LMFDB - Embedded newform 4026.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.46101901.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 12x^{3} + 6x^{2} - 5x - 2 $ x^6 - 3x^5 - 5x^4 + 12x^3 + 6x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.86911$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.199215 q^{5} -1.00000 q^{6} -0.938542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.199215 q^{5} -1.00000 q^{6} -0.938542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.199215 q^{10} -1.00000 q^{11} -1.00000 q^{12} -0.930566 q^{13} -0.938542 q^{14} -0.199215 q^{15} +1.00000 q^{16} -2.81829 q^{17} +1.00000 q^{18} -2.14373 q^{19} +0.199215 q^{20} +0.938542 q^{21} -1.00000 q^{22} +7.96999 q^{23} -1.00000 q^{24} -4.96031 q^{25} -0.930566 q^{26} -1.00000 q^{27} -0.938542 q^{28} +2.70246 q^{29} -0.199215 q^{30} -1.54964 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.81829 q^{34} -0.186971 q^{35} +1.00000 q^{36} -3.07370 q^{37} -2.14373 q^{38} +0.930566 q^{39} +0.199215 q^{40} +0.0554469 q^{41} +0.938542 q^{42} -9.33266 q^{43} -1.00000 q^{44} +0.199215 q^{45} +7.96999 q^{46} +1.16605 q^{47} -1.00000 q^{48} -6.11914 q^{49} -4.96031 q^{50} +2.81829 q^{51} -0.930566 q^{52} -2.09773 q^{53} -1.00000 q^{54} -0.199215 q^{55} -0.938542 q^{56} +2.14373 q^{57} +2.70246 q^{58} -12.0548 q^{59} -0.199215 q^{60} +1.00000 q^{61} -1.54964 q^{62} -0.938542 q^{63} +1.00000 q^{64} -0.185382 q^{65} +1.00000 q^{66} +13.9379 q^{67} -2.81829 q^{68} -7.96999 q^{69} -0.186971 q^{70} +5.25860 q^{71} +1.00000 q^{72} +1.42502 q^{73} -3.07370 q^{74} +4.96031 q^{75} -2.14373 q^{76} +0.938542 q^{77} +0.930566 q^{78} -13.6055 q^{79} +0.199215 q^{80} +1.00000 q^{81} +0.0554469 q^{82} -13.4433 q^{83} +0.938542 q^{84} -0.561444 q^{85} -9.33266 q^{86} -2.70246 q^{87} -1.00000 q^{88} -12.9033 q^{89} +0.199215 q^{90} +0.873375 q^{91} +7.96999 q^{92} +1.54964 q^{93} +1.16605 q^{94} -0.427062 q^{95} -1.00000 q^{96} +3.31812 q^{97} -6.11914 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + q^14 + 6 * q^15 + 6 * q^16 - 13 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - q^21 - 6 * q^22 - 11 * q^23 - 6 * q^24 + 8 * q^25 + 2 * q^26 - 6 * q^27 + q^28 - 14 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + 6 * q^33 - 13 * q^34 - 13 * q^35 + 6 * q^36 - 6 * q^37 + q^38 - 2 * q^39 - 6 * q^40 - 25 * q^41 - q^42 + 19 * q^43 - 6 * q^44 - 6 * q^45 - 11 * q^46 - 10 * q^47 - 6 * q^48 - 5 * q^49 + 8 * q^50 + 13 * q^51 + 2 * q^52 - 17 * q^53 - 6 * q^54 + 6 * q^55 + q^56 - q^57 - 14 * q^58 - 14 * q^59 + 6 * q^60 + 6 * q^61 - 5 * q^62 + q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 12 * q^67 - 13 * q^68 + 11 * q^69 - 13 * q^70 + 6 * q^71 + 6 * q^72 - 29 * q^73 - 6 * q^74 - 8 * q^75 + q^76 - q^77 - 2 * q^78 - 24 * q^79 - 6 * q^80 + 6 * q^81 - 25 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 19 * q^86 + 14 * q^87 - 6 * q^88 - 4 * q^89 - 6 * q^90 - 29 * q^91 - 11 * q^92 + 5 * q^93 - 10 * q^94 - 27 * q^95 - 6 * q^96 - 5 * q^97 - 5 * q^98 - 6 * 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
$5$	0.199215	0.0890915	0.0445457	−	0.999007i	$-0.485816\pi$
$5$	0.199215	0.0890915	0.0445457	+	0.999007i	$0.485816\pi$
$6$	−1.00000	−0.408248
$7$	−0.938542	−0.354735	−0.177368	−	0.984145i	$-0.556758\pi$
$7$	−0.938542	−0.354735	−0.177368	+	0.984145i	$0.556758\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.199215	0.0629972
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−0.930566	−0.258092	−0.129046	−	0.991639i	$-0.541192\pi$
$13$	−0.930566	−0.258092	−0.129046	+	0.991639i	$0.541192\pi$
$14$	−0.938542	−0.250836
$15$	−0.199215	−0.0514370
$16$	1.00000	0.250000
$17$	−2.81829	−0.683536	−0.341768	−	0.939784i	$-0.611026\pi$
$17$	−2.81829	−0.683536	−0.341768	+	0.939784i	$0.611026\pi$
$18$	1.00000	0.235702
$19$	−2.14373	−0.491806	−0.245903	−	0.969294i	$-0.579084\pi$
$19$	−2.14373	−0.491806	−0.245903	+	0.969294i	$0.579084\pi$
$20$	0.199215	0.0445457
$21$	0.938542	0.204807
$22$	−1.00000	−0.213201
$23$	7.96999	1.66186	0.830929	−	0.556378i	$-0.187809\pi$
$23$	7.96999	1.66186	0.830929	+	0.556378i	$0.187809\pi$
$24$	−1.00000	−0.204124
$25$	−4.96031	−0.992063
$26$	−0.930566	−0.182499
$27$	−1.00000	−0.192450
$28$	−0.938542	−0.177368
$29$	2.70246	0.501833	0.250917	−	0.968009i	$-0.419268\pi$
$29$	2.70246	0.501833	0.250917	+	0.968009i	$0.419268\pi$
$30$	−0.199215	−0.0363714
$31$	−1.54964	−0.278324	−0.139162	−	0.990270i	$-0.544441\pi$
$31$	−1.54964	−0.278324	−0.139162	+	0.990270i	$0.544441\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−2.81829	−0.483333
$35$	−0.186971	−0.0316039
$36$	1.00000	0.166667
$37$	−3.07370	−0.505313	−0.252657	−	0.967556i	$-0.581304\pi$
$37$	−3.07370	−0.505313	−0.252657	+	0.967556i	$0.581304\pi$
$38$	−2.14373	−0.347759
$39$	0.930566	0.149010
$40$	0.199215	0.0314986
$41$	0.0554469	0.00865935	0.00432967	−	0.999991i	$-0.498622\pi$
$41$	0.0554469	0.00865935	0.00432967	+	0.999991i	$0.498622\pi$
$42$	0.938542	0.144820
$43$	−9.33266	−1.42322	−0.711609	−	0.702576i	$-0.752033\pi$
$43$	−9.33266	−1.42322	−0.711609	+	0.702576i	$0.752033\pi$
$44$	−1.00000	−0.150756
$45$	0.199215	0.0296972
$46$	7.96999	1.17511
$47$	1.16605	0.170086	0.0850431	−	0.996377i	$-0.472897\pi$
$47$	1.16605	0.170086	0.0850431	+	0.996377i	$0.472897\pi$
$48$	−1.00000	−0.144338
$49$	−6.11914	−0.874163
$50$	−4.96031	−0.701494
$51$	2.81829	0.394640
$52$	−0.930566	−0.129046
$53$	−2.09773	−0.288145	−0.144073	−	0.989567i	$-0.546020\pi$
$53$	−2.09773	−0.288145	−0.144073	+	0.989567i	$0.546020\pi$
$54$	−1.00000	−0.136083
$55$	−0.199215	−0.0268621
$56$	−0.938542	−0.125418
$57$	2.14373	0.283944
$58$	2.70246	0.354850
$59$	−12.0548	−1.56941	−0.784704	−	0.619871i	$-0.787185\pi$
$59$	−12.0548	−1.56941	−0.784704	+	0.619871i	$0.787185\pi$
$60$	−0.199215	−0.0257185
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−1.54964	−0.196805
$63$	−0.938542	−0.118245
$64$	1.00000	0.125000
$65$	−0.185382	−0.0229938
$66$	1.00000	0.123091
$67$	13.9379	1.70279	0.851393	−	0.524528i	$-0.175758\pi$
$67$	13.9379	1.70279	0.851393	+	0.524528i	$0.175758\pi$
$68$	−2.81829	−0.341768
$69$	−7.96999	−0.959474
$70$	−0.186971	−0.0223473
$71$	5.25860	0.624081	0.312041	−	0.950069i	$-0.398987\pi$
$71$	5.25860	0.624081	0.312041	+	0.950069i	$0.398987\pi$
$72$	1.00000	0.117851
$73$	1.42502	0.166786	0.0833928	−	0.996517i	$-0.473424\pi$
$73$	1.42502	0.166786	0.0833928	+	0.996517i	$0.473424\pi$
$74$	−3.07370	−0.357311
$75$	4.96031	0.572768
$76$	−2.14373	−0.245903
$77$	0.938542	0.106957
$78$	0.930566	0.105366
$79$	−13.6055	−1.53074	−0.765371	−	0.643589i	$-0.777444\pi$
$79$	−13.6055	−1.53074	−0.765371	+	0.643589i	$0.777444\pi$
$80$	0.199215	0.0222729
$81$	1.00000	0.111111
$82$	0.0554469	0.00612308
$83$	−13.4433	−1.47560	−0.737800	−	0.675020i	$-0.764135\pi$
$83$	−13.4433	−1.47560	−0.737800	+	0.675020i	$0.764135\pi$
$84$	0.938542	0.102403
$85$	−0.561444	−0.0608972
$86$	−9.33266	−1.00637
$87$	−2.70246	−0.289734
$88$	−1.00000	−0.106600
$89$	−12.9033	−1.36774	−0.683872	−	0.729602i	$-0.739705\pi$
$89$	−12.9033	−1.36774	−0.683872	+	0.729602i	$0.739705\pi$
$90$	0.199215	0.0209991
$91$	0.873375	0.0915545
$92$	7.96999	0.830929
$93$	1.54964	0.160690
$94$	1.16605	0.120269
$95$	−0.427062	−0.0438157
$96$	−1.00000	−0.102062
$97$	3.31812	0.336904	0.168452	−	0.985710i	$-0.446123\pi$
$97$	3.31812	0.336904	0.168452	+	0.985710i	$0.446123\pi$
$98$	−6.11914	−0.618126
$99$	−1.00000	−0.100504
$100$	−4.96031	−0.496031
$101$	−3.39097	−0.337414	−0.168707	−	0.985666i	$-0.553959\pi$
$101$	−3.39097	−0.337414	−0.168707	+	0.985666i	$0.553959\pi$
$102$	2.81829	0.279052
$103$	−8.10200	−0.798313	−0.399157	−	0.916883i	$-0.630697\pi$
$103$	−8.10200	−0.798313	−0.399157	+	0.916883i	$0.630697\pi$
$104$	−0.930566	−0.0912495
$105$	0.186971	0.0182465
$106$	−2.09773	−0.203750
$107$	−9.80155	−0.947552	−0.473776	−	0.880645i	$-0.657109\pi$
$107$	−9.80155	−0.947552	−0.473776	+	0.880645i	$0.657109\pi$
$108$	−1.00000	−0.0962250
$109$	15.6029	1.49449	0.747243	−	0.664551i	$-0.231377\pi$
$109$	15.6029	1.49449	0.747243	+	0.664551i	$0.231377\pi$
$110$	−0.199215	−0.0189944
$111$	3.07370	0.291743
$112$	−0.938542	−0.0886839
$113$	−5.62215	−0.528888	−0.264444	−	0.964401i	$-0.585188\pi$
$113$	−5.62215	−0.528888	−0.264444	+	0.964401i	$0.585188\pi$
$114$	2.14373	0.200779
$115$	1.58774	0.148057
$116$	2.70246	0.250917
$117$	−0.930566	−0.0860308
$118$	−12.0548	−1.10974
$119$	2.64508	0.242474
$120$	−0.199215	−0.0181857
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−0.0554469	−0.00499948
$124$	−1.54964	−0.139162
$125$	−1.98424	−0.177476
$126$	−0.938542	−0.0836119
$127$	−0.0754406	−0.00669427	−0.00334714	−	0.999994i	$-0.501065\pi$
$127$	−0.0754406	−0.00669427	−0.00334714	+	0.999994i	$0.501065\pi$
$128$	1.00000	0.0883883
$129$	9.33266	0.821695
$130$	−0.185382	−0.0162591
$131$	5.79808	0.506581	0.253290	−	0.967390i	$-0.418487\pi$
$131$	5.79808	0.506581	0.253290	+	0.967390i	$0.418487\pi$
$132$	1.00000	0.0870388
$133$	2.01198	0.174461
$134$	13.9379	1.20405
$135$	−0.199215	−0.0171457
$136$	−2.81829	−0.241666
$137$	−15.3323	−1.30993	−0.654963	−	0.755661i	$-0.727316\pi$
$137$	−15.3323	−1.30993	−0.654963	+	0.755661i	$0.727316\pi$
$138$	−7.96999	−0.678451
$139$	12.6291	1.07119	0.535594	−	0.844475i	$-0.320088\pi$
$139$	12.6291	1.07119	0.535594	+	0.844475i	$0.320088\pi$
$140$	−0.186971	−0.0158019
$141$	−1.16605	−0.0981993
$142$	5.25860	0.441292
$143$	0.930566	0.0778178
$144$	1.00000	0.0833333
$145$	0.538369	0.0447091
$146$	1.42502	0.117935
$147$	6.11914	0.504698
$148$	−3.07370	−0.252657
$149$	−8.85231	−0.725209	−0.362605	−	0.931943i	$-0.618112\pi$
$149$	−8.85231	−0.725209	−0.362605	+	0.931943i	$0.618112\pi$
$150$	4.96031	0.405008
$151$	−9.29216	−0.756185	−0.378093	−	0.925768i	$-0.623420\pi$
$151$	−9.29216	−0.756185	−0.378093	+	0.925768i	$0.623420\pi$
$152$	−2.14373	−0.173880
$153$	−2.81829	−0.227845
$154$	0.938542	0.0756298
$155$	−0.308711	−0.0247963
$156$	0.930566	0.0745049
$157$	−14.9991	−1.19706	−0.598528	−	0.801102i	$-0.704247\pi$
$157$	−14.9991	−1.19706	−0.598528	+	0.801102i	$0.704247\pi$
$158$	−13.6055	−1.08240
$159$	2.09773	0.166361
$160$	0.199215	0.0157493
$161$	−7.48017	−0.589520
$162$	1.00000	0.0785674
$163$	17.8434	1.39760	0.698800	−	0.715317i	$-0.253718\pi$
$163$	17.8434	1.39760	0.698800	+	0.715317i	$0.253718\pi$
$164$	0.0554469	0.00432967
$165$	0.199215	0.0155088
$166$	−13.4433	−1.04341
$167$	−3.93394	−0.304418	−0.152209	−	0.988348i	$-0.548639\pi$
$167$	−3.93394	−0.304418	−0.152209	+	0.988348i	$0.548639\pi$
$168$	0.938542	0.0724101
$169$	−12.1340	−0.933388
$170$	−0.561444	−0.0430608
$171$	−2.14373	−0.163935
$172$	−9.33266	−0.711609
$173$	−1.12886	−0.0858256	−0.0429128	−	0.999079i	$-0.513664\pi$
$173$	−1.12886	−0.0858256	−0.0429128	+	0.999079i	$0.513664\pi$
$174$	−2.70246	−0.204873
$175$	4.65546	0.351920
$176$	−1.00000	−0.0753778
$177$	12.0548	0.906098
$178$	−12.9033	−0.967141
$179$	12.1157	0.905568	0.452784	−	0.891620i	$-0.350431\pi$
$179$	12.1157	0.905568	0.452784	+	0.891620i	$0.350431\pi$
$180$	0.199215	0.0148486
$181$	6.71371	0.499026	0.249513	−	0.968371i	$-0.419729\pi$
$181$	6.71371	0.499026	0.249513	+	0.968371i	$0.419729\pi$
$182$	0.873375	0.0647388
$183$	−1.00000	−0.0739221
$184$	7.96999	0.587556
$185$	−0.612326	−0.0450191
$186$	1.54964	0.113625
$187$	2.81829	0.206094
$188$	1.16605	0.0850431
$189$	0.938542	0.0682689
$190$	−0.427062	−0.0309824
$191$	20.5759	1.48882	0.744410	−	0.667723i	$-0.232731\pi$
$191$	20.5759	1.48882	0.744410	+	0.667723i	$0.232731\pi$
$192$	−1.00000	−0.0721688
$193$	−26.0578	−1.87568	−0.937841	−	0.347064i	$-0.887178\pi$
$193$	−26.0578	−1.87568	−0.937841	+	0.347064i	$0.887178\pi$
$194$	3.31812	0.238227
$195$	0.185382	0.0132755
$196$	−6.11914	−0.437081
$197$	16.5311	1.17779	0.588895	−	0.808210i	$-0.299563\pi$
$197$	16.5311	1.17779	0.588895	+	0.808210i	$0.299563\pi$
$198$	−1.00000	−0.0710669
$199$	−22.1799	−1.57229	−0.786145	−	0.618042i	$-0.787926\pi$
$199$	−22.1799	−1.57229	−0.786145	+	0.618042i	$0.787926\pi$
$200$	−4.96031	−0.350747
$201$	−13.9379	−0.983104
$202$	−3.39097	−0.238588
$203$	−2.53637	−0.178018
$204$	2.81829	0.197320
$205$	0.0110458	0.000771474 0
$206$	−8.10200	−0.564493
$207$	7.96999	0.553953
$208$	−0.930566	−0.0645231
$209$	2.14373	0.148285
$210$	0.186971	0.0129022
$211$	1.59697	0.109940	0.0549698	−	0.998488i	$-0.482494\pi$
$211$	1.59697	0.109940	0.0549698	+	0.998488i	$0.482494\pi$
$212$	−2.09773	−0.144073
$213$	−5.25860	−0.360314
$214$	−9.80155	−0.670020
$215$	−1.85920	−0.126797
$216$	−1.00000	−0.0680414
$217$	1.45440	0.0987313
$218$	15.6029	1.05676
$219$	−1.42502	−0.0962937
$220$	−0.199215	−0.0134310
$221$	2.62260	0.176415
$222$	3.07370	0.206293
$223$	26.0481	1.74431	0.872155	−	0.489229i	$-0.162722\pi$
$223$	26.0481	1.74431	0.872155	+	0.489229i	$0.162722\pi$
$224$	−0.938542	−0.0627090
$225$	−4.96031	−0.330688
$226$	−5.62215	−0.373980
$227$	−24.7573	−1.64320	−0.821601	−	0.570063i	$-0.806919\pi$
$227$	−24.7573	−1.64320	−0.821601	+	0.570063i	$0.806919\pi$
$228$	2.14373	0.141972
$229$	16.8840	1.11573	0.557863	−	0.829933i	$-0.311621\pi$
$229$	16.8840	1.11573	0.557863	+	0.829933i	$0.311621\pi$
$230$	1.58774	0.104692
$231$	−0.938542	−0.0617515
$232$	2.70246	0.177425
$233$	−12.1902	−0.798609	−0.399305	−	0.916818i	$-0.630748\pi$
$233$	−12.1902	−0.798609	−0.399305	+	0.916818i	$0.630748\pi$
$234$	−0.930566	−0.0608330
$235$	0.232294	0.0151532
$236$	−12.0548	−0.784704
$237$	13.6055	0.883774
$238$	2.64508	0.171455
$239$	0.484923	0.0313671	0.0156835	−	0.999877i	$-0.495008\pi$
$239$	0.484923	0.0313671	0.0156835	+	0.999877i	$0.495008\pi$
$240$	−0.199215	−0.0128592
$241$	−24.5810	−1.58340	−0.791701	−	0.610908i	$-0.790804\pi$
$241$	−24.5810	−1.58340	−0.791701	+	0.610908i	$0.790804\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−1.21902	−0.0778804
$246$	−0.0554469	−0.00353516
$247$	1.99488	0.126931
$248$	−1.54964	−0.0984023
$249$	13.4433	0.851938
$250$	−1.98424	−0.125494
$251$	−22.9068	−1.44586	−0.722932	−	0.690919i	$-0.757206\pi$
$251$	−22.9068	−1.44586	−0.722932	+	0.690919i	$0.757206\pi$
$252$	−0.938542	−0.0591226
$253$	−7.96999	−0.501069
$254$	−0.0754406	−0.00473357
$255$	0.561444	0.0351590
$256$	1.00000	0.0625000
$257$	−23.3154	−1.45437	−0.727187	−	0.686439i	$-0.759173\pi$
$257$	−23.3154	−1.45437	−0.727187	+	0.686439i	$0.759173\pi$
$258$	9.33266	0.581026
$259$	2.88480	0.179253
$260$	−0.185382	−0.0114969
$261$	2.70246	0.167278
$262$	5.79808	0.358207
$263$	15.0678	0.929120	0.464560	−	0.885542i	$-0.346213\pi$
$263$	15.0678	0.929120	0.464560	+	0.885542i	$0.346213\pi$
$264$	1.00000	0.0615457
$265$	−0.417898	−0.0256713
$266$	2.01198	0.123362
$267$	12.9033	0.789667
$268$	13.9379	0.851393
$269$	19.9678	1.21746	0.608728	−	0.793379i	$-0.291680\pi$
$269$	19.9678	1.21746	0.608728	+	0.793379i	$0.291680\pi$
$270$	−0.199215	−0.0121238
$271$	5.07884	0.308518	0.154259	−	0.988030i	$-0.450701\pi$
$271$	5.07884	0.308518	0.154259	+	0.988030i	$0.450701\pi$
$272$	−2.81829	−0.170884
$273$	−0.873375	−0.0528590
$274$	−15.3323	−0.926258
$275$	4.96031	0.299118
$276$	−7.96999	−0.479737
$277$	−23.7202	−1.42521	−0.712605	−	0.701565i	$-0.752485\pi$
$277$	−23.7202	−1.42521	−0.712605	+	0.701565i	$0.752485\pi$
$278$	12.6291	0.757445
$279$	−1.54964	−0.0927746
$280$	−0.186971	−0.0111737
$281$	−25.2415	−1.50578	−0.752890	−	0.658146i	$-0.771341\pi$
$281$	−25.2415	−1.50578	−0.752890	+	0.658146i	$0.771341\pi$
$282$	−1.16605	−0.0694374
$283$	−16.7970	−0.998478	−0.499239	−	0.866464i	$-0.666387\pi$
$283$	−16.7970	−0.998478	−0.499239	+	0.866464i	$0.666387\pi$
$284$	5.25860	0.312041
$285$	0.427062	0.0252970
$286$	0.930566	0.0550255
$287$	−0.0520392	−0.00307178
$288$	1.00000	0.0589256
$289$	−9.05724	−0.532779
$290$	0.538369	0.0316141
$291$	−3.31812	−0.194512
$292$	1.42502	0.0833928
$293$	−23.9767	−1.40074	−0.700368	−	0.713782i	$-0.746981\pi$
$293$	−23.9767	−1.40074	−0.700368	+	0.713782i	$0.746981\pi$
$294$	6.11914	0.356875
$295$	−2.40150	−0.139821
$296$	−3.07370	−0.178655
$297$	1.00000	0.0580259
$298$	−8.85231	−0.512800
$299$	−7.41660	−0.428913
$300$	4.96031	0.286384
$301$	8.75909	0.504866
$302$	−9.29216	−0.534704
$303$	3.39097	0.194806
$304$	−2.14373	−0.122951
$305$	0.199215	0.0114070
$306$	−2.81829	−0.161111
$307$	0.836498	0.0477415	0.0238707	−	0.999715i	$-0.492401\pi$
$307$	0.836498	0.0477415	0.0238707	+	0.999715i	$0.492401\pi$
$308$	0.938542	0.0534784
$309$	8.10200	0.460907
$310$	−0.308711	−0.0175336
$311$	3.19603	0.181230	0.0906152	−	0.995886i	$-0.471117\pi$
$311$	3.19603	0.181230	0.0906152	+	0.995886i	$0.471117\pi$
$312$	0.930566	0.0526829
$313$	22.3123	1.26117	0.630583	−	0.776122i	$-0.282816\pi$
$313$	22.3123	1.26117	0.630583	+	0.776122i	$0.282816\pi$
$314$	−14.9991	−0.846446
$315$	−0.186971	−0.0105346
$316$	−13.6055	−0.765371
$317$	−3.49725	−0.196425	−0.0982126	−	0.995165i	$-0.531313\pi$
$317$	−3.49725	−0.196425	−0.0982126	+	0.995165i	$0.531313\pi$
$318$	2.09773	0.117635
$319$	−2.70246	−0.151308
$320$	0.199215	0.0111364
$321$	9.80155	0.547069
$322$	−7.48017	−0.416854
$323$	6.04166	0.336167
$324$	1.00000	0.0555556
$325$	4.61590	0.256044
$326$	17.8434	0.988253
$327$	−15.6029	−0.862842
$328$	0.0554469	0.00306154
$329$	−1.09439	−0.0603356
$330$	0.199215	0.0109664
$331$	−1.29069	−0.0709425	−0.0354712	−	0.999371i	$-0.511293\pi$
$331$	−1.29069	−0.0709425	−0.0354712	+	0.999371i	$0.511293\pi$
$332$	−13.4433	−0.737800
$333$	−3.07370	−0.168438
$334$	−3.93394	−0.215256
$335$	2.77663	0.151704
$336$	0.938542	0.0512016
$337$	26.1145	1.42255	0.711275	−	0.702914i	$-0.248118\pi$
$337$	26.1145	1.42255	0.711275	+	0.702914i	$0.248118\pi$
$338$	−12.1340	−0.660005
$339$	5.62215	0.305353
$340$	−0.561444	−0.0304486
$341$	1.54964	0.0839178
$342$	−2.14373	−0.115920
$343$	12.3129	0.664832
$344$	−9.33266	−0.503183
$345$	−1.58774	−0.0854810
$346$	−1.12886	−0.0606879
$347$	20.4768	1.09925	0.549625	−	0.835412i	$-0.314771\pi$
$347$	20.4768	1.09925	0.549625	+	0.835412i	$0.314771\pi$
$348$	−2.70246	−0.144867
$349$	4.16398	0.222893	0.111446	−	0.993770i	$-0.464452\pi$
$349$	4.16398	0.222893	0.111446	+	0.993770i	$0.464452\pi$
$350$	4.65546	0.248845
$351$	0.930566	0.0496699
$352$	−1.00000	−0.0533002
$353$	11.3166	0.602323	0.301162	−	0.953573i	$-0.402626\pi$
$353$	11.3166	0.602323	0.301162	+	0.953573i	$0.402626\pi$
$354$	12.0548	0.640708
$355$	1.04759	0.0556003
$356$	−12.9033	−0.683872
$357$	−2.64508	−0.139993
$358$	12.1157	0.640333
$359$	7.60261	0.401250	0.200625	−	0.979668i	$-0.435703\pi$
$359$	7.60261	0.401250	0.200625	+	0.979668i	$0.435703\pi$
$360$	0.199215	0.0104995
$361$	−14.4044	−0.758127
$362$	6.71371	0.352865
$363$	−1.00000	−0.0524864
$364$	0.873375	0.0457773
$365$	0.283884	0.0148592
$366$	−1.00000	−0.0522708
$367$	19.2308	1.00384	0.501921	−	0.864914i	$-0.332627\pi$
$367$	19.2308	1.00384	0.501921	+	0.864914i	$0.332627\pi$
$368$	7.96999	0.415465
$369$	0.0554469	0.00288645
$370$	−0.612326	−0.0318333
$371$	1.96881	0.102215
$372$	1.54964	0.0803451
$373$	25.4162	1.31600	0.657999	−	0.753019i	$-0.271403\pi$
$373$	25.4162	1.31600	0.657999	+	0.753019i	$0.271403\pi$
$374$	2.81829	0.145730
$375$	1.98424	0.102466
$376$	1.16605	0.0601345
$377$	−2.51481	−0.129519
$378$	0.938542	0.0482734
$379$	27.5759	1.41648	0.708239	−	0.705973i	$-0.249490\pi$
$379$	27.5759	1.41648	0.708239	+	0.705973i	$0.249490\pi$
$380$	−0.427062	−0.0219078
$381$	0.0754406	0.00386494
$382$	20.5759	1.05275
$383$	27.0403	1.38170	0.690848	−	0.723000i	$-0.257237\pi$
$383$	27.0403	1.38170	0.690848	+	0.723000i	$0.257237\pi$
$384$	−1.00000	−0.0510310
$385$	0.186971	0.00952893
$386$	−26.0578	−1.32631
$387$	−9.33266	−0.474406
$388$	3.31812	0.168452
$389$	−31.3178	−1.58788	−0.793939	−	0.607998i	$-0.791973\pi$
$389$	−31.3178	−1.58788	−0.793939	+	0.607998i	$0.791973\pi$
$390$	0.185382	0.00938719
$391$	−22.4617	−1.13594
$392$	−6.11914	−0.309063
$393$	−5.79808	−0.292475
$394$	16.5311	0.832823
$395$	−2.71042	−0.136376
$396$	−1.00000	−0.0502519
$397$	24.8416	1.24676	0.623381	−	0.781918i	$-0.285759\pi$
$397$	24.8416	1.24676	0.623381	+	0.781918i	$0.285759\pi$
$398$	−22.1799	−1.11178
$399$	−2.01198	−0.100725
$400$	−4.96031	−0.248016
$401$	−34.5131	−1.72350	−0.861752	−	0.507330i	$-0.830633\pi$
$401$	−34.5131	−1.72350	−0.861752	+	0.507330i	$0.830633\pi$
$402$	−13.9379	−0.695160
$403$	1.44204	0.0718333
$404$	−3.39097	−0.168707
$405$	0.199215	0.00989905
$406$	−2.53637	−0.125878
$407$	3.07370	0.152358
$408$	2.81829	0.139526
$409$	15.4700	0.764944	0.382472	−	0.923967i	$-0.375073\pi$
$409$	15.4700	0.764944	0.382472	+	0.923967i	$0.375073\pi$
$410$	0.0110458	0.000545514 0
$411$	15.3323	0.756287
$412$	−8.10200	−0.399157
$413$	11.3140	0.556724
$414$	7.96999	0.391704
$415$	−2.67811	−0.131463
$416$	−0.930566	−0.0456247
$417$	−12.6291	−0.618451
$418$	2.14373	0.104853
$419$	2.24085	0.109473	0.0547364	−	0.998501i	$-0.482568\pi$
$419$	2.24085	0.109473	0.0547364	+	0.998501i	$0.482568\pi$
$420$	0.186971	0.00912326
$421$	−19.7845	−0.964239	−0.482119	−	0.876106i	$-0.660133\pi$
$421$	−19.7845	−0.964239	−0.482119	+	0.876106i	$0.660133\pi$
$422$	1.59697	0.0777391
$423$	1.16605	0.0566954
$424$	−2.09773	−0.101875
$425$	13.9796	0.678110
$426$	−5.25860	−0.254780
$427$	−0.938542	−0.0454192
$428$	−9.80155	−0.473776
$429$	−0.930566	−0.0449281
$430$	−1.85920	−0.0896587
$431$	11.6761	0.562417	0.281208	−	0.959647i	$-0.409265\pi$
$431$	11.6761	0.562417	0.281208	+	0.959647i	$0.409265\pi$
$432$	−1.00000	−0.0481125
$433$	−15.2260	−0.731715	−0.365858	−	0.930671i	$-0.619224\pi$
$433$	−15.2260	−0.731715	−0.365858	+	0.930671i	$0.619224\pi$
$434$	1.45440	0.0698136
$435$	−0.538369	−0.0258128
$436$	15.6029	0.747243
$437$	−17.0855	−0.817311
$438$	−1.42502	−0.0680899
$439$	6.09295	0.290801	0.145400	−	0.989373i	$-0.453553\pi$
$439$	6.09295	0.290801	0.145400	+	0.989373i	$0.453553\pi$
$440$	−0.199215	−0.00949718
$441$	−6.11914	−0.291388
$442$	2.62260	0.124745
$443$	33.9450	1.61278	0.806389	−	0.591386i	$-0.201419\pi$
$443$	33.9450	1.61278	0.806389	+	0.591386i	$0.201419\pi$
$444$	3.07370	0.145871
$445$	−2.57052	−0.121854
$446$	26.0481	1.23341
$447$	8.85231	0.418700
$448$	−0.938542	−0.0443419
$449$	3.99217	0.188402	0.0942010	−	0.995553i	$-0.469970\pi$
$449$	3.99217	0.188402	0.0942010	+	0.995553i	$0.469970\pi$
$450$	−4.96031	−0.233831
$451$	−0.0554469	−0.00261089
$452$	−5.62215	−0.264444
$453$	9.29216	0.436584
$454$	−24.7573	−1.16192
$455$	0.173989	0.00815673
$456$	2.14373	0.100389
$457$	27.0641	1.26600	0.633002	−	0.774151i	$-0.281823\pi$
$457$	27.0641	1.26600	0.633002	+	0.774151i	$0.281823\pi$
$458$	16.8840	0.788938
$459$	2.81829	0.131547
$460$	1.58774	0.0740287
$461$	−20.2773	−0.944409	−0.472204	−	0.881489i	$-0.656542\pi$
$461$	−20.2773	−0.944409	−0.472204	+	0.881489i	$0.656542\pi$
$462$	−0.938542	−0.0436649
$463$	23.4714	1.09081	0.545404	−	0.838173i	$-0.316376\pi$
$463$	23.4714	1.09081	0.545404	+	0.838173i	$0.316376\pi$
$464$	2.70246	0.125458
$465$	0.308711	0.0143161
$466$	−12.1902	−0.564702
$467$	−5.54314	−0.256506	−0.128253	−	0.991741i	$-0.540937\pi$
$467$	−5.54314	−0.256506	−0.128253	+	0.991741i	$0.540937\pi$
$468$	−0.930566	−0.0430154
$469$	−13.0813	−0.604039
$470$	0.232294	0.0107149
$471$	14.9991	0.691120
$472$	−12.0548	−0.554869
$473$	9.33266	0.429116
$474$	13.6055	0.624923
$475$	10.6336	0.487902
$476$	2.64508	0.121237
$477$	−2.09773	−0.0960484
$478$	0.484923	0.0221799
$479$	27.4024	1.25205	0.626024	−	0.779804i	$-0.284681\pi$
$479$	27.4024	1.25205	0.626024	+	0.779804i	$0.284681\pi$
$480$	−0.199215	−0.00909286
$481$	2.86028	0.130418
$482$	−24.5810	−1.11963
$483$	7.48017	0.340360
$484$	1.00000	0.0454545
$485$	0.661018	0.0300153
$486$	−1.00000	−0.0453609
$487$	8.78891	0.398264	0.199132	−	0.979973i	$-0.436188\pi$
$487$	8.78891	0.398264	0.199132	+	0.979973i	$0.436188\pi$
$488$	1.00000	0.0452679
$489$	−17.8434	−0.806905
$490$	−1.21902	−0.0550698
$491$	22.3994	1.01087	0.505434	−	0.862865i	$-0.331332\pi$
$491$	22.3994	1.01087	0.505434	+	0.862865i	$0.331332\pi$
$492$	−0.0554469	−0.00249974
$493$	−7.61630	−0.343021
$494$	1.99488	0.0897540
$495$	−0.199215	−0.00895403
$496$	−1.54964	−0.0695809
$497$	−4.93542	−0.221384
$498$	13.4433	0.602411
$499$	−11.3642	−0.508731	−0.254366	−	0.967108i	$-0.581867\pi$
$499$	−11.3642	−0.508731	−0.254366	+	0.967108i	$0.581867\pi$
$500$	−1.98424	−0.0887379
$501$	3.93394	0.175756
$502$	−22.9068	−1.02238
$503$	−34.9533	−1.55849	−0.779245	−	0.626719i	$-0.784397\pi$
$503$	−34.9533	−1.55849	−0.779245	+	0.626719i	$0.784397\pi$
$504$	−0.938542	−0.0418060
$505$	−0.675531	−0.0300607
$506$	−7.96999	−0.354309
$507$	12.1340	0.538892
$508$	−0.0754406	−0.00334714
$509$	−34.3363	−1.52193	−0.760966	−	0.648792i	$-0.775274\pi$
$509$	−34.3363	−1.52193	−0.760966	+	0.648792i	$0.775274\pi$
$510$	0.561444	0.0248612
$511$	−1.33744	−0.0591648
$512$	1.00000	0.0441942
$513$	2.14373	0.0946480
$514$	−23.3154	−1.02840
$515$	−1.61404	−0.0711229
$516$	9.33266	0.410848
$517$	−1.16605	−0.0512829
$518$	2.88480	0.126751
$519$	1.12886	0.0495514
$520$	−0.185382	−0.00812955
$521$	33.7575	1.47894	0.739471	−	0.673189i	$-0.235076\pi$
$521$	33.7575	1.47894	0.739471	+	0.673189i	$0.235076\pi$
$522$	2.70246	0.118283
$523$	26.7075	1.16784	0.583918	−	0.811813i	$-0.301519\pi$
$523$	26.7075	1.16784	0.583918	+	0.811813i	$0.301519\pi$
$524$	5.79808	0.253290
$525$	−4.65546	−0.203181
$526$	15.0678	0.656987
$527$	4.36734	0.190244
$528$	1.00000	0.0435194
$529$	40.5208	1.76177
$530$	−0.417898	−0.0181523
$531$	−12.0548	−0.523136
$532$	2.01198	0.0872304
$533$	−0.0515970	−0.00223491
$534$	12.9033	0.558379
$535$	−1.95261	−0.0844188
$536$	13.9379	0.602026
$537$	−12.1157	−0.522830
$538$	19.9678	0.860872
$539$	6.11914	0.263570
$540$	−0.199215	−0.00857283
$541$	41.5374	1.78583	0.892916	−	0.450224i	$-0.148656\pi$
$541$	41.5374	1.78583	0.892916	+	0.450224i	$0.148656\pi$
$542$	5.07884	0.218155
$543$	−6.71371	−0.288113
$544$	−2.81829	−0.120833
$545$	3.10832	0.133146
$546$	−0.873375	−0.0373770
$547$	31.0303	1.32676	0.663381	−	0.748282i	$-0.269121\pi$
$547$	31.0303	1.32676	0.663381	+	0.748282i	$0.269121\pi$
$548$	−15.3323	−0.654963
$549$	1.00000	0.0426790
$550$	4.96031	0.211508
$551$	−5.79334	−0.246804
$552$	−7.96999	−0.339225
$553$	12.7694	0.543008
$554$	−23.7202	−1.00778
$555$	0.612326	0.0259918
$556$	12.6291	0.535594
$557$	12.5287	0.530858	0.265429	−	0.964130i	$-0.414486\pi$
$557$	12.5287	0.530858	0.265429	+	0.964130i	$0.414486\pi$
$558$	−1.54964	−0.0656015
$559$	8.68465	0.367322
$560$	−0.186971	−0.00790097
$561$	−2.81829	−0.118988
$562$	−25.2415	−1.06475
$563$	−12.7520	−0.537432	−0.268716	−	0.963220i	$-0.586599\pi$
$563$	−12.7520	−0.537432	−0.268716	+	0.963220i	$0.586599\pi$
$564$	−1.16605	−0.0490996
$565$	−1.12001	−0.0471194
$566$	−16.7970	−0.706031
$567$	−0.938542	−0.0394150
$568$	5.25860	0.220646
$569$	−23.2054	−0.972820	−0.486410	−	0.873731i	$-0.661694\pi$
$569$	−23.2054	−0.972820	−0.486410	+	0.873731i	$0.661694\pi$
$570$	0.427062	0.0178877
$571$	−23.1629	−0.969339	−0.484670	−	0.874697i	$-0.661060\pi$
$571$	−23.1629	−0.969339	−0.484670	+	0.874697i	$0.661060\pi$
$572$	0.930566	0.0389089
$573$	−20.5759	−0.859571
$574$	−0.0520392	−0.00217207
$575$	−39.5337	−1.64867
$576$	1.00000	0.0416667
$577$	14.7675	0.614778	0.307389	−	0.951584i	$-0.400545\pi$
$577$	14.7675	0.614778	0.307389	+	0.951584i	$0.400545\pi$
$578$	−9.05724	−0.376732
$579$	26.0578	1.08293
$580$	0.538369	0.0223545
$581$	12.6171	0.523447
$582$	−3.31812	−0.137541
$583$	2.09773	0.0868791
$584$	1.42502	0.0589676
$585$	−0.185382	−0.00766461
$586$	−23.9767	−0.990470
$587$	−16.5984	−0.685089	−0.342545	−	0.939502i	$-0.611289\pi$
$587$	−16.5984	−0.685089	−0.342545	+	0.939502i	$0.611289\pi$
$588$	6.11914	0.252349
$589$	3.32201	0.136881
$590$	−2.40150	−0.0988682
$591$	−16.5311	−0.679997
$592$	−3.07370	−0.126328
$593$	9.09586	0.373522	0.186761	−	0.982405i	$-0.440201\pi$
$593$	9.09586	0.373522	0.186761	+	0.982405i	$0.440201\pi$
$594$	1.00000	0.0410305
$595$	0.526939	0.0216024
$596$	−8.85231	−0.362605
$597$	22.1799	0.907762
$598$	−7.41660	−0.303287
$599$	11.7677	0.480813	0.240407	−	0.970672i	$-0.422719\pi$
$599$	11.7677	0.480813	0.240407	+	0.970672i	$0.422719\pi$
$600$	4.96031	0.202504
$601$	−42.4127	−1.73005	−0.865024	−	0.501730i	$-0.832697\pi$
$601$	−42.4127	−1.73005	−0.865024	+	0.501730i	$0.832697\pi$
$602$	8.75909	0.356994
$603$	13.9379	0.567595
$604$	−9.29216	−0.378093
$605$	0.199215	0.00809922
$606$	3.39097	0.137749
$607$	21.7469	0.882680	0.441340	−	0.897340i	$-0.354503\pi$
$607$	21.7469	0.882680	0.441340	+	0.897340i	$0.354503\pi$
$608$	−2.14373	−0.0869398
$609$	2.53637	0.102779
$610$	0.199215	0.00806596
$611$	−1.08509	−0.0438979
$612$	−2.81829	−0.113923
$613$	−25.7719	−1.04092	−0.520459	−	0.853886i	$-0.674239\pi$
$613$	−25.7719	−1.04092	−0.520459	+	0.853886i	$0.674239\pi$
$614$	0.836498	0.0337583
$615$	−0.0110458	−0.000445411 0
$616$	0.938542	0.0378149
$617$	−26.4304	−1.06405	−0.532024	−	0.846729i	$-0.678568\pi$
$617$	−26.4304	−1.06405	−0.532024	+	0.846729i	$0.678568\pi$
$618$	8.10200	0.325910
$619$	6.49382	0.261009	0.130504	−	0.991448i	$-0.458340\pi$
$619$	6.49382	0.261009	0.130504	+	0.991448i	$0.458340\pi$
$620$	−0.308711	−0.0123981
$621$	−7.96999	−0.319825
$622$	3.19603	0.128149
$623$	12.1103	0.485187
$624$	0.930566	0.0372524
$625$	24.4063	0.976251
$626$	22.3123	0.891779
$627$	−2.14373	−0.0856124
$628$	−14.9991	−0.598528
$629$	8.66258	0.345400
$630$	−0.186971	−0.00744911
$631$	−22.5750	−0.898698	−0.449349	−	0.893356i	$-0.648344\pi$
$631$	−22.5750	−0.898698	−0.449349	+	0.893356i	$0.648344\pi$
$632$	−13.6055	−0.541199
$633$	−1.59697	−0.0634737
$634$	−3.49725	−0.138894
$635$	−0.0150289	−0.000596403 0
$636$	2.09773	0.0831804
$637$	5.69426	0.225615
$638$	−2.70246	−0.106991
$639$	5.25860	0.208027
$640$	0.199215	0.00787465
$641$	44.2425	1.74747	0.873736	−	0.486401i	$-0.161690\pi$
$641$	44.2425	1.74747	0.873736	+	0.486401i	$0.161690\pi$
$642$	9.80155	0.386837
$643$	−25.6461	−1.01138	−0.505692	−	0.862714i	$-0.668763\pi$
$643$	−25.6461	−1.01138	−0.505692	+	0.862714i	$0.668763\pi$
$644$	−7.48017	−0.294760
$645$	1.85920	0.0732060
$646$	6.04166	0.237706
$647$	−3.13328	−0.123182	−0.0615910	−	0.998101i	$-0.519617\pi$
$647$	−3.13328	−0.123182	−0.0615910	+	0.998101i	$0.519617\pi$
$648$	1.00000	0.0392837
$649$	12.0548	0.473194
$650$	4.61590	0.181050
$651$	−1.45440	−0.0570025
$652$	17.8434	0.698800
$653$	26.8131	1.04928	0.524638	−	0.851325i	$-0.324201\pi$
$653$	26.8131	1.04928	0.524638	+	0.851325i	$0.324201\pi$
$654$	−15.6029	−0.610122
$655$	1.15506	0.0451320
$656$	0.0554469	0.00216484
$657$	1.42502	0.0555952
$658$	−1.09439	−0.0426637
$659$	−2.19805	−0.0856237	−0.0428119	−	0.999083i	$-0.513632\pi$
$659$	−2.19805	−0.0856237	−0.0428119	+	0.999083i	$0.513632\pi$
$660$	0.199215	0.00775442
$661$	40.6428	1.58082	0.790412	−	0.612576i	$-0.209867\pi$
$661$	40.6428	1.58082	0.790412	+	0.612576i	$0.209867\pi$
$662$	−1.29069	−0.0501639
$663$	−2.62260	−0.101853
$664$	−13.4433	−0.521703
$665$	0.400816	0.0155430
$666$	−3.07370	−0.119104
$667$	21.5385	0.833976
$668$	−3.93394	−0.152209
$669$	−26.0481	−1.00708
$670$	2.77663	0.107271
$671$	−1.00000	−0.0386046
$672$	0.938542	0.0362050
$673$	−18.3820	−0.708575	−0.354287	−	0.935137i	$-0.615277\pi$
$673$	−18.3820	−0.708575	−0.354287	+	0.935137i	$0.615277\pi$
$674$	26.1145	1.00589
$675$	4.96031	0.190923
$676$	−12.1340	−0.466694
$677$	3.23297	0.124253	0.0621266	−	0.998068i	$-0.480212\pi$
$677$	3.23297	0.124253	0.0621266	+	0.998068i	$0.480212\pi$
$678$	5.62215	0.215917
$679$	−3.11419	−0.119512
$680$	−0.561444	−0.0215304
$681$	24.7573	0.948703
$682$	1.54964	0.0593388
$683$	−20.0172	−0.765938	−0.382969	−	0.923761i	$-0.625098\pi$
$683$	−20.0172	−0.765938	−0.382969	+	0.923761i	$0.625098\pi$
$684$	−2.14373	−0.0819676
$685$	−3.05442	−0.116703
$686$	12.3129	0.470107
$687$	−16.8840	−0.644165
$688$	−9.33266	−0.355804
$689$	1.95208	0.0743681
$690$	−1.58774	−0.0604442
$691$	26.8461	1.02127	0.510637	−	0.859796i	$-0.329410\pi$
$691$	26.8461	1.02127	0.510637	+	0.859796i	$0.329410\pi$
$692$	−1.12886	−0.0429128
$693$	0.938542	0.0356523
$694$	20.4768	0.777287
$695$	2.51591	0.0954337
$696$	−2.70246	−0.102436
$697$	−0.156265	−0.00591897
$698$	4.16398	0.157609
$699$	12.1902	0.461077
$700$	4.65546	0.175960
$701$	13.1369	0.496173	0.248087	−	0.968738i	$-0.420198\pi$
$701$	13.1369	0.496173	0.248087	+	0.968738i	$0.420198\pi$
$702$	0.930566	0.0351219
$703$	6.58919	0.248516
$704$	−1.00000	−0.0376889
$705$	−0.232294	−0.00874872
$706$	11.3166	0.425907
$707$	3.18257	0.119693
$708$	12.0548	0.453049
$709$	−20.9518	−0.786862	−0.393431	−	0.919354i	$-0.628712\pi$
$709$	−20.9518	−0.786862	−0.393431	+	0.919354i	$0.628712\pi$
$710$	1.04759	0.0393154
$711$	−13.6055	−0.510247
$712$	−12.9033	−0.483571
$713$	−12.3506	−0.462535
$714$	−2.64508	−0.0989897
$715$	0.185382	0.00693290
$716$	12.1157	0.452784
$717$	−0.484923	−0.0181098
$718$	7.60261	0.283727
$719$	−22.6934	−0.846321	−0.423160	−	0.906055i	$-0.639079\pi$
$719$	−22.6934	−0.846321	−0.423160	+	0.906055i	$0.639079\pi$
$720$	0.199215	0.00742429
$721$	7.60406	0.283190
$722$	−14.4044	−0.536077
$723$	24.5810	0.914178
$724$	6.71371	0.249513
$725$	−13.4050	−0.497850
$726$	−1.00000	−0.0371135
$727$	10.2405	0.379800	0.189900	−	0.981803i	$-0.439184\pi$
$727$	10.2405	0.379800	0.189900	+	0.981803i	$0.439184\pi$
$728$	0.873375	0.0323694
$729$	1.00000	0.0370370
$730$	0.283884	0.0105070
$731$	26.3021	0.972820
$732$	−1.00000	−0.0369611
$733$	−35.7426	−1.32018	−0.660092	−	0.751185i	$-0.729483\pi$
$733$	−35.7426	−1.32018	−0.660092	+	0.751185i	$0.729483\pi$
$734$	19.2308	0.709823
$735$	1.21902	0.0449643
$736$	7.96999	0.293778
$737$	−13.9379	−0.513409
$738$	0.0554469	0.00204103
$739$	−38.5874	−1.41946	−0.709731	−	0.704473i	$-0.751183\pi$
$739$	−38.5874	−1.41946	−0.709731	+	0.704473i	$0.751183\pi$
$740$	−0.612326	−0.0225096
$741$	−1.99488	−0.0732838
$742$	1.96881	0.0722772
$743$	3.54745	0.130143	0.0650716	−	0.997881i	$-0.479272\pi$
$743$	3.54745	0.130143	0.0650716	+	0.997881i	$0.479272\pi$
$744$	1.54964	0.0568126
$745$	−1.76351	−0.0646099
$746$	25.4162	0.930551
$747$	−13.4433	−0.491866
$748$	2.81829	0.103047
$749$	9.19917	0.336130
$750$	1.98424	0.0724542
$751$	36.3944	1.32805	0.664025	−	0.747710i	$-0.268847\pi$
$751$	36.3944	1.32805	0.664025	+	0.747710i	$0.268847\pi$
$752$	1.16605	0.0425215
$753$	22.9068	0.834770
$754$	−2.51481	−0.0915841
$755$	−1.85113	−0.0673696
$756$	0.938542	0.0341344
$757$	43.7812	1.59126	0.795628	−	0.605786i	$-0.207141\pi$
$757$	43.7812	1.59126	0.795628	+	0.605786i	$0.207141\pi$
$758$	27.5759	1.00160
$759$	7.96999	0.289292
$760$	−0.427062	−0.0154912
$761$	13.9320	0.505035	0.252517	−	0.967592i	$-0.418742\pi$
$761$	13.9320	0.505035	0.252517	+	0.967592i	$0.418742\pi$
$762$	0.0754406	0.00273293
$763$	−14.6440	−0.530147
$764$	20.5759	0.744410
$765$	−0.561444	−0.0202991
$766$	27.0403	0.977007
$767$	11.2178	0.405052
$768$	−1.00000	−0.0360844
$769$	1.34565	0.0485254	0.0242627	−	0.999706i	$-0.492276\pi$
$769$	1.34565	0.0485254	0.0242627	+	0.999706i	$0.492276\pi$
$770$	0.186971	0.00673797
$771$	23.3154	0.839683
$772$	−26.0578	−0.937841
$773$	−11.2542	−0.404784	−0.202392	−	0.979305i	$-0.564872\pi$
$773$	−11.2542	−0.404784	−0.202392	+	0.979305i	$0.564872\pi$
$774$	−9.33266	−0.335456
$775$	7.68671	0.276115
$776$	3.31812	0.119114
$777$	−2.88480	−0.103492
$778$	−31.3178	−1.12280
$779$	−0.118863	−0.00425872
$780$	0.185382	0.00663775
$781$	−5.25860	−0.188168
$782$	−22.4617	−0.803230
$783$	−2.70246	−0.0965779
$784$	−6.11914	−0.218541
$785$	−2.98803	−0.106647
$786$	−5.79808	−0.206811
$787$	−47.8303	−1.70497	−0.852484	−	0.522754i	$-0.824905\pi$
$787$	−47.8303	−1.70497	−0.852484	+	0.522754i	$0.824905\pi$
$788$	16.5311	0.588895
$789$	−15.0678	−0.536428
$790$	−2.71042	−0.0964324
$791$	5.27662	0.187615
$792$	−1.00000	−0.0355335
$793$	−0.930566	−0.0330454
$794$	24.8416	0.881594
$795$	0.417898	0.0148213
$796$	−22.1799	−0.786145
$797$	44.8011	1.58694	0.793469	−	0.608611i	$-0.208273\pi$
$797$	44.8011	1.58694	0.793469	+	0.608611i	$0.208273\pi$
$798$	−2.01198	−0.0712234
$799$	−3.28627	−0.116260
$800$	−4.96031	−0.175374
$801$	−12.9033	−0.455915
$802$	−34.5131	−1.21870
$803$	−1.42502	−0.0502878
$804$	−13.9379	−0.491552
$805$	−1.49016	−0.0525212
$806$	1.44204	0.0507938
$807$	−19.9678	−0.702899
$808$	−3.39097	−0.119294
$809$	−55.0757	−1.93636	−0.968179	−	0.250258i	$-0.919484\pi$
$809$	−55.0757	−1.93636	−0.968179	+	0.250258i	$0.919484\pi$
$810$	0.199215	0.00699969
$811$	37.9290	1.33187	0.665933	−	0.746011i	$-0.268033\pi$
$811$	37.9290	1.33187	0.665933	+	0.746011i	$0.268033\pi$
$812$	−2.53637	−0.0890090
$813$	−5.07884	−0.178123
$814$	3.07370	0.107733
$815$	3.55466	0.124514
$816$	2.81829	0.0986599
$817$	20.0067	0.699946
$818$	15.4700	0.540897
$819$	0.873375	0.0305182
$820$	0.0110458	0.000385737 0
$821$	54.2671	1.89393	0.946967	−	0.321332i	$-0.104131\pi$
$821$	54.2671	1.89393	0.946967	+	0.321332i	$0.104131\pi$
$822$	15.3323	0.534775
$823$	31.7253	1.10587	0.552936	−	0.833223i	$-0.313507\pi$
$823$	31.7253	1.10587	0.552936	+	0.833223i	$0.313507\pi$
$824$	−8.10200	−0.282246
$825$	−4.96031	−0.172696
$826$	11.3140	0.393664
$827$	13.6382	0.474245	0.237123	−	0.971480i	$-0.423796\pi$
$827$	13.6382	0.474245	0.237123	+	0.971480i	$0.423796\pi$
$828$	7.96999	0.276976
$829$	37.3762	1.29813	0.649064	−	0.760733i	$-0.275161\pi$
$829$	37.3762	1.29813	0.649064	+	0.760733i	$0.275161\pi$
$830$	−2.67811	−0.0929586
$831$	23.7202	0.822846
$832$	−0.930566	−0.0322616
$833$	17.2455	0.597521
$834$	−12.6291	−0.437311
$835$	−0.783699	−0.0271210
$836$	2.14373	0.0741425
$837$	1.54964	0.0535634
$838$	2.24085	0.0774089
$839$	−40.3172	−1.39191	−0.695953	−	0.718087i	$-0.745018\pi$
$839$	−40.3172	−1.39191	−0.695953	+	0.718087i	$0.745018\pi$
$840$	0.186971	0.00645112
$841$	−21.6967	−0.748163
$842$	−19.7845	−0.681820
$843$	25.2415	0.869363
$844$	1.59697	0.0549698
$845$	−2.41728	−0.0831569
$846$	1.16605	0.0400897
$847$	−0.938542	−0.0322487
$848$	−2.09773	−0.0720363
$849$	16.7970	0.576472
$850$	13.9796	0.479496
$851$	−24.4974	−0.839759
$852$	−5.25860	−0.180157
$853$	−43.2429	−1.48061	−0.740304	−	0.672272i	$-0.765319\pi$
$853$	−43.2429	−1.48061	−0.740304	+	0.672272i	$0.765319\pi$
$854$	−0.938542	−0.0321162
$855$	−0.427062	−0.0146052
$856$	−9.80155	−0.335010
$857$	−14.8079	−0.505827	−0.252913	−	0.967489i	$-0.581389\pi$
$857$	−14.8079	−0.505827	−0.252913	+	0.967489i	$0.581389\pi$
$858$	−0.930566	−0.0317690
$859$	31.0891	1.06075	0.530373	−	0.847764i	$-0.322052\pi$
$859$	31.0891	1.06075	0.530373	+	0.847764i	$0.322052\pi$
$860$	−1.85920	−0.0633983
$861$	0.0520392	0.00177349
$862$	11.6761	0.397689
$863$	−24.0179	−0.817579	−0.408789	−	0.912629i	$-0.634049\pi$
$863$	−24.0179	−0.817579	−0.408789	+	0.912629i	$0.634049\pi$
$864$	−1.00000	−0.0340207
$865$	−0.224885	−0.00764633
$866$	−15.2260	−0.517401
$867$	9.05724	0.307600
$868$	1.45440	0.0493656
$869$	13.6055	0.461536
$870$	−0.538369	−0.0182524
$871$	−12.9701	−0.439476
$872$	15.6029	0.528381
$873$	3.31812	0.112301
$874$	−17.0855	−0.577926
$875$	1.86229	0.0629569
$876$	−1.42502	−0.0481469
$877$	−14.8205	−0.500454	−0.250227	−	0.968187i	$-0.580505\pi$
$877$	−14.8205	−0.500454	−0.250227	+	0.968187i	$0.580505\pi$
$878$	6.09295	0.205627
$879$	23.9767	0.808715
$880$	−0.199215	−0.00671552
$881$	15.4417	0.520244	0.260122	−	0.965576i	$-0.416237\pi$
$881$	15.4417	0.520244	0.260122	+	0.965576i	$0.416237\pi$
$882$	−6.11914	−0.206042
$883$	39.6318	1.33371	0.666857	−	0.745185i	$-0.267639\pi$
$883$	39.6318	1.33371	0.666857	+	0.745185i	$0.267639\pi$
$884$	2.62260	0.0882077
$885$	2.40150	0.0807256
$886$	33.9450	1.14041
$887$	55.7710	1.87261	0.936303	−	0.351194i	$-0.114224\pi$
$887$	55.7710	1.87261	0.936303	+	0.351194i	$0.114224\pi$
$888$	3.07370	0.103147
$889$	0.0708042	0.00237470
$890$	−2.57052	−0.0861640
$891$	−1.00000	−0.0335013
$892$	26.0481	0.872155
$893$	−2.49970	−0.0836493
$894$	8.85231	0.296065
$895$	2.41362	0.0806784
$896$	−0.938542	−0.0313545
$897$	7.41660	0.247633
$898$	3.99217	0.133220
$899$	−4.18784	−0.139672
$900$	−4.96031	−0.165344
$901$	5.91201	0.196958
$902$	−0.0554469	−0.00184618
$903$	−8.75909	−0.291484
$904$	−5.62215	−0.186990
$905$	1.33747	0.0444589
$906$	9.29216	0.308711
$907$	−44.1857	−1.46716	−0.733580	−	0.679603i	$-0.762152\pi$
$907$	−44.1857	−1.46716	−0.733580	+	0.679603i	$0.762152\pi$
$908$	−24.7573	−0.821601
$909$	−3.39097	−0.112471
$910$	0.173989	0.00576768
$911$	−15.3537	−0.508689	−0.254345	−	0.967114i	$-0.581860\pi$
$911$	−15.3537	−0.508689	−0.254345	+	0.967114i	$0.581860\pi$
$912$	2.14373	0.0709860
$913$	13.4433	0.444910
$914$	27.0641	0.895199
$915$	−0.199215	−0.00658583
$916$	16.8840	0.557863
$917$	−5.44174	−0.179702
$918$	2.81829	0.0930174
$919$	−53.8386	−1.77597	−0.887986	−	0.459870i	$-0.847896\pi$
$919$	−53.8386	−1.77597	−0.887986	+	0.459870i	$0.847896\pi$
$920$	1.58774	0.0523462
$921$	−0.836498	−0.0275636
$922$	−20.2773	−0.667798
$923$	−4.89348	−0.161071
$924$	−0.938542	−0.0308758
$925$	15.2465	0.501303
$926$	23.4714	0.771318
$927$	−8.10200	−0.266104
$928$	2.70246	0.0887124
$929$	−34.4903	−1.13159	−0.565795	−	0.824546i	$-0.691431\pi$
$929$	−34.4903	−1.13159	−0.565795	+	0.824546i	$0.691431\pi$
$930$	0.308711	0.0101230
$931$	13.1178	0.429918
$932$	−12.1902	−0.399305
$933$	−3.19603	−0.104633
$934$	−5.54314	−0.181377
$935$	0.561444	0.0183612
$936$	−0.930566	−0.0304165
$937$	41.9490	1.37041	0.685207	−	0.728348i	$-0.259712\pi$
$937$	41.9490	1.37041	0.685207	+	0.728348i	$0.259712\pi$
$938$	−13.0813	−0.427120
$939$	−22.3123	−0.728134
$940$	0.232294	0.00757661
$941$	−9.72122	−0.316903	−0.158451	−	0.987367i	$-0.550650\pi$
$941$	−9.72122	−0.316903	−0.158451	+	0.987367i	$0.550650\pi$
$942$	14.9991	0.488696
$943$	0.441911	0.0143906
$944$	−12.0548	−0.392352
$945$	0.186971	0.00608217
$946$	9.33266	0.303431
$947$	31.9656	1.03874	0.519371	−	0.854549i	$-0.326166\pi$
$947$	31.9656	1.03874	0.519371	+	0.854549i	$0.326166\pi$
$948$	13.6055	0.441887
$949$	−1.32607	−0.0430461
$950$	10.6336	0.344999
$951$	3.49725	0.113406
$952$	2.64508	0.0857276
$953$	6.98466	0.226255	0.113128	−	0.993580i	$-0.463913\pi$
$953$	6.98466	0.226255	0.113128	+	0.993580i	$0.463913\pi$
$954$	−2.09773	−0.0679165
$955$	4.09902	0.132641
$956$	0.484923	0.0156835
$957$	2.70246	0.0873580
$958$	27.4024	0.885332
$959$	14.3900	0.464677
$960$	−0.199215	−0.00642962
$961$	−28.5986	−0.922536
$962$	2.86028	0.0922192
$963$	−9.80155	−0.315851
$964$	−24.5810	−0.791701
$965$	−5.19110	−0.167107
$966$	7.48017	0.240671
$967$	43.0194	1.38341	0.691706	−	0.722179i	$-0.256860\pi$
$967$	43.0194	1.38341	0.691706	+	0.722179i	$0.256860\pi$
$968$	1.00000	0.0321412
$969$	−6.04166	−0.194086
$970$	0.661018	0.0212240
$971$	−33.2011	−1.06547	−0.532737	−	0.846281i	$-0.678836\pi$
$971$	−33.2011	−1.06547	−0.532737	+	0.846281i	$0.678836\pi$
$972$	−1.00000	−0.0320750
$973$	−11.8530	−0.379988
$974$	8.78891	0.281615
$975$	−4.61590	−0.147827
$976$	1.00000	0.0320092
$977$	22.5679	0.722011	0.361005	−	0.932564i	$-0.382434\pi$
$977$	22.5679	0.722011	0.361005	+	0.932564i	$0.382434\pi$
$978$	−17.8434	−0.570568
$979$	12.9033	0.412390
$980$	−1.21902	−0.0389402
$981$	15.6029	0.498162
$982$	22.3994	0.714792
$983$	−35.5309	−1.13326	−0.566630	−	0.823973i	$-0.691753\pi$
$983$	−35.5309	−1.13326	−0.566630	+	0.823973i	$0.691753\pi$
$984$	−0.0554469	−0.00176758
$985$	3.29323	0.104931
$986$	−7.61630	−0.242553
$987$	1.09439	0.0348348
$988$	1.99488	0.0634657
$989$	−74.3812	−2.36519
$990$	−0.199215	−0.00633145
$991$	14.0232	0.445461	0.222731	−	0.974880i	$-0.428503\pi$
$991$	14.0232	0.445461	0.222731	+	0.974880i	$0.428503\pi$
$992$	−1.54964	−0.0492012
$993$	1.29069	0.0409587
$994$	−4.93542	−0.156542
$995$	−4.41855	−0.140078
$996$	13.4433	0.425969
$997$	35.4015	1.12118	0.560588	−	0.828095i	$-0.310575\pi$
$997$	35.4015	1.12118	0.560588	+	0.828095i	$0.310575\pi$
$998$	−11.3642	−0.359727
$999$	3.07370	0.0972476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.x.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.x.1.4	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.199215 q^{5} -1.00000 q^{6} -0.938542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.199215 q^{5} -1.00000 q^{6} -0.938542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.199215 q^{10} -1.00000 q^{11} -1.00000 q^{12} -0.930566 q^{13} -0.938542 q^{14} -0.199215 q^{15} +1.00000 q^{16} -2.81829 q^{17} +1.00000 q^{18} -2.14373 q^{19} +0.199215 q^{20} +0.938542 q^{21} -1.00000 q^{22} +7.96999 q^{23} -1.00000 q^{24} -4.96031 q^{25} -0.930566 q^{26} -1.00000 q^{27} -0.938542 q^{28} +2.70246 q^{29} -0.199215 q^{30} -1.54964 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.81829 q^{34} -0.186971 q^{35} +1.00000 q^{36} -3.07370 q^{37} -2.14373 q^{38} +0.930566 q^{39} +0.199215 q^{40} +0.0554469 q^{41} +0.938542 q^{42} -9.33266 q^{43} -1.00000 q^{44} +0.199215 q^{45} +7.96999 q^{46} +1.16605 q^{47} -1.00000 q^{48} -6.11914 q^{49} -4.96031 q^{50} +2.81829 q^{51} -0.930566 q^{52} -2.09773 q^{53} -1.00000 q^{54} -0.199215 q^{55} -0.938542 q^{56} +2.14373 q^{57} +2.70246 q^{58} -12.0548 q^{59} -0.199215 q^{60} +1.00000 q^{61} -1.54964 q^{62} -0.938542 q^{63} +1.00000 q^{64} -0.185382 q^{65} +1.00000 q^{66} +13.9379 q^{67} -2.81829 q^{68} -7.96999 q^{69} -0.186971 q^{70} +5.25860 q^{71} +1.00000 q^{72} +1.42502 q^{73} -3.07370 q^{74} +4.96031 q^{75} -2.14373 q^{76} +0.938542 q^{77} +0.930566 q^{78} -13.6055 q^{79} +0.199215 q^{80} +1.00000 q^{81} +0.0554469 q^{82} -13.4433 q^{83} +0.938542 q^{84} -0.561444 q^{85} -9.33266 q^{86} -2.70246 q^{87} -1.00000 q^{88} -12.9033 q^{89} +0.199215 q^{90} +0.873375 q^{91} +7.96999 q^{92} +1.54964 q^{93} +1.16605 q^{94} -0.427062 q^{95} -1.00000 q^{96} +3.31812 q^{97} -6.11914 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + q^14 + 6 * q^15 + 6 * q^16 - 13 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - q^21 - 6 * q^22 - 11 * q^23 - 6 * q^24 + 8 * q^25 + 2 * q^26 - 6 * q^27 + q^28 - 14 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + 6 * q^33 - 13 * q^34 - 13 * q^35 + 6 * q^36 - 6 * q^37 + q^38 - 2 * q^39 - 6 * q^40 - 25 * q^41 - q^42 + 19 * q^43 - 6 * q^44 - 6 * q^45 - 11 * q^46 - 10 * q^47 - 6 * q^48 - 5 * q^49 + 8 * q^50 + 13 * q^51 + 2 * q^52 - 17 * q^53 - 6 * q^54 + 6 * q^55 + q^56 - q^57 - 14 * q^58 - 14 * q^59 + 6 * q^60 + 6 * q^61 - 5 * q^62 + q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 12 * q^67 - 13 * q^68 + 11 * q^69 - 13 * q^70 + 6 * q^71 + 6 * q^72 - 29 * q^73 - 6 * q^74 - 8 * q^75 + q^76 - q^77 - 2 * q^78 - 24 * q^79 - 6 * q^80 + 6 * q^81 - 25 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 19 * q^86 + 14 * q^87 - 6 * q^88 - 4 * q^89 - 6 * q^90 - 29 * q^91 - 11 * q^92 + 5 * q^93 - 10 * q^94 - 27 * q^95 - 6 * q^96 - 5 * q^97 - 5 * q^98 - 6 * q^99

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