LMFDB - Embedded newform 4334.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 8 x^{13} + 94 x^{12} - 13 x^{11} - 582 x^{10} + 295 x^{9} + 1814 x^{8} - 1056 x^{7} + \cdots - 45 $ x^15 - 6x^14 - 8x^13 + 94x^12 - 13x^11 - 582x^10 + 295x^9 + 1814x^8 - 1056x^7 - 2966x^6 + 1621x^5 + 2328x^4 - 1160x^3 - 589x^2 + 364x - 45
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.956062$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.95606 q^{3} +1.00000 q^{4} -1.56251 q^{5} -1.95606 q^{6} +1.47305 q^{7} +1.00000 q^{8} +0.826177 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.95606 q^{3} +1.00000 q^{4} -1.56251 q^{5} -1.95606 q^{6} +1.47305 q^{7} +1.00000 q^{8} +0.826177 q^{9} -1.56251 q^{10} +1.00000 q^{11} -1.95606 q^{12} -1.42492 q^{13} +1.47305 q^{14} +3.05636 q^{15} +1.00000 q^{16} -5.43250 q^{17} +0.826177 q^{18} +3.19088 q^{19} -1.56251 q^{20} -2.88138 q^{21} +1.00000 q^{22} +5.12122 q^{23} -1.95606 q^{24} -2.55857 q^{25} -1.42492 q^{26} +4.25213 q^{27} +1.47305 q^{28} +2.49894 q^{29} +3.05636 q^{30} +0.687649 q^{31} +1.00000 q^{32} -1.95606 q^{33} -5.43250 q^{34} -2.30165 q^{35} +0.826177 q^{36} -3.11058 q^{37} +3.19088 q^{38} +2.78722 q^{39} -1.56251 q^{40} -9.26906 q^{41} -2.88138 q^{42} +1.12195 q^{43} +1.00000 q^{44} -1.29091 q^{45} +5.12122 q^{46} +2.17401 q^{47} -1.95606 q^{48} -4.83012 q^{49} -2.55857 q^{50} +10.6263 q^{51} -1.42492 q^{52} +8.13008 q^{53} +4.25213 q^{54} -1.56251 q^{55} +1.47305 q^{56} -6.24156 q^{57} +2.49894 q^{58} -9.33492 q^{59} +3.05636 q^{60} +3.38218 q^{61} +0.687649 q^{62} +1.21700 q^{63} +1.00000 q^{64} +2.22644 q^{65} -1.95606 q^{66} -3.81090 q^{67} -5.43250 q^{68} -10.0174 q^{69} -2.30165 q^{70} +2.58619 q^{71} +0.826177 q^{72} -6.76996 q^{73} -3.11058 q^{74} +5.00472 q^{75} +3.19088 q^{76} +1.47305 q^{77} +2.78722 q^{78} +3.30517 q^{79} -1.56251 q^{80} -10.7960 q^{81} -9.26906 q^{82} +7.08287 q^{83} -2.88138 q^{84} +8.48832 q^{85} +1.12195 q^{86} -4.88807 q^{87} +1.00000 q^{88} +16.5286 q^{89} -1.29091 q^{90} -2.09898 q^{91} +5.12122 q^{92} -1.34508 q^{93} +2.17401 q^{94} -4.98578 q^{95} -1.95606 q^{96} -8.76432 q^{97} -4.83012 q^{98} +0.826177 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.95606	−1.12933	−0.564666	−	0.825319i	$-0.690995\pi$
$3$	−1.95606	−1.12933	−0.564666	+	0.825319i	$0.690995\pi$
$4$	1.00000	0.500000
$5$	−1.56251	−0.698774	−0.349387	−	0.936978i	$-0.613610\pi$
$5$	−1.56251	−0.698774	−0.349387	+	0.936978i	$0.613610\pi$
$6$	−1.95606	−0.798559
$7$	1.47305	0.556761	0.278381	−	0.960471i	$-0.410202\pi$
$7$	1.47305	0.556761	0.278381	+	0.960471i	$0.410202\pi$
$8$	1.00000	0.353553
$9$	0.826177	0.275392
$10$	−1.56251	−0.494108
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.95606	−0.564666
$13$	−1.42492	−0.395201	−0.197600	−	0.980283i	$-0.563315\pi$
$13$	−1.42492	−0.395201	−0.197600	+	0.980283i	$0.563315\pi$
$14$	1.47305	0.393690
$15$	3.05636	0.789149
$16$	1.00000	0.250000
$17$	−5.43250	−1.31758	−0.658788	−	0.752329i	$-0.728930\pi$
$17$	−5.43250	−1.31758	−0.658788	+	0.752329i	$0.728930\pi$
$18$	0.826177	0.194732
$19$	3.19088	0.732038	0.366019	−	0.930607i	$-0.380720\pi$
$19$	3.19088	0.732038	0.366019	+	0.930607i	$0.380720\pi$
$20$	−1.56251	−0.349387
$21$	−2.88138	−0.628769
$22$	1.00000	0.213201
$23$	5.12122	1.06785	0.533924	−	0.845533i	$-0.320717\pi$
$23$	5.12122	1.06785	0.533924	+	0.845533i	$0.320717\pi$
$24$	−1.95606	−0.399279
$25$	−2.55857	−0.511714
$26$	−1.42492	−0.279449
$27$	4.25213	0.818323
$28$	1.47305	0.278381
$29$	2.49894	0.464041	0.232020	−	0.972711i	$-0.425466\pi$
$29$	2.49894	0.464041	0.232020	+	0.972711i	$0.425466\pi$
$30$	3.05636	0.558013
$31$	0.687649	0.123505	0.0617527	−	0.998091i	$-0.480331\pi$
$31$	0.687649	0.123505	0.0617527	+	0.998091i	$0.480331\pi$
$32$	1.00000	0.176777
$33$	−1.95606	−0.340507
$34$	−5.43250	−0.931666
$35$	−2.30165	−0.389050
$36$	0.826177	0.137696
$37$	−3.11058	−0.511377	−0.255688	−	0.966759i	$-0.582302\pi$
$37$	−3.11058	−0.511377	−0.255688	+	0.966759i	$0.582302\pi$
$38$	3.19088	0.517629
$39$	2.78722	0.446313
$40$	−1.56251	−0.247054
$41$	−9.26906	−1.44758	−0.723792	−	0.690018i	$-0.757603\pi$
$41$	−9.26906	−1.44758	−0.723792	+	0.690018i	$0.757603\pi$
$42$	−2.88138	−0.444607
$43$	1.12195	0.171096	0.0855478	−	0.996334i	$-0.472736\pi$
$43$	1.12195	0.171096	0.0855478	+	0.996334i	$0.472736\pi$
$44$	1.00000	0.150756
$45$	−1.29091	−0.192437
$46$	5.12122	0.755082
$47$	2.17401	0.317113	0.158556	−	0.987350i	$-0.449316\pi$
$47$	2.17401	0.317113	0.158556	+	0.987350i	$0.449316\pi$
$48$	−1.95606	−0.282333
$49$	−4.83012	−0.690017
$50$	−2.55857	−0.361837
$51$	10.6263	1.48798
$52$	−1.42492	−0.197600
$53$	8.13008	1.11675	0.558376	−	0.829588i	$-0.311425\pi$
$53$	8.13008	1.11675	0.558376	+	0.829588i	$0.311425\pi$
$54$	4.25213	0.578642
$55$	−1.56251	−0.210688
$56$	1.47305	0.196845
$57$	−6.24156	−0.826715
$58$	2.49894	0.328126
$59$	−9.33492	−1.21530	−0.607652	−	0.794204i	$-0.707888\pi$
$59$	−9.33492	−1.21530	−0.607652	+	0.794204i	$0.707888\pi$
$60$	3.05636	0.394574
$61$	3.38218	0.433043	0.216522	−	0.976278i	$-0.430529\pi$
$61$	3.38218	0.433043	0.216522	+	0.976278i	$0.430529\pi$
$62$	0.687649	0.0873315
$63$	1.21700	0.153328
$64$	1.00000	0.125000
$65$	2.22644	0.276156
$66$	−1.95606	−0.240775
$67$	−3.81090	−0.465576	−0.232788	−	0.972528i	$-0.574785\pi$
$67$	−3.81090	−0.465576	−0.232788	+	0.972528i	$0.574785\pi$
$68$	−5.43250	−0.658788
$69$	−10.0174	−1.20596
$70$	−2.30165	−0.275100
$71$	2.58619	0.306924	0.153462	−	0.988155i	$-0.450958\pi$
$71$	2.58619	0.306924	0.153462	+	0.988155i	$0.450958\pi$
$72$	0.826177	0.0973659
$73$	−6.76996	−0.792363	−0.396182	−	0.918172i	$-0.629665\pi$
$73$	−6.76996	−0.792363	−0.396182	+	0.918172i	$0.629665\pi$
$74$	−3.11058	−0.361598
$75$	5.00472	0.577896
$76$	3.19088	0.366019
$77$	1.47305	0.167870
$78$	2.78722	0.315591
$79$	3.30517	0.371860	0.185930	−	0.982563i	$-0.440470\pi$
$79$	3.30517	0.371860	0.185930	+	0.982563i	$0.440470\pi$
$80$	−1.56251	−0.174694
$81$	−10.7960	−1.19955
$82$	−9.26906	−1.02360
$83$	7.08287	0.777446	0.388723	−	0.921355i	$-0.372916\pi$
$83$	7.08287	0.777446	0.388723	+	0.921355i	$0.372916\pi$
$84$	−2.88138	−0.314384
$85$	8.48832	0.920688
$86$	1.12195	0.120983
$87$	−4.88807	−0.524056
$88$	1.00000	0.106600
$89$	16.5286	1.75203	0.876013	−	0.482288i	$-0.160194\pi$
$89$	16.5286	1.75203	0.876013	+	0.482288i	$0.160194\pi$
$90$	−1.29091	−0.136074
$91$	−2.09898	−0.220032
$92$	5.12122	0.533924
$93$	−1.34508	−0.139479
$94$	2.17401	0.224233
$95$	−4.98578	−0.511530
$96$	−1.95606	−0.199640
$97$	−8.76432	−0.889882	−0.444941	−	0.895560i	$-0.646775\pi$
$97$	−8.76432	−0.889882	−0.444941	+	0.895560i	$0.646775\pi$
$98$	−4.83012	−0.487916
$99$	0.826177	0.0830339
$100$	−2.55857	−0.255857
$101$	−19.7168	−1.96189	−0.980947	−	0.194273i	$-0.937765\pi$
$101$	−19.7168	−1.96189	−0.980947	+	0.194273i	$0.937765\pi$
$102$	10.6263	1.05216
$103$	−9.79739	−0.965365	−0.482683	−	0.875795i	$-0.660338\pi$
$103$	−9.79739	−0.965365	−0.482683	+	0.875795i	$0.660338\pi$
$104$	−1.42492	−0.139725
$105$	4.50218	0.439367
$106$	8.13008	0.789663
$107$	−11.0572	−1.06894	−0.534472	−	0.845186i	$-0.679490\pi$
$107$	−11.0572	−1.06894	−0.534472	+	0.845186i	$0.679490\pi$
$108$	4.25213	0.409162
$109$	−5.76847	−0.552519	−0.276260	−	0.961083i	$-0.589095\pi$
$109$	−5.76847	−0.552519	−0.276260	+	0.961083i	$0.589095\pi$
$110$	−1.56251	−0.148979
$111$	6.08449	0.577515
$112$	1.47305	0.139190
$113$	−16.5878	−1.56045	−0.780223	−	0.625501i	$-0.784895\pi$
$113$	−16.5878	−1.56045	−0.780223	+	0.625501i	$0.784895\pi$
$114$	−6.24156	−0.584576
$115$	−8.00194	−0.746185
$116$	2.49894	0.232020
$117$	−1.17723	−0.108835
$118$	−9.33492	−0.859349
$119$	−8.00236	−0.733575
$120$	3.05636	0.279006
$121$	1.00000	0.0909091
$122$	3.38218	0.306208
$123$	18.1309	1.63480
$124$	0.687649	0.0617527
$125$	11.8103	1.05635
$126$	1.21700	0.108419
$127$	7.05596	0.626115	0.313058	−	0.949734i	$-0.398647\pi$
$127$	7.05596	0.626115	0.313058	+	0.949734i	$0.398647\pi$
$128$	1.00000	0.0883883
$129$	−2.19460	−0.193224
$130$	2.22644	0.195272
$131$	3.09254	0.270197	0.135098	−	0.990832i	$-0.456865\pi$
$131$	3.09254	0.270197	0.135098	+	0.990832i	$0.456865\pi$
$132$	−1.95606	−0.170253
$133$	4.70033	0.407571
$134$	−3.81090	−0.329212
$135$	−6.64399	−0.571823
$136$	−5.43250	−0.465833
$137$	−2.67423	−0.228475	−0.114237	−	0.993453i	$-0.536442\pi$
$137$	−2.67423	−0.228475	−0.114237	+	0.993453i	$0.536442\pi$
$138$	−10.0174	−0.852739
$139$	−18.1754	−1.54161	−0.770807	−	0.637068i	$-0.780147\pi$
$139$	−18.1754	−1.54161	−0.770807	+	0.637068i	$0.780147\pi$
$140$	−2.30165	−0.194525
$141$	−4.25251	−0.358126
$142$	2.58619	0.217028
$143$	−1.42492	−0.119158
$144$	0.826177	0.0688481
$145$	−3.90461	−0.324260
$146$	−6.76996	−0.560285
$147$	9.44801	0.779259
$148$	−3.11058	−0.255688
$149$	4.22590	0.346199	0.173100	−	0.984904i	$-0.444622\pi$
$149$	4.22590	0.346199	0.173100	+	0.984904i	$0.444622\pi$
$150$	5.00472	0.408634
$151$	10.0460	0.817531	0.408766	−	0.912639i	$-0.365959\pi$
$151$	10.0460	0.817531	0.408766	+	0.912639i	$0.365959\pi$
$152$	3.19088	0.258815
$153$	−4.48821	−0.362850
$154$	1.47305	0.118702
$155$	−1.07446	−0.0863024
$156$	2.78722	0.223157
$157$	−10.6620	−0.850920	−0.425460	−	0.904977i	$-0.639888\pi$
$157$	−10.6620	−0.850920	−0.425460	+	0.904977i	$0.639888\pi$
$158$	3.30517	0.262945
$159$	−15.9029	−1.26119
$160$	−1.56251	−0.123527
$161$	7.54382	0.594536
$162$	−10.7960	−0.848211
$163$	−11.8164	−0.925534	−0.462767	−	0.886480i	$-0.653143\pi$
$163$	−11.8164	−0.925534	−0.462767	+	0.886480i	$0.653143\pi$
$164$	−9.26906	−0.723792
$165$	3.05636	0.237937
$166$	7.08287	0.549738
$167$	18.5479	1.43528	0.717641	−	0.696413i	$-0.245222\pi$
$167$	18.5479	1.43528	0.717641	+	0.696413i	$0.245222\pi$
$168$	−2.88138	−0.222303
$169$	−10.9696	−0.843816
$170$	8.48832	0.651025
$171$	2.63623	0.201598
$172$	1.12195	0.0855478
$173$	−17.9743	−1.36656	−0.683280	−	0.730157i	$-0.739447\pi$
$173$	−17.9743	−1.36656	−0.683280	+	0.730157i	$0.739447\pi$
$174$	−4.88807	−0.370564
$175$	−3.76891	−0.284903
$176$	1.00000	0.0753778
$177$	18.2597	1.37248
$178$	16.5286	1.23887
$179$	−16.0428	−1.19909	−0.599547	−	0.800340i	$-0.704652\pi$
$179$	−16.0428	−1.19909	−0.599547	+	0.800340i	$0.704652\pi$
$180$	−1.29091	−0.0962186
$181$	2.34551	0.174340	0.0871701	−	0.996193i	$-0.472218\pi$
$181$	2.34551	0.174340	0.0871701	+	0.996193i	$0.472218\pi$
$182$	−2.09898	−0.155586
$183$	−6.61575	−0.489050
$184$	5.12122	0.377541
$185$	4.86031	0.357337
$186$	−1.34508	−0.0986263
$187$	−5.43250	−0.397264
$188$	2.17401	0.158556
$189$	6.26361	0.455610
$190$	−4.98578	−0.361706
$191$	11.4146	0.825933	0.412966	−	0.910746i	$-0.364493\pi$
$191$	11.4146	0.825933	0.412966	+	0.910746i	$0.364493\pi$
$192$	−1.95606	−0.141167
$193$	7.18081	0.516886	0.258443	−	0.966027i	$-0.416791\pi$
$193$	7.18081	0.516886	0.258443	+	0.966027i	$0.416791\pi$
$194$	−8.76432	−0.629241
$195$	−4.35506	−0.311872
$196$	−4.83012	−0.345009
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	0.826177	0.0587139
$199$	−8.00693	−0.567596	−0.283798	−	0.958884i	$-0.591595\pi$
$199$	−8.00693	−0.567596	−0.283798	+	0.958884i	$0.591595\pi$
$200$	−2.55857	−0.180918
$201$	7.45436	0.525790
$202$	−19.7168	−1.38727
$203$	3.68106	0.258360
$204$	10.6263	0.743990
$205$	14.4830	1.01153
$206$	−9.79739	−0.682616
$207$	4.23103	0.294077
$208$	−1.42492	−0.0988002
$209$	3.19088	0.220718
$210$	4.50218	0.310680
$211$	−18.4369	−1.26925	−0.634625	−	0.772820i	$-0.718846\pi$
$211$	−18.4369	−1.26925	−0.634625	+	0.772820i	$0.718846\pi$
$212$	8.13008	0.558376
$213$	−5.05874	−0.346619
$214$	−11.0572	−0.755858
$215$	−1.75305	−0.119557
$216$	4.25213	0.289321
$217$	1.01294	0.0687630
$218$	−5.76847	−0.390690
$219$	13.2425	0.894842
$220$	−1.56251	−0.105344
$221$	7.74086	0.520707
$222$	6.08449	0.408365
$223$	−14.3742	−0.962570	−0.481285	−	0.876564i	$-0.659830\pi$
$223$	−14.3742	−0.962570	−0.481285	+	0.876564i	$0.659830\pi$
$224$	1.47305	0.0984224
$225$	−2.11383	−0.140922
$226$	−16.5878	−1.10340
$227$	−1.26170	−0.0837422	−0.0418711	−	0.999123i	$-0.513332\pi$
$227$	−1.26170	−0.0837422	−0.0418711	+	0.999123i	$0.513332\pi$
$228$	−6.24156	−0.413358
$229$	−20.4310	−1.35012	−0.675059	−	0.737764i	$-0.735882\pi$
$229$	−20.4310	−1.35012	−0.675059	+	0.737764i	$0.735882\pi$
$230$	−8.00194	−0.527632
$231$	−2.88138	−0.189581
$232$	2.49894	0.164063
$233$	1.21420	0.0795450	0.0397725	−	0.999209i	$-0.487337\pi$
$233$	1.21420	0.0795450	0.0397725	+	0.999209i	$0.487337\pi$
$234$	−1.17723	−0.0769582
$235$	−3.39691	−0.221590
$236$	−9.33492	−0.607652
$237$	−6.46511	−0.419954
$238$	−8.00236	−0.518716
$239$	−15.4043	−0.996423	−0.498212	−	0.867055i	$-0.666010\pi$
$239$	−15.4043	−0.996423	−0.498212	+	0.867055i	$0.666010\pi$
$240$	3.05636	0.197287
$241$	−26.9930	−1.73877	−0.869386	−	0.494133i	$-0.835486\pi$
$241$	−26.9930	−1.73877	−0.869386	+	0.494133i	$0.835486\pi$
$242$	1.00000	0.0642824
$243$	8.36118	0.536370
$244$	3.38218	0.216522
$245$	7.54710	0.482166
$246$	18.1309	1.15598
$247$	−4.54674	−0.289302
$248$	0.687649	0.0436658
$249$	−13.8545	−0.877996
$250$	11.8103	0.746950
$251$	−18.7324	−1.18238	−0.591191	−	0.806532i	$-0.701342\pi$
$251$	−18.7324	−1.18238	−0.591191	+	0.806532i	$0.701342\pi$
$252$	1.21700	0.0766639
$253$	5.12122	0.321968
$254$	7.05596	0.442730
$255$	−16.6037	−1.03976
$256$	1.00000	0.0625000
$257$	−26.2704	−1.63870	−0.819351	−	0.573292i	$-0.805666\pi$
$257$	−26.2704	−1.63870	−0.819351	+	0.573292i	$0.805666\pi$
$258$	−2.19460	−0.136630
$259$	−4.58205	−0.284715
$260$	2.22644	0.138078
$261$	2.06456	0.127793
$262$	3.09254	0.191058
$263$	−4.97174	−0.306571	−0.153285	−	0.988182i	$-0.548985\pi$
$263$	−4.97174	−0.306571	−0.153285	+	0.988182i	$0.548985\pi$
$264$	−1.95606	−0.120387
$265$	−12.7033	−0.780358
$266$	4.70033	0.288196
$267$	−32.3309	−1.97862
$268$	−3.81090	−0.232788
$269$	16.8447	1.02704	0.513520	−	0.858078i	$-0.328341\pi$
$269$	16.8447	1.02704	0.513520	+	0.858078i	$0.328341\pi$
$270$	−6.64399	−0.404340
$271$	9.16999	0.557037	0.278519	−	0.960431i	$-0.410157\pi$
$271$	9.16999	0.557037	0.278519	+	0.960431i	$0.410157\pi$
$272$	−5.43250	−0.329394
$273$	4.10573	0.248490
$274$	−2.67423	−0.161556
$275$	−2.55857	−0.154288
$276$	−10.0174	−0.602978
$277$	28.9699	1.74064	0.870318	−	0.492491i	$-0.163914\pi$
$277$	28.9699	1.74064	0.870318	+	0.492491i	$0.163914\pi$
$278$	−18.1754	−1.09009
$279$	0.568120	0.0340125
$280$	−2.30165	−0.137550
$281$	0.632988	0.0377609	0.0188805	−	0.999822i	$-0.493990\pi$
$281$	0.632988	0.0377609	0.0188805	+	0.999822i	$0.493990\pi$
$282$	−4.25251	−0.253233
$283$	−13.9530	−0.829420	−0.414710	−	0.909954i	$-0.636117\pi$
$283$	−13.9530	−0.829420	−0.414710	+	0.909954i	$0.636117\pi$
$284$	2.58619	0.153462
$285$	9.75248	0.577687
$286$	−1.42492	−0.0842571
$287$	−13.6538	−0.805959
$288$	0.826177	0.0486830
$289$	12.5121	0.736005
$290$	−3.90461	−0.229286
$291$	17.1435	1.00497
$292$	−6.76996	−0.396182
$293$	14.9735	0.874761	0.437380	−	0.899277i	$-0.355906\pi$
$293$	14.9735	0.874761	0.437380	+	0.899277i	$0.355906\pi$
$294$	9.44801	0.551019
$295$	14.5859	0.849223
$296$	−3.11058	−0.180799
$297$	4.25213	0.246734
$298$	4.22590	0.244800
$299$	−7.29731	−0.422014
$300$	5.00472	0.288948
$301$	1.65269	0.0952594
$302$	10.0460	0.578082
$303$	38.5673	2.21563
$304$	3.19088	0.183010
$305$	−5.28468	−0.302600
$306$	−4.48821	−0.256574
$307$	−3.59920	−0.205417	−0.102709	−	0.994711i	$-0.532751\pi$
$307$	−3.59920	−0.205417	−0.102709	+	0.994711i	$0.532751\pi$
$308$	1.47305	0.0839349
$309$	19.1643	1.09022
$310$	−1.07446	−0.0610250
$311$	1.03203	0.0585209	0.0292604	−	0.999572i	$-0.490685\pi$
$311$	1.03203	0.0585209	0.0292604	+	0.999572i	$0.490685\pi$
$312$	2.78722	0.157796
$313$	10.1250	0.572302	0.286151	−	0.958185i	$-0.407624\pi$
$313$	10.1250	0.572302	0.286151	+	0.958185i	$0.407624\pi$
$314$	−10.6620	−0.601691
$315$	−1.90157	−0.107142
$316$	3.30517	0.185930
$317$	−10.7513	−0.603851	−0.301926	−	0.953331i	$-0.597629\pi$
$317$	−10.7513	−0.603851	−0.301926	+	0.953331i	$0.597629\pi$
$318$	−15.9029	−0.891793
$319$	2.49894	0.139914
$320$	−1.56251	−0.0873468
$321$	21.6287	1.20719
$322$	7.54382	0.420401
$323$	−17.3345	−0.964516
$324$	−10.7960	−0.599776
$325$	3.64575	0.202230
$326$	−11.8164	−0.654451
$327$	11.2835	0.623978
$328$	−9.26906	−0.511798
$329$	3.20244	0.176556
$330$	3.05636	0.168247
$331$	−14.1093	−0.775519	−0.387760	−	0.921761i	$-0.626751\pi$
$331$	−14.1093	−0.775519	−0.387760	+	0.921761i	$0.626751\pi$
$332$	7.08287	0.388723
$333$	−2.56989	−0.140829
$334$	18.5479	1.01490
$335$	5.95456	0.325333
$336$	−2.88138	−0.157192
$337$	14.0990	0.768021	0.384011	−	0.923329i	$-0.374543\pi$
$337$	14.0990	0.768021	0.384011	+	0.923329i	$0.374543\pi$
$338$	−10.9696	−0.596668
$339$	32.4467	1.76226
$340$	8.48832	0.460344
$341$	0.687649	0.0372383
$342$	2.63623	0.142551
$343$	−17.4264	−0.940936
$344$	1.12195	0.0604914
$345$	15.6523	0.842691
$346$	−17.9743	−0.966304
$347$	−23.0460	−1.23717	−0.618586	−	0.785717i	$-0.712294\pi$
$347$	−23.0460	−1.23717	−0.618586	+	0.785717i	$0.712294\pi$
$348$	−4.88807	−0.262028
$349$	−28.4009	−1.52027	−0.760133	−	0.649767i	$-0.774866\pi$
$349$	−28.4009	−1.52027	−0.760133	+	0.649767i	$0.774866\pi$
$350$	−3.76891	−0.201457
$351$	−6.05893	−0.323402
$352$	1.00000	0.0533002
$353$	7.74380	0.412161	0.206081	−	0.978535i	$-0.433929\pi$
$353$	7.74380	0.412161	0.206081	+	0.978535i	$0.433929\pi$
$354$	18.2597	0.970491
$355$	−4.04094	−0.214471
$356$	16.5286	0.876013
$357$	15.6531	0.828450
$358$	−16.0428	−0.847887
$359$	28.3589	1.49672	0.748362	−	0.663290i	$-0.230840\pi$
$359$	28.3589	1.49672	0.748362	+	0.663290i	$0.230840\pi$
$360$	−1.29091	−0.0680368
$361$	−8.81827	−0.464120
$362$	2.34551	0.123277
$363$	−1.95606	−0.102667
$364$	−2.09898	−0.110016
$365$	10.5781	0.553683
$366$	−6.61575	−0.345811
$367$	−14.8459	−0.774948	−0.387474	−	0.921881i	$-0.626652\pi$
$367$	−14.8459	−0.774948	−0.387474	+	0.921881i	$0.626652\pi$
$368$	5.12122	0.266962
$369$	−7.65789	−0.398654
$370$	4.86031	0.252675
$371$	11.9760	0.621764
$372$	−1.34508	−0.0697393
$373$	−15.7416	−0.815069	−0.407534	−	0.913190i	$-0.633611\pi$
$373$	−15.7416	−0.815069	−0.407534	+	0.913190i	$0.633611\pi$
$374$	−5.43250	−0.280908
$375$	−23.1017	−1.19297
$376$	2.17401	0.112116
$377$	−3.56078	−0.183389
$378$	6.26361	0.322165
$379$	−15.5411	−0.798292	−0.399146	−	0.916887i	$-0.630693\pi$
$379$	−15.5411	−0.798292	−0.399146	+	0.916887i	$0.630693\pi$
$380$	−4.98578	−0.255765
$381$	−13.8019	−0.707093
$382$	11.4146	0.584023
$383$	21.1001	1.07816	0.539082	−	0.842253i	$-0.318771\pi$
$383$	21.1001	1.07816	0.539082	+	0.842253i	$0.318771\pi$
$384$	−1.95606	−0.0998199
$385$	−2.30165	−0.117303
$386$	7.18081	0.365494
$387$	0.926929	0.0471184
$388$	−8.76432	−0.444941
$389$	−4.84105	−0.245451	−0.122725	−	0.992441i	$-0.539163\pi$
$389$	−4.84105	−0.245451	−0.122725	+	0.992441i	$0.539163\pi$
$390$	−4.35506	−0.220527
$391$	−27.8210	−1.40697
$392$	−4.83012	−0.243958
$393$	−6.04921	−0.305142
$394$	−1.00000	−0.0503793
$395$	−5.16434	−0.259846
$396$	0.826177	0.0415170
$397$	34.0232	1.70758	0.853788	−	0.520620i	$-0.174299\pi$
$397$	34.0232	1.70758	0.853788	+	0.520620i	$0.174299\pi$
$398$	−8.00693	−0.401351
$399$	−9.19414	−0.460283
$400$	−2.55857	−0.127929
$401$	6.11489	0.305363	0.152681	−	0.988275i	$-0.451209\pi$
$401$	6.11489	0.305363	0.152681	+	0.988275i	$0.451209\pi$
$402$	7.45436	0.371790
$403$	−0.979842	−0.0488094
$404$	−19.7168	−0.980947
$405$	16.8688	0.838216
$406$	3.68106	0.182688
$407$	−3.11058	−0.154186
$408$	10.6263	0.526081
$409$	−4.05604	−0.200558	−0.100279	−	0.994959i	$-0.531974\pi$
$409$	−4.05604	−0.200558	−0.100279	+	0.994959i	$0.531974\pi$
$410$	14.4830	0.715263
$411$	5.23095	0.258024
$412$	−9.79739	−0.482683
$413$	−13.7508	−0.676634
$414$	4.23103	0.207944
$415$	−11.0670	−0.543260
$416$	−1.42492	−0.0698623
$417$	35.5521	1.74100
$418$	3.19088	0.156071
$419$	6.03291	0.294727	0.147363	−	0.989082i	$-0.452921\pi$
$419$	6.03291	0.294727	0.147363	+	0.989082i	$0.452921\pi$
$420$	4.50218	0.219684
$421$	−28.9215	−1.40955	−0.704773	−	0.709433i	$-0.748951\pi$
$421$	−28.9215	−1.40955	−0.704773	+	0.709433i	$0.748951\pi$
$422$	−18.4369	−0.897496
$423$	1.79612	0.0873304
$424$	8.13008	0.394832
$425$	13.8994	0.674222
$426$	−5.05874	−0.245097
$427$	4.98212	0.241102
$428$	−11.0572	−0.534472
$429$	2.78722	0.134568
$430$	−1.75305	−0.0845398
$431$	18.0323	0.868585	0.434293	−	0.900772i	$-0.356998\pi$
$431$	18.0323	0.868585	0.434293	+	0.900772i	$0.356998\pi$
$432$	4.25213	0.204581
$433$	25.2180	1.21190	0.605949	−	0.795503i	$-0.292794\pi$
$433$	25.2180	1.21190	0.605949	+	0.795503i	$0.292794\pi$
$434$	1.01294	0.0486228
$435$	7.63765	0.366197
$436$	−5.76847	−0.276260
$437$	16.3412	0.781706
$438$	13.2425	0.632749
$439$	1.82930	0.0873077	0.0436539	−	0.999047i	$-0.486100\pi$
$439$	1.82930	0.0873077	0.0436539	+	0.999047i	$0.486100\pi$
$440$	−1.56251	−0.0744896
$441$	−3.99053	−0.190025
$442$	7.74086	0.368195
$443$	30.0581	1.42810	0.714052	−	0.700093i	$-0.246858\pi$
$443$	30.0581	1.42810	0.714052	+	0.700093i	$0.246858\pi$
$444$	6.08449	0.288757
$445$	−25.8260	−1.22427
$446$	−14.3742	−0.680640
$447$	−8.26613	−0.390974
$448$	1.47305	0.0695951
$449$	41.1261	1.94086	0.970431	−	0.241380i	$-0.0776001\pi$
$449$	41.1261	1.94086	0.970431	+	0.241380i	$0.0776001\pi$
$450$	−2.11383	−0.0996471
$451$	−9.26906	−0.436463
$452$	−16.5878	−0.780223
$453$	−19.6506	−0.923265
$454$	−1.26170	−0.0592147
$455$	3.27966	0.153753
$456$	−6.24156	−0.292288
$457$	40.6927	1.90352	0.951762	−	0.306836i	$-0.0992703\pi$
$457$	40.6927	1.90352	0.951762	+	0.306836i	$0.0992703\pi$
$458$	−20.4310	−0.954677
$459$	−23.0997	−1.07820
$460$	−8.00194	−0.373092
$461$	7.59610	0.353786	0.176893	−	0.984230i	$-0.443395\pi$
$461$	7.59610	0.353786	0.176893	+	0.984230i	$0.443395\pi$
$462$	−2.88138	−0.134054
$463$	25.4919	1.18471	0.592354	−	0.805677i	$-0.298199\pi$
$463$	25.4919	1.18471	0.592354	+	0.805677i	$0.298199\pi$
$464$	2.49894	0.116010
$465$	2.10170	0.0974641
$466$	1.21420	0.0562468
$467$	−27.9289	−1.29239	−0.646197	−	0.763170i	$-0.723642\pi$
$467$	−27.9289	−1.29239	−0.646197	+	0.763170i	$0.723642\pi$
$468$	−1.17723	−0.0544176
$469$	−5.61366	−0.259215
$470$	−3.39691	−0.156688
$471$	20.8555	0.960971
$472$	−9.33492	−0.429675
$473$	1.12195	0.0515873
$474$	−6.46511	−0.296952
$475$	−8.16410	−0.374595
$476$	−8.00236	−0.366787
$477$	6.71689	0.307545
$478$	−15.4043	−0.704578
$479$	−9.39973	−0.429485	−0.214742	−	0.976671i	$-0.568891\pi$
$479$	−9.39973	−0.429485	−0.214742	+	0.976671i	$0.568891\pi$
$480$	3.05636	0.139503
$481$	4.43232	0.202097
$482$	−26.9930	−1.22950
$483$	−14.7562	−0.671429
$484$	1.00000	0.0454545
$485$	13.6943	0.621826
$486$	8.36118	0.379271
$487$	26.9266	1.22016	0.610079	−	0.792340i	$-0.291138\pi$
$487$	26.9266	1.22016	0.610079	+	0.792340i	$0.291138\pi$
$488$	3.38218	0.153104
$489$	23.1137	1.04524
$490$	7.54710	0.340943
$491$	10.4586	0.471992	0.235996	−	0.971754i	$-0.424165\pi$
$491$	10.4586	0.471992	0.235996	+	0.971754i	$0.424165\pi$
$492$	18.1309	0.817402
$493$	−13.5755	−0.611409
$494$	−4.54674	−0.204568
$495$	−1.29091	−0.0580220
$496$	0.687649	0.0308763
$497$	3.80959	0.170883
$498$	−13.8545	−0.620837
$499$	30.3944	1.36064	0.680321	−	0.732915i	$-0.261841\pi$
$499$	30.3944	1.36064	0.680321	+	0.732915i	$0.261841\pi$
$500$	11.8103	0.528174
$501$	−36.2809	−1.62091
$502$	−18.7324	−0.836070
$503$	−18.7757	−0.837165	−0.418582	−	0.908179i	$-0.637473\pi$
$503$	−18.7757	−0.837165	−0.418582	+	0.908179i	$0.637473\pi$
$504$	1.21700	0.0542096
$505$	30.8076	1.37092
$506$	5.12122	0.227666
$507$	21.4572	0.952949
$508$	7.05596	0.313058
$509$	9.31083	0.412695	0.206348	−	0.978479i	$-0.433842\pi$
$509$	9.31083	0.412695	0.206348	+	0.978479i	$0.433842\pi$
$510$	−16.6037	−0.735223
$511$	−9.97249	−0.441157
$512$	1.00000	0.0441942
$513$	13.5680	0.599044
$514$	−26.2704	−1.15874
$515$	15.3085	0.674573
$516$	−2.19460	−0.0966120
$517$	2.17401	0.0956131
$518$	−4.58205	−0.201324
$519$	35.1588	1.54330
$520$	2.22644	0.0976360
$521$	19.9952	0.876006	0.438003	−	0.898974i	$-0.355686\pi$
$521$	19.9952	0.876006	0.438003	+	0.898974i	$0.355686\pi$
$522$	2.06456	0.0903635
$523$	−13.2117	−0.577709	−0.288854	−	0.957373i	$-0.593274\pi$
$523$	−13.2117	−0.577709	−0.288854	+	0.957373i	$0.593274\pi$
$524$	3.09254	0.135098
$525$	7.37222	0.321750
$526$	−4.97174	−0.216778
$527$	−3.73565	−0.162728
$528$	−1.95606	−0.0851267
$529$	3.22688	0.140299
$530$	−12.7033	−0.551797
$531$	−7.71230	−0.334685
$532$	4.70033	0.203785
$533$	13.2076	0.572086
$534$	−32.3309	−1.39910
$535$	17.2770	0.746951
$536$	−3.81090	−0.164606
$537$	31.3807	1.35418
$538$	16.8447	0.726227
$539$	−4.83012	−0.208048
$540$	−6.64399	−0.285912
$541$	9.36961	0.402831	0.201416	−	0.979506i	$-0.435446\pi$
$541$	9.36961	0.402831	0.201416	+	0.979506i	$0.435446\pi$
$542$	9.16999	0.393885
$543$	−4.58796	−0.196888
$544$	−5.43250	−0.232917
$545$	9.01328	0.386086
$546$	4.10573	0.175709
$547$	36.8478	1.57550	0.787749	−	0.615997i	$-0.211247\pi$
$547$	36.8478	1.57550	0.787749	+	0.615997i	$0.211247\pi$
$548$	−2.67423	−0.114237
$549$	2.79428	0.119257
$550$	−2.55857	−0.109098
$551$	7.97381	0.339696
$552$	−10.0174	−0.426370
$553$	4.86868	0.207037
$554$	28.9699	1.23081
$555$	−9.50707	−0.403552
$556$	−18.1754	−0.770807
$557$	14.1076	0.597759	0.298879	−	0.954291i	$-0.403387\pi$
$557$	14.1076	0.597759	0.298879	+	0.954291i	$0.403387\pi$
$558$	0.568120	0.0240504
$559$	−1.59868	−0.0676171
$560$	−2.30165	−0.0972626
$561$	10.6263	0.448643
$562$	0.632988	0.0267010
$563$	7.81036	0.329167	0.164584	−	0.986363i	$-0.447372\pi$
$563$	7.81036	0.329167	0.164584	+	0.986363i	$0.447372\pi$
$564$	−4.25251	−0.179063
$565$	25.9185	1.09040
$566$	−13.9530	−0.586488
$567$	−15.9030	−0.667864
$568$	2.58619	0.108514
$569$	−7.09978	−0.297638	−0.148819	−	0.988864i	$-0.547547\pi$
$569$	−7.09978	−0.297638	−0.148819	+	0.988864i	$0.547547\pi$
$570$	9.75248	0.408487
$571$	−1.21337	−0.0507778	−0.0253889	−	0.999678i	$-0.508082\pi$
$571$	−1.21337	−0.0507778	−0.0253889	+	0.999678i	$0.508082\pi$
$572$	−1.42492	−0.0595788
$573$	−22.3277	−0.932753
$574$	−13.6538	−0.569899
$575$	−13.1030	−0.546433
$576$	0.826177	0.0344241
$577$	33.6812	1.40216	0.701082	−	0.713080i	$-0.252701\pi$
$577$	33.6812	1.40216	0.701082	+	0.713080i	$0.252701\pi$
$578$	12.5121	0.520434
$579$	−14.0461	−0.583736
$580$	−3.90461	−0.162130
$581$	10.4334	0.432852
$582$	17.1435	0.710623
$583$	8.13008	0.336714
$584$	−6.76996	−0.280143
$585$	1.83944	0.0760513
$586$	14.9735	0.618549
$587$	14.4824	0.597751	0.298875	−	0.954292i	$-0.403389\pi$
$587$	14.4824	0.597751	0.298875	+	0.954292i	$0.403389\pi$
$588$	9.44801	0.389629
$589$	2.19421	0.0904107
$590$	14.5859	0.600491
$591$	1.95606	0.0804616
$592$	−3.11058	−0.127844
$593$	−3.55407	−0.145948	−0.0729742	−	0.997334i	$-0.523249\pi$
$593$	−3.55407	−0.145948	−0.0729742	+	0.997334i	$0.523249\pi$
$594$	4.25213	0.174467
$595$	12.5037	0.512603
$596$	4.22590	0.173100
$597$	15.6620	0.641005
$598$	−7.29731	−0.298409
$599$	−20.0122	−0.817678	−0.408839	−	0.912607i	$-0.634066\pi$
$599$	−20.0122	−0.817678	−0.408839	+	0.912607i	$0.634066\pi$
$600$	5.00472	0.204317
$601$	−14.4363	−0.588868	−0.294434	−	0.955672i	$-0.595131\pi$
$601$	−14.4363	−0.588868	−0.294434	+	0.955672i	$0.595131\pi$
$602$	1.65269	0.0673586
$603$	−3.14848	−0.128216
$604$	10.0460	0.408766
$605$	−1.56251	−0.0635249
$606$	38.5673	1.56669
$607$	−0.517211	−0.0209930	−0.0104965	−	0.999945i	$-0.503341\pi$
$607$	−0.517211	−0.0209930	−0.0104965	+	0.999945i	$0.503341\pi$
$608$	3.19088	0.129407
$609$	−7.20038	−0.291774
$610$	−5.28468	−0.213970
$611$	−3.09779	−0.125323
$612$	−4.48821	−0.181425
$613$	7.96751	0.321805	0.160902	−	0.986970i	$-0.448560\pi$
$613$	7.96751	0.321805	0.160902	+	0.986970i	$0.448560\pi$
$614$	−3.59920	−0.145252
$615$	−28.3296	−1.14236
$616$	1.47305	0.0593509
$617$	3.96338	0.159560	0.0797799	−	0.996813i	$-0.474578\pi$
$617$	3.96338	0.159560	0.0797799	+	0.996813i	$0.474578\pi$
$618$	19.1643	0.770901
$619$	−44.8214	−1.80152	−0.900762	−	0.434314i	$-0.856991\pi$
$619$	−44.8214	−1.80152	−0.900762	+	0.434314i	$0.856991\pi$
$620$	−1.07446	−0.0431512
$621$	21.7761	0.873845
$622$	1.03203	0.0413805
$623$	24.3474	0.975460
$624$	2.78722	0.111578
$625$	−5.66086	−0.226434
$626$	10.1250	0.404678
$627$	−6.24156	−0.249264
$628$	−10.6620	−0.425460
$629$	16.8983	0.673778
$630$	−1.90157	−0.0757605
$631$	35.7208	1.42202	0.711012	−	0.703180i	$-0.248237\pi$
$631$	35.7208	1.42202	0.711012	+	0.703180i	$0.248237\pi$
$632$	3.30517	0.131472
$633$	36.0638	1.43341
$634$	−10.7513	−0.426987
$635$	−11.0250	−0.437513
$636$	−15.9029	−0.630593
$637$	6.88252	0.272695
$638$	2.49894	0.0989338
$639$	2.13665	0.0845245
$640$	−1.56251	−0.0617635
$641$	−17.3106	−0.683729	−0.341864	−	0.939749i	$-0.611058\pi$
$641$	−17.3106	−0.683729	−0.341864	+	0.939749i	$0.611058\pi$
$642$	21.6287	0.853615
$643$	−33.9908	−1.34046	−0.670232	−	0.742151i	$-0.733806\pi$
$643$	−33.9908	−1.34046	−0.670232	+	0.742151i	$0.733806\pi$
$644$	7.54382	0.297268
$645$	3.42908	0.135020
$646$	−17.3345	−0.682016
$647$	16.9701	0.667164	0.333582	−	0.942721i	$-0.391743\pi$
$647$	16.9701	0.667164	0.333582	+	0.942721i	$0.391743\pi$
$648$	−10.7960	−0.424105
$649$	−9.33492	−0.366428
$650$	3.64575	0.142998
$651$	−1.98138	−0.0776563
$652$	−11.8164	−0.462767
$653$	−23.4561	−0.917909	−0.458955	−	0.888460i	$-0.651776\pi$
$653$	−23.4561	−0.917909	−0.458955	+	0.888460i	$0.651776\pi$
$654$	11.2835	0.441219
$655$	−4.83212	−0.188807
$656$	−9.26906	−0.361896
$657$	−5.59318	−0.218211
$658$	3.20244	0.124844
$659$	4.23456	0.164955	0.0824776	−	0.996593i	$-0.473717\pi$
$659$	4.23456	0.164955	0.0824776	+	0.996593i	$0.473717\pi$
$660$	3.05636	0.118969
$661$	−15.9777	−0.621459	−0.310729	−	0.950498i	$-0.600573\pi$
$661$	−15.9777	−0.621459	−0.310729	+	0.950498i	$0.600573\pi$
$662$	−14.1093	−0.548375
$663$	−15.1416	−0.588051
$664$	7.08287	0.274869
$665$	−7.34430	−0.284800
$666$	−2.56989	−0.0995814
$667$	12.7976	0.495525
$668$	18.5479	0.717641
$669$	28.1169	1.08706
$670$	5.95456	0.230045
$671$	3.38218	0.130567
$672$	−2.88138	−0.111152
$673$	−46.6285	−1.79740	−0.898699	−	0.438566i	$-0.855487\pi$
$673$	−46.6285	−1.79740	−0.898699	+	0.438566i	$0.855487\pi$
$674$	14.0990	0.543073
$675$	−10.8794	−0.418748
$676$	−10.9696	−0.421908
$677$	5.87617	0.225839	0.112920	−	0.993604i	$-0.463980\pi$
$677$	5.87617	0.225839	0.112920	+	0.993604i	$0.463980\pi$
$678$	32.4467	1.24611
$679$	−12.9103	−0.495451
$680$	8.48832	0.325512
$681$	2.46797	0.0945729
$682$	0.687649	0.0263314
$683$	33.4905	1.28148	0.640739	−	0.767759i	$-0.278628\pi$
$683$	33.4905	1.28148	0.640739	+	0.767759i	$0.278628\pi$
$684$	2.63623	0.100799
$685$	4.17850	0.159652
$686$	−17.4264	−0.665342
$687$	39.9643	1.52473
$688$	1.12195	0.0427739
$689$	−11.5847	−0.441341
$690$	15.6523	0.595872
$691$	−20.5879	−0.783202	−0.391601	−	0.920135i	$-0.628079\pi$
$691$	−20.5879	−0.783202	−0.391601	+	0.920135i	$0.628079\pi$
$692$	−17.9743	−0.683280
$693$	1.21700	0.0462301
$694$	−23.0460	−0.874813
$695$	28.3991	1.07724
$696$	−4.88807	−0.185282
$697$	50.3542	1.90730
$698$	−28.4009	−1.07499
$699$	−2.37505	−0.0898327
$700$	−3.76891	−0.142451
$701$	11.1495	0.421111	0.210555	−	0.977582i	$-0.432473\pi$
$701$	11.1495	0.421111	0.210555	+	0.977582i	$0.432473\pi$
$702$	−6.05893	−0.228680
$703$	−9.92551	−0.374348
$704$	1.00000	0.0376889
$705$	6.64457	0.250249
$706$	7.74380	0.291442
$707$	−29.0439	−1.09231
$708$	18.2597	0.686241
$709$	−16.4352	−0.617236	−0.308618	−	0.951186i	$-0.599866\pi$
$709$	−16.4352	−0.617236	−0.308618	+	0.951186i	$0.599866\pi$
$710$	−4.04094	−0.151654
$711$	2.73065	0.102407
$712$	16.5286	0.619434
$713$	3.52160	0.131885
$714$	15.6531	0.585803
$715$	2.22644	0.0832642
$716$	−16.0428	−0.599547
$717$	30.1318	1.12529
$718$	28.3589	1.05834
$719$	25.8771	0.965053	0.482526	−	0.875881i	$-0.339719\pi$
$719$	25.8771	0.965053	0.482526	+	0.875881i	$0.339719\pi$
$720$	−1.29091	−0.0481093
$721$	−14.4321	−0.537478
$722$	−8.81827	−0.328182
$723$	52.8000	1.96365
$724$	2.34551	0.0871701
$725$	−6.39371	−0.237456
$726$	−1.95606	−0.0725963
$727$	32.9366	1.22155	0.610775	−	0.791804i	$-0.290858\pi$
$727$	32.9366	1.22155	0.610775	+	0.791804i	$0.290858\pi$
$728$	−2.09898	−0.0777932
$729$	16.0329	0.593812
$730$	10.5781	0.391513
$731$	−6.09499	−0.225431
$732$	−6.61575	−0.244525
$733$	−14.1163	−0.521398	−0.260699	−	0.965420i	$-0.583953\pi$
$733$	−14.1163	−0.521398	−0.260699	+	0.965420i	$0.583953\pi$
$734$	−14.8459	−0.547971
$735$	−14.7626	−0.544526
$736$	5.12122	0.188771
$737$	−3.81090	−0.140376
$738$	−7.65789	−0.281891
$739$	−20.1536	−0.741362	−0.370681	−	0.928760i	$-0.620876\pi$
$739$	−20.1536	−0.741362	−0.370681	+	0.928760i	$0.620876\pi$
$740$	4.86031	0.178669
$741$	8.89370	0.326718
$742$	11.9760	0.439654
$743$	−44.3868	−1.62839	−0.814196	−	0.580590i	$-0.802822\pi$
$743$	−44.3868	−1.62839	−0.814196	+	0.580590i	$0.802822\pi$
$744$	−1.34508	−0.0493132
$745$	−6.60300	−0.241915
$746$	−15.7416	−0.576341
$747$	5.85171	0.214103
$748$	−5.43250	−0.198632
$749$	−16.2879	−0.595147
$750$	−23.1017	−0.843555
$751$	14.9056	0.543912	0.271956	−	0.962310i	$-0.412330\pi$
$751$	14.9056	0.543912	0.271956	+	0.962310i	$0.412330\pi$
$752$	2.17401	0.0792782
$753$	36.6418	1.33530
$754$	−3.56078	−0.129676
$755$	−15.6969	−0.571270
$756$	6.26361	0.227805
$757$	−47.6627	−1.73233	−0.866166	−	0.499757i	$-0.833423\pi$
$757$	−47.6627	−1.73233	−0.866166	+	0.499757i	$0.833423\pi$
$758$	−15.5411	−0.564478
$759$	−10.0174	−0.363609
$760$	−4.98578	−0.180853
$761$	0.251419	0.00911392	0.00455696	−	0.999990i	$-0.498549\pi$
$761$	0.251419	0.00911392	0.00455696	+	0.999990i	$0.498549\pi$
$762$	−13.8019	−0.499990
$763$	−8.49726	−0.307621
$764$	11.4146	0.412966
$765$	7.01286	0.253550
$766$	21.1001	0.762378
$767$	13.3015	0.480289
$768$	−1.95606	−0.0705833
$769$	−22.7737	−0.821241	−0.410620	−	0.911806i	$-0.634688\pi$
$769$	−22.7737	−0.821241	−0.410620	+	0.911806i	$0.634688\pi$
$770$	−2.30165	−0.0829458
$771$	51.3865	1.85064
$772$	7.18081	0.258443
$773$	−21.7595	−0.782634	−0.391317	−	0.920256i	$-0.627980\pi$
$773$	−21.7595	−0.782634	−0.391317	+	0.920256i	$0.627980\pi$
$774$	0.926929	0.0333178
$775$	−1.75940	−0.0631995
$776$	−8.76432	−0.314621
$777$	8.96277	0.321538
$778$	−4.84105	−0.173560
$779$	−29.5765	−1.05969
$780$	−4.35506	−0.155936
$781$	2.58619	0.0925411
$782$	−27.8210	−0.994878
$783$	10.6258	0.379735
$784$	−4.83012	−0.172504
$785$	16.6594	0.594601
$786$	−6.04921	−0.215768
$787$	−40.5105	−1.44404	−0.722022	−	0.691870i	$-0.756787\pi$
$787$	−40.5105	−1.44404	−0.722022	+	0.691870i	$0.756787\pi$
$788$	−1.00000	−0.0356235
$789$	9.72503	0.346220
$790$	−5.16434	−0.183739
$791$	−24.4346	−0.868796
$792$	0.826177	0.0293569
$793$	−4.81932	−0.171139
$794$	34.0232	1.20744
$795$	24.8485	0.881284
$796$	−8.00693	−0.283798
$797$	19.6098	0.694613	0.347307	−	0.937752i	$-0.387096\pi$
$797$	19.6098	0.694613	0.347307	+	0.937752i	$0.387096\pi$
$798$	−9.19414	−0.325469
$799$	−11.8103	−0.417820
$800$	−2.55857	−0.0904592
$801$	13.6555	0.482494
$802$	6.11489	0.215924
$803$	−6.76996	−0.238907
$804$	7.45436	0.262895
$805$	−11.7873	−0.415447
$806$	−0.979842	−0.0345135
$807$	−32.9493	−1.15987
$808$	−19.7168	−0.693635
$809$	12.9880	0.456635	0.228318	−	0.973587i	$-0.426678\pi$
$809$	12.9880	0.456635	0.228318	+	0.973587i	$0.426678\pi$
$810$	16.8688	0.592708
$811$	37.5380	1.31814	0.659068	−	0.752083i	$-0.270951\pi$
$811$	37.5380	1.31814	0.659068	+	0.752083i	$0.270951\pi$
$812$	3.68106	0.129180
$813$	−17.9371	−0.629080
$814$	−3.11058	−0.109026
$815$	18.4633	0.646740
$816$	10.6263	0.371995
$817$	3.58001	0.125249
$818$	−4.05604	−0.141816
$819$	−1.73413	−0.0605953
$820$	14.4830	0.505767
$821$	−21.3852	−0.746349	−0.373174	−	0.927761i	$-0.621731\pi$
$821$	−21.3852	−0.746349	−0.373174	+	0.927761i	$0.621731\pi$
$822$	5.23095	0.182450
$823$	16.5038	0.575285	0.287643	−	0.957738i	$-0.407129\pi$
$823$	16.5038	0.575285	0.287643	+	0.957738i	$0.407129\pi$
$824$	−9.79739	−0.341308
$825$	5.00472	0.174242
$826$	−13.7508	−0.478452
$827$	9.27612	0.322562	0.161281	−	0.986908i	$-0.448437\pi$
$827$	9.27612	0.322562	0.161281	+	0.986908i	$0.448437\pi$
$828$	4.23103	0.147039
$829$	45.7251	1.58810	0.794049	−	0.607854i	$-0.207969\pi$
$829$	45.7251	1.58810	0.794049	+	0.607854i	$0.207969\pi$
$830$	−11.0670	−0.384143
$831$	−56.6670	−1.96576
$832$	−1.42492	−0.0494001
$833$	26.2396	0.909149
$834$	35.5521	1.23107
$835$	−28.9813	−1.00294
$836$	3.19088	0.110359
$837$	2.92397	0.101067
$838$	6.03291	0.208403
$839$	19.7500	0.681845	0.340922	−	0.940091i	$-0.389261\pi$
$839$	19.7500	0.681845	0.340922	+	0.940091i	$0.389261\pi$
$840$	4.50218	0.155340
$841$	−22.7553	−0.784666
$842$	−28.9215	−0.996700
$843$	−1.23816	−0.0426447
$844$	−18.4369	−0.634625
$845$	17.1401	0.589637
$846$	1.79612	0.0617519
$847$	1.47305	0.0506146
$848$	8.13008	0.279188
$849$	27.2929	0.936691
$850$	13.8994	0.476747
$851$	−15.9300	−0.546073
$852$	−5.05874	−0.173310
$853$	33.7285	1.15484	0.577421	−	0.816446i	$-0.304059\pi$
$853$	33.7285	1.15484	0.577421	+	0.816446i	$0.304059\pi$
$854$	4.98212	0.170485
$855$	−4.11913	−0.140871
$856$	−11.0572	−0.377929
$857$	−21.5612	−0.736516	−0.368258	−	0.929724i	$-0.620046\pi$
$857$	−21.5612	−0.736516	−0.368258	+	0.929724i	$0.620046\pi$
$858$	2.78722	0.0951543
$859$	55.3260	1.88770	0.943850	−	0.330375i	$-0.107175\pi$
$859$	55.3260	1.88770	0.943850	+	0.330375i	$0.107175\pi$
$860$	−1.75305	−0.0597786
$861$	26.7077	0.910196
$862$	18.0323	0.614183
$863$	−32.7425	−1.11457	−0.557284	−	0.830322i	$-0.688157\pi$
$863$	−32.7425	−1.11457	−0.557284	+	0.830322i	$0.688157\pi$
$864$	4.25213	0.144660
$865$	28.0850	0.954917
$866$	25.2180	0.856941
$867$	−24.4744	−0.831194
$868$	1.01294	0.0343815
$869$	3.30517	0.112120
$870$	7.63765	0.258941
$871$	5.43022	0.183996
$872$	−5.76847	−0.195345
$873$	−7.24088	−0.245067
$874$	16.3412	0.552749
$875$	17.3972	0.588133
$876$	13.2425	0.447421
$877$	−48.2627	−1.62971	−0.814857	−	0.579662i	$-0.803185\pi$
$877$	−48.2627	−1.62971	−0.814857	+	0.579662i	$0.803185\pi$
$878$	1.82930	0.0617359
$879$	−29.2891	−0.987896
$880$	−1.56251	−0.0526721
$881$	−23.6360	−0.796318	−0.398159	−	0.917316i	$-0.630351\pi$
$881$	−23.6360	−0.796318	−0.398159	+	0.917316i	$0.630351\pi$
$882$	−3.99053	−0.134368
$883$	6.35187	0.213757	0.106879	−	0.994272i	$-0.465914\pi$
$883$	6.35187	0.213757	0.106879	+	0.994272i	$0.465914\pi$
$884$	7.74086	0.260353
$885$	−28.5309	−0.959055
$886$	30.0581	1.00982
$887$	51.4619	1.72792	0.863961	−	0.503559i	$-0.167976\pi$
$887$	51.4619	1.72792	0.863961	+	0.503559i	$0.167976\pi$
$888$	6.08449	0.204182
$889$	10.3938	0.348597
$890$	−25.8260	−0.865690
$891$	−10.7960	−0.361678
$892$	−14.3742	−0.481285
$893$	6.93702	0.232139
$894$	−8.26613	−0.276461
$895$	25.0670	0.837896
$896$	1.47305	0.0492112
$897$	14.2740	0.476595
$898$	41.1261	1.37240
$899$	1.71839	0.0573115
$900$	−2.11383	−0.0704611
$901$	−44.1667	−1.47141
$902$	−9.26906	−0.308626
$903$	−3.23276	−0.107580
$904$	−16.5878	−0.551701
$905$	−3.66487	−0.121824
$906$	−19.6506	−0.652847
$907$	−14.7899	−0.491091	−0.245546	−	0.969385i	$-0.578967\pi$
$907$	−14.7899	−0.491091	−0.245546	+	0.969385i	$0.578967\pi$
$908$	−1.26170	−0.0418711
$909$	−16.2896	−0.540291
$910$	3.27966	0.108720
$911$	−50.2089	−1.66350	−0.831748	−	0.555154i	$-0.812659\pi$
$911$	−50.2089	−1.66350	−0.831748	+	0.555154i	$0.812659\pi$
$912$	−6.24156	−0.206679
$913$	7.08287	0.234409
$914$	40.6927	1.34600
$915$	10.3372	0.341736
$916$	−20.4310	−0.675059
$917$	4.55548	0.150435
$918$	−23.0997	−0.762404
$919$	−13.1758	−0.434630	−0.217315	−	0.976102i	$-0.569730\pi$
$919$	−13.1758	−0.434630	−0.217315	+	0.976102i	$0.569730\pi$
$920$	−8.00194	−0.263816
$921$	7.04025	0.231984
$922$	7.59610	0.250164
$923$	−3.68510	−0.121297
$924$	−2.88138	−0.0947904
$925$	7.95865	0.261679
$926$	25.4919	0.837716
$927$	−8.09438	−0.265854
$928$	2.49894	0.0820316
$929$	40.7783	1.33789	0.668946	−	0.743311i	$-0.266746\pi$
$929$	40.7783	1.33789	0.668946	+	0.743311i	$0.266746\pi$
$930$	2.10170	0.0689176
$931$	−15.4123	−0.505119
$932$	1.21420	0.0397725
$933$	−2.01871	−0.0660895
$934$	−27.9289	−0.913861
$935$	8.48832	0.277598
$936$	−1.17723	−0.0384791
$937$	−10.2149	−0.333706	−0.166853	−	0.985982i	$-0.553361\pi$
$937$	−10.2149	−0.333706	−0.166853	+	0.985982i	$0.553361\pi$
$938$	−5.61366	−0.183292
$939$	−19.8052	−0.646319
$940$	−3.39691	−0.110795
$941$	10.1842	0.331994	0.165997	−	0.986126i	$-0.446916\pi$
$941$	10.1842	0.331994	0.165997	+	0.986126i	$0.446916\pi$
$942$	20.8555	0.679509
$943$	−47.4689	−1.54580
$944$	−9.33492	−0.303826
$945$	−9.78693	−0.318369
$946$	1.12195	0.0364777
$947$	49.1407	1.59686	0.798429	−	0.602089i	$-0.205665\pi$
$947$	49.1407	1.59686	0.798429	+	0.602089i	$0.205665\pi$
$948$	−6.46511	−0.209977
$949$	9.64662	0.313143
$950$	−8.16410	−0.264878
$951$	21.0301	0.681949
$952$	−8.00236	−0.259358
$953$	50.9001	1.64882	0.824408	−	0.565996i	$-0.191508\pi$
$953$	50.9001	1.64882	0.824408	+	0.565996i	$0.191508\pi$
$954$	6.71689	0.217467
$955$	−17.8354	−0.577141
$956$	−15.4043	−0.498212
$957$	−4.88807	−0.158009
$958$	−9.39973	−0.303692
$959$	−3.93927	−0.127206
$960$	3.05636	0.0986436
$961$	−30.5271	−0.984746
$962$	4.43232	0.142904
$963$	−9.13525	−0.294379
$964$	−26.9930	−0.869386
$965$	−11.2201	−0.361187
$966$	−14.7562	−0.474772
$967$	5.87717	0.188997	0.0944986	−	0.995525i	$-0.469875\pi$
$967$	5.87717	0.188997	0.0944986	+	0.995525i	$0.469875\pi$
$968$	1.00000	0.0321412
$969$	33.9073	1.08926
$970$	13.6943	0.439698
$971$	−44.8411	−1.43902	−0.719509	−	0.694483i	$-0.755633\pi$
$971$	−44.8411	−1.43902	−0.719509	+	0.694483i	$0.755633\pi$
$972$	8.36118	0.268185
$973$	−26.7733	−0.858311
$974$	26.9266	0.862783
$975$	−7.13131	−0.228385
$976$	3.38218	0.108261
$977$	55.2302	1.76697	0.883486	−	0.468458i	$-0.155190\pi$
$977$	55.2302	1.76697	0.883486	+	0.468458i	$0.155190\pi$
$978$	23.1137	0.739093
$979$	16.5286	0.528255
$980$	7.54710	0.241083
$981$	−4.76578	−0.152160
$982$	10.4586	0.333749
$983$	59.1157	1.88550	0.942750	−	0.333501i	$-0.108230\pi$
$983$	59.1157	1.88550	0.942750	+	0.333501i	$0.108230\pi$
$984$	18.1309	0.577991
$985$	1.56251	0.0497856
$986$	−13.5755	−0.432331
$987$	−6.26416	−0.199390
$988$	−4.54674	−0.144651
$989$	5.74575	0.182704
$990$	−1.29091	−0.0410277
$991$	12.1990	0.387512	0.193756	−	0.981050i	$-0.437933\pi$
$991$	12.1990	0.387512	0.193756	+	0.981050i	$0.437933\pi$
$992$	0.687649	0.0218329
$993$	27.5987	0.875819
$994$	3.80959	0.120833
$995$	12.5109	0.396622
$996$	−13.8545	−0.438998
$997$	15.4458	0.489174	0.244587	−	0.969627i	$-0.421348\pi$
$997$	15.4458	0.489174	0.244587	+	0.969627i	$0.421348\pi$
$998$	30.3944	0.962119
$999$	−13.2266	−0.418471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.b.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.b.1.6	✓	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.95606 q^{3} +1.00000 q^{4} -1.56251 q^{5} -1.95606 q^{6} +1.47305 q^{7} +1.00000 q^{8} +0.826177 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.95606 q^{3} +1.00000 q^{4} -1.56251 q^{5} -1.95606 q^{6} +1.47305 q^{7} +1.00000 q^{8} +0.826177 q^{9} -1.56251 q^{10} +1.00000 q^{11} -1.95606 q^{12} -1.42492 q^{13} +1.47305 q^{14} +3.05636 q^{15} +1.00000 q^{16} -5.43250 q^{17} +0.826177 q^{18} +3.19088 q^{19} -1.56251 q^{20} -2.88138 q^{21} +1.00000 q^{22} +5.12122 q^{23} -1.95606 q^{24} -2.55857 q^{25} -1.42492 q^{26} +4.25213 q^{27} +1.47305 q^{28} +2.49894 q^{29} +3.05636 q^{30} +0.687649 q^{31} +1.00000 q^{32} -1.95606 q^{33} -5.43250 q^{34} -2.30165 q^{35} +0.826177 q^{36} -3.11058 q^{37} +3.19088 q^{38} +2.78722 q^{39} -1.56251 q^{40} -9.26906 q^{41} -2.88138 q^{42} +1.12195 q^{43} +1.00000 q^{44} -1.29091 q^{45} +5.12122 q^{46} +2.17401 q^{47} -1.95606 q^{48} -4.83012 q^{49} -2.55857 q^{50} +10.6263 q^{51} -1.42492 q^{52} +8.13008 q^{53} +4.25213 q^{54} -1.56251 q^{55} +1.47305 q^{56} -6.24156 q^{57} +2.49894 q^{58} -9.33492 q^{59} +3.05636 q^{60} +3.38218 q^{61} +0.687649 q^{62} +1.21700 q^{63} +1.00000 q^{64} +2.22644 q^{65} -1.95606 q^{66} -3.81090 q^{67} -5.43250 q^{68} -10.0174 q^{69} -2.30165 q^{70} +2.58619 q^{71} +0.826177 q^{72} -6.76996 q^{73} -3.11058 q^{74} +5.00472 q^{75} +3.19088 q^{76} +1.47305 q^{77} +2.78722 q^{78} +3.30517 q^{79} -1.56251 q^{80} -10.7960 q^{81} -9.26906 q^{82} +7.08287 q^{83} -2.88138 q^{84} +8.48832 q^{85} +1.12195 q^{86} -4.88807 q^{87} +1.00000 q^{88} +16.5286 q^{89} -1.29091 q^{90} -2.09898 q^{91} +5.12122 q^{92} -1.34508 q^{93} +2.17401 q^{94} -4.98578 q^{95} -1.95606 q^{96} -8.76432 q^{97} -4.83012 q^{98} +0.826177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

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