LMFDB - Embedded newform 429.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(1,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, 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("429.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.27841$ of defining polynomial
Character	$\chi$	$=$	429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0872450 q^{2} -1.00000 q^{3} -1.99239 q^{4} -0.477194 q^{5} +0.0872450 q^{6} +0.435561 q^{7} +0.348316 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0872450 q^{2} -1.00000 q^{3} -1.99239 q^{4} -0.477194 q^{5} +0.0872450 q^{6} +0.435561 q^{7} +0.348316 q^{8} +1.00000 q^{9} +0.0416328 q^{10} -1.00000 q^{11} +1.99239 q^{12} +1.00000 q^{13} -0.0380005 q^{14} +0.477194 q^{15} +3.95439 q^{16} +3.29509 q^{17} -0.0872450 q^{18} +4.43556 q^{19} +0.950756 q^{20} -0.435561 q^{21} +0.0872450 q^{22} +3.16688 q^{23} -0.348316 q^{24} -4.77229 q^{25} -0.0872450 q^{26} -1.00000 q^{27} -0.867807 q^{28} +6.02641 q^{29} -0.0416328 q^{30} +10.6365 q^{31} -1.04163 q^{32} +1.00000 q^{33} -0.287480 q^{34} -0.207847 q^{35} -1.99239 q^{36} +3.42795 q^{37} -0.386981 q^{38} -1.00000 q^{39} -0.166214 q^{40} -7.54922 q^{41} +0.0380005 q^{42} +12.4240 q^{43} +1.99239 q^{44} -0.477194 q^{45} -0.276294 q^{46} -3.25346 q^{47} -3.95439 q^{48} -6.81029 q^{49} +0.416358 q^{50} -3.29509 q^{51} -1.99239 q^{52} -9.81029 q^{53} +0.0872450 q^{54} +0.477194 q^{55} +0.151713 q^{56} -4.43556 q^{57} -0.525774 q^{58} -12.9239 q^{59} -0.950756 q^{60} +10.3671 q^{61} -0.927978 q^{62} +0.435561 q^{63} -7.81790 q^{64} -0.477194 q^{65} -0.0872450 q^{66} +7.50758 q^{67} -6.56510 q^{68} -3.16688 q^{69} +0.0181336 q^{70} +14.5416 q^{71} +0.348316 q^{72} +0.344337 q^{73} -0.299072 q^{74} +4.77229 q^{75} -8.83736 q^{76} -0.435561 q^{77} +0.0872450 q^{78} -7.55285 q^{79} -1.88701 q^{80} +1.00000 q^{81} +0.658632 q^{82} -9.03039 q^{83} +0.867807 q^{84} -1.57240 q^{85} -1.08393 q^{86} -6.02641 q^{87} -0.348316 q^{88} +5.90514 q^{89} +0.0416328 q^{90} +0.435561 q^{91} -6.30965 q^{92} -10.6365 q^{93} +0.283848 q^{94} -2.11662 q^{95} +1.04163 q^{96} +12.8906 q^{97} +0.594164 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{9} - 2 q^{10} - 4 q^{11} - 8 q^{12} + 4 q^{13} + 12 q^{14} + 12 q^{16} - 8 q^{17} - 2 q^{18} + 18 q^{19} - 10 q^{20} - 2 q^{21} + 2 q^{22} + 4 q^{25} - 2 q^{26} - 4 q^{27} - 6 q^{28} - 10 q^{29} + 2 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 36 q^{34} + 22 q^{35} + 8 q^{36} - 2 q^{37} + 4 q^{38} - 4 q^{39} + 20 q^{40} + 2 q^{41} - 12 q^{42} + 28 q^{43} - 8 q^{44} - 30 q^{46} + 6 q^{47} - 12 q^{48} + 8 q^{49} - 36 q^{50} + 8 q^{51} + 8 q^{52} - 4 q^{53} + 2 q^{54} + 48 q^{56} - 18 q^{57} - 6 q^{58} + 16 q^{59} + 10 q^{60} - 10 q^{61} - 34 q^{62} + 2 q^{63} - 12 q^{64} - 2 q^{66} - 34 q^{68} - 58 q^{70} + 10 q^{71} - 6 q^{73} + 14 q^{74} - 4 q^{75} + 26 q^{76} - 2 q^{77} + 2 q^{78} - 8 q^{79} - 48 q^{80} + 4 q^{81} + 12 q^{82} - 8 q^{83} + 6 q^{84} - 18 q^{85} - 8 q^{86} + 10 q^{87} + 6 q^{89} - 2 q^{90} + 2 q^{91} - 28 q^{92} - 12 q^{93} - 46 q^{94} + 22 q^{95} + 2 q^{96} + 10 q^{97} - 34 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^9 - 2 * q^10 - 4 * q^11 - 8 * q^12 + 4 * q^13 + 12 * q^14 + 12 * q^16 - 8 * q^17 - 2 * q^18 + 18 * q^19 - 10 * q^20 - 2 * q^21 + 2 * q^22 + 4 * q^25 - 2 * q^26 - 4 * q^27 - 6 * q^28 - 10 * q^29 + 2 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 36 * q^34 + 22 * q^35 + 8 * q^36 - 2 * q^37 + 4 * q^38 - 4 * q^39 + 20 * q^40 + 2 * q^41 - 12 * q^42 + 28 * q^43 - 8 * q^44 - 30 * q^46 + 6 * q^47 - 12 * q^48 + 8 * q^49 - 36 * q^50 + 8 * q^51 + 8 * q^52 - 4 * q^53 + 2 * q^54 + 48 * q^56 - 18 * q^57 - 6 * q^58 + 16 * q^59 + 10 * q^60 - 10 * q^61 - 34 * q^62 + 2 * q^63 - 12 * q^64 - 2 * q^66 - 34 * q^68 - 58 * q^70 + 10 * q^71 - 6 * q^73 + 14 * q^74 - 4 * q^75 + 26 * q^76 - 2 * q^77 + 2 * q^78 - 8 * q^79 - 48 * q^80 + 4 * q^81 + 12 * q^82 - 8 * q^83 + 6 * q^84 - 18 * q^85 - 8 * q^86 + 10 * q^87 + 6 * q^89 - 2 * q^90 + 2 * q^91 - 28 * q^92 - 12 * q^93 - 46 * q^94 + 22 * q^95 + 2 * q^96 + 10 * q^97 - 34 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0872450	−0.0616916	−0.0308458	−	0.999524i	$-0.509820\pi$
$2$	−0.0872450	−0.0616916	−0.0308458	+	0.999524i	$0.509820\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99239	−0.996194
$5$	−0.477194	−0.213408	−0.106704	−	0.994291i	$-0.534030\pi$
$5$	−0.477194	−0.213408	−0.106704	+	0.994291i	$0.534030\pi$
$6$	0.0872450	0.0356176
$7$	0.435561	0.164627	0.0823133	−	0.996607i	$-0.473769\pi$
$7$	0.435561	0.164627	0.0823133	+	0.996607i	$0.473769\pi$
$8$	0.348316	0.123148
$9$	1.00000	0.333333
$10$	0.0416328	0.0131654
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.99239	0.575153
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.0380005	−0.0101561
$15$	0.477194	0.123211
$16$	3.95439	0.988597
$17$	3.29509	0.799177	0.399589	−	0.916695i	$-0.369153\pi$
$17$	3.29509	0.799177	0.399589	+	0.916695i	$0.369153\pi$
$18$	−0.0872450	−0.0205639
$19$	4.43556	1.01759	0.508794	−	0.860888i	$-0.330092\pi$
$19$	4.43556	1.01759	0.508794	+	0.860888i	$0.330092\pi$
$20$	0.950756	0.212595
$21$	−0.435561	−0.0950472
$22$	0.0872450	0.0186007
$23$	3.16688	0.660340	0.330170	−	0.943922i	$-0.392894\pi$
$23$	3.16688	0.660340	0.330170	+	0.943922i	$0.392894\pi$
$24$	−0.348316	−0.0710997
$25$	−4.77229	−0.954457
$26$	−0.0872450	−0.0171102
$27$	−1.00000	−0.192450
$28$	−0.867807	−0.164000
$29$	6.02641	1.11908	0.559538	−	0.828805i	$-0.310979\pi$
$29$	6.02641	1.11908	0.559538	+	0.828805i	$0.310979\pi$
$30$	−0.0416328	−0.00760107
$31$	10.6365	1.91036	0.955182	−	0.296018i	$-0.0956588\pi$
$31$	10.6365	1.91036	0.955182	+	0.296018i	$0.0956588\pi$
$32$	−1.04163	−0.184136
$33$	1.00000	0.174078
$34$	−0.287480	−0.0493025
$35$	−0.207847	−0.0351326
$36$	−1.99239	−0.332065
$37$	3.42795	0.563551	0.281776	−	0.959480i	$-0.409077\pi$
$37$	3.42795	0.563551	0.281776	+	0.959480i	$0.409077\pi$
$38$	−0.386981	−0.0627766
$39$	−1.00000	−0.160128
$40$	−0.166214	−0.0262808
$41$	−7.54922	−1.17899	−0.589495	−	0.807772i	$-0.700673\pi$
$41$	−7.54922	−1.17899	−0.589495	+	0.807772i	$0.700673\pi$
$42$	0.0380005	0.00586361
$43$	12.4240	1.89464	0.947319	−	0.320292i	$-0.103781\pi$
$43$	12.4240	1.89464	0.947319	+	0.320292i	$0.103781\pi$
$44$	1.99239	0.300364
$45$	−0.477194	−0.0711359
$46$	−0.276294	−0.0407374
$47$	−3.25346	−0.474566	−0.237283	−	0.971441i	$-0.576257\pi$
$47$	−3.25346	−0.474566	−0.237283	+	0.971441i	$0.576257\pi$
$48$	−3.95439	−0.570767
$49$	−6.81029	−0.972898
$50$	0.416358	0.0588819
$51$	−3.29509	−0.461405
$52$	−1.99239	−0.276295
$53$	−9.81029	−1.34755	−0.673773	−	0.738938i	$-0.735328\pi$
$53$	−9.81029	−1.34755	−0.673773	+	0.738938i	$0.735328\pi$
$54$	0.0872450	0.0118725
$55$	0.477194	0.0643448
$56$	0.151713	0.0202735
$57$	−4.43556	−0.587504
$58$	−0.525774	−0.0690375
$59$	−12.9239	−1.68255	−0.841277	−	0.540604i	$-0.818196\pi$
$59$	−12.9239	−1.68255	−0.841277	+	0.540604i	$0.818196\pi$
$60$	−0.950756	−0.122742
$61$	10.3671	1.32737	0.663686	−	0.748011i	$-0.268991\pi$
$61$	10.3671	1.32737	0.663686	+	0.748011i	$0.268991\pi$
$62$	−0.927978	−0.117853
$63$	0.435561	0.0548755
$64$	−7.81790	−0.977237
$65$	−0.477194	−0.0591886
$66$	−0.0872450	−0.0107391
$67$	7.50758	0.917197	0.458599	−	0.888644i	$-0.348352\pi$
$67$	7.50758	0.917197	0.458599	+	0.888644i	$0.348352\pi$
$68$	−6.56510	−0.796136
$69$	−3.16688	−0.381247
$70$	0.0181336	0.00216738
$71$	14.5416	1.72577	0.862885	−	0.505400i	$-0.168655\pi$
$71$	14.5416	1.72577	0.862885	+	0.505400i	$0.168655\pi$
$72$	0.348316	0.0410494
$73$	0.344337	0.0403016	0.0201508	−	0.999797i	$-0.493585\pi$
$73$	0.344337	0.0403016	0.0201508	+	0.999797i	$0.493585\pi$
$74$	−0.299072	−0.0347664
$75$	4.77229	0.551056
$76$	−8.83736	−1.01371
$77$	−0.435561	−0.0496368
$78$	0.0872450	0.00987855
$79$	−7.55285	−0.849762	−0.424881	−	0.905249i	$-0.639684\pi$
$79$	−7.55285	−0.849762	−0.424881	+	0.905249i	$0.639684\pi$
$80$	−1.88701	−0.210974
$81$	1.00000	0.111111
$82$	0.658632	0.0727337
$83$	−9.03039	−0.991214	−0.495607	−	0.868547i	$-0.665054\pi$
$83$	−9.03039	−0.991214	−0.495607	+	0.868547i	$0.665054\pi$
$84$	0.867807	0.0946855
$85$	−1.57240	−0.170550
$86$	−1.08393	−0.116883
$87$	−6.02641	−0.646099
$88$	−0.348316	−0.0371306
$89$	5.90514	0.625944	0.312972	−	0.949762i	$-0.398675\pi$
$89$	5.90514	0.625944	0.312972	+	0.949762i	$0.398675\pi$
$90$	0.0416328	0.00438848
$91$	0.435561	0.0456592
$92$	−6.30965	−0.657827
$93$	−10.6365	−1.10295
$94$	0.283848	0.0292767
$95$	−2.11662	−0.217161
$96$	1.04163	0.106311
$97$	12.8906	1.30884	0.654420	−	0.756131i	$-0.272913\pi$
$97$	12.8906	1.30884	0.654420	+	0.756131i	$0.272913\pi$
$98$	0.594164	0.0600196
$99$	−1.00000	−0.100504
$100$	9.50825	0.950825
$101$	−6.07499	−0.604484	−0.302242	−	0.953231i	$-0.597735\pi$
$101$	−6.07499	−0.604484	−0.302242	+	0.953231i	$0.597735\pi$
$102$	0.287480	0.0284648
$103$	−1.98478	−0.195566	−0.0977829	−	0.995208i	$-0.531175\pi$
$103$	−1.98478	−0.195566	−0.0977829	+	0.995208i	$0.531175\pi$
$104$	0.348316	0.0341552
$105$	0.207847	0.0202838
$106$	0.855899	0.0831322
$107$	16.5750	1.60236	0.801181	−	0.598422i	$-0.204205\pi$
$107$	16.5750	1.60236	0.801181	+	0.598422i	$0.204205\pi$
$108$	1.99239	0.191718
$109$	5.21546	0.499550	0.249775	−	0.968304i	$-0.419643\pi$
$109$	5.21546	0.499550	0.249775	+	0.968304i	$0.419643\pi$
$110$	−0.0416328	−0.00396953
$111$	−3.42795	−0.325367
$112$	1.72238	0.162749
$113$	−17.2881	−1.62633	−0.813166	−	0.582032i	$-0.802258\pi$
$113$	−17.2881	−1.62633	−0.813166	+	0.582032i	$0.802258\pi$
$114$	0.386981	0.0362441
$115$	−1.51121	−0.140922
$116$	−12.0069	−1.11482
$117$	1.00000	0.0924500
$118$	1.12755	0.103799
$119$	1.43521	0.131566
$120$	0.166214	0.0151732
$121$	1.00000	0.0909091
$122$	−0.904479	−0.0818877
$123$	7.54922	0.680690
$124$	−21.1920	−1.90309
$125$	4.66328	0.417096
$126$	−0.0380005	−0.00338536
$127$	−4.37539	−0.388253	−0.194127	−	0.980977i	$-0.562187\pi$
$127$	−4.37539	−0.388253	−0.194127	+	0.980977i	$0.562187\pi$
$128$	2.76534	0.244424
$129$	−12.4240	−1.09387
$130$	0.0416328	0.00365144
$131$	15.8936	1.38863	0.694313	−	0.719673i	$-0.255708\pi$
$131$	15.8936	1.38863	0.694313	+	0.719673i	$0.255708\pi$
$132$	−1.99239	−0.173415
$133$	1.93196	0.167522
$134$	−0.654999	−0.0565833
$135$	0.477194	0.0410703
$136$	1.14773	0.0984173
$137$	7.01880	0.599656	0.299828	−	0.953993i	$-0.403071\pi$
$137$	7.01880	0.599656	0.299828	+	0.953993i	$0.403071\pi$
$138$	0.276294	0.0235197
$139$	7.86714	0.667282	0.333641	−	0.942700i	$-0.391723\pi$
$139$	7.86714	0.667282	0.333641	+	0.942700i	$0.391723\pi$
$140$	0.414112	0.0349989
$141$	3.25346	0.273991
$142$	−1.26868	−0.106465
$143$	−1.00000	−0.0836242
$144$	3.95439	0.329532
$145$	−2.87577	−0.238819
$146$	−0.0300417	−0.00248627
$147$	6.81029	0.561703
$148$	−6.82981	−0.561407
$149$	−10.6781	−0.874783	−0.437392	−	0.899271i	$-0.644098\pi$
$149$	−10.6781	−0.874783	−0.437392	+	0.899271i	$0.644098\pi$
$150$	−0.416358	−0.0339955
$151$	−12.3291	−1.00333	−0.501665	−	0.865062i	$-0.667279\pi$
$151$	−12.3291	−1.00333	−0.501665	+	0.865062i	$0.667279\pi$
$152$	1.54498	0.125314
$153$	3.29509	0.266392
$154$	0.0380005	0.00306217
$155$	−5.07565	−0.407686
$156$	1.99239	0.159519
$157$	2.56741	0.204901	0.102451	−	0.994738i	$-0.467332\pi$
$157$	2.56741	0.204901	0.102451	+	0.994738i	$0.467332\pi$
$158$	0.658948	0.0524231
$159$	9.81029	0.778006
$160$	0.497061	0.0392961
$161$	1.37937	0.108710
$162$	−0.0872450	−0.00685462
$163$	−1.47423	−0.115470	−0.0577351	−	0.998332i	$-0.518388\pi$
$163$	−1.47423	−0.115470	−0.0577351	+	0.998332i	$0.518388\pi$
$164$	15.0410	1.17450
$165$	−0.477194	−0.0371495
$166$	0.787857	0.0611495
$167$	−19.0984	−1.47788	−0.738940	−	0.673771i	$-0.764674\pi$
$167$	−19.0984	−1.47788	−0.738940	+	0.673771i	$0.764674\pi$
$168$	−0.151713	−0.0117049
$169$	1.00000	0.0769231
$170$	0.137184	0.0105215
$171$	4.43556	0.339196
$172$	−24.7534	−1.88743
$173$	8.67446	0.659507	0.329754	−	0.944067i	$-0.393034\pi$
$173$	8.67446	0.659507	0.329754	+	0.944067i	$0.393034\pi$
$174$	0.525774	0.0398588
$175$	−2.07862	−0.157129
$176$	−3.95439	−0.298073
$177$	12.9239	0.971423
$178$	−0.515194	−0.0386155
$179$	18.4550	1.37939	0.689697	−	0.724098i	$-0.257744\pi$
$179$	18.4550	1.37939	0.689697	+	0.724098i	$0.257744\pi$
$180$	0.950756	0.0708651
$181$	6.99239	0.519740	0.259870	−	0.965644i	$-0.416320\pi$
$181$	6.99239	0.519740	0.259870	+	0.965644i	$0.416320\pi$
$182$	−0.0380005	−0.00281679
$183$	−10.3671	−0.766359
$184$	1.10307	0.0813197
$185$	−1.63580	−0.120266
$186$	0.927978	0.0680427
$187$	−3.29509	−0.240961
$188$	6.48215	0.472760
$189$	−0.435561	−0.0316824
$190$	0.184665	0.0133970
$191$	21.4461	1.55178	0.775892	−	0.630866i	$-0.217300\pi$
$191$	21.4461	1.55178	0.775892	+	0.630866i	$0.217300\pi$
$192$	7.81790	0.564208
$193$	−21.6100	−1.55552	−0.777761	−	0.628561i	$-0.783644\pi$
$193$	−21.6100	−1.55552	−0.777761	+	0.628561i	$0.783644\pi$
$194$	−1.12464	−0.0807444
$195$	0.477194	0.0341726
$196$	13.5687	0.969195
$197$	−8.42760	−0.600442	−0.300221	−	0.953870i	$-0.597060\pi$
$197$	−8.42760	−0.600442	−0.300221	+	0.953870i	$0.597060\pi$
$198$	0.0872450	0.00620023
$199$	13.0072	0.922056	0.461028	−	0.887385i	$-0.347481\pi$
$199$	13.0072	0.922056	0.461028	+	0.887385i	$0.347481\pi$
$200$	−1.66226	−0.117540
$201$	−7.50758	−0.529544
$202$	0.530013	0.0372916
$203$	2.62487	0.184230
$204$	6.56510	0.459649
$205$	3.60244	0.251605
$206$	0.173162	0.0120648
$207$	3.16688	0.220113
$208$	3.95439	0.274187
$209$	−4.43556	−0.306814
$210$	−0.0181336	−0.00125134
$211$	7.39358	0.508995	0.254498	−	0.967073i	$-0.418090\pi$
$211$	7.39358	0.508995	0.254498	+	0.967073i	$0.418090\pi$
$212$	19.5459	1.34242
$213$	−14.5416	−0.996374
$214$	−1.44608	−0.0988522
$215$	−5.92864	−0.404330
$216$	−0.348316	−0.0236999
$217$	4.63283	0.314497
$218$	−0.455023	−0.0308180
$219$	−0.344337	−0.0232681
$220$	−0.950756	−0.0640999
$221$	3.29509	0.221652
$222$	0.299072	0.0200724
$223$	−15.0826	−1.01001	−0.505003	−	0.863118i	$-0.668509\pi$
$223$	−15.0826	−1.01001	−0.505003	+	0.863118i	$0.668509\pi$
$224$	−0.453695	−0.0303138
$225$	−4.77229	−0.318152
$226$	1.50830	0.100331
$227$	21.3899	1.41970	0.709850	−	0.704352i	$-0.248763\pi$
$227$	21.3899	1.41970	0.709850	+	0.704352i	$0.248763\pi$
$228$	8.83736	0.585268
$229$	3.69366	0.244084	0.122042	−	0.992525i	$-0.461056\pi$
$229$	3.69366	0.244084	0.122042	+	0.992525i	$0.461056\pi$
$230$	0.131846	0.00869367
$231$	0.435561	0.0286578
$232$	2.09910	0.137812
$233$	−24.6398	−1.61421	−0.807103	−	0.590411i	$-0.798966\pi$
$233$	−24.6398	−1.61421	−0.807103	+	0.590411i	$0.798966\pi$
$234$	−0.0872450	−0.00570339
$235$	1.55253	0.101276
$236$	25.7495	1.67615
$237$	7.55285	0.490610
$238$	−0.125215	−0.00811650
$239$	−15.2683	−0.987623	−0.493811	−	0.869569i	$-0.664397\pi$
$239$	−15.2683	−0.987623	−0.493811	+	0.869569i	$0.664397\pi$
$240$	1.88701	0.121806
$241$	2.50825	0.161570	0.0807852	−	0.996732i	$-0.474257\pi$
$241$	2.50825	0.161570	0.0807852	+	0.996732i	$0.474257\pi$
$242$	−0.0872450	−0.00560832
$243$	−1.00000	−0.0641500
$244$	−20.6553	−1.32232
$245$	3.24983	0.207624
$246$	−0.658632	−0.0419928
$247$	4.43556	0.282228
$248$	3.70485	0.235258
$249$	9.03039	0.572278
$250$	−0.406848	−0.0257313
$251$	11.7343	0.740662	0.370331	−	0.928900i	$-0.379244\pi$
$251$	11.7343	0.740662	0.370331	+	0.928900i	$0.379244\pi$
$252$	−0.867807	−0.0546667
$253$	−3.16688	−0.199100
$254$	0.381731	0.0239519
$255$	1.57240	0.0984674
$256$	15.3945	0.962158
$257$	12.2273	0.762719	0.381359	−	0.924427i	$-0.375456\pi$
$257$	12.2273	0.762719	0.381359	+	0.924427i	$0.375456\pi$
$258$	1.08393	0.0674825
$259$	1.49308	0.0927756
$260$	0.950756	0.0589634
$261$	6.02641	0.373025
$262$	−1.38663	−0.0856665
$263$	17.7191	1.09260	0.546302	−	0.837588i	$-0.316035\pi$
$263$	17.7191	1.09260	0.546302	+	0.837588i	$0.316035\pi$
$264$	0.348316	0.0214374
$265$	4.68141	0.287577
$266$	−0.168554	−0.0103347
$267$	−5.90514	−0.361389
$268$	−14.9580	−0.913706
$269$	17.7038	1.07942	0.539711	−	0.841850i	$-0.318533\pi$
$269$	17.7038	1.07942	0.539711	+	0.841850i	$0.318533\pi$
$270$	−0.0416328	−0.00253369
$271$	9.45666	0.574451	0.287226	−	0.957863i	$-0.407267\pi$
$271$	9.45666	0.574451	0.287226	+	0.957863i	$0.407267\pi$
$272$	13.0301	0.790064
$273$	−0.435561	−0.0263614
$274$	−0.612355	−0.0369937
$275$	4.77229	0.287780
$276$	6.30965	0.379796
$277$	−18.4917	−1.11106	−0.555529	−	0.831497i	$-0.687484\pi$
$277$	−18.4917	−1.11106	−0.555529	+	0.831497i	$0.687484\pi$
$278$	−0.686369	−0.0411657
$279$	10.6365	0.636788
$280$	−0.0723965	−0.00432652
$281$	−15.0198	−0.896007	−0.448003	−	0.894032i	$-0.647865\pi$
$281$	−15.0198	−0.896007	−0.448003	+	0.894032i	$0.647865\pi$
$282$	−0.283848	−0.0169029
$283$	−12.2921	−0.730691	−0.365345	−	0.930872i	$-0.619049\pi$
$283$	−12.2921	−0.730691	−0.365345	+	0.930872i	$0.619049\pi$
$284$	−28.9725	−1.71920
$285$	2.11662	0.125378
$286$	0.0872450	0.00515891
$287$	−3.28814	−0.194093
$288$	−1.04163	−0.0613788
$289$	−6.14237	−0.361316
$290$	0.250896	0.0147331
$291$	−12.8906	−0.755659
$292$	−0.686052	−0.0401482
$293$	−30.4579	−1.77937	−0.889686	−	0.456573i	$-0.849077\pi$
$293$	−30.4579	−1.77937	−0.889686	+	0.456573i	$0.849077\pi$
$294$	−0.594164	−0.0346523
$295$	6.16723	0.359070
$296$	1.19401	0.0694004
$297$	1.00000	0.0580259
$298$	0.931611	0.0539668
$299$	3.16688	0.183145
$300$	−9.50825	−0.548959
$301$	5.41140	0.311908
$302$	1.07565	0.0618969
$303$	6.07499	0.348999
$304$	17.5399	1.00598
$305$	−4.94712	−0.283271
$306$	−0.287480	−0.0164342
$307$	−1.82883	−0.104377	−0.0521883	−	0.998637i	$-0.516620\pi$
$307$	−1.82883	−0.104377	−0.0521883	+	0.998637i	$0.516620\pi$
$308$	0.867807	0.0494479
$309$	1.98478	0.112910
$310$	0.442826	0.0251508
$311$	−0.144448	−0.00819092	−0.00409546	−	0.999992i	$-0.501304\pi$
$311$	−0.144448	−0.00819092	−0.00409546	+	0.999992i	$0.501304\pi$
$312$	−0.348316	−0.0197195
$313$	6.69623	0.378493	0.189247	−	0.981930i	$-0.439395\pi$
$313$	6.69623	0.378493	0.189247	+	0.981930i	$0.439395\pi$
$314$	−0.223994	−0.0126407
$315$	−0.207847	−0.0117109
$316$	15.0482	0.846528
$317$	−21.0175	−1.18046	−0.590229	−	0.807236i	$-0.700963\pi$
$317$	−21.0175	−1.18046	−0.590229	+	0.807236i	$0.700963\pi$
$318$	−0.855899	−0.0479964
$319$	−6.02641	−0.337414
$320$	3.73065	0.208550
$321$	−16.5750	−0.925124
$322$	−0.120343	−0.00670646
$323$	14.6156	0.813233
$324$	−1.99239	−0.110688
$325$	−4.77229	−0.264719
$326$	0.128619	0.00712354
$327$	−5.21546	−0.288416
$328$	−2.62951	−0.145191
$329$	−1.41708	−0.0781262
$330$	0.0416328	0.00229181
$331$	2.00363	0.110130	0.0550648	−	0.998483i	$-0.482463\pi$
$331$	2.00363	0.110130	0.0550648	+	0.998483i	$0.482463\pi$
$332$	17.9920	0.987442
$333$	3.42795	0.187850
$334$	1.66624	0.0911728
$335$	−3.58257	−0.195737
$336$	−1.72238	−0.0939634
$337$	−18.5750	−1.01184	−0.505921	−	0.862580i	$-0.668847\pi$
$337$	−18.5750	−1.01184	−0.505921	+	0.862580i	$0.668847\pi$
$338$	−0.0872450	−0.00474550
$339$	17.2881	0.938963
$340$	3.13283	0.169901
$341$	−10.6365	−0.575997
$342$	−0.386981	−0.0209255
$343$	−6.01522	−0.324792
$344$	4.32747	0.233321
$345$	1.51121	0.0813611
$346$	−0.756804	−0.0406860
$347$	−31.3063	−1.68061	−0.840305	−	0.542115i	$-0.817624\pi$
$347$	−31.3063	−1.68061	−0.840305	+	0.542115i	$0.817624\pi$
$348$	12.0069	0.643640
$349$	−28.9847	−1.55152	−0.775758	−	0.631030i	$-0.782632\pi$
$349$	−28.9847	−1.55152	−0.775758	+	0.631030i	$0.782632\pi$
$350$	0.181349	0.00969354
$351$	−1.00000	−0.0533761
$352$	1.04163	0.0555192
$353$	−1.11305	−0.0592416	−0.0296208	−	0.999561i	$-0.509430\pi$
$353$	−1.11305	−0.0592416	−0.0296208	+	0.999561i	$0.509430\pi$
$354$	−1.12755	−0.0599286
$355$	−6.93916	−0.368293
$356$	−11.7653	−0.623562
$357$	−1.43521	−0.0759596
$358$	−1.61011	−0.0850969
$359$	14.0575	0.741924	0.370962	−	0.928648i	$-0.379028\pi$
$359$	14.0575	0.741924	0.370962	+	0.928648i	$0.379028\pi$
$360$	−0.166214	−0.00876026
$361$	0.674202	0.0354843
$362$	−0.610051	−0.0320636
$363$	−1.00000	−0.0524864
$364$	−0.867807	−0.0454854
$365$	−0.164315	−0.00860066
$366$	0.904479	0.0472779
$367$	11.0456	0.576576	0.288288	−	0.957544i	$-0.406914\pi$
$367$	11.0456	0.576576	0.288288	+	0.957544i	$0.406914\pi$
$368$	12.5231	0.652810
$369$	−7.54922	−0.392996
$370$	0.142715	0.00741941
$371$	−4.27298	−0.221842
$372$	21.1920	1.09875
$373$	8.41702	0.435817	0.217908	−	0.975969i	$-0.430077\pi$
$373$	8.41702	0.435817	0.217908	+	0.975969i	$0.430077\pi$
$374$	0.287480	0.0148653
$375$	−4.66328	−0.240810
$376$	−1.13323	−0.0584420
$377$	6.02641	0.310376
$378$	0.0380005	0.00195454
$379$	−18.4953	−0.950041	−0.475021	−	0.879975i	$-0.657559\pi$
$379$	−18.4953	−0.950041	−0.475021	+	0.879975i	$0.657559\pi$
$380$	4.21713	0.216334
$381$	4.37539	0.224158
$382$	−1.87106	−0.0957320
$383$	−6.93916	−0.354575	−0.177287	−	0.984159i	$-0.556732\pi$
$383$	−6.93916	−0.354575	−0.177287	+	0.984159i	$0.556732\pi$
$384$	−2.76534	−0.141118
$385$	0.207847	0.0105929
$386$	1.88536	0.0959625
$387$	12.4240	0.631546
$388$	−25.6830	−1.30386
$389$	7.13684	0.361852	0.180926	−	0.983497i	$-0.442091\pi$
$389$	7.13684	0.361852	0.180926	+	0.983497i	$0.442091\pi$
$390$	−0.0416328	−0.00210816
$391$	10.4352	0.527729
$392$	−2.37213	−0.119811
$393$	−15.8936	−0.801724
$394$	0.735266	0.0370422
$395$	3.60417	0.181346
$396$	1.99239	0.100121
$397$	−37.2091	−1.86747	−0.933736	−	0.357962i	$-0.883472\pi$
$397$	−37.2091	−1.86747	−0.933736	+	0.357962i	$0.883472\pi$
$398$	−1.13481	−0.0568831
$399$	−1.93196	−0.0967189
$400$	−18.8715	−0.943573
$401$	−6.97022	−0.348076	−0.174038	−	0.984739i	$-0.555682\pi$
$401$	−6.97022	−0.348076	−0.174038	+	0.984739i	$0.555682\pi$
$402$	0.654999	0.0326684
$403$	10.6365	0.529840
$404$	12.1037	0.602184
$405$	−0.477194	−0.0237120
$406$	−0.229007	−0.0113654
$407$	−3.42795	−0.169917
$408$	−1.14773	−0.0568213
$409$	8.66287	0.428351	0.214176	−	0.976795i	$-0.431293\pi$
$409$	8.66287	0.428351	0.214176	+	0.976795i	$0.431293\pi$
$410$	−0.314295	−0.0155219
$411$	−7.01880	−0.346212
$412$	3.95445	0.194822
$413$	−5.62917	−0.276993
$414$	−0.276294	−0.0135791
$415$	4.30925	0.211533
$416$	−1.04163	−0.0510702
$417$	−7.86714	−0.385256
$418$	0.386981	0.0189278
$419$	−13.3869	−0.653994	−0.326997	−	0.945025i	$-0.606037\pi$
$419$	−13.3869	−0.653994	−0.326997	+	0.945025i	$0.606037\pi$
$420$	−0.414112	−0.0202066
$421$	23.6053	1.15045	0.575227	−	0.817994i	$-0.304914\pi$
$421$	23.6053	1.15045	0.575227	+	0.817994i	$0.304914\pi$
$422$	−0.645053	−0.0314007
$423$	−3.25346	−0.158189
$424$	−3.41708	−0.165948
$425$	−15.7251	−0.762780
$426$	1.26868	0.0614679
$427$	4.51551	0.218521
$428$	−33.0238	−1.59626
$429$	1.00000	0.0482805
$430$	0.517245	0.0249437
$431$	−34.4005	−1.65701	−0.828506	−	0.559980i	$-0.810809\pi$
$431$	−34.4005	−1.65701	−0.828506	+	0.559980i	$0.810809\pi$
$432$	−3.95439	−0.190256
$433$	7.55980	0.363301	0.181650	−	0.983363i	$-0.441856\pi$
$433$	7.55980	0.363301	0.181650	+	0.983363i	$0.441856\pi$
$434$	−0.404191	−0.0194018
$435$	2.87577	0.137882
$436$	−10.3912	−0.497649
$437$	14.0469	0.671954
$438$	0.0300417	0.00143545
$439$	−25.4239	−1.21342	−0.606709	−	0.794924i	$-0.707510\pi$
$439$	−25.4239	−1.21342	−0.606709	+	0.794924i	$0.707510\pi$
$440$	0.166214	0.00792396
$441$	−6.81029	−0.324299
$442$	−0.287480	−0.0136740
$443$	5.04428	0.239661	0.119831	−	0.992794i	$-0.461765\pi$
$443$	5.04428	0.239661	0.119831	+	0.992794i	$0.461765\pi$
$444$	6.82981	0.324128
$445$	−2.81790	−0.133581
$446$	1.31588	0.0623088
$447$	10.6781	0.505056
$448$	−3.40517	−0.160879
$449$	4.97615	0.234839	0.117420	−	0.993082i	$-0.462538\pi$
$449$	4.97615	0.234839	0.117420	+	0.993082i	$0.462538\pi$
$450$	0.416358	0.0196273
$451$	7.54922	0.355479
$452$	34.4447	1.62014
$453$	12.3291	0.579272
$454$	−1.86617	−0.0875835
$455$	−0.207847	−0.00974402
$456$	−1.54498	−0.0723502
$457$	12.6827	0.593273	0.296637	−	0.954990i	$-0.404135\pi$
$457$	12.6827	0.593273	0.296637	+	0.954990i	$0.404135\pi$
$458$	−0.322254	−0.0150579
$459$	−3.29509	−0.153802
$460$	3.01093	0.140385
$461$	10.8605	0.505826	0.252913	−	0.967489i	$-0.418611\pi$
$461$	10.8605	0.505826	0.252913	+	0.967489i	$0.418611\pi$
$462$	−0.0380005	−0.00176795
$463$	−36.3208	−1.68797	−0.843986	−	0.536365i	$-0.819797\pi$
$463$	−36.3208	−1.68797	−0.843986	+	0.536365i	$0.819797\pi$
$464$	23.8308	1.10632
$465$	5.07565	0.235378
$466$	2.14970	0.0995828
$467$	−6.54492	−0.302863	−0.151431	−	0.988468i	$-0.548388\pi$
$467$	−6.54492	−0.302863	−0.151431	+	0.988468i	$0.548388\pi$
$468$	−1.99239	−0.0920982
$469$	3.27001	0.150995
$470$	−0.135451	−0.00624787
$471$	−2.56741	−0.118300
$472$	−4.50162	−0.207204
$473$	−12.4240	−0.571255
$474$	−0.658948	−0.0302665
$475$	−21.1678	−0.971244
$476$	−2.85950	−0.131065
$477$	−9.81029	−0.449182
$478$	1.33208	0.0609280
$479$	−2.42760	−0.110920	−0.0554600	−	0.998461i	$-0.517663\pi$
$479$	−2.42760	−0.110920	−0.0554600	+	0.998461i	$0.517663\pi$
$480$	−0.497061	−0.0226876
$481$	3.42795	0.156301
$482$	−0.218832	−0.00996753
$483$	−1.37937	−0.0627635
$484$	−1.99239	−0.0905631
$485$	−6.15131	−0.279316
$486$	0.0872450	0.00395752
$487$	−27.1628	−1.23087	−0.615433	−	0.788189i	$-0.711019\pi$
$487$	−27.1628	−1.23087	−0.615433	+	0.788189i	$0.711019\pi$
$488$	3.61103	0.163464
$489$	1.47423	0.0666668
$490$	−0.283531	−0.0128086
$491$	23.0637	1.04085	0.520426	−	0.853907i	$-0.325773\pi$
$491$	23.0637	1.04085	0.520426	+	0.853907i	$0.325773\pi$
$492$	−15.0410	−0.678099
$493$	19.8576	0.894340
$494$	−0.386981	−0.0174111
$495$	0.477194	0.0214483
$496$	42.0607	1.88858
$497$	6.33376	0.284108
$498$	−0.787857	−0.0353047
$499$	−10.0978	−0.452038	−0.226019	−	0.974123i	$-0.572571\pi$
$499$	−10.0978	−0.452038	−0.226019	+	0.974123i	$0.572571\pi$
$500$	−9.29105	−0.415509
$501$	19.0984	0.853255
$502$	−1.02376	−0.0456926
$503$	−17.3034	−0.771519	−0.385760	−	0.922599i	$-0.626061\pi$
$503$	−17.3034	−0.771519	−0.385760	+	0.922599i	$0.626061\pi$
$504$	0.151713	0.00675783
$505$	2.89895	0.129001
$506$	0.276294	0.0122828
$507$	−1.00000	−0.0444116
$508$	8.71747	0.386775
$509$	29.3664	1.30164	0.650822	−	0.759230i	$-0.274424\pi$
$509$	29.3664	1.30164	0.650822	+	0.759230i	$0.274424\pi$
$510$	−0.137184	−0.00607461
$511$	0.149980	0.00663471
$512$	−6.87377	−0.303781
$513$	−4.43556	−0.195835
$514$	−1.06677	−0.0470533
$515$	0.947123	0.0417352
$516$	24.7534	1.08971
$517$	3.25346	0.143087
$518$	−0.130264	−0.00572347
$519$	−8.67446	−0.380767
$520$	−0.166214	−0.00728898
$521$	−26.2881	−1.15170	−0.575851	−	0.817555i	$-0.695329\pi$
$521$	−26.2881	−1.15170	−0.575851	+	0.817555i	$0.695329\pi$
$522$	−0.525774	−0.0230125
$523$	41.7729	1.82660	0.913301	−	0.407286i	$-0.133525\pi$
$523$	41.7729	1.82660	0.913301	+	0.407286i	$0.133525\pi$
$524$	−31.6661	−1.38334
$525$	2.07862	0.0907185
$526$	−1.54590	−0.0674045
$527$	35.0481	1.52672
$528$	3.95439	0.172093
$529$	−12.9709	−0.563951
$530$	−0.408430	−0.0177411
$531$	−12.9239	−0.560851
$532$	−3.84921	−0.166884
$533$	−7.54922	−0.326993
$534$	0.515194	0.0222946
$535$	−7.90947	−0.341956
$536$	2.61501	0.112951
$537$	−18.4550	−0.796393
$538$	−1.54457	−0.0665912
$539$	6.81029	0.293340
$540$	−0.950756	−0.0409140
$541$	−1.62057	−0.0696739	−0.0348369	−	0.999393i	$-0.511091\pi$
$541$	−1.62057	−0.0696739	−0.0348369	+	0.999393i	$0.511091\pi$
$542$	−0.825047	−0.0354388
$543$	−6.99239	−0.300072
$544$	−3.43228	−0.147158
$545$	−2.48879	−0.106608
$546$	0.0380005	0.00162627
$547$	−5.74547	−0.245659	−0.122829	−	0.992428i	$-0.539197\pi$
$547$	−5.74547	−0.245659	−0.122829	+	0.992428i	$0.539197\pi$
$548$	−13.9842	−0.597374
$549$	10.3671	0.442458
$550$	−0.416358	−0.0177536
$551$	26.7305	1.13876
$552$	−1.10307	−0.0469500
$553$	−3.28973	−0.139893
$554$	1.61331	0.0685429
$555$	1.63580	0.0694357
$556$	−15.6744	−0.664743
$557$	−15.5399	−0.658448	−0.329224	−	0.944252i	$-0.606787\pi$
$557$	−15.5399	−0.658448	−0.329224	+	0.944252i	$0.606787\pi$
$558$	−0.927978	−0.0392845
$559$	12.4240	0.525478
$560$	−0.821908	−0.0347320
$561$	3.29509	0.139119
$562$	1.31040	0.0552760
$563$	−29.4533	−1.24131	−0.620655	−	0.784084i	$-0.713133\pi$
$563$	−29.4533	−1.24131	−0.620655	+	0.784084i	$0.713133\pi$
$564$	−6.48215	−0.272948
$565$	8.24980	0.347072
$566$	1.07243	0.0450775
$567$	0.435561	0.0182918
$568$	5.06507	0.212526
$569$	17.1206	0.717733	0.358866	−	0.933389i	$-0.383163\pi$
$569$	17.1206	0.717733	0.358866	+	0.933389i	$0.383163\pi$
$570$	−0.184665	−0.00773476
$571$	20.3036	0.849680	0.424840	−	0.905268i	$-0.360330\pi$
$571$	20.3036	0.849680	0.424840	+	0.905268i	$0.360330\pi$
$572$	1.99239	0.0833059
$573$	−21.4461	−0.895923
$574$	0.286874	0.0119739
$575$	−15.1132	−0.630266
$576$	−7.81790	−0.325746
$577$	−9.09843	−0.378773	−0.189386	−	0.981903i	$-0.560650\pi$
$577$	−9.09843	−0.378773	−0.189386	+	0.981903i	$0.560650\pi$
$578$	0.535891	0.0222901
$579$	21.6100	0.898081
$580$	5.72964	0.237910
$581$	−3.93329	−0.163180
$582$	1.12464	0.0466178
$583$	9.81029	0.406301
$584$	0.119938	0.00496307
$585$	−0.477194	−0.0197295
$586$	2.65730	0.109772
$587$	36.1288	1.49120	0.745598	−	0.666396i	$-0.232164\pi$
$587$	36.1288	1.49120	0.745598	+	0.666396i	$0.232164\pi$
$588$	−13.5687	−0.559565
$589$	47.1787	1.94396
$590$	−0.538060	−0.0221516
$591$	8.42760	0.346665
$592$	13.5554	0.557125
$593$	−7.60203	−0.312178	−0.156089	−	0.987743i	$-0.549889\pi$
$593$	−7.60203	−0.312178	−0.156089	+	0.987743i	$0.549889\pi$
$594$	−0.0872450	−0.00357971
$595$	−0.684875	−0.0280771
$596$	21.2749	0.871454
$597$	−13.0072	−0.532350
$598$	−0.276294	−0.0112985
$599$	27.5373	1.12514	0.562572	−	0.826748i	$-0.309812\pi$
$599$	27.5373	1.12514	0.562572	+	0.826748i	$0.309812\pi$
$600$	1.66226	0.0678616
$601$	34.2028	1.39516	0.697581	−	0.716506i	$-0.254260\pi$
$601$	34.2028	1.39516	0.697581	+	0.716506i	$0.254260\pi$
$602$	−0.472118	−0.0192421
$603$	7.50758	0.305732
$604$	24.5644	0.999510
$605$	−0.477194	−0.0194007
$606$	−0.530013	−0.0215303
$607$	26.5194	1.07639	0.538195	−	0.842820i	$-0.319106\pi$
$607$	26.5194	1.07639	0.538195	+	0.842820i	$0.319106\pi$
$608$	−4.62023	−0.187375
$609$	−2.62487	−0.106365
$610$	0.431612	0.0174755
$611$	−3.25346	−0.131621
$612$	−6.56510	−0.265379
$613$	−23.0938	−0.932749	−0.466375	−	0.884587i	$-0.654440\pi$
$613$	−23.0938	−0.932749	−0.466375	+	0.884587i	$0.654440\pi$
$614$	0.159556	0.00643915
$615$	−3.60244	−0.145264
$616$	−0.151713	−0.00611269
$617$	−6.14344	−0.247325	−0.123663	−	0.992324i	$-0.539464\pi$
$617$	−6.14344	−0.247325	−0.123663	+	0.992324i	$0.539464\pi$
$618$	−0.173162	−0.00696559
$619$	11.1767	0.449231	0.224615	−	0.974447i	$-0.427887\pi$
$619$	11.1767	0.449231	0.224615	+	0.974447i	$0.427887\pi$
$620$	10.1127	0.406135
$621$	−3.16688	−0.127082
$622$	0.0126024	0.000505310 0
$623$	2.57205	0.103047
$624$	−3.95439	−0.158302
$625$	21.6361	0.865446
$626$	−0.584213	−0.0233498
$627$	4.43556	0.177139
$628$	−5.11527	−0.204122
$629$	11.2954	0.450377
$630$	0.0181336	0.000722461 0
$631$	−22.1325	−0.881079	−0.440540	−	0.897733i	$-0.645213\pi$
$631$	−22.1325	−0.881079	−0.440540	+	0.897733i	$0.645213\pi$
$632$	−2.63078	−0.104647
$633$	−7.39358	−0.293868
$634$	1.83367	0.0728243
$635$	2.08791	0.0828561
$636$	−19.5459	−0.775045
$637$	−6.81029	−0.269833
$638$	0.525774	0.0208156
$639$	14.5416	0.575257
$640$	−1.31960	−0.0521619
$641$	11.3562	0.448542	0.224271	−	0.974527i	$-0.428000\pi$
$641$	11.3562	0.448542	0.224271	+	0.974527i	$0.428000\pi$
$642$	1.44608	0.0570723
$643$	19.8334	0.782152	0.391076	−	0.920358i	$-0.372103\pi$
$643$	19.8334	0.782152	0.391076	+	0.920358i	$0.372103\pi$
$644$	−2.74824	−0.108296
$645$	5.92864	0.233440
$646$	−1.27514	−0.0501696
$647$	8.58425	0.337482	0.168741	−	0.985660i	$-0.446030\pi$
$647$	8.58425	0.337482	0.168741	+	0.985660i	$0.446030\pi$
$648$	0.348316	0.0136831
$649$	12.9239	0.507309
$650$	0.416358	0.0163309
$651$	−4.63283	−0.181575
$652$	2.93723	0.115031
$653$	19.8783	0.777899	0.388950	−	0.921259i	$-0.372838\pi$
$653$	19.8783	0.777899	0.388950	+	0.921259i	$0.372838\pi$
$654$	0.455023	0.0177928
$655$	−7.58431	−0.296343
$656$	−29.8525	−1.16555
$657$	0.344337	0.0134339
$658$	0.123633	0.00481972
$659$	−29.9818	−1.16792	−0.583962	−	0.811781i	$-0.698498\pi$
$659$	−29.9818	−1.16792	−0.583962	+	0.811781i	$0.698498\pi$
$660$	0.950756	0.0370081
$661$	37.9919	1.47771	0.738857	−	0.673862i	$-0.235366\pi$
$661$	37.9919	1.47771	0.738857	+	0.673862i	$0.235366\pi$
$662$	−0.174807	−0.00679407
$663$	−3.29509	−0.127971
$664$	−3.14543	−0.122066
$665$	−0.921918	−0.0357505
$666$	−0.299072	−0.0115888
$667$	19.0849	0.738970
$668$	38.0515	1.47226
$669$	15.0826	0.583127
$670$	0.312562	0.0120753
$671$	−10.3671	−0.400218
$672$	0.453695	0.0175017
$673$	25.5859	0.986263	0.493132	−	0.869955i	$-0.335852\pi$
$673$	25.5859	0.986263	0.493132	+	0.869955i	$0.335852\pi$
$674$	1.62057	0.0624221
$675$	4.77229	0.183685
$676$	−1.99239	−0.0766303
$677$	−24.4362	−0.939158	−0.469579	−	0.882890i	$-0.655594\pi$
$677$	−24.4362	−0.939158	−0.469579	+	0.882890i	$0.655594\pi$
$678$	−1.50830	−0.0579261
$679$	5.61464	0.215470
$680$	−0.547691	−0.0210030
$681$	−21.3899	−0.819665
$682$	0.927978	0.0355341
$683$	−39.0934	−1.49587	−0.747933	−	0.663774i	$-0.768954\pi$
$683$	−39.0934	−1.49587	−0.747933	+	0.663774i	$0.768954\pi$
$684$	−8.83736	−0.337905
$685$	−3.34933	−0.127971
$686$	0.524798	0.0200369
$687$	−3.69366	−0.140922
$688$	49.1292	1.87303
$689$	−9.81029	−0.373742
$690$	−0.131846	−0.00501929
$691$	−40.6394	−1.54599	−0.772997	−	0.634409i	$-0.781243\pi$
$691$	−40.6394	−1.54599	−0.772997	+	0.634409i	$0.781243\pi$
$692$	−17.2829	−0.656997
$693$	−0.435561	−0.0165456
$694$	2.73132	0.103679
$695$	−3.75415	−0.142403
$696$	−2.09910	−0.0795660
$697$	−24.8754	−0.942221
$698$	2.52877	0.0957155
$699$	24.6398	0.931962
$700$	4.14142	0.156531
$701$	−4.06905	−0.153686	−0.0768430	−	0.997043i	$-0.524484\pi$
$701$	−4.06905	−0.153686	−0.0768430	+	0.997043i	$0.524484\pi$
$702$	0.0872450	0.00329285
$703$	15.2049	0.573463
$704$	7.81790	0.294648
$705$	−1.55253	−0.0584717
$706$	0.0971079	0.00365471
$707$	−2.64603	−0.0995142
$708$	−25.7495	−0.967726
$709$	30.7457	1.15468	0.577340	−	0.816504i	$-0.304091\pi$
$709$	30.7457	1.15468	0.577340	+	0.816504i	$0.304091\pi$
$710$	0.605408	0.0227205
$711$	−7.55285	−0.283254
$712$	2.05686	0.0770839
$713$	33.6844	1.26149
$714$	0.125215	0.00468606
$715$	0.477194	0.0178460
$716$	−36.7696	−1.37414
$717$	15.2683	0.570204
$718$	−1.22644	−0.0457705
$719$	25.7422	0.960024	0.480012	−	0.877262i	$-0.340632\pi$
$719$	25.7422	0.960024	0.480012	+	0.877262i	$0.340632\pi$
$720$	−1.88701	−0.0703247
$721$	−0.864491	−0.0321953
$722$	−0.0588208	−0.00218908
$723$	−2.50825	−0.0932827
$724$	−13.9316	−0.517762
$725$	−28.7597	−1.06811
$726$	0.0872450	0.00323797
$727$	3.21877	0.119378	0.0596889	−	0.998217i	$-0.480989\pi$
$727$	3.21877	0.119378	0.0596889	+	0.998217i	$0.480989\pi$
$728$	0.151713	0.00562285
$729$	1.00000	0.0370370
$730$	0.0143357	0.000530588 0
$731$	40.9381	1.51415
$732$	20.6553	0.763442
$733$	38.8208	1.43388	0.716940	−	0.697135i	$-0.245542\pi$
$733$	38.8208	1.43388	0.716940	+	0.697135i	$0.245542\pi$
$734$	−0.963675	−0.0355699
$735$	−3.24983	−0.119872
$736$	−3.29872	−0.121593
$737$	−7.50758	−0.276545
$738$	0.658632	0.0242446
$739$	14.7389	0.542178	0.271089	−	0.962554i	$-0.412616\pi$
$739$	14.7389	0.542178	0.271089	+	0.962554i	$0.412616\pi$
$740$	3.25914	0.119808
$741$	−4.43556	−0.162944
$742$	0.372796	0.0136858
$743$	−21.1064	−0.774318	−0.387159	−	0.922013i	$-0.626544\pi$
$743$	−21.1064	−0.774318	−0.387159	+	0.922013i	$0.626544\pi$
$744$	−3.70485	−0.135826
$745$	5.09552	0.186685
$746$	−0.734343	−0.0268862
$747$	−9.03039	−0.330405
$748$	6.56510	0.240044
$749$	7.21941	0.263791
$750$	0.406848	0.0148560
$751$	−13.3701	−0.487881	−0.243941	−	0.969790i	$-0.578440\pi$
$751$	−13.3701	−0.487881	−0.243941	+	0.969790i	$0.578440\pi$
$752$	−12.8654	−0.469154
$753$	−11.7343	−0.427621
$754$	−0.525774	−0.0191476
$755$	5.88338	0.214118
$756$	0.867807	0.0315618
$757$	2.09082	0.0759921	0.0379961	−	0.999278i	$-0.487903\pi$
$757$	2.09082	0.0759921	0.0379961	+	0.999278i	$0.487903\pi$
$758$	1.61363	0.0586095
$759$	3.16688	0.114950
$760$	−0.737254	−0.0267430
$761$	30.7680	1.11534	0.557669	−	0.830063i	$-0.311696\pi$
$761$	30.7680	1.11534	0.557669	+	0.830063i	$0.311696\pi$
$762$	−0.381731	−0.0138287
$763$	2.27165	0.0822393
$764$	−42.7289	−1.54588
$765$	−1.57240	−0.0568502
$766$	0.605408	0.0218743
$767$	−12.9239	−0.466656
$768$	−15.3945	−0.555502
$769$	−37.4540	−1.35063	−0.675314	−	0.737531i	$-0.735992\pi$
$769$	−37.4540	−1.35063	−0.675314	+	0.737531i	$0.735992\pi$
$770$	−0.0181336	−0.000653491 0
$771$	−12.2273	−0.440356
$772$	43.0555	1.54960
$773$	40.3657	1.45185	0.725927	−	0.687772i	$-0.241411\pi$
$773$	40.3657	1.45185	0.725927	+	0.687772i	$0.241411\pi$
$774$	−1.08393	−0.0389610
$775$	−50.7602	−1.82336
$776$	4.49000	0.161182
$777$	−1.49308	−0.0535640
$778$	−0.622654	−0.0223232
$779$	−33.4850	−1.19972
$780$	−0.950756	−0.0340425
$781$	−14.5416	−0.520339
$782$	−0.910416	−0.0325564
$783$	−6.02641	−0.215366
$784$	−26.9305	−0.961804
$785$	−1.22515	−0.0437275
$786$	1.38663	0.0494596
$787$	14.7389	0.525384	0.262692	−	0.964880i	$-0.415390\pi$
$787$	14.7389	0.525384	0.262692	+	0.964880i	$0.415390\pi$
$788$	16.7911	0.598157
$789$	−17.7191	−0.630815
$790$	−0.314446	−0.0111875
$791$	−7.53004	−0.267738
$792$	−0.348316	−0.0123769
$793$	10.3671	0.368147
$794$	3.24631	0.115207
$795$	−4.68141	−0.166032
$796$	−25.9154	−0.918547
$797$	−43.3925	−1.53704	−0.768520	−	0.639826i	$-0.779006\pi$
$797$	−43.3925	−1.53704	−0.768520	+	0.639826i	$0.779006\pi$
$798$	0.168554	0.00596674
$799$	−10.7204	−0.379262
$800$	4.97097	0.175750
$801$	5.90514	0.208648
$802$	0.608117	0.0214734
$803$	−0.344337	−0.0121514
$804$	14.9580	0.527529
$805$	−0.658226	−0.0231994
$806$	−0.927978	−0.0326866
$807$	−17.7038	−0.623205
$808$	−2.11602	−0.0744412
$809$	28.0821	0.987315	0.493658	−	0.869656i	$-0.335660\pi$
$809$	28.0821	0.987315	0.493658	+	0.869656i	$0.335660\pi$
$810$	0.0416328	0.00146283
$811$	42.2927	1.48510	0.742549	−	0.669791i	$-0.233616\pi$
$811$	42.2927	1.48510	0.742549	+	0.669791i	$0.233616\pi$
$812$	−5.22976	−0.183529
$813$	−9.45666	−0.331660
$814$	0.299072	0.0104825
$815$	0.703491	0.0246422
$816$	−13.0301	−0.456144
$817$	55.1073	1.92796
$818$	−0.755792	−0.0264257
$819$	0.435561	0.0152197
$820$	−7.17746	−0.250648
$821$	−47.6687	−1.66365	−0.831825	−	0.555037i	$-0.812704\pi$
$821$	−47.6687	−1.66365	−0.831825	+	0.555037i	$0.812704\pi$
$822$	0.612355	0.0213583
$823$	−29.8618	−1.04092	−0.520458	−	0.853887i	$-0.674239\pi$
$823$	−29.8618	−1.04092	−0.520458	+	0.853887i	$0.674239\pi$
$824$	−0.691330	−0.0240836
$825$	−4.77229	−0.166150
$826$	0.491117	0.0170881
$827$	53.2133	1.85041	0.925204	−	0.379470i	$-0.123893\pi$
$827$	53.2133	1.85041	0.925204	+	0.379470i	$0.123893\pi$
$828$	−6.30965	−0.219276
$829$	−14.2881	−0.496246	−0.248123	−	0.968729i	$-0.579814\pi$
$829$	−14.2881	−0.496246	−0.248123	+	0.968729i	$0.579814\pi$
$830$	−0.375960	−0.0130498
$831$	18.4917	0.641470
$832$	−7.81790	−0.271037
$833$	−22.4405	−0.777518
$834$	0.686369	0.0237670
$835$	9.11365	0.315391
$836$	8.83736	0.305646
$837$	−10.6365	−0.367650
$838$	1.16794	0.0403459
$839$	31.0680	1.07259	0.536293	−	0.844032i	$-0.319824\pi$
$839$	31.0680	1.07259	0.536293	+	0.844032i	$0.319824\pi$
$840$	0.0723965	0.00249792
$841$	7.31761	0.252331
$842$	−2.05945	−0.0709733
$843$	15.0198	0.517310
$844$	−14.7309	−0.507058
$845$	−0.477194	−0.0164160
$846$	0.283848	0.00975890
$847$	0.435561	0.0149661
$848$	−38.7937	−1.33218
$849$	12.2921	0.421865
$850$	1.37194	0.0470571
$851$	10.8559	0.372135
$852$	28.9725	0.992582
$853$	−16.0515	−0.549593	−0.274796	−	0.961502i	$-0.588610\pi$
$853$	−16.0515	−0.549593	−0.274796	+	0.961502i	$0.588610\pi$
$854$	−0.393956	−0.0134809
$855$	−2.11662	−0.0723870
$856$	5.77332	0.197328
$857$	−11.4725	−0.391893	−0.195946	−	0.980615i	$-0.562778\pi$
$857$	−11.4725	−0.391893	−0.195946	+	0.980615i	$0.562778\pi$
$858$	−0.0872450	−0.00297850
$859$	−26.7956	−0.914255	−0.457128	−	0.889401i	$-0.651122\pi$
$859$	−26.7956	−0.914255	−0.457128	+	0.889401i	$0.651122\pi$
$860$	11.8122	0.402791
$861$	3.28814	0.112060
$862$	3.00127	0.102224
$863$	−43.5095	−1.48108	−0.740541	−	0.672012i	$-0.765430\pi$
$863$	−43.5095	−1.48108	−0.740541	+	0.672012i	$0.765430\pi$
$864$	1.04163	0.0354371
$865$	−4.13940	−0.140744
$866$	−0.659555	−0.0224126
$867$	6.14237	0.208606
$868$	−9.23039	−0.313300
$869$	7.55285	0.256213
$870$	−0.250896	−0.00850618
$871$	7.50758	0.254385
$872$	1.81663	0.0615188
$873$	12.8906	0.436280
$874$	−1.22552	−0.0414539
$875$	2.03114	0.0686651
$876$	0.686052	0.0231796
$877$	−11.9320	−0.402914	−0.201457	−	0.979497i	$-0.564568\pi$
$877$	−11.9320	−0.402914	−0.201457	+	0.979497i	$0.564568\pi$
$878$	2.21811	0.0748576
$879$	30.4579	1.02732
$880$	1.88701	0.0636111
$881$	13.8176	0.465525	0.232763	−	0.972534i	$-0.425223\pi$
$881$	13.8176	0.465525	0.232763	+	0.972534i	$0.425223\pi$
$882$	0.594164	0.0200065
$883$	29.8413	1.00424	0.502119	−	0.864799i	$-0.332554\pi$
$883$	29.8413	1.00424	0.502119	+	0.864799i	$0.332554\pi$
$884$	−6.56510	−0.220808
$885$	−6.16723	−0.207309
$886$	−0.440089	−0.0147851
$887$	−53.2070	−1.78652	−0.893258	−	0.449545i	$-0.851586\pi$
$887$	−53.2070	−1.78652	−0.893258	+	0.449545i	$0.851586\pi$
$888$	−1.19401	−0.0400683
$889$	−1.90575	−0.0639168
$890$	0.245848	0.00824083
$891$	−1.00000	−0.0335013
$892$	30.0504	1.00616
$893$	−14.4309	−0.482912
$894$	−0.931611	−0.0311577
$895$	−8.80662	−0.294373
$896$	1.20447	0.0402386
$897$	−3.16688	−0.105739
$898$	−0.434145	−0.0144876
$899$	64.0997	2.13784
$900$	9.50825	0.316942
$901$	−32.3258	−1.07693
$902$	−0.658632	−0.0219300
$903$	−5.41140	−0.180080
$904$	−6.02174	−0.200280
$905$	−3.33672	−0.110916
$906$	−1.07565	−0.0357362
$907$	−45.8017	−1.52082	−0.760410	−	0.649443i	$-0.775002\pi$
$907$	−45.8017	−1.52082	−0.760410	+	0.649443i	$0.775002\pi$
$908$	−42.6171	−1.41430
$909$	−6.07499	−0.201495
$910$	0.0181336	0.000601124 0
$911$	−10.9696	−0.363439	−0.181720	−	0.983350i	$-0.558166\pi$
$911$	−10.9696	−0.363439	−0.181720	+	0.983350i	$0.558166\pi$
$912$	−17.5399	−0.580805
$913$	9.03039	0.298862
$914$	−1.10651	−0.0366000
$915$	4.94712	0.163547
$916$	−7.35921	−0.243155
$917$	6.92261	0.228605
$918$	0.287480	0.00948827
$919$	−19.2008	−0.633377	−0.316689	−	0.948530i	$-0.602571\pi$
$919$	−19.2008	−0.633377	−0.316689	+	0.948530i	$0.602571\pi$
$920$	−0.526380	−0.0173542
$921$	1.82883	0.0602618
$922$	−0.947528	−0.0312052
$923$	14.5416	0.478643
$924$	−0.867807	−0.0285487
$925$	−16.3592	−0.537886
$926$	3.16881	0.104134
$927$	−1.98478	−0.0651886
$928$	−6.27731	−0.206063
$929$	−3.91310	−0.128385	−0.0641924	−	0.997938i	$-0.520447\pi$
$929$	−3.91310	−0.128385	−0.0641924	+	0.997938i	$0.520447\pi$
$930$	−0.442826	−0.0145208
$931$	−30.2074	−0.990009
$932$	49.0920	1.60806
$933$	0.144448	0.00472903
$934$	0.571012	0.0186841
$935$	1.57240	0.0514229
$936$	0.348316	0.0113851
$937$	49.4490	1.61543	0.807714	−	0.589574i	$-0.200704\pi$
$937$	49.4490	1.61543	0.807714	+	0.589574i	$0.200704\pi$
$938$	−0.285292	−0.00931512
$939$	−6.69623	−0.218523
$940$	−3.09324	−0.100891
$941$	−27.1698	−0.885710	−0.442855	−	0.896593i	$-0.646034\pi$
$941$	−27.1698	−0.885710	−0.442855	+	0.896593i	$0.646034\pi$
$942$	0.223994	0.00729810
$943$	−23.9074	−0.778534
$944$	−51.1063	−1.66337
$945$	0.207847	0.00676127
$946$	1.08393	0.0352416
$947$	3.67844	0.119533	0.0597666	−	0.998212i	$-0.480964\pi$
$947$	3.67844	0.119533	0.0597666	+	0.998212i	$0.480964\pi$
$948$	−15.0482	−0.488743
$949$	0.344337	0.0111776
$950$	1.84678	0.0599175
$951$	21.0175	0.681538
$952$	0.499908	0.0162021
$953$	−14.3681	−0.465429	−0.232715	−	0.972545i	$-0.574761\pi$
$953$	−14.3681	−0.465429	−0.232715	+	0.972545i	$0.574761\pi$
$954$	0.855899	0.0277107
$955$	−10.2339	−0.331163
$956$	30.4203	0.983864
$957$	6.02641	0.194806
$958$	0.211796	0.00684283
$959$	3.05712	0.0987194
$960$	−3.73065	−0.120406
$961$	82.1343	2.64949
$962$	−0.299072	−0.00964245
$963$	16.5750	0.534121
$964$	−4.99740	−0.160955
$965$	10.3122	0.331960
$966$	0.120343	0.00387198
$967$	−15.7904	−0.507786	−0.253893	−	0.967232i	$-0.581711\pi$
$967$	−15.7904	−0.507786	−0.253893	+	0.967232i	$0.581711\pi$
$968$	0.348316	0.0111953
$969$	−14.6156	−0.469520
$970$	0.536671	0.0172315
$971$	34.6447	1.11180	0.555901	−	0.831248i	$-0.312373\pi$
$971$	34.6447	1.11180	0.555901	+	0.831248i	$0.312373\pi$
$972$	1.99239	0.0639059
$973$	3.42662	0.109852
$974$	2.36982	0.0759340
$975$	4.77229	0.152835
$976$	40.9956	1.31224
$977$	1.18666	0.0379645	0.0189823	−	0.999820i	$-0.493957\pi$
$977$	1.18666	0.0379645	0.0189823	+	0.999820i	$0.493957\pi$
$978$	−0.128619	−0.00411278
$979$	−5.90514	−0.188729
$980$	−6.47492	−0.206834
$981$	5.21546	0.166517
$982$	−2.01220	−0.0642118
$983$	0.173162	0.00552301	0.00276150	−	0.999996i	$-0.499121\pi$
$983$	0.173162	0.00552301	0.00276150	+	0.999996i	$0.499121\pi$
$984$	2.62951	0.0838258
$985$	4.02160	0.128139
$986$	−1.73247	−0.0551732
$987$	1.41708	0.0451062
$988$	−8.83736	−0.281154
$989$	39.3452	1.25110
$990$	−0.0416328	−0.00132318
$991$	−60.8935	−1.93435	−0.967173	−	0.254120i	$-0.918214\pi$
$991$	−60.8935	−1.93435	−0.967173	+	0.254120i	$0.918214\pi$
$992$	−11.0793	−0.351768
$993$	−2.00363	−0.0635833
$994$	−0.552589	−0.0175271
$995$	−6.20696	−0.196774
$996$	−17.9920	−0.570100
$997$	−50.8776	−1.61131	−0.805655	−	0.592386i	$-0.798186\pi$
$997$	−50.8776	−1.61131	−0.805655	+	0.592386i	$0.798186\pi$
$998$	0.880980	0.0278869
$999$	−3.42795	−0.108456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.a.h.1.3	✓	4
3.2	odd	2		1287.2.a.m.1.2		4
4.3	odd	2		6864.2.a.bz.1.3		4
11.10	odd	2		4719.2.a.z.1.2		4
13.12	even	2		5577.2.a.m.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.a.h.1.3	✓	4	1.1	even	1	trivial
1287.2.a.m.1.2		4	3.2	odd	2
4719.2.a.z.1.2		4	11.10	odd	2
5577.2.a.m.1.2		4	13.12	even	2
6864.2.a.bz.1.3		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0872450 q^{2} -1.00000 q^{3} -1.99239 q^{4} -0.477194 q^{5} +0.0872450 q^{6} +0.435561 q^{7} +0.348316 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0872450 q^{2} -1.00000 q^{3} -1.99239 q^{4} -0.477194 q^{5} +0.0872450 q^{6} +0.435561 q^{7} +0.348316 q^{8} +1.00000 q^{9} +0.0416328 q^{10} -1.00000 q^{11} +1.99239 q^{12} +1.00000 q^{13} -0.0380005 q^{14} +0.477194 q^{15} +3.95439 q^{16} +3.29509 q^{17} -0.0872450 q^{18} +4.43556 q^{19} +0.950756 q^{20} -0.435561 q^{21} +0.0872450 q^{22} +3.16688 q^{23} -0.348316 q^{24} -4.77229 q^{25} -0.0872450 q^{26} -1.00000 q^{27} -0.867807 q^{28} +6.02641 q^{29} -0.0416328 q^{30} +10.6365 q^{31} -1.04163 q^{32} +1.00000 q^{33} -0.287480 q^{34} -0.207847 q^{35} -1.99239 q^{36} +3.42795 q^{37} -0.386981 q^{38} -1.00000 q^{39} -0.166214 q^{40} -7.54922 q^{41} +0.0380005 q^{42} +12.4240 q^{43} +1.99239 q^{44} -0.477194 q^{45} -0.276294 q^{46} -3.25346 q^{47} -3.95439 q^{48} -6.81029 q^{49} +0.416358 q^{50} -3.29509 q^{51} -1.99239 q^{52} -9.81029 q^{53} +0.0872450 q^{54} +0.477194 q^{55} +0.151713 q^{56} -4.43556 q^{57} -0.525774 q^{58} -12.9239 q^{59} -0.950756 q^{60} +10.3671 q^{61} -0.927978 q^{62} +0.435561 q^{63} -7.81790 q^{64} -0.477194 q^{65} -0.0872450 q^{66} +7.50758 q^{67} -6.56510 q^{68} -3.16688 q^{69} +0.0181336 q^{70} +14.5416 q^{71} +0.348316 q^{72} +0.344337 q^{73} -0.299072 q^{74} +4.77229 q^{75} -8.83736 q^{76} -0.435561 q^{77} +0.0872450 q^{78} -7.55285 q^{79} -1.88701 q^{80} +1.00000 q^{81} +0.658632 q^{82} -9.03039 q^{83} +0.867807 q^{84} -1.57240 q^{85} -1.08393 q^{86} -6.02641 q^{87} -0.348316 q^{88} +5.90514 q^{89} +0.0416328 q^{90} +0.435561 q^{91} -6.30965 q^{92} -10.6365 q^{93} +0.283848 q^{94} -2.11662 q^{95} +1.04163 q^{96} +12.8906 q^{97} +0.594164 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{9} - 2 q^{10} - 4 q^{11} - 8 q^{12} + 4 q^{13} + 12 q^{14} + 12 q^{16} - 8 q^{17} - 2 q^{18} + 18 q^{19} - 10 q^{20} - 2 q^{21} + 2 q^{22} + 4 q^{25} - 2 q^{26} - 4 q^{27} - 6 q^{28} - 10 q^{29} + 2 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 36 q^{34} + 22 q^{35} + 8 q^{36} - 2 q^{37} + 4 q^{38} - 4 q^{39} + 20 q^{40} + 2 q^{41} - 12 q^{42} + 28 q^{43} - 8 q^{44} - 30 q^{46} + 6 q^{47} - 12 q^{48} + 8 q^{49} - 36 q^{50} + 8 q^{51} + 8 q^{52} - 4 q^{53} + 2 q^{54} + 48 q^{56} - 18 q^{57} - 6 q^{58} + 16 q^{59} + 10 q^{60} - 10 q^{61} - 34 q^{62} + 2 q^{63} - 12 q^{64} - 2 q^{66} - 34 q^{68} - 58 q^{70} + 10 q^{71} - 6 q^{73} + 14 q^{74} - 4 q^{75} + 26 q^{76} - 2 q^{77} + 2 q^{78} - 8 q^{79} - 48 q^{80} + 4 q^{81} + 12 q^{82} - 8 q^{83} + 6 q^{84} - 18 q^{85} - 8 q^{86} + 10 q^{87} + 6 q^{89} - 2 q^{90} + 2 q^{91} - 28 q^{92} - 12 q^{93} - 46 q^{94} + 22 q^{95} + 2 q^{96} + 10 q^{97} - 34 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^9 - 2 * q^10 - 4 * q^11 - 8 * q^12 + 4 * q^13 + 12 * q^14 + 12 * q^16 - 8 * q^17 - 2 * q^18 + 18 * q^19 - 10 * q^20 - 2 * q^21 + 2 * q^22 + 4 * q^25 - 2 * q^26 - 4 * q^27 - 6 * q^28 - 10 * q^29 + 2 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 36 * q^34 + 22 * q^35 + 8 * q^36 - 2 * q^37 + 4 * q^38 - 4 * q^39 + 20 * q^40 + 2 * q^41 - 12 * q^42 + 28 * q^43 - 8 * q^44 - 30 * q^46 + 6 * q^47 - 12 * q^48 + 8 * q^49 - 36 * q^50 + 8 * q^51 + 8 * q^52 - 4 * q^53 + 2 * q^54 + 48 * q^56 - 18 * q^57 - 6 * q^58 + 16 * q^59 + 10 * q^60 - 10 * q^61 - 34 * q^62 + 2 * q^63 - 12 * q^64 - 2 * q^66 - 34 * q^68 - 58 * q^70 + 10 * q^71 - 6 * q^73 + 14 * q^74 - 4 * q^75 + 26 * q^76 - 2 * q^77 + 2 * q^78 - 8 * q^79 - 48 * q^80 + 4 * q^81 + 12 * q^82 - 8 * q^83 + 6 * q^84 - 18 * q^85 - 8 * q^86 + 10 * q^87 + 6 * q^89 - 2 * q^90 + 2 * q^91 - 28 * q^92 - 12 * q^93 - 46 * q^94 + 22 * q^95 + 2 * q^96 + 10 * q^97 - 34 * q^98 - 4 * q^99

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