.0711	1.27831	0.639156	+	0.769077i	$0.279284\pi$
$140$	−3.41421	−0.288554
$141$	2.17157	0.182879
$142$	−13.7279	−1.15202
$143$	−1.41421	−0.118262
$144$	−2.82843	−0.235702
$145$	−4.17157	−0.346430
$146$	2.17157	0.179721
$147$	1.92893	0.159096
$148$	6.24264	0.513142
$149$	10.2426	0.839110	0.419555	−	0.907730i	$-0.362186\pi$
$149$	10.2426	0.839110	0.419555	+	0.907730i	$0.362186\pi$
$150$	0.414214	0.0338204
$151$	0.828427	0.0674164	0.0337082	−	0.999432i	$-0.489268\pi$
$151$	0.828427	0.0674164	0.0337082	+	0.999432i	$0.489268\pi$
$152$	−0.414214	−0.0335972
$153$	0	0
$154$	−4.82843	−0.389086
$155$	−3.24264	−0.260455
$156$	−0.414214	−0.0331636
$157$	2.82843	0.225733	0.112867	−	0.993610i	$-0.463997\pi$
$157$	2.82843	0.225733	0.112867	+	0.993610i	$0.463997\pi$
$158$	−0.343146	−0.0272992
$159$	−5.58579	−0.442982
$160$	1.00000	0.0790569
$161$	30.1421	2.37553
$162$	7.48528	0.588099
$163$	−16.4853	−1.29123	−0.645613	−	0.763664i	$-0.723398\pi$
$163$	−16.4853	−1.29123	−0.645613	+	0.763664i	$0.723398\pi$
$164$	−6.58579	−0.514264
$165$	0.585786	0.0456034
$166$	9.89949	0.768350
$167$	−20.8284	−1.61175	−0.805876	−	0.592084i	$-0.798305\pi$
$167$	−20.8284	−1.61175	−0.805876	+	0.592084i	$0.798305\pi$
$168$	−1.41421	−0.109109
$169$	−12.0000	−0.923077
$170$	0	0
$171$	1.17157	0.0895924
$172$	1.75736	0.133997
$173$	21.3137	1.62045	0.810226	−	0.586118i	$-0.199345\pi$
$173$	21.3137	1.62045	0.810226	+	0.586118i	$0.199345\pi$
$174$	−1.72792	−0.130993
$175$	−3.41421	−0.258090
$176$	1.41421	0.106600
$177$	3.68629	0.277079
$178$	−3.34315	−0.250579
$179$	1.17157	0.0875675	0.0437837	−	0.999041i	$-0.486059\pi$
$179$	1.17157	0.0875675	0.0437837	+	0.999041i	$0.486059\pi$
$180$	−2.82843	−0.210819
$181$	1.65685	0.123153	0.0615765	−	0.998102i	$-0.480387\pi$
$181$	1.65685	0.123153	0.0615765	+	0.998102i	$0.480387\pi$
$182$	3.41421	0.253078
$183$	−5.72792	−0.423420
$184$	−8.82843	−0.650840
$185$	6.24264	0.458968
$186$	−1.34315	−0.0984842
$187$	0	0
$188$	5.24264	0.382359
$189$	8.24264	0.599564
$190$	−0.414214	−0.0300502
$191$	8.24264	0.596417	0.298208	−	0.954501i	$-0.403611\pi$
$191$	8.24264	0.596417	0.298208	+	0.954501i	$0.403611\pi$
$192$	0.414214	0.0298933
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−8.31371	−0.596889
$195$	−0.414214	−0.0296624
$196$	4.65685	0.332632
$197$	5.55635	0.395873	0.197937	−	0.980215i	$-0.436576\pi$
$197$	5.55635	0.395873	0.197937	+	0.980215i	$0.436576\pi$
$198$	−4.00000	−0.284268
$199$	25.3848	1.79948	0.899740	−	0.436427i	$-0.143756\pi$
$199$	25.3848	1.79948	0.899740	+	0.436427i	$0.143756\pi$
$200$	1.00000	0.0707107
$201$	1.31371	0.0926619
$202$	−15.6569	−1.10161
$203$	14.2426	0.999637
$204$	0	0
$205$	−6.58579	−0.459971
$206$	−13.6569	−0.951518
$207$	24.9706	1.73557
$208$	−1.00000	−0.0693375
$209$	−0.585786	−0.0405197
$210$	−1.41421	−0.0975900
$211$	−0.828427	−0.0570313	−0.0285156	−	0.999593i	$-0.509078\pi$
$211$	−0.828427	−0.0570313	−0.0285156	+	0.999593i	$0.509078\pi$
$212$	−13.4853	−0.926173
$213$	−5.68629	−0.389618
$214$	4.48528	0.306608
$215$	1.75736	0.119851
$216$	−2.41421	−0.164266
$217$	11.0711	0.751553
$218$	−6.17157	−0.417992
$219$	0.899495	0.0607822
$220$	1.41421	0.0953463
$221$	0	0
$222$	2.58579	0.173547
$223$	11.3848	0.762381	0.381191	−	0.924497i	$-0.375514\pi$
$223$	11.3848	0.762381	0.381191	+	0.924497i	$0.375514\pi$
$224$	−3.41421	−0.228122
$225$	−2.82843	−0.188562
$226$	13.4853	0.897028
$227$	−10.5563	−0.700650	−0.350325	−	0.936628i	$-0.613929\pi$
$227$	−10.5563	−0.700650	−0.350325	+	0.936628i	$0.613929\pi$
$228$	−0.171573	−0.0113627
$229$	−7.75736	−0.512621	−0.256310	−	0.966595i	$-0.582507\pi$
$229$	−7.75736	−0.512621	−0.256310	+	0.966595i	$0.582507\pi$
$230$	−8.82843	−0.582129
$231$	−2.00000	−0.131590
$232$	−4.17157	−0.273877
$233$	−6.17157	−0.404313	−0.202157	−	0.979353i	$-0.564795\pi$
$233$	−6.17157	−0.404313	−0.202157	+	0.979353i	$0.564795\pi$
$234$	2.82843	0.184900
$235$	5.24264	0.341992
$236$	8.89949	0.579308
$237$	−0.142136	−0.00923270
$238$	0	0
$239$	24.5858	1.59032	0.795161	−	0.606398i	$-0.207386\pi$
$239$	24.5858	1.59032	0.795161	+	0.606398i	$0.207386\pi$
$240$	0.414214	0.0267374
$241$	−20.0416	−1.29099	−0.645497	−	0.763762i	$-0.723350\pi$
$241$	−20.0416	−1.29099	−0.645497	+	0.763762i	$0.723350\pi$
$242$	−9.00000	−0.578542
$243$	10.3431	0.663513
$244$	−13.8284	−0.885274
$245$	4.65685	0.297516
$246$	−2.72792	−0.173926
$247$	0.414214	0.0263558
$248$	−3.24264	−0.205908
$249$	4.10051	0.259859
$250$	1.00000	0.0632456
$251$	−26.1421	−1.65008	−0.825038	−	0.565077i	$-0.808847\pi$
$251$	−26.1421	−1.65008	−0.825038	+	0.565077i	$0.808847\pi$
$252$	9.65685	0.608325
$253$	−12.4853	−0.784943
$254$	17.7279	1.11235
$255$	0	0
$256$	1.00000	0.0625000
$257$	25.4142	1.58530	0.792648	−	0.609680i	$-0.208702\pi$
$257$	25.4142	1.58530	0.792648	+	0.609680i	$0.208702\pi$
$258$	0.727922	0.0453184
$259$	−21.3137	−1.32437
$260$	−1.00000	−0.0620174
$261$	11.7990	0.730339
$262$	0.100505	0.00620922
$263$	−4.27208	−0.263428	−0.131714	−	0.991288i	$-0.542048\pi$
$263$	−4.27208	−0.263428	−0.131714	+	0.991288i	$0.542048\pi$
$264$	0.585786	0.0360527
$265$	−13.4853	−0.828394
$266$	1.41421	0.0867110
$267$	−1.38478	−0.0847469
$268$	3.17157	0.193735
$269$	−13.4853	−0.822212	−0.411106	−	0.911588i	$-0.634857\pi$
$269$	−13.4853	−0.822212	−0.411106	+	0.911588i	$0.634857\pi$
$270$	−2.41421	−0.146924
$271$	−17.6569	−1.07258	−0.536289	−	0.844035i	$-0.680174\pi$
$271$	−17.6569	−1.07258	−0.536289	+	0.844035i	$0.680174\pi$
$272$	0	0
$273$	1.41421	0.0855921
$274$	8.72792	0.527273
$275$	1.41421	0.0852803
$276$	−3.65685	−0.220117
$277$	19.6569	1.18107	0.590533	−	0.807014i	$-0.298918\pi$
$277$	19.6569	1.18107	0.590533	+	0.807014i	$0.298918\pi$
$278$	15.0711	0.903903
$279$	9.17157	0.549088
$280$	−3.41421	−0.204038
$281$	15.4853	0.923774	0.461887	−	0.886939i	$-0.347172\pi$
$281$	15.4853	0.923774	0.461887	+	0.886939i	$0.347172\pi$
$282$	2.17157	0.129315
$283$	−12.4142	−0.737948	−0.368974	−	0.929440i	$-0.620291\pi$
$283$	−12.4142	−0.737948	−0.368974	+	0.929440i	$0.620291\pi$
$284$	−13.7279	−0.814602
$285$	−0.171573	−0.0101631
$286$	−1.41421	−0.0836242
$287$	22.4853	1.32726
$288$	−2.82843	−0.166667
$289$	0	0
$290$	−4.17157	−0.244963
$291$	−3.44365	−0.201870
$292$	2.17157	0.127082
$293$	11.4853	0.670977	0.335489	−	0.942044i	$-0.391099\pi$
$293$	11.4853	0.670977	0.335489	+	0.942044i	$0.391099\pi$
$294$	1.92893	0.112498
$295$	8.89949	0.518149
$296$	6.24264	0.362846
$297$	−3.41421	−0.198113
$298$	10.2426	0.593340
$299$	8.82843	0.510561
$300$	0.414214	0.0239146
$301$	−6.00000	−0.345834
$302$	0.828427	0.0476706
$303$	−6.48528	−0.372570
$304$	−0.414214	−0.0237568
$305$	−13.8284	−0.791813
$306$	0	0
$307$	−9.89949	−0.564994	−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949	−0.564994	−0.282497	+	0.959268i	$0.591163\pi$
$308$	−4.82843	−0.275125
$309$	−5.65685	−0.321807
$310$	−3.24264	−0.184170
$311$	7.65685	0.434180	0.217090	−	0.976152i	$-0.430343\pi$
$311$	7.65685	0.434180	0.217090	+	0.976152i	$0.430343\pi$
$312$	−0.414214	−0.0234502
$313$	14.8284	0.838152	0.419076	−	0.907951i	$-0.362354\pi$
$313$	14.8284	0.838152	0.419076	+	0.907951i	$0.362354\pi$
$314$	2.82843	0.159617
$315$	9.65685	0.544102
$316$	−0.343146	−0.0193035
$317$	−10.6274	−0.596895	−0.298448	−	0.954426i	$-0.596469\pi$
$317$	−10.6274	−0.596895	−0.298448	+	0.954426i	$0.596469\pi$
$318$	−5.58579	−0.313235
$319$	−5.89949	−0.330308
$320$	1.00000	0.0559017
$321$	1.85786	0.103696
$322$	30.1421	1.67976
$323$	0	0
$324$	7.48528	0.415849
$325$	−1.00000	−0.0554700
$326$	−16.4853	−0.913035
$327$	−2.55635	−0.141366
$328$	−6.58579	−0.363639
$329$	−17.8995	−0.986831
$330$	0.585786	0.0322465
$331$	22.5563	1.23981	0.619905	−	0.784677i	$-0.287171\pi$
$331$	22.5563	1.23981	0.619905	+	0.784677i	$0.287171\pi$
$332$	9.89949	0.543305
$333$	−17.6569	−0.967590
$334$	−20.8284	−1.13968
$335$	3.17157	0.173282
$336$	−1.41421	−0.0771517
$337$	7.68629	0.418699	0.209349	−	0.977841i	$-0.432865\pi$
$337$	7.68629	0.418699	0.209349	+	0.977841i	$0.432865\pi$
$338$	−12.0000	−0.652714
$339$	5.58579	0.303378
$340$	0	0
$341$	−4.58579	−0.248334
$342$	1.17157	0.0633514
$343$	8.00000	0.431959
$344$	1.75736	0.0947505
$345$	−3.65685	−0.196878
$346$	21.3137	1.14583
$347$	−23.2426	−1.24773	−0.623865	−	0.781532i	$-0.714439\pi$
$347$	−23.2426	−1.24773	−0.623865	+	0.781532i	$0.714439\pi$
$348$	−1.72792	−0.0926263
$349$	−24.9706	−1.33664	−0.668322	−	0.743872i	$-0.732987\pi$
$349$	−24.9706	−1.33664	−0.668322	+	0.743872i	$0.732987\pi$
$350$	−3.41421	−0.182497
$351$	2.41421	0.128861
$352$	1.41421	0.0753778
$353$	17.3137	0.921516	0.460758	−	0.887526i	$-0.347578\pi$
$353$	17.3137	0.921516	0.460758	+	0.887526i	$0.347578\pi$
$354$	3.68629	0.195924
$355$	−13.7279	−0.728602
$356$	−3.34315	−0.177186
$357$	0	0
$358$	1.17157	0.0619196
$359$	−24.3848	−1.28698	−0.643490	−	0.765455i	$-0.722514\pi$
$359$	−24.3848	−1.28698	−0.643490	+	0.765455i	$0.722514\pi$
$360$	−2.82843	−0.149071
$361$	−18.8284	−0.990970
$362$	1.65685	0.0870823
$363$	−3.72792	−0.195665
$364$	3.41421	0.178953
$365$	2.17157	0.113665
$366$	−5.72792	−0.299403
$367$	36.1421	1.88660	0.943302	−	0.331936i	$-0.107702\pi$
$367$	36.1421	1.88660	0.943302	+	0.331936i	$0.107702\pi$
$368$	−8.82843	−0.460214
$369$	18.6274	0.969705
$370$	6.24264	0.324539
$371$	46.0416	2.39036
$372$	−1.34315	−0.0696389
$373$	−32.2843	−1.67162	−0.835808	−	0.549022i	$-0.815000\pi$
$373$	−32.2843	−1.67162	−0.835808	+	0.549022i	$0.815000\pi$
$374$	0	0
$375$	0.414214	0.0213899
$376$	5.24264	0.270369
$377$	4.17157	0.214847
$378$	8.24264	0.423956
$379$	5.65685	0.290573	0.145287	−	0.989390i	$-0.453590\pi$
$379$	5.65685	0.290573	0.145287	+	0.989390i	$0.453590\pi$
$380$	−0.414214	−0.0212487
$381$	7.34315	0.376201
$382$	8.24264	0.421730
$383$	−20.2132	−1.03285	−0.516423	−	0.856333i	$-0.672737\pi$
$383$	−20.2132	−1.03285	−0.516423	+	0.856333i	$0.672737\pi$
$384$	0.414214	0.0211377
$385$	−4.82843	−0.246079
$386$	−4.00000	−0.203595
$387$	−4.97056	−0.252668
$388$	−8.31371	−0.422065
$389$	−34.6274	−1.75568	−0.877840	−	0.478954i	$-0.841016\pi$
$389$	−34.6274	−1.75568	−0.877840	+	0.478954i	$0.841016\pi$
$390$	−0.414214	−0.0209745
$391$	0	0
$392$	4.65685	0.235207
$393$	0.0416306	0.00209998
$394$	5.55635	0.279925
$395$	−0.343146	−0.0172655
$396$	−4.00000	−0.201008
$397$	0.686292	0.0344440	0.0172220	−	0.999852i	$-0.494518\pi$
$397$	0.686292	0.0344440	0.0172220	+	0.999852i	$0.494518\pi$
$398$	25.3848	1.27242
$399$	0.585786	0.0293260
$400$	1.00000	0.0500000
$401$	−12.9706	−0.647719	−0.323859	−	0.946105i	$-0.604981\pi$
$401$	−12.9706	−0.647719	−0.323859	+	0.946105i	$0.604981\pi$
$402$	1.31371	0.0655218
$403$	3.24264	0.161527
$404$	−15.6569	−0.778958
$405$	7.48528	0.371947
$406$	14.2426	0.706850
$407$	8.82843	0.437609
$408$	0	0
$409$	−5.48528	−0.271230	−0.135615	−	0.990762i	$-0.543301\pi$
$409$	−5.48528	−0.271230	−0.135615	+	0.990762i	$0.543301\pi$
$410$	−6.58579	−0.325249
$411$	3.61522	0.178326
$412$	−13.6569	−0.672825
$413$	−30.3848	−1.49514
$414$	24.9706	1.22724
$415$	9.89949	0.485947
$416$	−1.00000	−0.0490290
$417$	6.24264	0.305703
$418$	−0.585786	−0.0286518
$419$	25.7990	1.26036	0.630182	−	0.776448i	$-0.282980\pi$
$419$	25.7990	1.26036	0.630182	+	0.776448i	$0.282980\pi$
$420$	−1.41421	−0.0690066
$421$	−37.0711	−1.80673	−0.903367	−	0.428869i	$-0.858912\pi$
$421$	−37.0711	−1.80673	−0.903367	+	0.428869i	$0.858912\pi$
$422$	−0.828427	−0.0403272
$423$	−14.8284	−0.720983
$424$	−13.4853	−0.654903
$425$	0	0
$426$	−5.68629	−0.275502
$427$	47.2132	2.28481
$428$	4.48528	0.216804
$429$	−0.585786	−0.0282820
$430$	1.75736	0.0847474
$431$	22.6274	1.08992	0.544962	−	0.838461i	$-0.316544\pi$
$431$	22.6274	1.08992	0.544962	+	0.838461i	$0.316544\pi$
$432$	−2.41421	−0.116154
$433$	−15.0711	−0.724269	−0.362135	−	0.932126i	$-0.617952\pi$
$433$	−15.0711	−0.724269	−0.362135	+	0.932126i	$0.617952\pi$
$434$	11.0711	0.531428
$435$	−1.72792	−0.0828475
$436$	−6.17157	−0.295565
$437$	3.65685	0.174931
$438$	0.899495	0.0429795
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	1.41421	0.0674200
$441$	−13.1716	−0.627218
$442$	0	0
$443$	−20.0000	−0.950229	−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000	−0.950229	−0.475114	+	0.879924i	$0.657593\pi$
$444$	2.58579	0.122716
$445$	−3.34315	−0.158480
$446$	11.3848	0.539085
$447$	4.24264	0.200670
$448$	−3.41421	−0.161306
$449$	−10.4437	−0.492866	−0.246433	−	0.969160i	$-0.579259\pi$
$449$	−10.4437	−0.492866	−0.246433	+	0.969160i	$0.579259\pi$
$450$	−2.82843	−0.133333
$451$	−9.31371	−0.438565
$452$	13.4853	0.634294
$453$	0.343146	0.0161224
$454$	−10.5563	−0.495434
$455$	3.41421	0.160061
$456$	−0.171573	−0.00803464
$457$	−3.55635	−0.166359	−0.0831795	−	0.996535i	$-0.526507\pi$
$457$	−3.55635	−0.166359	−0.0831795	+	0.996535i	$0.526507\pi$
$458$	−7.75736	−0.362478
$459$	0	0
$460$	−8.82843	−0.411628
$461$	−26.9706	−1.25614	−0.628072	−	0.778155i	$-0.716156\pi$
$461$	−26.9706	−1.25614	−0.628072	+	0.778155i	$0.716156\pi$
$462$	−2.00000	−0.0930484
$463$	20.8995	0.971282	0.485641	−	0.874158i	$-0.338586\pi$
$463$	20.8995	0.971282	0.485641	+	0.874158i	$0.338586\pi$
$464$	−4.17157	−0.193660
$465$	−1.34315	−0.0622869
$466$	−6.17157	−0.285893
$467$	−17.2132	−0.796532	−0.398266	−	0.917270i	$-0.630388\pi$
$467$	−17.2132	−0.796532	−0.398266	+	0.917270i	$0.630388\pi$
$468$	2.82843	0.130744
$469$	−10.8284	−0.500010
$470$	5.24264	0.241825
$471$	1.17157	0.0539832
$472$	8.89949	0.409632
$473$	2.48528	0.114273
$474$	−0.142136	−0.00652851
$475$	−0.414214	−0.0190054
$476$	0	0
$477$	38.1421	1.74641
$478$	24.5858	1.12453
$479$	−7.10051	−0.324430	−0.162215	−	0.986755i	$-0.551864\pi$
$479$	−7.10051	−0.324430	−0.162215	+	0.986755i	$0.551864\pi$
$480$	0.414214	0.0189062
$481$	−6.24264	−0.284640
$482$	−20.0416	−0.912871
$483$	12.4853	0.568100
$484$	−9.00000	−0.409091
$485$	−8.31371	−0.377506
$486$	10.3431	0.469175
$487$	16.3848	0.742465	0.371233	−	0.928540i	$-0.378935\pi$
$487$	16.3848	0.742465	0.371233	+	0.928540i	$0.378935\pi$
$488$	−13.8284	−0.625983
$489$	−6.82843	−0.308792
$490$	4.65685	0.210375
$491$	33.7279	1.52212	0.761060	−	0.648682i	$-0.224679\pi$
$491$	33.7279	1.52212	0.761060	+	0.648682i	$0.224679\pi$
$492$	−2.72792	−0.122984
$493$	0	0
$494$	0.414214	0.0186363
$495$	−4.00000	−0.179787
$496$	−3.24264	−0.145599
$497$	46.8701	2.10241
$498$	4.10051	0.183748
$499$	−15.2132	−0.681037	−0.340518	−	0.940238i	$-0.610603\pi$
$499$	−15.2132	−0.681037	−0.340518	+	0.940238i	$0.610603\pi$
$500$	1.00000	0.0447214
$501$	−8.62742	−0.385445
$502$	−26.1421	−1.16678
$503$	3.02944	0.135076	0.0675380	−	0.997717i	$-0.478486\pi$
$503$	3.02944	0.135076	0.0675380	+	0.997717i	$0.478486\pi$
$504$	9.65685	0.430150
$505$	−15.6569	−0.696721
$506$	−12.4853	−0.555038
$507$	−4.97056	−0.220750
$508$	17.7279	0.786549
$509$	32.0000	1.41838	0.709188	−	0.705020i	$-0.249062\pi$
$509$	32.0000	1.41838	0.709188	+	0.705020i	$0.249062\pi$
$510$	0	0
$511$	−7.41421	−0.327985
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	25.4142	1.12097
$515$	−13.6569	−0.601793
$516$	0.727922	0.0320450
$517$	7.41421	0.326077
$518$	−21.3137	−0.936471
$519$	8.82843	0.387525
$520$	−1.00000	−0.0438529
$521$	38.6274	1.69230	0.846149	−	0.532947i	$-0.178915\pi$
$521$	38.6274	1.69230	0.846149	+	0.532947i	$0.178915\pi$
$522$	11.7990	0.516428
$523$	0.828427	0.0362246	0.0181123	−	0.999836i	$-0.494234\pi$
$523$	0.828427	0.0362246	0.0181123	+	0.999836i	$0.494234\pi$
$524$	0.100505	0.00439058
$525$	−1.41421	−0.0617213
$526$	−4.27208	−0.186271
$527$	0	0
$528$	0.585786	0.0254931
$529$	54.9411	2.38874
$530$	−13.4853	−0.585763
$531$	−25.1716	−1.09235
$532$	1.41421	0.0613139
$533$	6.58579	0.285262
$534$	−1.38478	−0.0599251
$535$	4.48528	0.193916
$536$	3.17157	0.136991
$537$	0.485281	0.0209414
$538$	−13.4853	−0.581392
$539$	6.58579	0.283670
$540$	−2.41421	−0.103891
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	−17.6569	−0.758427
$543$	0.686292	0.0294516
$544$	0	0
$545$	−6.17157	−0.264361
$546$	1.41421	0.0605228
$547$	26.2132	1.12080	0.560398	−	0.828224i	$-0.310648\pi$
$547$	26.2132	1.12080	0.560398	+	0.828224i	$0.310648\pi$
$548$	8.72792	0.372838
$549$	39.1127	1.66929
$550$	1.41421	0.0603023
$551$	1.72792	0.0736120
$552$	−3.65685	−0.155646
$553$	1.17157	0.0498203
$554$	19.6569	0.835140
$555$	2.58579	0.109761
$556$	15.0711	0.639156
$557$	−2.17157	−0.0920125	−0.0460062	−	0.998941i	$-0.514649\pi$
$557$	−2.17157	−0.0920125	−0.0460062	+	0.998941i	$0.514649\pi$
$558$	9.17157	0.388264
$559$	−1.75736	−0.0743284
$560$	−3.41421	−0.144277
$561$	0	0
$562$	15.4853	0.653207
$563$	3.85786	0.162590	0.0812948	−	0.996690i	$-0.474094\pi$
$563$	3.85786	0.162590	0.0812948	+	0.996690i	$0.474094\pi$
$564$	2.17157	0.0914397
$565$	13.4853	0.567330
$566$	−12.4142	−0.521808
$567$	−25.5563	−1.07327
$568$	−13.7279	−0.576011
$569$	−7.97056	−0.334143	−0.167072	−	0.985945i	$-0.553431\pi$
$569$	−7.97056	−0.334143	−0.167072	+	0.985945i	$0.553431\pi$
$570$	−0.171573	−0.00718640
$571$	35.4142	1.48204	0.741019	−	0.671484i	$-0.234343\pi$
$571$	35.4142	1.48204	0.741019	+	0.671484i	$0.234343\pi$
$572$	−1.41421	−0.0591312
$573$	3.41421	0.142631
$574$	22.4853	0.938518
$575$	−8.82843	−0.368171
$576$	−2.82843	−0.117851
$577$	29.6569	1.23463	0.617315	−	0.786716i	$-0.288220\pi$
$577$	29.6569	1.23463	0.617315	+	0.786716i	$0.288220\pi$
$578$	0	0
$579$	−1.65685	−0.0688565
$580$	−4.17157	−0.173215
$581$	−33.7990	−1.40222
$582$	−3.44365	−0.142744
$583$	−19.0711	−0.789843
$584$	2.17157	0.0898603
$585$	2.82843	0.116941
$586$	11.4853	0.474453
$587$	−8.82843	−0.364388	−0.182194	−	0.983263i	$-0.558320\pi$
$587$	−8.82843	−0.364388	−0.182194	+	0.983263i	$0.558320\pi$
$588$	1.92893	0.0795478
$589$	1.34315	0.0553434
$590$	8.89949	0.366386
$591$	2.30152	0.0946717
$592$	6.24264	0.256571
$593$	−42.2843	−1.73641	−0.868203	−	0.496208i	$-0.834725\pi$
$593$	−42.2843	−1.73641	−0.868203	+	0.496208i	$0.834725\pi$
$594$	−3.41421	−0.140087
$595$	0	0
$596$	10.2426	0.419555
$597$	10.5147	0.430339
$598$	8.82843	0.361021
$599$	30.7696	1.25721	0.628605	−	0.777725i	$-0.283626\pi$
$599$	30.7696	1.25721	0.628605	+	0.777725i	$0.283626\pi$
$600$	0.414214	0.0169102
$601$	26.6274	1.08615	0.543077	−	0.839683i	$-0.317259\pi$
$601$	26.6274	1.08615	0.543077	+	0.839683i	$0.317259\pi$
$602$	−6.00000	−0.244542
$603$	−8.97056	−0.365310
$604$	0.828427	0.0337082
$605$	−9.00000	−0.365902
$606$	−6.48528	−0.263447
$607$	−14.2426	−0.578091	−0.289045	−	0.957315i	$-0.593338\pi$
$607$	−14.2426	−0.578091	−0.289045	+	0.957315i	$0.593338\pi$
$608$	−0.414214	−0.0167986
$609$	5.89949	0.239060
$610$	−13.8284	−0.559897
$611$	−5.24264	−0.212095
$612$	0	0
$613$	33.2843	1.34434	0.672170	−	0.740397i	$-0.265363\pi$
$613$	33.2843	1.34434	0.672170	+	0.740397i	$0.265363\pi$
$614$	−9.89949	−0.399511
$615$	−2.72792	−0.110000
$616$	−4.82843	−0.194543
$617$	−38.7990	−1.56199	−0.780994	−	0.624538i	$-0.785287\pi$
$617$	−38.7990	−1.56199	−0.780994	+	0.624538i	$0.785287\pi$
$618$	−5.65685	−0.227552
$619$	2.48528	0.0998919	0.0499459	−	0.998752i	$-0.484095\pi$
$619$	2.48528	0.0998919	0.0499459	+	0.998752i	$0.484095\pi$
$620$	−3.24264	−0.130228
$621$	21.3137	0.855290
$622$	7.65685	0.307012
$623$	11.4142	0.457301
$624$	−0.414214	−0.0165818
$625$	1.00000	0.0400000
$626$	14.8284	0.592663
$627$	−0.242641	−0.00969014
$628$	2.82843	0.112867
$629$	0	0
$630$	9.65685	0.384738
$631$	−38.3431	−1.52642	−0.763208	−	0.646153i	$-0.776377\pi$
$631$	−38.3431	−1.52642	−0.763208	+	0.646153i	$0.776377\pi$
$632$	−0.343146	−0.0136496
$633$	−0.343146	−0.0136388
$634$	−10.6274	−0.422069
$635$	17.7279	0.703511
$636$	−5.58579	−0.221491
$637$	−4.65685	−0.184511
$638$	−5.89949	−0.233563
$639$	38.8284	1.53603
$640$	1.00000	0.0395285
$641$	−4.34315	−0.171544	−0.0857720	−	0.996315i	$-0.527336\pi$
$641$	−4.34315	−0.171544	−0.0857720	+	0.996315i	$0.527336\pi$
$642$	1.85786	0.0733241
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	30.1421	1.18777
$645$	0.727922	0.0286619
$646$	0	0
$647$	5.78680	0.227502	0.113751	−	0.993509i	$-0.463713\pi$
$647$	5.78680	0.227502	0.113751	+	0.993509i	$0.463713\pi$
$648$	7.48528	0.294050
$649$	12.5858	0.494035
$650$	−1.00000	−0.0392232
$651$	4.58579	0.179731
$652$	−16.4853	−0.645613
$653$	−33.2132	−1.29973	−0.649867	−	0.760048i	$-0.725175\pi$
$653$	−33.2132	−1.29973	−0.649867	+	0.760048i	$0.725175\pi$
$654$	−2.55635	−0.0999612
$655$	0.100505	0.00392706
$656$	−6.58579	−0.257132
$657$	−6.14214	−0.239628
$658$	−17.8995	−0.697795
$659$	19.2426	0.749587	0.374793	−	0.927108i	$-0.377714\pi$
$659$	19.2426	0.749587	0.374793	+	0.927108i	$0.377714\pi$
$660$	0.585786	0.0228017
$661$	−11.3137	−0.440052	−0.220026	−	0.975494i	$-0.570614\pi$
$661$	−11.3137	−0.440052	−0.220026	+	0.975494i	$0.570614\pi$
$662$	22.5563	0.876677
$663$	0	0
$664$	9.89949	0.384175
$665$	1.41421	0.0548408
$666$	−17.6569	−0.684189
$667$	36.8284	1.42600
$668$	−20.8284	−0.805876
$669$	4.71573	0.182321
$670$	3.17157	0.122529
$671$	−19.5563	−0.754964
$672$	−1.41421	−0.0545545
$673$	21.9706	0.846903	0.423451	−	0.905919i	$-0.360818\pi$
$673$	21.9706	0.846903	0.423451	+	0.905919i	$0.360818\pi$
$674$	7.68629	0.296065
$675$	−2.41421	−0.0929231
$676$	−12.0000	−0.461538
$677$	−37.0122	−1.42249	−0.711247	−	0.702942i	$-0.751869\pi$
$677$	−37.0122	−1.42249	−0.711247	+	0.702942i	$0.751869\pi$
$678$	5.58579	0.214521
$679$	28.3848	1.08931
$680$	0	0
$681$	−4.37258	−0.167558
$682$	−4.58579	−0.175599
$683$	−14.4142	−0.551545	−0.275772	−	0.961223i	$-0.588934\pi$
$683$	−14.4142	−0.551545	−0.275772	+	0.961223i	$0.588934\pi$
$684$	1.17157	0.0447962
$685$	8.72792	0.333477
$686$	8.00000	0.305441
$687$	−3.21320	−0.122591
$688$	1.75736	0.0669987
$689$	13.4853	0.513748
$690$	−3.65685	−0.139214
$691$	−25.6985	−0.977616	−0.488808	−	0.872391i	$-0.662568\pi$
$691$	−25.6985	−0.977616	−0.488808	+	0.872391i	$0.662568\pi$
$692$	21.3137	0.810226
$693$	13.6569	0.518781
$694$	−23.2426	−0.882279
$695$	15.0711	0.571678
$696$	−1.72792	−0.0654967
$697$	0	0
$698$	−24.9706	−0.945150
$699$	−2.55635	−0.0966900
$700$	−3.41421	−0.129045
$701$	24.9706	0.943125	0.471563	−	0.881833i	$-0.343690\pi$
$701$	24.9706	0.943125	0.471563	+	0.881833i	$0.343690\pi$
$702$	2.41421	0.0911186
$703$	−2.58579	−0.0975248
$704$	1.41421	0.0533002
$705$	2.17157	0.0817862
$706$	17.3137	0.651610
$707$	53.4558	2.01041
$708$	3.68629	0.138539
$709$	−34.6569	−1.30157	−0.650783	−	0.759264i	$-0.725559\pi$
$709$	−34.6569	−1.30157	−0.650783	+	0.759264i	$0.725559\pi$
$710$	−13.7279	−0.515200
$711$	0.970563	0.0363989
$712$	−3.34315	−0.125290
$713$	28.6274	1.07211
$714$	0	0
$715$	−1.41421	−0.0528886
$716$	1.17157	0.0437837
$717$	10.1838	0.380320
$718$	−24.3848	−0.910032
$719$	1.87006	0.0697414	0.0348707	−	0.999392i	$-0.488898\pi$
$719$	1.87006	0.0697414	0.0348707	+	0.999392i	$0.488898\pi$
$720$	−2.82843	−0.105409
$721$	46.6274	1.73650
$722$	−18.8284	−0.700721
$723$	−8.30152	−0.308737
$724$	1.65685	0.0615765
$725$	−4.17157	−0.154928
$726$	−3.72792	−0.138356
$727$	−20.2132	−0.749666	−0.374833	−	0.927092i	$-0.622300\pi$
$727$	−20.2132	−0.749666	−0.374833	+	0.927092i	$0.622300\pi$
$728$	3.41421	0.126539
$729$	−18.1716	−0.673021
$730$	2.17157	0.0803735
$731$	0	0
$732$	−5.72792	−0.211710
$733$	5.17157	0.191016	0.0955082	−	0.995429i	$-0.469552\pi$
$733$	5.17157	0.191016	0.0955082	+	0.995429i	$0.469552\pi$
$734$	36.1421	1.33403
$735$	1.92893	0.0711497
$736$	−8.82843	−0.325420
$737$	4.48528	0.165217
$738$	18.6274	0.685685
$739$	−47.8701	−1.76093	−0.880464	−	0.474113i	$-0.842769\pi$
$739$	−47.8701	−1.76093	−0.880464	+	0.474113i	$0.842769\pi$
$740$	6.24264	0.229484
$741$	0.171573	0.00630289
$742$	46.0416	1.69024
$743$	37.5563	1.37781	0.688904	−	0.724852i	$-0.258092\pi$
$743$	37.5563	1.37781	0.688904	+	0.724852i	$0.258092\pi$
$744$	−1.34315	−0.0492421
$745$	10.2426	0.375261
$746$	−32.2843	−1.18201
$747$	−28.0000	−1.02447
$748$	0	0
$749$	−15.3137	−0.559551
$750$	0.414214	0.0151249
$751$	−45.0416	−1.64359	−0.821796	−	0.569782i	$-0.807028\pi$
$751$	−45.0416	−1.64359	−0.821796	+	0.569782i	$0.807028\pi$
$752$	5.24264	0.191179
$753$	−10.8284	−0.394610
$754$	4.17157	0.151920
$755$	0.828427	0.0301496
$756$	8.24264	0.299782
$757$	34.1716	1.24199	0.620993	−	0.783816i	$-0.286729\pi$
$757$	34.1716	1.24199	0.620993	+	0.783816i	$0.286729\pi$
$758$	5.65685	0.205466
$759$	−5.17157	−0.187716
$760$	−0.414214	−0.0150251
$761$	19.1127	0.692835	0.346417	−	0.938080i	$-0.387398\pi$
$761$	19.1127	0.692835	0.346417	+	0.938080i	$0.387398\pi$
$762$	7.34315	0.266014
$763$	21.0711	0.762824
$764$	8.24264	0.298208
$765$	0	0
$766$	−20.2132	−0.730333
$767$	−8.89949	−0.321342
$768$	0.414214	0.0149466
$769$	5.14214	0.185430	0.0927151	−	0.995693i	$-0.470445\pi$
$769$	5.14214	0.185430	0.0927151	+	0.995693i	$0.470445\pi$
$770$	−4.82843	−0.174004
$771$	10.5269	0.379117
$772$	−4.00000	−0.143963
$773$	−40.4853	−1.45615	−0.728077	−	0.685495i	$-0.759586\pi$
$773$	−40.4853	−1.45615	−0.728077	+	0.685495i	$0.759586\pi$
$774$	−4.97056	−0.178663
$775$	−3.24264	−0.116479
$776$	−8.31371	−0.298445
$777$	−8.82843	−0.316718
$778$	−34.6274	−1.24145
$779$	2.72792	0.0977380
$780$	−0.414214	−0.0148312
$781$	−19.4142	−0.694695
$782$	0	0
$783$	10.0711	0.359911
$784$	4.65685	0.166316
$785$	2.82843	0.100951
$786$	0.0416306	0.00148491
$787$	30.5563	1.08922	0.544608	−	0.838691i	$-0.316678\pi$
$787$	30.5563	1.08922	0.544608	+	0.838691i	$0.316678\pi$
$788$	5.55635	0.197937
$789$	−1.76955	−0.0629977
$790$	−0.343146	−0.0122086
$791$	−46.0416	−1.63705
$792$	−4.00000	−0.142134
$793$	13.8284	0.491062
$794$	0.686292	0.0243556
$795$	−5.58579	−0.198107
$796$	25.3848	0.899740
$797$	18.6274	0.659817	0.329908	−	0.944013i	$-0.392982\pi$
$797$	18.6274	0.659817	0.329908	+	0.944013i	$0.392982\pi$
$798$	0.585786	0.0207366
$799$	0	0
$800$	1.00000	0.0353553
$801$	9.45584	0.334106
$802$	−12.9706	−0.458006
$803$	3.07107	0.108376
$804$	1.31371	0.0463309
$805$	30.1421	1.06237
$806$	3.24264	0.114217
$807$	−5.58579	−0.196629
$808$	−15.6569	−0.550806
$809$	−28.5269	−1.00295	−0.501476	−	0.865171i	$-0.667210\pi$
$809$	−28.5269	−1.00295	−0.501476	+	0.865171i	$0.667210\pi$
$810$	7.48528	0.263006
$811$	−31.0122	−1.08899	−0.544493	−	0.838766i	$-0.683278\pi$
$811$	−31.0122	−1.08899	−0.544493	+	0.838766i	$0.683278\pi$
$812$	14.2426	0.499819
$813$	−7.31371	−0.256503
$814$	8.82843	0.309436
$815$	−16.4853	−0.577454
$816$	0	0
$817$	−0.727922	−0.0254668
$818$	−5.48528	−0.191788
$819$	−9.65685	−0.337438
$820$	−6.58579	−0.229986
$821$	−56.4558	−1.97032	−0.985161	−	0.171631i	$-0.945096\pi$
$821$	−56.4558	−1.97032	−0.985161	+	0.171631i	$0.945096\pi$
$822$	3.61522	0.126095
$823$	−16.1421	−0.562679	−0.281340	−	0.959608i	$-0.590779\pi$
$823$	−16.1421	−0.562679	−0.281340	+	0.959608i	$0.590779\pi$
$824$	−13.6569	−0.475759
$825$	0.585786	0.0203945
$826$	−30.3848	−1.05722
$827$	−25.6569	−0.892176	−0.446088	−	0.894989i	$-0.647183\pi$
$827$	−25.6569	−0.892176	−0.446088	+	0.894989i	$0.647183\pi$
$828$	24.9706	0.867787
$829$	−11.3137	−0.392941	−0.196471	−	0.980510i	$-0.562948\pi$
$829$	−11.3137	−0.392941	−0.196471	+	0.980510i	$0.562948\pi$
$830$	9.89949	0.343616
$831$	8.14214	0.282448
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	6.24264	0.216165
$835$	−20.8284	−0.720797
$836$	−0.585786	−0.0202598
$837$	7.82843	0.270590
$838$	25.7990	0.891211
$839$	−18.5563	−0.640636	−0.320318	−	0.947310i	$-0.603790\pi$
$839$	−18.5563	−0.640636	−0.320318	+	0.947310i	$0.603790\pi$
$840$	−1.41421	−0.0487950
$841$	−11.5980	−0.399930
$842$	−37.0711	−1.27755
$843$	6.41421	0.220917
$844$	−0.828427	−0.0285156
$845$	−12.0000	−0.412813
$846$	−14.8284	−0.509812
$847$	30.7279	1.05582
$848$	−13.4853	−0.463086
$849$	−5.14214	−0.176478
$850$	0	0
$851$	−55.1127	−1.88924
$852$	−5.68629	−0.194809
$853$	−24.7279	−0.846668	−0.423334	−	0.905974i	$-0.639140\pi$
$853$	−24.7279	−0.846668	−0.423334	+	0.905974i	$0.639140\pi$
$854$	47.2132	1.61560
$855$	1.17157	0.0400669
$856$	4.48528	0.153304
$857$	−16.1716	−0.552410	−0.276205	−	0.961099i	$-0.589077\pi$
$857$	−16.1716	−0.552410	−0.276205	+	0.961099i	$0.589077\pi$
$858$	−0.585786	−0.0199984
$859$	5.87006	0.200284	0.100142	−	0.994973i	$-0.468070\pi$
$859$	5.87006	0.200284	0.100142	+	0.994973i	$0.468070\pi$
$860$	1.75736	0.0599255
$861$	9.31371	0.317410
$862$	22.6274	0.770693
$863$	−49.4558	−1.68350	−0.841748	−	0.539870i	$-0.818473\pi$
$863$	−49.4558	−1.68350	−0.841748	+	0.539870i	$0.818473\pi$
$864$	−2.41421	−0.0821332
$865$	21.3137	0.724688
$866$	−15.0711	−0.512136
$867$	0	0
$868$	11.0711	0.375777
$869$	−0.485281	−0.0164620
$870$	−1.72792	−0.0585820
$871$	−3.17157	−0.107465
$872$	−6.17157	−0.208996
$873$	23.5147	0.795853
$874$	3.65685	0.123695
$875$	−3.41421	−0.115421
$876$	0.899495	0.0303911
$877$	−11.6152	−0.392218	−0.196109	−	0.980582i	$-0.562831\pi$
$877$	−11.6152	−0.392218	−0.196109	+	0.980582i	$0.562831\pi$
$878$	32.0000	1.07995
$879$	4.75736	0.160462
$880$	1.41421	0.0476731
$881$	−28.3431	−0.954905	−0.477452	−	0.878658i	$-0.658440\pi$
$881$	−28.3431	−0.954905	−0.477452	+	0.878658i	$0.658440\pi$
$882$	−13.1716	−0.443510
$883$	43.4975	1.46381	0.731903	−	0.681409i	$-0.238632\pi$
$883$	43.4975	1.46381	0.731903	+	0.681409i	$0.238632\pi$
$884$	0	0
$885$	3.68629	0.123913
$886$	−20.0000	−0.671913
$887$	24.1838	0.812011	0.406006	−	0.913871i	$-0.366921\pi$
$887$	24.1838	0.812011	0.406006	+	0.913871i	$0.366921\pi$
$888$	2.58579	0.0867733
$889$	−60.5269	−2.03001
$890$	−3.34315	−0.112063
$891$	10.5858	0.354637
$892$	11.3848	0.381191
$893$	−2.17157	−0.0726689
$894$	4.24264	0.141895
$895$	1.17157	0.0391614
$896$	−3.41421	−0.114061
$897$	3.65685	0.122099
$898$	−10.4437	−0.348509
$899$	13.5269	0.451148
$900$	−2.82843	−0.0942809
$901$	0	0
$902$	−9.31371	−0.310113
$903$	−2.48528	−0.0827050
$904$	13.4853	0.448514
$905$	1.65685	0.0550757
$906$	0.343146	0.0114003
$907$	38.2132	1.26885	0.634424	−	0.772985i	$-0.281237\pi$
$907$	38.2132	1.26885	0.634424	+	0.772985i	$0.281237\pi$
$908$	−10.5563	−0.350325
$909$	44.2843	1.46882
$910$	3.41421	0.113180
$911$	−27.3137	−0.904944	−0.452472	−	0.891779i	$-0.649458\pi$
$911$	−27.3137	−0.904944	−0.452472	+	0.891779i	$0.649458\pi$
$912$	−0.171573	−0.00568135
$913$	14.0000	0.463332
$914$	−3.55635	−0.117634
$915$	−5.72792	−0.189359
$916$	−7.75736	−0.256310
$917$	−0.343146	−0.0113317
$918$	0	0
$919$	39.0122	1.28689	0.643447	−	0.765491i	$-0.277504\pi$
$919$	39.0122	1.28689	0.643447	+	0.765491i	$0.277504\pi$
$920$	−8.82843	−0.291065
$921$	−4.10051	−0.135116
$922$	−26.9706	−0.888228
$923$	13.7279	0.451860
$924$	−2.00000	−0.0657952
$925$	6.24264	0.205257
$926$	20.8995	0.686800
$927$	38.6274	1.26869
$928$	−4.17157	−0.136939
$929$	−4.92893	−0.161713	−0.0808565	−	0.996726i	$-0.525766\pi$
$929$	−4.92893	−0.161713	−0.0808565	+	0.996726i	$0.525766\pi$
$930$	−1.34315	−0.0440435
$931$	−1.92893	−0.0632182
$932$	−6.17157	−0.202157
$933$	3.17157	0.103833
$934$	−17.2132	−0.563233
$935$	0	0
$936$	2.82843	0.0924500
$937$	41.8406	1.36687	0.683437	−	0.730010i	$-0.260485\pi$
$937$	41.8406	1.36687	0.683437	+	0.730010i	$0.260485\pi$
$938$	−10.8284	−0.353561
$939$	6.14214	0.200441
$940$	5.24264	0.170996
$941$	31.6863	1.03294	0.516472	−	0.856304i	$-0.327245\pi$
$941$	31.6863	1.03294	0.516472	+	0.856304i	$0.327245\pi$
$942$	1.17157	0.0381719
$943$	58.1421	1.89337
$944$	8.89949	0.289654
$945$	8.24264	0.268133
$946$	2.48528	0.0808035
$947$	−1.10051	−0.0357616	−0.0178808	−	0.999840i	$-0.505692\pi$
$947$	−1.10051	−0.0357616	−0.0178808	+	0.999840i	$0.505692\pi$
$948$	−0.142136	−0.00461635
$949$	−2.17157	−0.0704922
$950$	−0.414214	−0.0134389
$951$	−4.40202	−0.142745
$952$	0	0
$953$	−23.4142	−0.758461	−0.379230	−	0.925302i	$-0.623811\pi$
$953$	−23.4142	−0.758461	−0.379230	+	0.925302i	$0.623811\pi$
$954$	38.1421	1.23490
$955$	8.24264	0.266726
$956$	24.5858	0.795161
$957$	−2.44365	−0.0789920
$958$	−7.10051	−0.229407
$959$	−29.7990	−0.962260
$960$	0.414214	0.0133687
$961$	−20.4853	−0.660816
$962$	−6.24264	−0.201271
$963$	−12.6863	−0.408810
$964$	−20.0416	−0.645497
$965$	−4.00000	−0.128765
$966$	12.4853	0.401707
$967$	−45.5980	−1.46633	−0.733166	−	0.680050i	$-0.761958\pi$
$967$	−45.5980	−1.46633	−0.733166	+	0.680050i	$0.761958\pi$
$968$	−9.00000	−0.289271
$969$	0	0
$970$	−8.31371	−0.266937
$971$	−60.0122	−1.92588	−0.962941	−	0.269710i	$-0.913072\pi$
$971$	−60.0122	−1.92588	−0.962941	+	0.269710i	$0.913072\pi$
$972$	10.3431	0.331757
$973$	−51.4558	−1.64960
$974$	16.3848	0.525002
$975$	−0.414214	−0.0132655
$976$	−13.8284	−0.442637
$977$	−25.7574	−0.824051	−0.412025	−	0.911172i	$-0.635179\pi$
$977$	−25.7574	−0.824051	−0.412025	+	0.911172i	$0.635179\pi$
$978$	−6.82843	−0.218349
$979$	−4.72792	−0.151105
$980$	4.65685	0.148758
$981$	17.4558	0.557322
$982$	33.7279	1.07630
$983$	8.58579	0.273844	0.136922	−	0.990582i	$-0.456279\pi$
$983$	8.58579	0.273844	0.136922	+	0.990582i	$0.456279\pi$
$984$	−2.72792	−0.0869630
$985$	5.55635	0.177040
$986$	0	0
$987$	−7.41421	−0.235997
$988$	0.414214	0.0131779
$989$	−15.5147	−0.493339
$990$	−4.00000	−0.127128
$991$	22.7574	0.722911	0.361456	−	0.932389i	$-0.382280\pi$
$991$	22.7574	0.722911	0.361456	+	0.932389i	$0.382280\pi$
$992$	−3.24264	−0.102954
$993$	9.34315	0.296496
$994$	46.8701	1.48663
$995$	25.3848	0.804752
$996$	4.10051	0.129929
$997$	−32.9289	−1.04287	−0.521435	−	0.853291i	$-0.674603\pi$
$997$	−32.9289	−1.04287	−0.521435	+	0.853291i	$0.674603\pi$
$998$	−15.2132	−0.481566
$999$	−15.0711	−0.476827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2890.2.a.t.1.2		2
17.2	even	8		170.2.h.a.21.1	✓	4
17.4	even	4		2890.2.b.j.2311.2		4
17.9	even	8		170.2.h.a.81.1	yes	4
17.13	even	4		2890.2.b.j.2311.3		4
17.16	even	2		2890.2.a.v.1.1		2
51.2	odd	8		1530.2.q.c.361.2		4
51.26	odd	8		1530.2.q.c.1441.2		4
68.19	odd	8		1360.2.bt.a.1041.2		4
68.43	odd	8		1360.2.bt.a.81.2		4
85.2	odd	8		850.2.g.e.599.2		4
85.9	even	8		850.2.h.g.251.2		4
85.19	even	8		850.2.h.g.701.2		4
85.43	odd	8		850.2.g.e.149.2		4
85.53	odd	8		850.2.g.h.599.1		4
85.77	odd	8		850.2.g.h.149.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.a.21.1	✓	4	17.2	even	8
170.2.h.a.81.1	yes	4	17.9	even	8
850.2.g.e.149.2		4	85.43	odd	8
850.2.g.e.599.2		4	85.2	odd	8
850.2.g.h.149.1		4	85.77	odd	8
850.2.g.h.599.1		4	85.53	odd	8
850.2.h.g.251.2		4	85.9	even	8
850.2.h.g.701.2		4	85.19	even	8
1360.2.bt.a.81.2		4	68.43	odd	8
1360.2.bt.a.1041.2		4	68.19	odd	8
1530.2.q.c.361.2		4	51.2	odd	8
1530.2.q.c.1441.2		4	51.26	odd	8
2890.2.a.t.1.2		2	1.1	even	1	trivial
2890.2.a.v.1.1		2	17.16	even	2
2890.2.b.j.2311.2		4	17.4	even	4
2890.2.b.j.2311.3		4	17.13	even	4

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:	\( N \)	\(=\)	\( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2890.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -3.41421 q^{7} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.414214 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.414214 q^{6} -3.41421 q^{7} +1.00000 q^{8} -2.82843 q^{9} +1.00000 q^{10} +1.41421 q^{11} +0.414214 q^{12} -1.00000 q^{13} -3.41421 q^{14} +0.414214 q^{15} +1.00000 q^{16} -2.82843 q^{18} -0.414214 q^{19} +1.00000 q^{20} -1.41421 q^{21} +1.41421 q^{22} -8.82843 q^{23} +0.414214 q^{24} +1.00000 q^{25} -1.00000 q^{26} -2.41421 q^{27} -3.41421 q^{28} -4.17157 q^{29} +0.414214 q^{30} -3.24264 q^{31} +1.00000 q^{32} +0.585786 q^{33} -3.41421 q^{35} -2.82843 q^{36} +6.24264 q^{37} -0.414214 q^{38} -0.414214 q^{39} +1.00000 q^{40} -6.58579 q^{41} -1.41421 q^{42} +1.75736 q^{43} +1.41421 q^{44} -2.82843 q^{45} -8.82843 q^{46} +5.24264 q^{47} +0.414214 q^{48} +4.65685 q^{49} +1.00000 q^{50} -1.00000 q^{52} -13.4853 q^{53} -2.41421 q^{54} +1.41421 q^{55} -3.41421 q^{56} -0.171573 q^{57} -4.17157 q^{58} +8.89949 q^{59} +0.414214 q^{60} -13.8284 q^{61} -3.24264 q^{62} +9.65685 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.585786 q^{66} +3.17157 q^{67} -3.65685 q^{69} -3.41421 q^{70} -13.7279 q^{71} -2.82843 q^{72} +2.17157 q^{73} +6.24264 q^{74} +0.414214 q^{75} -0.414214 q^{76} -4.82843 q^{77} -0.414214 q^{78} -0.343146 q^{79} +1.00000 q^{80} +7.48528 q^{81} -6.58579 q^{82} +9.89949 q^{83} -1.41421 q^{84} +1.75736 q^{86} -1.72792 q^{87} +1.41421 q^{88} -3.34315 q^{89} -2.82843 q^{90} +3.41421 q^{91} -8.82843 q^{92} -1.34315 q^{93} +5.24264 q^{94} -0.414214 q^{95} +0.414214 q^{96} -8.31371 q^{97} +4.65685 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{10} - 2 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{20} - 12 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 4 q^{28} - 14 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} + 4 q^{33} - 4 q^{35} + 4 q^{37} + 2 q^{38} + 2 q^{39} + 2 q^{40} - 16 q^{41} + 12 q^{43} - 12 q^{46} + 2 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} - 2 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{56} - 6 q^{57} - 14 q^{58} - 2 q^{59} - 2 q^{60} - 22 q^{61} + 2 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 4 q^{66} + 12 q^{67} + 4 q^{69} - 4 q^{70} - 2 q^{71} + 10 q^{73} + 4 q^{74} - 2 q^{75} + 2 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 2 q^{80} - 2 q^{81} - 16 q^{82} + 12 q^{86} + 22 q^{87} - 18 q^{89} + 4 q^{91} - 12 q^{92} - 14 q^{93} + 2 q^{94} + 2 q^{95} - 2 q^{96} + 6 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 2 * q^10 - 2 * q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^20 - 12 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 4 * q^28 - 14 * q^29 - 2 * q^30 + 2 * q^31 + 2 * q^32 + 4 * q^33 - 4 * q^35 + 4 * q^37 + 2 * q^38 + 2 * q^39 + 2 * q^40 - 16 * q^41 + 12 * q^43 - 12 * q^46 + 2 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 - 2 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^56 - 6 * q^57 - 14 * q^58 - 2 * q^59 - 2 * q^60 - 22 * q^61 + 2 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^65 + 4 * q^66 + 12 * q^67 + 4 * q^69 - 4 * q^70 - 2 * q^71 + 10 * q^73 + 4 * q^74 - 2 * q^75 + 2 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 2 * q^80 - 2 * q^81 - 16 * q^82 + 12 * q^86 + 22 * q^87 - 18 * q^89 + 4 * q^91 - 12 * q^92 - 14 * q^93 + 2 * q^94 + 2 * q^95 - 2 * q^96 + 6 * q^97 - 2 * q^98 - 8 * q^99

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