LMFDB - Embedded newform 8034.2.a.bb.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-3.07028$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.07028 q^{5} -1.00000 q^{6} -1.20257 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.07028 q^{5} -1.00000 q^{6} -1.20257 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.07028 q^{10} +1.64327 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.20257 q^{14} +3.07028 q^{15} +1.00000 q^{16} +5.16756 q^{17} -1.00000 q^{18} -6.97237 q^{19} +3.07028 q^{20} -1.20257 q^{21} -1.64327 q^{22} -4.45098 q^{23} -1.00000 q^{24} +4.42660 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.20257 q^{28} -5.46012 q^{29} -3.07028 q^{30} -0.105312 q^{31} -1.00000 q^{32} +1.64327 q^{33} -5.16756 q^{34} -3.69223 q^{35} +1.00000 q^{36} -4.85429 q^{37} +6.97237 q^{38} -1.00000 q^{39} -3.07028 q^{40} -1.62153 q^{41} +1.20257 q^{42} -12.7227 q^{43} +1.64327 q^{44} +3.07028 q^{45} +4.45098 q^{46} -9.64077 q^{47} +1.00000 q^{48} -5.55382 q^{49} -4.42660 q^{50} +5.16756 q^{51} -1.00000 q^{52} -8.08025 q^{53} -1.00000 q^{54} +5.04531 q^{55} +1.20257 q^{56} -6.97237 q^{57} +5.46012 q^{58} -4.90361 q^{59} +3.07028 q^{60} -2.19611 q^{61} +0.105312 q^{62} -1.20257 q^{63} +1.00000 q^{64} -3.07028 q^{65} -1.64327 q^{66} -15.1928 q^{67} +5.16756 q^{68} -4.45098 q^{69} +3.69223 q^{70} +12.9797 q^{71} -1.00000 q^{72} +0.0855982 q^{73} +4.85429 q^{74} +4.42660 q^{75} -6.97237 q^{76} -1.97615 q^{77} +1.00000 q^{78} -11.5359 q^{79} +3.07028 q^{80} +1.00000 q^{81} +1.62153 q^{82} +5.79368 q^{83} -1.20257 q^{84} +15.8658 q^{85} +12.7227 q^{86} -5.46012 q^{87} -1.64327 q^{88} +4.12175 q^{89} -3.07028 q^{90} +1.20257 q^{91} -4.45098 q^{92} -0.105312 q^{93} +9.64077 q^{94} -21.4071 q^{95} -1.00000 q^{96} -3.96607 q^{97} +5.55382 q^{98} +1.64327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.07028	1.37307	0.686535	−	0.727097i	$-0.259131\pi$
$5$	3.07028	1.37307	0.686535	+	0.727097i	$0.259131\pi$
$6$	−1.00000	−0.408248
$7$	−1.20257	−0.454529	−0.227265	−	0.973833i	$-0.572978\pi$
$7$	−1.20257	−0.454529	−0.227265	+	0.973833i	$0.572978\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.07028	−0.970907
$11$	1.64327	0.495466	0.247733	−	0.968828i	$-0.420314\pi$
$11$	1.64327	0.495466	0.247733	+	0.968828i	$0.420314\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.20257	0.321401
$15$	3.07028	0.792742
$16$	1.00000	0.250000
$17$	5.16756	1.25332	0.626659	−	0.779294i	$-0.284422\pi$
$17$	5.16756	1.25332	0.626659	+	0.779294i	$0.284422\pi$
$18$	−1.00000	−0.235702
$19$	−6.97237	−1.59957	−0.799786	−	0.600286i	$-0.795054\pi$
$19$	−6.97237	−1.59957	−0.799786	+	0.600286i	$0.795054\pi$
$20$	3.07028	0.686535
$21$	−1.20257	−0.262423
$22$	−1.64327	−0.350347
$23$	−4.45098	−0.928094	−0.464047	−	0.885811i	$-0.653603\pi$
$23$	−4.45098	−0.928094	−0.464047	+	0.885811i	$0.653603\pi$
$24$	−1.00000	−0.204124
$25$	4.42660	0.885320
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−1.20257	−0.227265
$29$	−5.46012	−1.01392	−0.506959	−	0.861970i	$-0.669231\pi$
$29$	−5.46012	−1.01392	−0.506959	+	0.861970i	$0.669231\pi$
$30$	−3.07028	−0.560553
$31$	−0.105312	−0.0189146	−0.00945731	−	0.999955i	$-0.503010\pi$
$31$	−0.105312	−0.0189146	−0.00945731	+	0.999955i	$0.503010\pi$
$32$	−1.00000	−0.176777
$33$	1.64327	0.286057
$34$	−5.16756	−0.886230
$35$	−3.69223	−0.624101
$36$	1.00000	0.166667
$37$	−4.85429	−0.798040	−0.399020	−	0.916942i	$-0.630650\pi$
$37$	−4.85429	−0.798040	−0.399020	+	0.916942i	$0.630650\pi$
$38$	6.97237	1.13107
$39$	−1.00000	−0.160128
$40$	−3.07028	−0.485453
$41$	−1.62153	−0.253240	−0.126620	−	0.991951i	$-0.540413\pi$
$41$	−1.62153	−0.253240	−0.126620	+	0.991951i	$0.540413\pi$
$42$	1.20257	0.185561
$43$	−12.7227	−1.94020	−0.970100	−	0.242707i	$-0.921964\pi$
$43$	−12.7227	−1.94020	−0.970100	+	0.242707i	$0.921964\pi$
$44$	1.64327	0.247733
$45$	3.07028	0.457690
$46$	4.45098	0.656261
$47$	−9.64077	−1.40625	−0.703126	−	0.711066i	$-0.748213\pi$
$47$	−9.64077	−1.40625	−0.703126	+	0.711066i	$0.748213\pi$
$48$	1.00000	0.144338
$49$	−5.55382	−0.793403
$50$	−4.42660	−0.626016
$51$	5.16756	0.723603
$52$	−1.00000	−0.138675
$53$	−8.08025	−1.10991	−0.554954	−	0.831881i	$-0.687264\pi$
$53$	−8.08025	−1.10991	−0.554954	+	0.831881i	$0.687264\pi$
$54$	−1.00000	−0.136083
$55$	5.04531	0.680309
$56$	1.20257	0.160700
$57$	−6.97237	−0.923513
$58$	5.46012	0.716949
$59$	−4.90361	−0.638396	−0.319198	−	0.947688i	$-0.603413\pi$
$59$	−4.90361	−0.638396	−0.319198	+	0.947688i	$0.603413\pi$
$60$	3.07028	0.396371
$61$	−2.19611	−0.281184	−0.140592	−	0.990068i	$-0.544901\pi$
$61$	−2.19611	−0.281184	−0.140592	+	0.990068i	$0.544901\pi$
$62$	0.105312	0.0133747
$63$	−1.20257	−0.151510
$64$	1.00000	0.125000
$65$	−3.07028	−0.380821
$66$	−1.64327	−0.202273
$67$	−15.1928	−1.85609	−0.928047	−	0.372463i	$-0.878513\pi$
$67$	−15.1928	−1.85609	−0.928047	+	0.372463i	$0.878513\pi$
$68$	5.16756	0.626659
$69$	−4.45098	−0.535835
$70$	3.69223	0.441306
$71$	12.9797	1.54040	0.770201	−	0.637801i	$-0.220156\pi$
$71$	12.9797	1.54040	0.770201	+	0.637801i	$0.220156\pi$
$72$	−1.00000	−0.117851
$73$	0.0855982	0.0100185	0.00500925	−	0.999987i	$-0.498405\pi$
$73$	0.0855982	0.0100185	0.00500925	+	0.999987i	$0.498405\pi$
$74$	4.85429	0.564300
$75$	4.42660	0.511140
$76$	−6.97237	−0.799786
$77$	−1.97615	−0.225204
$78$	1.00000	0.113228
$79$	−11.5359	−1.29789	−0.648943	−	0.760837i	$-0.724789\pi$
$79$	−11.5359	−1.29789	−0.648943	+	0.760837i	$0.724789\pi$
$80$	3.07028	0.343267
$81$	1.00000	0.111111
$82$	1.62153	0.179068
$83$	5.79368	0.635939	0.317970	−	0.948101i	$-0.396999\pi$
$83$	5.79368	0.635939	0.317970	+	0.948101i	$0.396999\pi$
$84$	−1.20257	−0.131211
$85$	15.8658	1.72089
$86$	12.7227	1.37193
$87$	−5.46012	−0.585386
$88$	−1.64327	−0.175174
$89$	4.12175	0.436905	0.218452	−	0.975848i	$-0.429899\pi$
$89$	4.12175	0.436905	0.218452	+	0.975848i	$0.429899\pi$
$90$	−3.07028	−0.323636
$91$	1.20257	0.126064
$92$	−4.45098	−0.464047
$93$	−0.105312	−0.0109204
$94$	9.64077	0.994370
$95$	−21.4071	−2.19632
$96$	−1.00000	−0.102062
$97$	−3.96607	−0.402694	−0.201347	−	0.979520i	$-0.564532\pi$
$97$	−3.96607	−0.402694	−0.201347	+	0.979520i	$0.564532\pi$
$98$	5.55382	0.561021
$99$	1.64327	0.165155
$100$	4.42660	0.442660
$101$	5.55432	0.552675	0.276338	−	0.961061i	$-0.410879\pi$
$101$	5.55432	0.552675	0.276338	+	0.961061i	$0.410879\pi$
$102$	−5.16756	−0.511665
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−3.69223	−0.360325
$106$	8.08025	0.784824
$107$	3.11236	0.300883	0.150442	−	0.988619i	$-0.451930\pi$
$107$	3.11236	0.300883	0.150442	+	0.988619i	$0.451930\pi$
$108$	1.00000	0.0962250
$109$	−10.7609	−1.03070	−0.515352	−	0.856978i	$-0.672339\pi$
$109$	−10.7609	−1.03070	−0.515352	+	0.856978i	$0.672339\pi$
$110$	−5.04531	−0.481051
$111$	−4.85429	−0.460749
$112$	−1.20257	−0.113632
$113$	20.4678	1.92545	0.962726	−	0.270480i	$-0.0871823\pi$
$113$	20.4678	1.92545	0.962726	+	0.270480i	$0.0871823\pi$
$114$	6.97237	0.653022
$115$	−13.6657	−1.27434
$116$	−5.46012	−0.506959
$117$	−1.00000	−0.0924500
$118$	4.90361	0.451414
$119$	−6.21437	−0.569670
$120$	−3.07028	−0.280277
$121$	−8.29965	−0.754514
$122$	2.19611	0.198827
$123$	−1.62153	−0.146208
$124$	−0.105312	−0.00945731
$125$	−1.76049	−0.157463
$126$	1.20257	0.107134
$127$	11.0748	0.982728	0.491364	−	0.870954i	$-0.336498\pi$
$127$	11.0748	0.982728	0.491364	+	0.870954i	$0.336498\pi$
$128$	−1.00000	−0.0883883
$129$	−12.7227	−1.12017
$130$	3.07028	0.269281
$131$	−4.30992	−0.376560	−0.188280	−	0.982115i	$-0.560291\pi$
$131$	−4.30992	−0.376560	−0.188280	+	0.982115i	$0.560291\pi$
$132$	1.64327	0.143029
$133$	8.38478	0.727052
$134$	15.1928	1.31246
$135$	3.07028	0.264247
$136$	−5.16756	−0.443115
$137$	2.72360	0.232693	0.116346	−	0.993209i	$-0.462882\pi$
$137$	2.72360	0.232693	0.116346	+	0.993209i	$0.462882\pi$
$138$	4.45098	0.378893
$139$	12.1741	1.03259	0.516296	−	0.856410i	$-0.327311\pi$
$139$	12.1741	1.03259	0.516296	+	0.856410i	$0.327311\pi$
$140$	−3.69223	−0.312050
$141$	−9.64077	−0.811899
$142$	−12.9797	−1.08923
$143$	−1.64327	−0.137417
$144$	1.00000	0.0833333
$145$	−16.7641	−1.39218
$146$	−0.0855982	−0.00708416
$147$	−5.55382	−0.458071
$148$	−4.85429	−0.399020
$149$	−11.2270	−0.919751	−0.459875	−	0.887984i	$-0.652106\pi$
$149$	−11.2270	−0.919751	−0.459875	+	0.887984i	$0.652106\pi$
$150$	−4.42660	−0.361431
$151$	−11.9752	−0.974529	−0.487265	−	0.873254i	$-0.662005\pi$
$151$	−11.9752	−0.974529	−0.487265	+	0.873254i	$0.662005\pi$
$152$	6.97237	0.565534
$153$	5.16756	0.417773
$154$	1.97615	0.159243
$155$	−0.323338	−0.0259711
$156$	−1.00000	−0.0800641
$157$	9.53725	0.761156	0.380578	−	0.924749i	$-0.375725\pi$
$157$	9.53725	0.761156	0.380578	+	0.924749i	$0.375725\pi$
$158$	11.5359	0.917744
$159$	−8.08025	−0.640806
$160$	−3.07028	−0.242727
$161$	5.35263	0.421846
$162$	−1.00000	−0.0785674
$163$	17.6275	1.38070	0.690348	−	0.723477i	$-0.257457\pi$
$163$	17.6275	1.38070	0.690348	+	0.723477i	$0.257457\pi$
$164$	−1.62153	−0.126620
$165$	5.04531	0.392776
$166$	−5.79368	−0.449677
$167$	−19.3747	−1.49926	−0.749630	−	0.661857i	$-0.769769\pi$
$167$	−19.3747	−1.49926	−0.749630	+	0.661857i	$0.769769\pi$
$168$	1.20257	0.0927804
$169$	1.00000	0.0769231
$170$	−15.8658	−1.21686
$171$	−6.97237	−0.533190
$172$	−12.7227	−0.970100
$173$	18.6200	1.41565	0.707827	−	0.706386i	$-0.249675\pi$
$173$	18.6200	1.41565	0.707827	+	0.706386i	$0.249675\pi$
$174$	5.46012	0.413931
$175$	−5.32331	−0.402404
$176$	1.64327	0.123866
$177$	−4.90361	−0.368578
$178$	−4.12175	−0.308938
$179$	−1.68183	−0.125706	−0.0628528	−	0.998023i	$-0.520020\pi$
$179$	−1.68183	−0.125706	−0.0628528	+	0.998023i	$0.520020\pi$
$180$	3.07028	0.228845
$181$	0.182749	0.0135836	0.00679182	−	0.999977i	$-0.497838\pi$
$181$	0.182749	0.0135836	0.00679182	+	0.999977i	$0.497838\pi$
$182$	−1.20257	−0.0891406
$183$	−2.19611	−0.162341
$184$	4.45098	0.328131
$185$	−14.9040	−1.09577
$186$	0.105312	0.00772186
$187$	8.49172	0.620976
$188$	−9.64077	−0.703126
$189$	−1.20257	−0.0874742
$190$	21.4071	1.55303
$191$	10.0979	0.730660	0.365330	−	0.930878i	$-0.380956\pi$
$191$	10.0979	0.730660	0.365330	+	0.930878i	$0.380956\pi$
$192$	1.00000	0.0721688
$193$	17.7644	1.27871	0.639354	−	0.768913i	$-0.279202\pi$
$193$	17.7644	1.27871	0.639354	+	0.768913i	$0.279202\pi$
$194$	3.96607	0.284747
$195$	−3.07028	−0.219867
$196$	−5.55382	−0.396701
$197$	13.3735	0.952821	0.476410	−	0.879223i	$-0.341938\pi$
$197$	13.3735	0.952821	0.476410	+	0.879223i	$0.341938\pi$
$198$	−1.64327	−0.116782
$199$	9.16019	0.649348	0.324674	−	0.945826i	$-0.394745\pi$
$199$	9.16019	0.649348	0.324674	+	0.945826i	$0.394745\pi$
$200$	−4.42660	−0.313008
$201$	−15.1928	−1.07162
$202$	−5.55432	−0.390800
$203$	6.56619	0.460856
$204$	5.16756	0.361802
$205$	−4.97853	−0.347716
$206$	−1.00000	−0.0696733
$207$	−4.45098	−0.309365
$208$	−1.00000	−0.0693375
$209$	−11.4575	−0.792533
$210$	3.69223	0.254788
$211$	−24.9722	−1.71915	−0.859577	−	0.511006i	$-0.829273\pi$
$211$	−24.9722	−1.71915	−0.859577	+	0.511006i	$0.829273\pi$
$212$	−8.08025	−0.554954
$213$	12.9797	0.889351
$214$	−3.11236	−0.212757
$215$	−39.0623	−2.66403
$216$	−1.00000	−0.0680414
$217$	0.126645	0.00859726
$218$	10.7609	0.728818
$219$	0.0855982	0.00578419
$220$	5.04531	0.340154
$221$	−5.16756	−0.347608
$222$	4.85429	0.325799
$223$	19.9780	1.33782	0.668912	−	0.743341i	$-0.266760\pi$
$223$	19.9780	1.33782	0.668912	+	0.743341i	$0.266760\pi$
$224$	1.20257	0.0803502
$225$	4.42660	0.295107
$226$	−20.4678	−1.36150
$227$	−7.71833	−0.512283	−0.256142	−	0.966639i	$-0.582451\pi$
$227$	−7.71833	−0.512283	−0.256142	+	0.966639i	$0.582451\pi$
$228$	−6.97237	−0.461756
$229$	16.6721	1.10172	0.550862	−	0.834596i	$-0.314299\pi$
$229$	16.6721	1.10172	0.550862	+	0.834596i	$0.314299\pi$
$230$	13.6657	0.901093
$231$	−1.97615	−0.130021
$232$	5.46012	0.358474
$233$	10.8908	0.713481	0.356740	−	0.934204i	$-0.383888\pi$
$233$	10.8908	0.713481	0.356740	+	0.934204i	$0.383888\pi$
$234$	1.00000	0.0653720
$235$	−29.5998	−1.93088
$236$	−4.90361	−0.319198
$237$	−11.5359	−0.749335
$238$	6.21437	0.402817
$239$	−22.7544	−1.47186	−0.735929	−	0.677058i	$-0.763254\pi$
$239$	−22.7544	−1.47186	−0.735929	+	0.677058i	$0.763254\pi$
$240$	3.07028	0.198186
$241$	18.4300	1.18718	0.593592	−	0.804766i	$-0.297709\pi$
$241$	18.4300	1.18718	0.593592	+	0.804766i	$0.297709\pi$
$242$	8.29965	0.533522
$243$	1.00000	0.0641500
$244$	−2.19611	−0.140592
$245$	−17.0518	−1.08940
$246$	1.62153	0.103385
$247$	6.97237	0.443641
$248$	0.105312	0.00668733
$249$	5.79368	0.367160
$250$	1.76049	0.111343
$251$	3.06979	0.193763	0.0968816	−	0.995296i	$-0.469113\pi$
$251$	3.06979	0.193763	0.0968816	+	0.995296i	$0.469113\pi$
$252$	−1.20257	−0.0757549
$253$	−7.31418	−0.459839
$254$	−11.0748	−0.694894
$255$	15.8658	0.993558
$256$	1.00000	0.0625000
$257$	−6.34044	−0.395506	−0.197753	−	0.980252i	$-0.563364\pi$
$257$	−6.34044	−0.395506	−0.197753	+	0.980252i	$0.563364\pi$
$258$	12.7227	0.792083
$259$	5.83763	0.362733
$260$	−3.07028	−0.190411
$261$	−5.46012	−0.337973
$262$	4.30992	0.266268
$263$	3.14227	0.193761	0.0968803	−	0.995296i	$-0.469114\pi$
$263$	3.14227	0.193761	0.0968803	+	0.995296i	$0.469114\pi$
$264$	−1.64327	−0.101136
$265$	−24.8086	−1.52398
$266$	−8.38478	−0.514104
$267$	4.12175	0.252247
$268$	−15.1928	−0.928047
$269$	11.5731	0.705622	0.352811	−	0.935695i	$-0.385226\pi$
$269$	11.5731	0.705622	0.352811	+	0.935695i	$0.385226\pi$
$270$	−3.07028	−0.186851
$271$	6.67362	0.405394	0.202697	−	0.979242i	$-0.435029\pi$
$271$	6.67362	0.405394	0.202697	+	0.979242i	$0.435029\pi$
$272$	5.16756	0.313329
$273$	1.20257	0.0727830
$274$	−2.72360	−0.164539
$275$	7.27412	0.438646
$276$	−4.45098	−0.267918
$277$	17.7381	1.06578	0.532891	−	0.846184i	$-0.321106\pi$
$277$	17.7381	1.06578	0.532891	+	0.846184i	$0.321106\pi$
$278$	−12.1741	−0.730152
$279$	−0.105312	−0.00630488
$280$	3.69223	0.220653
$281$	−5.19281	−0.309777	−0.154889	−	0.987932i	$-0.549502\pi$
$281$	−5.19281	−0.309777	−0.154889	+	0.987932i	$0.549502\pi$
$282$	9.64077	0.574100
$283$	−20.2995	−1.20668	−0.603341	−	0.797484i	$-0.706164\pi$
$283$	−20.2995	−1.20668	−0.603341	+	0.797484i	$0.706164\pi$
$284$	12.9797	0.770201
$285$	−21.4071	−1.26805
$286$	1.64327	0.0971688
$287$	1.95000	0.115105
$288$	−1.00000	−0.0589256
$289$	9.70370	0.570806
$290$	16.7641	0.984421
$291$	−3.96607	−0.232495
$292$	0.0855982	0.00500925
$293$	−19.9094	−1.16312	−0.581561	−	0.813503i	$-0.697558\pi$
$293$	−19.9094	−1.16312	−0.581561	+	0.813503i	$0.697558\pi$
$294$	5.55382	0.323905
$295$	−15.0554	−0.876562
$296$	4.85429	0.282150
$297$	1.64327	0.0953524
$298$	11.2270	0.650362
$299$	4.45098	0.257407
$300$	4.42660	0.255570
$301$	15.3000	0.881878
$302$	11.9752	0.689096
$303$	5.55432	0.319087
$304$	−6.97237	−0.399893
$305$	−6.74268	−0.386085
$306$	−5.16756	−0.295410
$307$	6.24787	0.356585	0.178292	−	0.983978i	$-0.442943\pi$
$307$	6.24787	0.356585	0.178292	+	0.983978i	$0.442943\pi$
$308$	−1.97615	−0.112602
$309$	1.00000	0.0568880
$310$	0.323338	0.0183643
$311$	−27.1527	−1.53969	−0.769845	−	0.638231i	$-0.779667\pi$
$311$	−27.1527	−1.53969	−0.769845	+	0.638231i	$0.779667\pi$
$312$	1.00000	0.0566139
$313$	−15.7601	−0.890812	−0.445406	−	0.895329i	$-0.646941\pi$
$313$	−15.7601	−0.890812	−0.445406	+	0.895329i	$0.646941\pi$
$314$	−9.53725	−0.538218
$315$	−3.69223	−0.208034
$316$	−11.5359	−0.648943
$317$	−33.4872	−1.88083	−0.940415	−	0.340028i	$-0.889564\pi$
$317$	−33.4872	−1.88083	−0.940415	+	0.340028i	$0.889564\pi$
$318$	8.08025	0.453118
$319$	−8.97247	−0.502362
$320$	3.07028	0.171634
$321$	3.11236	0.173715
$322$	−5.35263	−0.298290
$323$	−36.0302	−2.00477
$324$	1.00000	0.0555556
$325$	−4.42660	−0.245544
$326$	−17.6275	−0.976300
$327$	−10.7609	−0.595078
$328$	1.62153	0.0895338
$329$	11.5937	0.639183
$330$	−5.04531	−0.277735
$331$	21.6617	1.19063	0.595316	−	0.803492i	$-0.297027\pi$
$331$	21.6617	1.19063	0.595316	+	0.803492i	$0.297027\pi$
$332$	5.79368	0.317970
$333$	−4.85429	−0.266013
$334$	19.3747	1.06014
$335$	−46.6461	−2.54855
$336$	−1.20257	−0.0656057
$337$	−3.74274	−0.203880	−0.101940	−	0.994791i	$-0.532505\pi$
$337$	−3.74274	−0.203880	−0.101940	+	0.994791i	$0.532505\pi$
$338$	−1.00000	−0.0543928
$339$	20.4678	1.11166
$340$	15.8658	0.860446
$341$	−0.173057	−0.00937155
$342$	6.97237	0.377023
$343$	15.0969	0.815155
$344$	12.7227	0.685964
$345$	−13.6657	−0.735739
$346$	−18.6200	−1.00102
$347$	24.1538	1.29664	0.648321	−	0.761367i	$-0.275472\pi$
$347$	24.1538	1.29664	0.648321	+	0.761367i	$0.275472\pi$
$348$	−5.46012	−0.292693
$349$	33.4838	1.79234	0.896172	−	0.443707i	$-0.146337\pi$
$349$	33.4838	1.79234	0.896172	+	0.443707i	$0.146337\pi$
$350$	5.32331	0.284543
$351$	−1.00000	−0.0533761
$352$	−1.64327	−0.0875868
$353$	15.3361	0.816257	0.408129	−	0.912924i	$-0.366181\pi$
$353$	15.3361	0.816257	0.408129	+	0.912924i	$0.366181\pi$
$354$	4.90361	0.260624
$355$	39.8511	2.11508
$356$	4.12175	0.218452
$357$	−6.21437	−0.328899
$358$	1.68183	0.0888873
$359$	−19.2016	−1.01342	−0.506711	−	0.862116i	$-0.669139\pi$
$359$	−19.2016	−1.01342	−0.506711	+	0.862116i	$0.669139\pi$
$360$	−3.07028	−0.161818
$361$	29.6139	1.55863
$362$	−0.182749	−0.00960508
$363$	−8.29965	−0.435619
$364$	1.20257	0.0630319
$365$	0.262810	0.0137561
$366$	2.19611	0.114793
$367$	11.5935	0.605177	0.302588	−	0.953121i	$-0.402149\pi$
$367$	11.5935	0.605177	0.302588	+	0.953121i	$0.402149\pi$
$368$	−4.45098	−0.232023
$369$	−1.62153	−0.0844133
$370$	14.9040	0.774823
$371$	9.71709	0.504486
$372$	−0.105312	−0.00546018
$373$	21.8239	1.13000	0.565000	−	0.825091i	$-0.308876\pi$
$373$	21.8239	1.13000	0.565000	+	0.825091i	$0.308876\pi$
$374$	−8.49172	−0.439096
$375$	−1.76049	−0.0909113
$376$	9.64077	0.497185
$377$	5.46012	0.281210
$378$	1.20257	0.0618536
$379$	9.10148	0.467512	0.233756	−	0.972295i	$-0.424898\pi$
$379$	9.10148	0.467512	0.233756	+	0.972295i	$0.424898\pi$
$380$	−21.4071	−1.09816
$381$	11.0748	0.567378
$382$	−10.0979	−0.516655
$383$	32.9427	1.68329	0.841647	−	0.540029i	$-0.181587\pi$
$383$	32.9427	1.68329	0.841647	+	0.540029i	$0.181587\pi$
$384$	−1.00000	−0.0510310
$385$	−6.06734	−0.309220
$386$	−17.7644	−0.904183
$387$	−12.7227	−0.646733
$388$	−3.96607	−0.201347
$389$	23.9395	1.21378	0.606890	−	0.794786i	$-0.292417\pi$
$389$	23.9395	1.21378	0.606890	+	0.794786i	$0.292417\pi$
$390$	3.07028	0.155470
$391$	−23.0007	−1.16320
$392$	5.55382	0.280510
$393$	−4.30992	−0.217407
$394$	−13.3735	−0.673746
$395$	−35.4183	−1.78209
$396$	1.64327	0.0825776
$397$	−37.8751	−1.90090	−0.950449	−	0.310882i	$-0.899376\pi$
$397$	−37.8751	−1.90090	−0.950449	+	0.310882i	$0.899376\pi$
$398$	−9.16019	−0.459159
$399$	8.38478	0.419764
$400$	4.42660	0.221330
$401$	−16.3655	−0.817254	−0.408627	−	0.912701i	$-0.633992\pi$
$401$	−16.3655	−0.817254	−0.408627	+	0.912701i	$0.633992\pi$
$402$	15.1928	0.757747
$403$	0.105312	0.00524597
$404$	5.55432	0.276338
$405$	3.07028	0.152563
$406$	−6.56619	−0.325874
$407$	−7.97693	−0.395402
$408$	−5.16756	−0.255832
$409$	−31.5789	−1.56148	−0.780738	−	0.624858i	$-0.785157\pi$
$409$	−31.5789	−1.56148	−0.780738	+	0.624858i	$0.785157\pi$
$410$	4.97853	0.245872
$411$	2.72360	0.134345
$412$	1.00000	0.0492665
$413$	5.89694	0.290170
$414$	4.45098	0.218754
$415$	17.7882	0.873189
$416$	1.00000	0.0490290
$417$	12.1741	0.596167
$418$	11.4575	0.560405
$419$	22.0491	1.07717	0.538584	−	0.842572i	$-0.318960\pi$
$419$	22.0491	1.07717	0.538584	+	0.842572i	$0.318960\pi$
$420$	−3.69223	−0.180162
$421$	24.6640	1.20205	0.601024	−	0.799231i	$-0.294759\pi$
$421$	24.6640	1.20205	0.601024	+	0.799231i	$0.294759\pi$
$422$	24.9722	1.21563
$423$	−9.64077	−0.468750
$424$	8.08025	0.392412
$425$	22.8747	1.10959
$426$	−12.9797	−0.628866
$427$	2.64098	0.127806
$428$	3.11236	0.150442
$429$	−1.64327	−0.0793380
$430$	39.0623	1.88375
$431$	−39.9767	−1.92561	−0.962804	−	0.270201i	$-0.912910\pi$
$431$	−39.9767	−1.92561	−0.962804	+	0.270201i	$0.912910\pi$
$432$	1.00000	0.0481125
$433$	−7.46041	−0.358524	−0.179262	−	0.983801i	$-0.557371\pi$
$433$	−7.46041	−0.358524	−0.179262	+	0.983801i	$0.557371\pi$
$434$	−0.126645	−0.00607918
$435$	−16.7641	−0.803776
$436$	−10.7609	−0.515352
$437$	31.0339	1.48455
$438$	−0.0855982	−0.00409004
$439$	−24.6346	−1.17574	−0.587872	−	0.808954i	$-0.700034\pi$
$439$	−24.6346	−1.17574	−0.587872	+	0.808954i	$0.700034\pi$
$440$	−5.04531	−0.240525
$441$	−5.55382	−0.264468
$442$	5.16756	0.245796
$443$	39.3345	1.86884	0.934420	−	0.356173i	$-0.115918\pi$
$443$	39.3345	1.86884	0.934420	+	0.356173i	$0.115918\pi$
$444$	−4.85429	−0.230374
$445$	12.6549	0.599900
$446$	−19.9780	−0.945985
$447$	−11.2270	−0.531018
$448$	−1.20257	−0.0568162
$449$	−11.6656	−0.550535	−0.275267	−	0.961368i	$-0.588766\pi$
$449$	−11.6656	−0.550535	−0.275267	+	0.961368i	$0.588766\pi$
$450$	−4.42660	−0.208672
$451$	−2.66461	−0.125472
$452$	20.4678	0.962726
$453$	−11.9752	−0.562645
$454$	7.71833	0.362239
$455$	3.69223	0.173094
$456$	6.97237	0.326511
$457$	25.6576	1.20021	0.600106	−	0.799920i	$-0.295125\pi$
$457$	25.6576	1.20021	0.600106	+	0.799920i	$0.295125\pi$
$458$	−16.6721	−0.779037
$459$	5.16756	0.241201
$460$	−13.6657	−0.637169
$461$	17.6951	0.824145	0.412072	−	0.911151i	$-0.364805\pi$
$461$	17.6951	0.824145	0.412072	+	0.911151i	$0.364805\pi$
$462$	1.97615	0.0919390
$463$	27.3038	1.26892	0.634458	−	0.772958i	$-0.281223\pi$
$463$	27.3038	1.26892	0.634458	+	0.772958i	$0.281223\pi$
$464$	−5.46012	−0.253480
$465$	−0.323338	−0.0149944
$466$	−10.8908	−0.504507
$467$	1.21442	0.0561969	0.0280984	−	0.999605i	$-0.491055\pi$
$467$	1.21442	0.0561969	0.0280984	+	0.999605i	$0.491055\pi$
$468$	−1.00000	−0.0462250
$469$	18.2704	0.843649
$470$	29.5998	1.36534
$471$	9.53725	0.439453
$472$	4.90361	0.225707
$473$	−20.9069	−0.961302
$474$	11.5359	0.529860
$475$	−30.8639	−1.41613
$476$	−6.21437	−0.284835
$477$	−8.08025	−0.369969
$478$	22.7544	1.04076
$479$	−39.2516	−1.79345	−0.896725	−	0.442589i	$-0.854060\pi$
$479$	−39.2516	−1.79345	−0.896725	+	0.442589i	$0.854060\pi$
$480$	−3.07028	−0.140138
$481$	4.85429	0.221337
$482$	−18.4300	−0.839466
$483$	5.35263	0.243553
$484$	−8.29965	−0.377257
$485$	−12.1769	−0.552926
$486$	−1.00000	−0.0453609
$487$	−21.0855	−0.955477	−0.477739	−	0.878502i	$-0.658543\pi$
$487$	−21.0855	−0.955477	−0.477739	+	0.878502i	$0.658543\pi$
$488$	2.19611	0.0994134
$489$	17.6275	0.797145
$490$	17.0518	0.770320
$491$	−3.30888	−0.149328	−0.0746638	−	0.997209i	$-0.523788\pi$
$491$	−3.30888	−0.149328	−0.0746638	+	0.997209i	$0.523788\pi$
$492$	−1.62153	−0.0731040
$493$	−28.2155	−1.27076
$494$	−6.97237	−0.313702
$495$	5.04531	0.226770
$496$	−0.105312	−0.00472866
$497$	−15.6090	−0.700158
$498$	−5.79368	−0.259621
$499$	35.6352	1.59525	0.797625	−	0.603154i	$-0.206090\pi$
$499$	35.6352	1.59525	0.797625	+	0.603154i	$0.206090\pi$
$500$	−1.76049	−0.0787315
$501$	−19.3747	−0.865599
$502$	−3.06979	−0.137011
$503$	24.5682	1.09544	0.547722	−	0.836660i	$-0.315495\pi$
$503$	24.5682	1.09544	0.547722	+	0.836660i	$0.315495\pi$
$504$	1.20257	0.0535668
$505$	17.0533	0.758862
$506$	7.31418	0.325155
$507$	1.00000	0.0444116
$508$	11.0748	0.491364
$509$	30.2639	1.34142	0.670711	−	0.741719i	$-0.265989\pi$
$509$	30.2639	1.34142	0.670711	+	0.741719i	$0.265989\pi$
$510$	−15.8658	−0.702552
$511$	−0.102938	−0.00455371
$512$	−1.00000	−0.0441942
$513$	−6.97237	−0.307838
$514$	6.34044	0.279665
$515$	3.07028	0.135293
$516$	−12.7227	−0.560087
$517$	−15.8424	−0.696749
$518$	−5.83763	−0.256491
$519$	18.6200	0.817329
$520$	3.07028	0.134641
$521$	−2.64228	−0.115760	−0.0578802	−	0.998324i	$-0.518434\pi$
$521$	−2.64228	−0.115760	−0.0578802	+	0.998324i	$0.518434\pi$
$522$	5.46012	0.238983
$523$	6.62048	0.289493	0.144747	−	0.989469i	$-0.453763\pi$
$523$	6.62048	0.289493	0.144747	+	0.989469i	$0.453763\pi$
$524$	−4.30992	−0.188280
$525$	−5.32331	−0.232328
$526$	−3.14227	−0.137009
$527$	−0.544207	−0.0237060
$528$	1.64327	0.0715143
$529$	−3.18876	−0.138642
$530$	24.8086	1.07762
$531$	−4.90361	−0.212799
$532$	8.38478	0.363526
$533$	1.62153	0.0702361
$534$	−4.12175	−0.178366
$535$	9.55582	0.413134
$536$	15.1928	0.656228
$537$	−1.68183	−0.0725762
$538$	−11.5731	−0.498950
$539$	−9.12645	−0.393104
$540$	3.07028	0.132124
$541$	13.1057	0.563459	0.281730	−	0.959494i	$-0.409092\pi$
$541$	13.1057	0.563459	0.281730	+	0.959494i	$0.409092\pi$
$542$	−6.67362	−0.286657
$543$	0.182749	0.00784252
$544$	−5.16756	−0.221557
$545$	−33.0389	−1.41523
$546$	−1.20257	−0.0514653
$547$	18.0492	0.771729	0.385865	−	0.922555i	$-0.373903\pi$
$547$	18.0492	0.771729	0.385865	+	0.922555i	$0.373903\pi$
$548$	2.72360	0.116346
$549$	−2.19611	−0.0937278
$550$	−7.27412	−0.310169
$551$	38.0700	1.62184
$552$	4.45098	0.189446
$553$	13.8727	0.589928
$554$	−17.7381	−0.753621
$555$	−14.9040	−0.632640
$556$	12.1741	0.516296
$557$	6.55802	0.277872	0.138936	−	0.990301i	$-0.455632\pi$
$557$	6.55802	0.277872	0.138936	+	0.990301i	$0.455632\pi$
$558$	0.105312	0.00445822
$559$	12.7227	0.538114
$560$	−3.69223	−0.156025
$561$	8.49172	0.358521
$562$	5.19281	0.219046
$563$	−21.4589	−0.904385	−0.452192	−	0.891920i	$-0.649358\pi$
$563$	−21.4589	−0.904385	−0.452192	+	0.891920i	$0.649358\pi$
$564$	−9.64077	−0.405950
$565$	62.8419	2.64378
$566$	20.2995	0.853252
$567$	−1.20257	−0.0505033
$568$	−12.9797	−0.544614
$569$	11.2933	0.473440	0.236720	−	0.971578i	$-0.423928\pi$
$569$	11.2933	0.473440	0.236720	+	0.971578i	$0.423928\pi$
$570$	21.4071	0.896645
$571$	32.6803	1.36763	0.683813	−	0.729657i	$-0.260320\pi$
$571$	32.6803	1.36763	0.683813	+	0.729657i	$0.260320\pi$
$572$	−1.64327	−0.0687087
$573$	10.0979	0.421847
$574$	−1.95000	−0.0813915
$575$	−19.7027	−0.821661
$576$	1.00000	0.0416667
$577$	10.4058	0.433201	0.216600	−	0.976260i	$-0.430503\pi$
$577$	10.4058	0.433201	0.216600	+	0.976260i	$0.430503\pi$
$578$	−9.70370	−0.403621
$579$	17.7644	0.738262
$580$	−16.7641	−0.696091
$581$	−6.96732	−0.289053
$582$	3.96607	0.164399
$583$	−13.2781	−0.549921
$584$	−0.0855982	−0.00354208
$585$	−3.07028	−0.126940
$586$	19.9094	0.822451
$587$	14.2361	0.587586	0.293793	−	0.955869i	$-0.405082\pi$
$587$	14.2361	0.587586	0.293793	+	0.955869i	$0.405082\pi$
$588$	−5.55382	−0.229036
$589$	0.734276	0.0302553
$590$	15.0554	0.619823
$591$	13.3735	0.550111
$592$	−4.85429	−0.199510
$593$	−47.7002	−1.95881	−0.979405	−	0.201903i	$-0.935287\pi$
$593$	−47.7002	−1.95881	−0.979405	+	0.201903i	$0.935287\pi$
$594$	−1.64327	−0.0674243
$595$	−19.0798	−0.782197
$596$	−11.2270	−0.459875
$597$	9.16019	0.374902
$598$	−4.45098	−0.182014
$599$	−11.1070	−0.453821	−0.226910	−	0.973916i	$-0.572862\pi$
$599$	−11.1070	−0.453821	−0.226910	+	0.973916i	$0.572862\pi$
$600$	−4.42660	−0.180715
$601$	20.3015	0.828116	0.414058	−	0.910250i	$-0.364111\pi$
$601$	20.3015	0.828116	0.414058	+	0.910250i	$0.364111\pi$
$602$	−15.3000	−0.623582
$603$	−15.1928	−0.618698
$604$	−11.9752	−0.487265
$605$	−25.4822	−1.03600
$606$	−5.55432	−0.225629
$607$	−23.1722	−0.940530	−0.470265	−	0.882525i	$-0.655842\pi$
$607$	−23.1722	−0.940530	−0.470265	+	0.882525i	$0.655842\pi$
$608$	6.97237	0.282767
$609$	6.56619	0.266075
$610$	6.74268	0.273003
$611$	9.64077	0.390024
$612$	5.16756	0.208886
$613$	−19.8141	−0.800284	−0.400142	−	0.916453i	$-0.631039\pi$
$613$	−19.8141	−0.800284	−0.400142	+	0.916453i	$0.631039\pi$
$614$	−6.24787	−0.252143
$615$	−4.97853	−0.200754
$616$	1.97615	0.0796215
$617$	−31.1091	−1.25241	−0.626203	−	0.779660i	$-0.715392\pi$
$617$	−31.1091	−1.25241	−0.626203	+	0.779660i	$0.715392\pi$
$618$	−1.00000	−0.0402259
$619$	−32.2240	−1.29519	−0.647595	−	0.761985i	$-0.724225\pi$
$619$	−32.2240	−1.29519	−0.647595	+	0.761985i	$0.724225\pi$
$620$	−0.323338	−0.0129856
$621$	−4.45098	−0.178612
$622$	27.1527	1.08873
$623$	−4.95670	−0.198586
$624$	−1.00000	−0.0400320
$625$	−27.5382	−1.10153
$626$	15.7601	0.629899
$627$	−11.4575	−0.457569
$628$	9.53725	0.380578
$629$	−25.0848	−1.00020
$630$	3.69223	0.147102
$631$	−24.4836	−0.974678	−0.487339	−	0.873213i	$-0.662032\pi$
$631$	−24.4836	−0.974678	−0.487339	+	0.873213i	$0.662032\pi$
$632$	11.5359	0.458872
$633$	−24.9722	−0.992554
$634$	33.4872	1.32995
$635$	34.0027	1.34935
$636$	−8.08025	−0.320403
$637$	5.55382	0.220050
$638$	8.97247	0.355223
$639$	12.9797	0.513467
$640$	−3.07028	−0.121363
$641$	37.3835	1.47656	0.738279	−	0.674496i	$-0.235639\pi$
$641$	37.3835	1.47656	0.738279	+	0.674496i	$0.235639\pi$
$642$	−3.11236	−0.122835
$643$	2.66560	0.105121	0.0525605	−	0.998618i	$-0.483262\pi$
$643$	2.66560	0.105121	0.0525605	+	0.998618i	$0.483262\pi$
$644$	5.35263	0.210923
$645$	−39.0623	−1.53808
$646$	36.0302	1.41759
$647$	−35.3663	−1.39039	−0.695195	−	0.718821i	$-0.744682\pi$
$647$	−35.3663	−1.39039	−0.695195	+	0.718821i	$0.744682\pi$
$648$	−1.00000	−0.0392837
$649$	−8.05797	−0.316303
$650$	4.42660	0.173626
$651$	0.126645	0.00496363
$652$	17.6275	0.690348
$653$	−16.9690	−0.664049	−0.332025	−	0.943271i	$-0.607732\pi$
$653$	−16.9690	−0.664049	−0.332025	+	0.943271i	$0.607732\pi$
$654$	10.7609	0.420784
$655$	−13.2327	−0.517042
$656$	−1.62153	−0.0633100
$657$	0.0855982	0.00333950
$658$	−11.5937	−0.451970
$659$	32.3090	1.25858	0.629289	−	0.777171i	$-0.283346\pi$
$659$	32.3090	1.25858	0.629289	+	0.777171i	$0.283346\pi$
$660$	5.04531	0.196388
$661$	−7.72472	−0.300457	−0.150228	−	0.988651i	$-0.548001\pi$
$661$	−7.72472	−0.300457	−0.150228	+	0.988651i	$0.548001\pi$
$662$	−21.6617	−0.841904
$663$	−5.16756	−0.200691
$664$	−5.79368	−0.224838
$665$	25.7436	0.998294
$666$	4.85429	0.188100
$667$	24.3029	0.941012
$668$	−19.3747	−0.749630
$669$	19.9780	0.772393
$670$	46.6461	1.80209
$671$	−3.60882	−0.139317
$672$	1.20257	0.0463902
$673$	−14.3304	−0.552397	−0.276198	−	0.961101i	$-0.589075\pi$
$673$	−14.3304	−0.552397	−0.276198	+	0.961101i	$0.589075\pi$
$674$	3.74274	0.144165
$675$	4.42660	0.170380
$676$	1.00000	0.0384615
$677$	−15.9596	−0.613377	−0.306688	−	0.951810i	$-0.599221\pi$
$677$	−15.9596	−0.613377	−0.306688	+	0.951810i	$0.599221\pi$
$678$	−20.4678	−0.786062
$679$	4.76949	0.183036
$680$	−15.8658	−0.608428
$681$	−7.71833	−0.295767
$682$	0.173057	0.00662669
$683$	14.1424	0.541142	0.270571	−	0.962700i	$-0.412787\pi$
$683$	14.1424	0.541142	0.270571	+	0.962700i	$0.412787\pi$
$684$	−6.97237	−0.266595
$685$	8.36221	0.319504
$686$	−15.0969	−0.576401
$687$	16.6721	0.636081
$688$	−12.7227	−0.485050
$689$	8.08025	0.307833
$690$	13.6657	0.520246
$691$	17.1292	0.651627	0.325813	−	0.945434i	$-0.394362\pi$
$691$	17.1292	0.651627	0.325813	+	0.945434i	$0.394362\pi$
$692$	18.6200	0.707827
$693$	−1.97615	−0.0750679
$694$	−24.1538	−0.916864
$695$	37.3778	1.41782
$696$	5.46012	0.206965
$697$	−8.37934	−0.317390
$698$	−33.4838	−1.26738
$699$	10.8908	0.411928
$700$	−5.32331	−0.201202
$701$	−23.6808	−0.894412	−0.447206	−	0.894431i	$-0.647581\pi$
$701$	−23.6808	−0.894412	−0.447206	+	0.894431i	$0.647581\pi$
$702$	1.00000	0.0377426
$703$	33.8459	1.27652
$704$	1.64327	0.0619332
$705$	−29.5998	−1.11479
$706$	−15.3361	−0.577181
$707$	−6.67947	−0.251207
$708$	−4.90361	−0.184289
$709$	40.3891	1.51684	0.758422	−	0.651764i	$-0.225971\pi$
$709$	40.3891	1.51684	0.758422	+	0.651764i	$0.225971\pi$
$710$	−39.8511	−1.49559
$711$	−11.5359	−0.432629
$712$	−4.12175	−0.154469
$713$	0.468743	0.0175546
$714$	6.21437	0.232567
$715$	−5.04531	−0.188684
$716$	−1.68183	−0.0628528
$717$	−22.7544	−0.849778
$718$	19.2016	0.716598
$719$	18.8348	0.702420	0.351210	−	0.936297i	$-0.385770\pi$
$719$	18.8348	0.702420	0.351210	+	0.936297i	$0.385770\pi$
$720$	3.07028	0.114422
$721$	−1.20257	−0.0447861
$722$	−29.6139	−1.10212
$723$	18.4300	0.685421
$724$	0.182749	0.00679182
$725$	−24.1698	−0.897643
$726$	8.29965	0.308029
$727$	−23.0428	−0.854611	−0.427306	−	0.904107i	$-0.640537\pi$
$727$	−23.0428	−0.854611	−0.427306	+	0.904107i	$0.640537\pi$
$728$	−1.20257	−0.0445703
$729$	1.00000	0.0370370
$730$	−0.262810	−0.00972704
$731$	−65.7455	−2.43169
$732$	−2.19611	−0.0811707
$733$	23.7889	0.878665	0.439332	−	0.898325i	$-0.355215\pi$
$733$	23.7889	0.878665	0.439332	+	0.898325i	$0.355215\pi$
$734$	−11.5935	−0.427925
$735$	−17.0518	−0.628964
$736$	4.45098	0.164065
$737$	−24.9659	−0.919631
$738$	1.62153	0.0596892
$739$	−15.4492	−0.568308	−0.284154	−	0.958779i	$-0.591713\pi$
$739$	−15.4492	−0.568308	−0.284154	+	0.958779i	$0.591713\pi$
$740$	−14.9040	−0.547883
$741$	6.97237	0.256136
$742$	−9.71709	−0.356725
$743$	−32.4360	−1.18996	−0.594981	−	0.803740i	$-0.702840\pi$
$743$	−32.4360	−1.18996	−0.594981	+	0.803740i	$0.702840\pi$
$744$	0.105312	0.00386093
$745$	−34.4700	−1.26288
$746$	−21.8239	−0.799031
$747$	5.79368	0.211980
$748$	8.49172	0.310488
$749$	−3.74284	−0.136760
$750$	1.76049	0.0642840
$751$	46.0229	1.67940	0.839700	−	0.543051i	$-0.182731\pi$
$751$	46.0229	1.67940	0.839700	+	0.543051i	$0.182731\pi$
$752$	−9.64077	−0.351563
$753$	3.06979	0.111869
$754$	−5.46012	−0.198846
$755$	−36.7672	−1.33810
$756$	−1.20257	−0.0437371
$757$	−23.7709	−0.863970	−0.431985	−	0.901881i	$-0.642187\pi$
$757$	−23.7709	−0.863970	−0.431985	+	0.901881i	$0.642187\pi$
$758$	−9.10148	−0.330581
$759$	−7.31418	−0.265488
$760$	21.4071	0.776517
$761$	9.66927	0.350511	0.175255	−	0.984523i	$-0.443925\pi$
$761$	9.66927	0.350511	0.175255	+	0.984523i	$0.443925\pi$
$762$	−11.0748	−0.401197
$763$	12.9407	0.468486
$764$	10.0979	0.365330
$765$	15.8658	0.573631
$766$	−32.9427	−1.19027
$767$	4.90361	0.177059
$768$	1.00000	0.0360844
$769$	−42.4028	−1.52908	−0.764541	−	0.644575i	$-0.777034\pi$
$769$	−42.4028	−1.52908	−0.764541	+	0.644575i	$0.777034\pi$
$770$	6.06734	0.218652
$771$	−6.34044	−0.228345
$772$	17.7644	0.639354
$773$	−26.9094	−0.967865	−0.483933	−	0.875105i	$-0.660792\pi$
$773$	−26.9094	−0.967865	−0.483933	+	0.875105i	$0.660792\pi$
$774$	12.7227	0.457309
$775$	−0.466175	−0.0167455
$776$	3.96607	0.142374
$777$	5.83763	0.209424
$778$	−23.9395	−0.858272
$779$	11.3059	0.405075
$780$	−3.07028	−0.109934
$781$	21.3291	0.763216
$782$	23.0007	0.822504
$783$	−5.46012	−0.195129
$784$	−5.55382	−0.198351
$785$	29.2820	1.04512
$786$	4.30992	0.153730
$787$	−54.1803	−1.93132	−0.965660	−	0.259810i	$-0.916340\pi$
$787$	−54.1803	−1.93132	−0.965660	+	0.259810i	$0.916340\pi$
$788$	13.3735	0.476410
$789$	3.14227	0.111868
$790$	35.4183	1.26013
$791$	−24.6140	−0.875174
$792$	−1.64327	−0.0583912
$793$	2.19611	0.0779863
$794$	37.8751	1.34414
$795$	−24.8086	−0.879871
$796$	9.16019	0.324674
$797$	−38.6249	−1.36816	−0.684082	−	0.729405i	$-0.739797\pi$
$797$	−38.6249	−1.36816	−0.684082	+	0.729405i	$0.739797\pi$
$798$	−8.38478	−0.296818
$799$	−49.8193	−1.76248
$800$	−4.42660	−0.156504
$801$	4.12175	0.145635
$802$	16.3655	0.577886
$803$	0.140661	0.00496383
$804$	−15.1928	−0.535808
$805$	16.4340	0.579224
$806$	−0.105312	−0.00370946
$807$	11.5731	0.407391
$808$	−5.55432	−0.195400
$809$	0.561972	0.0197579	0.00987895	−	0.999951i	$-0.496855\pi$
$809$	0.561972	0.0197579	0.00987895	+	0.999951i	$0.496855\pi$
$810$	−3.07028	−0.107879
$811$	−8.60816	−0.302273	−0.151137	−	0.988513i	$-0.548293\pi$
$811$	−8.60816	−0.302273	−0.151137	+	0.988513i	$0.548293\pi$
$812$	6.56619	0.230428
$813$	6.67362	0.234054
$814$	7.97693	0.279591
$815$	54.1215	1.89579
$816$	5.16756	0.180901
$817$	88.7076	3.10349
$818$	31.5789	1.10413
$819$	1.20257	0.0420213
$820$	−4.97853	−0.173858
$821$	43.7122	1.52557	0.762783	−	0.646654i	$-0.223832\pi$
$821$	43.7122	1.52557	0.762783	+	0.646654i	$0.223832\pi$
$822$	−2.72360	−0.0949965
$823$	−47.8699	−1.66864	−0.834320	−	0.551280i	$-0.814139\pi$
$823$	−47.8699	−1.66864	−0.834320	+	0.551280i	$0.814139\pi$
$824$	−1.00000	−0.0348367
$825$	7.27412	0.253252
$826$	−5.89694	−0.205181
$827$	44.4387	1.54529	0.772643	−	0.634841i	$-0.218934\pi$
$827$	44.4387	1.54529	0.772643	+	0.634841i	$0.218934\pi$
$828$	−4.45098	−0.154682
$829$	−2.52204	−0.0875939	−0.0437970	−	0.999040i	$-0.513945\pi$
$829$	−2.52204	−0.0875939	−0.0437970	+	0.999040i	$0.513945\pi$
$830$	−17.7882	−0.617438
$831$	17.7381	0.615329
$832$	−1.00000	−0.0346688
$833$	−28.6997	−0.994386
$834$	−12.1741	−0.421554
$835$	−59.4858	−2.05859
$836$	−11.4575	−0.396266
$837$	−0.105312	−0.00364012
$838$	−22.0491	−0.761672
$839$	−32.9801	−1.13860	−0.569300	−	0.822130i	$-0.692786\pi$
$839$	−32.9801	−1.13860	−0.569300	+	0.822130i	$0.692786\pi$
$840$	3.69223	0.127394
$841$	0.812907	0.0280313
$842$	−24.6640	−0.849977
$843$	−5.19281	−0.178850
$844$	−24.9722	−0.859577
$845$	3.07028	0.105621
$846$	9.64077	0.331457
$847$	9.98093	0.342949
$848$	−8.08025	−0.277477
$849$	−20.2995	−0.696678
$850$	−22.8747	−0.784597
$851$	21.6064	0.740656
$852$	12.9797	0.444676
$853$	−45.2186	−1.54826	−0.774128	−	0.633029i	$-0.781812\pi$
$853$	−45.2186	−1.54826	−0.774128	+	0.633029i	$0.781812\pi$
$854$	−2.64098	−0.0903726
$855$	−21.4071	−0.732108
$856$	−3.11236	−0.106378
$857$	−34.9215	−1.19289	−0.596447	−	0.802652i	$-0.703421\pi$
$857$	−34.9215	−1.19289	−0.596447	+	0.802652i	$0.703421\pi$
$858$	1.64327	0.0561004
$859$	−50.5313	−1.72411	−0.862053	−	0.506819i	$-0.830821\pi$
$859$	−50.5313	−1.72411	−0.862053	+	0.506819i	$0.830821\pi$
$860$	−39.0623	−1.33201
$861$	1.95000	0.0664559
$862$	39.9767	1.36161
$863$	4.09305	0.139329	0.0696645	−	0.997570i	$-0.477807\pi$
$863$	4.09305	0.139329	0.0696645	+	0.997570i	$0.477807\pi$
$864$	−1.00000	−0.0340207
$865$	57.1686	1.94379
$866$	7.46041	0.253515
$867$	9.70370	0.329555
$868$	0.126645	0.00429863
$869$	−18.9566	−0.643058
$870$	16.7641	0.568356
$871$	15.1928	0.514788
$872$	10.7609	0.364409
$873$	−3.96607	−0.134231
$874$	−31.0339	−1.04974
$875$	2.11712	0.0715716
$876$	0.0855982	0.00289209
$877$	−12.6943	−0.428657	−0.214329	−	0.976762i	$-0.568756\pi$
$877$	−12.6943	−0.428657	−0.214329	+	0.976762i	$0.568756\pi$
$878$	24.6346	0.831376
$879$	−19.9094	−0.671529
$880$	5.04531	0.170077
$881$	−14.7407	−0.496628	−0.248314	−	0.968680i	$-0.579876\pi$
$881$	−14.7407	−0.496628	−0.248314	+	0.968680i	$0.579876\pi$
$882$	5.55382	0.187007
$883$	−6.77196	−0.227895	−0.113947	−	0.993487i	$-0.536350\pi$
$883$	−6.77196	−0.227895	−0.113947	+	0.993487i	$0.536350\pi$
$884$	−5.16756	−0.173804
$885$	−15.0554	−0.506083
$886$	−39.3345	−1.32147
$887$	−9.33024	−0.313279	−0.156639	−	0.987656i	$-0.550066\pi$
$887$	−9.33024	−0.313279	−0.156639	+	0.987656i	$0.550066\pi$
$888$	4.85429	0.162899
$889$	−13.3182	−0.446679
$890$	−12.6549	−0.424194
$891$	1.64327	0.0550517
$892$	19.9780	0.668912
$893$	67.2190	2.24940
$894$	11.2270	0.375487
$895$	−5.16368	−0.172603
$896$	1.20257	0.0401751
$897$	4.45098	0.148614
$898$	11.6656	0.389287
$899$	0.575017	0.0191779
$900$	4.42660	0.147553
$901$	−41.7552	−1.39107
$902$	2.66461	0.0887218
$903$	15.3000	0.509152
$904$	−20.4678	−0.680750
$905$	0.561091	0.0186513
$906$	11.9752	0.397850
$907$	−36.4415	−1.21002	−0.605010	−	0.796218i	$-0.706831\pi$
$907$	−36.4415	−1.21002	−0.605010	+	0.796218i	$0.706831\pi$
$908$	−7.71833	−0.256142
$909$	5.55432	0.184225
$910$	−3.69223	−0.122396
$911$	−17.0168	−0.563790	−0.281895	−	0.959445i	$-0.590963\pi$
$911$	−17.0168	−0.563790	−0.281895	+	0.959445i	$0.590963\pi$
$912$	−6.97237	−0.230878
$913$	9.52060	0.315086
$914$	−25.6576	−0.848678
$915$	−6.74268	−0.222906
$916$	16.6721	0.550862
$917$	5.18299	0.171157
$918$	−5.16756	−0.170555
$919$	−14.4786	−0.477606	−0.238803	−	0.971068i	$-0.576755\pi$
$919$	−14.4786	−0.477606	−0.238803	+	0.971068i	$0.576755\pi$
$920$	13.6657	0.450546
$921$	6.24787	0.205874
$922$	−17.6951	−0.582759
$923$	−12.9797	−0.427231
$924$	−1.97615	−0.0650107
$925$	−21.4880	−0.706521
$926$	−27.3038	−0.897259
$927$	1.00000	0.0328443
$928$	5.46012	0.179237
$929$	33.7938	1.10874	0.554369	−	0.832271i	$-0.312960\pi$
$929$	33.7938	1.10874	0.554369	+	0.832271i	$0.312960\pi$
$930$	0.323338	0.0106027
$931$	38.7233	1.26910
$932$	10.8908	0.356740
$933$	−27.1527	−0.888941
$934$	−1.21442	−0.0397372
$935$	26.0719	0.852643
$936$	1.00000	0.0326860
$937$	12.9072	0.421660	0.210830	−	0.977523i	$-0.432383\pi$
$937$	12.9072	0.421660	0.210830	+	0.977523i	$0.432383\pi$
$938$	−18.2704	−0.596550
$939$	−15.7601	−0.514310
$940$	−29.5998	−0.965440
$941$	−45.2959	−1.47660	−0.738302	−	0.674470i	$-0.764372\pi$
$941$	−45.2959	−1.47660	−0.738302	+	0.674470i	$0.764372\pi$
$942$	−9.53725	−0.310741
$943$	7.21738	0.235030
$944$	−4.90361	−0.159599
$945$	−3.69223	−0.120108
$946$	20.9069	0.679743
$947$	−14.8623	−0.482960	−0.241480	−	0.970406i	$-0.577633\pi$
$947$	−14.8623	−0.482960	−0.241480	+	0.970406i	$0.577633\pi$
$948$	−11.5359	−0.374668
$949$	−0.0855982	−0.00277863
$950$	30.8639	1.00136
$951$	−33.4872	−1.08590
$952$	6.21437	0.201409
$953$	−24.5583	−0.795522	−0.397761	−	0.917489i	$-0.630213\pi$
$953$	−24.5583	−0.795522	−0.397761	+	0.917489i	$0.630213\pi$
$954$	8.08025	0.261608
$955$	31.0034	1.00325
$956$	−22.7544	−0.735929
$957$	−8.97247	−0.290039
$958$	39.2516	1.26816
$959$	−3.27533	−0.105766
$960$	3.07028	0.0990928
$961$	−30.9889	−0.999642
$962$	−4.85429	−0.156509
$963$	3.11236	0.100294
$964$	18.4300	0.593592
$965$	54.5416	1.75576
$966$	−5.35263	−0.172218
$967$	−36.6901	−1.17988	−0.589938	−	0.807449i	$-0.700848\pi$
$967$	−36.6901	−1.17988	−0.589938	+	0.807449i	$0.700848\pi$
$968$	8.29965	0.266761
$969$	−36.0302	−1.15746
$970$	12.1769	0.390978
$971$	−57.1794	−1.83498	−0.917488	−	0.397764i	$-0.869786\pi$
$971$	−57.1794	−1.83498	−0.917488	+	0.397764i	$0.869786\pi$
$972$	1.00000	0.0320750
$973$	−14.6402	−0.469343
$974$	21.0855	0.675624
$975$	−4.42660	−0.141765
$976$	−2.19611	−0.0702959
$977$	57.7285	1.84690	0.923450	−	0.383719i	$-0.125357\pi$
$977$	57.7285	1.84690	0.923450	+	0.383719i	$0.125357\pi$
$978$	−17.6275	−0.563667
$979$	6.77316	0.216471
$980$	−17.0518	−0.544699
$981$	−10.7609	−0.343568
$982$	3.30888	0.105591
$983$	−21.7251	−0.692924	−0.346462	−	0.938064i	$-0.612617\pi$
$983$	−21.7251	−0.692924	−0.346462	+	0.938064i	$0.612617\pi$
$984$	1.62153	0.0516924
$985$	41.0603	1.30829
$986$	28.2155	0.898565
$987$	11.5937	0.369032
$988$	6.97237	0.221821
$989$	56.6287	1.80069
$990$	−5.04531	−0.160350
$991$	−36.8378	−1.17019	−0.585095	−	0.810965i	$-0.698943\pi$
$991$	−36.8378	−1.17019	−0.585095	+	0.810965i	$0.698943\pi$
$992$	0.105312	0.00334367
$993$	21.6617	0.687412
$994$	15.6090	0.495087
$995$	28.1243	0.891601
$996$	5.79368	0.183580
$997$	19.7875	0.626677	0.313339	−	0.949641i	$-0.398553\pi$
$997$	19.7875	0.626677	0.313339	+	0.949641i	$0.398553\pi$
$998$	−35.6352	−1.12801
$999$	−4.85429	−0.153583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.13	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.13	✓	14	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.07028 q^{5} -1.00000 q^{6} -1.20257 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.07028 q^{5} -1.00000 q^{6} -1.20257 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.07028 q^{10} +1.64327 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.20257 q^{14} +3.07028 q^{15} +1.00000 q^{16} +5.16756 q^{17} -1.00000 q^{18} -6.97237 q^{19} +3.07028 q^{20} -1.20257 q^{21} -1.64327 q^{22} -4.45098 q^{23} -1.00000 q^{24} +4.42660 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.20257 q^{28} -5.46012 q^{29} -3.07028 q^{30} -0.105312 q^{31} -1.00000 q^{32} +1.64327 q^{33} -5.16756 q^{34} -3.69223 q^{35} +1.00000 q^{36} -4.85429 q^{37} +6.97237 q^{38} -1.00000 q^{39} -3.07028 q^{40} -1.62153 q^{41} +1.20257 q^{42} -12.7227 q^{43} +1.64327 q^{44} +3.07028 q^{45} +4.45098 q^{46} -9.64077 q^{47} +1.00000 q^{48} -5.55382 q^{49} -4.42660 q^{50} +5.16756 q^{51} -1.00000 q^{52} -8.08025 q^{53} -1.00000 q^{54} +5.04531 q^{55} +1.20257 q^{56} -6.97237 q^{57} +5.46012 q^{58} -4.90361 q^{59} +3.07028 q^{60} -2.19611 q^{61} +0.105312 q^{62} -1.20257 q^{63} +1.00000 q^{64} -3.07028 q^{65} -1.64327 q^{66} -15.1928 q^{67} +5.16756 q^{68} -4.45098 q^{69} +3.69223 q^{70} +12.9797 q^{71} -1.00000 q^{72} +0.0855982 q^{73} +4.85429 q^{74} +4.42660 q^{75} -6.97237 q^{76} -1.97615 q^{77} +1.00000 q^{78} -11.5359 q^{79} +3.07028 q^{80} +1.00000 q^{81} +1.62153 q^{82} +5.79368 q^{83} -1.20257 q^{84} +15.8658 q^{85} +12.7227 q^{86} -5.46012 q^{87} -1.64327 q^{88} +4.12175 q^{89} -3.07028 q^{90} +1.20257 q^{91} -4.45098 q^{92} -0.105312 q^{93} +9.64077 q^{94} -21.4071 q^{95} -1.00000 q^{96} -3.96607 q^{97} +5.55382 q^{98} +1.64327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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