LMFDB - Embedded newform 4026.2.a.z.1.5

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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 18x^{5} - 10x^{4} + 91x^{3} + 90x^{2} - 66x - 56 $ x^7 - 18x^5 - 10x^4 + 91x^3 + 90x^2 - 66*x - 56
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.63895$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.19404 q^{5} +1.00000 q^{6} +1.89767 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.19404 q^{5} +1.00000 q^{6} +1.89767 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.19404 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.371358 q^{13} -1.89767 q^{14} -2.19404 q^{15} +1.00000 q^{16} +6.08408 q^{17} -1.00000 q^{18} +0.286668 q^{19} +2.19404 q^{20} -1.89767 q^{21} -1.00000 q^{22} -2.45625 q^{23} +1.00000 q^{24} -0.186181 q^{25} -0.371358 q^{26} -1.00000 q^{27} +1.89767 q^{28} +2.92393 q^{29} +2.19404 q^{30} +4.95241 q^{31} -1.00000 q^{32} -1.00000 q^{33} -6.08408 q^{34} +4.16357 q^{35} +1.00000 q^{36} +1.79170 q^{37} -0.286668 q^{38} -0.371358 q^{39} -2.19404 q^{40} -7.72555 q^{41} +1.89767 q^{42} +9.98983 q^{43} +1.00000 q^{44} +2.19404 q^{45} +2.45625 q^{46} +3.88802 q^{47} -1.00000 q^{48} -3.39884 q^{49} +0.186181 q^{50} -6.08408 q^{51} +0.371358 q^{52} +3.61101 q^{53} +1.00000 q^{54} +2.19404 q^{55} -1.89767 q^{56} -0.286668 q^{57} -2.92393 q^{58} +8.06260 q^{59} -2.19404 q^{60} -1.00000 q^{61} -4.95241 q^{62} +1.89767 q^{63} +1.00000 q^{64} +0.814774 q^{65} +1.00000 q^{66} -9.76167 q^{67} +6.08408 q^{68} +2.45625 q^{69} -4.16357 q^{70} +13.1729 q^{71} -1.00000 q^{72} -4.55463 q^{73} -1.79170 q^{74} +0.186181 q^{75} +0.286668 q^{76} +1.89767 q^{77} +0.371358 q^{78} +8.68046 q^{79} +2.19404 q^{80} +1.00000 q^{81} +7.72555 q^{82} -8.34840 q^{83} -1.89767 q^{84} +13.3487 q^{85} -9.98983 q^{86} -2.92393 q^{87} -1.00000 q^{88} -1.14636 q^{89} -2.19404 q^{90} +0.704716 q^{91} -2.45625 q^{92} -4.95241 q^{93} -3.88802 q^{94} +0.628961 q^{95} +1.00000 q^{96} -8.56741 q^{97} +3.39884 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} + 7 q^{11} - 7 q^{12} - 7 q^{13} + 4 q^{14} - 2 q^{15} + 7 q^{16} - 4 q^{17} - 7 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{21} - 7 q^{22} - q^{23} + 7 q^{24} + 5 q^{25} + 7 q^{26} - 7 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 7 q^{32} - 7 q^{33} + 4 q^{34} + 13 q^{35} + 7 q^{36} - 15 q^{37} + 4 q^{38} + 7 q^{39} - 2 q^{40} + q^{41} - 4 q^{42} - 13 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} + 11 q^{47} - 7 q^{48} + 9 q^{49} - 5 q^{50} + 4 q^{51} - 7 q^{52} + 14 q^{53} + 7 q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{57} - 6 q^{58} + 39 q^{59} - 2 q^{60} - 7 q^{61} - 7 q^{62} - 4 q^{63} + 7 q^{64} - 2 q^{65} + 7 q^{66} - 3 q^{67} - 4 q^{68} + q^{69} - 13 q^{70} + 12 q^{71} - 7 q^{72} - 21 q^{73} + 15 q^{74} - 5 q^{75} - 4 q^{76} - 4 q^{77} - 7 q^{78} + 15 q^{79} + 2 q^{80} + 7 q^{81} - q^{82} + 5 q^{83} + 4 q^{84} - 34 q^{85} + 13 q^{86} - 6 q^{87} - 7 q^{88} - 8 q^{89} - 2 q^{90} + 29 q^{91} - q^{92} - 7 q^{93} - 11 q^{94} + 13 q^{95} + 7 q^{96} - 20 q^{97} - 9 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 + 7 * q^11 - 7 * q^12 - 7 * q^13 + 4 * q^14 - 2 * q^15 + 7 * q^16 - 4 * q^17 - 7 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^21 - 7 * q^22 - q^23 + 7 * q^24 + 5 * q^25 + 7 * q^26 - 7 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 7 * q^32 - 7 * q^33 + 4 * q^34 + 13 * q^35 + 7 * q^36 - 15 * q^37 + 4 * q^38 + 7 * q^39 - 2 * q^40 + q^41 - 4 * q^42 - 13 * q^43 + 7 * q^44 + 2 * q^45 + q^46 + 11 * q^47 - 7 * q^48 + 9 * q^49 - 5 * q^50 + 4 * q^51 - 7 * q^52 + 14 * q^53 + 7 * q^54 + 2 * q^55 + 4 * q^56 + 4 * q^57 - 6 * q^58 + 39 * q^59 - 2 * q^60 - 7 * q^61 - 7 * q^62 - 4 * q^63 + 7 * q^64 - 2 * q^65 + 7 * q^66 - 3 * q^67 - 4 * q^68 + q^69 - 13 * q^70 + 12 * q^71 - 7 * q^72 - 21 * q^73 + 15 * q^74 - 5 * q^75 - 4 * q^76 - 4 * q^77 - 7 * q^78 + 15 * q^79 + 2 * q^80 + 7 * q^81 - q^82 + 5 * q^83 + 4 * q^84 - 34 * q^85 + 13 * q^86 - 6 * q^87 - 7 * q^88 - 8 * q^89 - 2 * q^90 + 29 * q^91 - q^92 - 7 * q^93 - 11 * q^94 + 13 * q^95 + 7 * q^96 - 20 * q^97 - 9 * q^98 + 7 * 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
$5$	2.19404	0.981205	0.490603	−	0.871383i	$-0.336777\pi$
$5$	2.19404	0.981205	0.490603	+	0.871383i	$0.336777\pi$
$6$	1.00000	0.408248
$7$	1.89767	0.717253	0.358627	−	0.933481i	$-0.383245\pi$
$7$	1.89767	0.717253	0.358627	+	0.933481i	$0.383245\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.19404	−0.693817
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	0.371358	0.102996	0.0514980	−	0.998673i	$-0.483600\pi$
$13$	0.371358	0.102996	0.0514980	+	0.998673i	$0.483600\pi$
$14$	−1.89767	−0.507175
$15$	−2.19404	−0.566499
$16$	1.00000	0.250000
$17$	6.08408	1.47560	0.737802	−	0.675017i	$-0.235864\pi$
$17$	6.08408	1.47560	0.737802	+	0.675017i	$0.235864\pi$
$18$	−1.00000	−0.235702
$19$	0.286668	0.0657660	0.0328830	−	0.999459i	$-0.489531\pi$
$19$	0.286668	0.0657660	0.0328830	+	0.999459i	$0.489531\pi$
$20$	2.19404	0.490603
$21$	−1.89767	−0.414106
$22$	−1.00000	−0.213201
$23$	−2.45625	−0.512163	−0.256081	−	0.966655i	$-0.582432\pi$
$23$	−2.45625	−0.512163	−0.256081	+	0.966655i	$0.582432\pi$
$24$	1.00000	0.204124
$25$	−0.186181	−0.0372361
$26$	−0.371358	−0.0728292
$27$	−1.00000	−0.192450
$28$	1.89767	0.358627
$29$	2.92393	0.542960	0.271480	−	0.962444i	$-0.412487\pi$
$29$	2.92393	0.542960	0.271480	+	0.962444i	$0.412487\pi$
$30$	2.19404	0.400575
$31$	4.95241	0.889480	0.444740	−	0.895660i	$-0.353296\pi$
$31$	4.95241	0.889480	0.444740	+	0.895660i	$0.353296\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−6.08408	−1.04341
$35$	4.16357	0.703773
$36$	1.00000	0.166667
$37$	1.79170	0.294554	0.147277	−	0.989095i	$-0.452949\pi$
$37$	1.79170	0.294554	0.147277	+	0.989095i	$0.452949\pi$
$38$	−0.286668	−0.0465036
$39$	−0.371358	−0.0594648
$40$	−2.19404	−0.346908
$41$	−7.72555	−1.20653	−0.603264	−	0.797542i	$-0.706133\pi$
$41$	−7.72555	−1.20653	−0.603264	+	0.797542i	$0.706133\pi$
$42$	1.89767	0.292817
$43$	9.98983	1.52343	0.761717	−	0.647910i	$-0.224357\pi$
$43$	9.98983	1.52343	0.761717	+	0.647910i	$0.224357\pi$
$44$	1.00000	0.150756
$45$	2.19404	0.327068
$46$	2.45625	0.362154
$47$	3.88802	0.567126	0.283563	−	0.958954i	$-0.408483\pi$
$47$	3.88802	0.567126	0.283563	+	0.958954i	$0.408483\pi$
$48$	−1.00000	−0.144338
$49$	−3.39884	−0.485548
$50$	0.186181	0.0263299
$51$	−6.08408	−0.851941
$52$	0.371358	0.0514980
$53$	3.61101	0.496010	0.248005	−	0.968759i	$-0.420225\pi$
$53$	3.61101	0.496010	0.248005	+	0.968759i	$0.420225\pi$
$54$	1.00000	0.136083
$55$	2.19404	0.295845
$56$	−1.89767	−0.253587
$57$	−0.286668	−0.0379700
$58$	−2.92393	−0.383930
$59$	8.06260	1.04966	0.524831	−	0.851207i	$-0.324129\pi$
$59$	8.06260	1.04966	0.524831	+	0.851207i	$0.324129\pi$
$60$	−2.19404	−0.283250
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−4.95241	−0.628957
$63$	1.89767	0.239084
$64$	1.00000	0.125000
$65$	0.814774	0.101060
$66$	1.00000	0.123091
$67$	−9.76167	−1.19258	−0.596289	−	0.802770i	$-0.703359\pi$
$67$	−9.76167	−1.19258	−0.596289	+	0.802770i	$0.703359\pi$
$68$	6.08408	0.737802
$69$	2.45625	0.295697
$70$	−4.16357	−0.497642
$71$	13.1729	1.56334	0.781670	−	0.623692i	$-0.214368\pi$
$71$	13.1729	1.56334	0.781670	+	0.623692i	$0.214368\pi$
$72$	−1.00000	−0.117851
$73$	−4.55463	−0.533079	−0.266540	−	0.963824i	$-0.585880\pi$
$73$	−4.55463	−0.533079	−0.266540	+	0.963824i	$0.585880\pi$
$74$	−1.79170	−0.208281
$75$	0.186181	0.0214983
$76$	0.286668	0.0328830
$77$	1.89767	0.216260
$78$	0.371358	0.0420480
$79$	8.68046	0.976628	0.488314	−	0.872668i	$-0.337612\pi$
$79$	8.68046	0.976628	0.488314	+	0.872668i	$0.337612\pi$
$80$	2.19404	0.245301
$81$	1.00000	0.111111
$82$	7.72555	0.853144
$83$	−8.34840	−0.916356	−0.458178	−	0.888860i	$-0.651498\pi$
$83$	−8.34840	−0.916356	−0.458178	+	0.888860i	$0.651498\pi$
$84$	−1.89767	−0.207053
$85$	13.3487	1.44787
$86$	−9.98983	−1.07723
$87$	−2.92393	−0.313478
$88$	−1.00000	−0.106600
$89$	−1.14636	−0.121514	−0.0607571	−	0.998153i	$-0.519352\pi$
$89$	−1.14636	−0.121514	−0.0607571	+	0.998153i	$0.519352\pi$
$90$	−2.19404	−0.231272
$91$	0.704716	0.0738743
$92$	−2.45625	−0.256081
$93$	−4.95241	−0.513541
$94$	−3.88802	−0.401019
$95$	0.628961	0.0645300
$96$	1.00000	0.102062
$97$	−8.56741	−0.869889	−0.434944	−	0.900457i	$-0.643232\pi$
$97$	−8.56741	−0.869889	−0.434944	+	0.900457i	$0.643232\pi$
$98$	3.39884	0.343334
$99$	1.00000	0.100504
$100$	−0.186181	−0.0186181
$101$	9.14449	0.909911	0.454955	−	0.890514i	$-0.349655\pi$
$101$	9.14449	0.909911	0.454955	+	0.890514i	$0.349655\pi$
$102$	6.08408	0.602413
$103$	5.89973	0.581318	0.290659	−	0.956827i	$-0.406125\pi$
$103$	5.89973	0.581318	0.290659	+	0.956827i	$0.406125\pi$
$104$	−0.371358	−0.0364146
$105$	−4.16357	−0.406323
$106$	−3.61101	−0.350732
$107$	5.12090	0.495056	0.247528	−	0.968881i	$-0.420382\pi$
$107$	5.12090	0.495056	0.247528	+	0.968881i	$0.420382\pi$
$108$	−1.00000	−0.0962250
$109$	−17.0172	−1.62995	−0.814977	−	0.579493i	$-0.803251\pi$
$109$	−17.0172	−1.62995	−0.814977	+	0.579493i	$0.803251\pi$
$110$	−2.19404	−0.209194
$111$	−1.79170	−0.170061
$112$	1.89767	0.179313
$113$	−5.35385	−0.503647	−0.251824	−	0.967773i	$-0.581030\pi$
$113$	−5.35385	−0.503647	−0.251824	+	0.967773i	$0.581030\pi$
$114$	0.286668	0.0268489
$115$	−5.38911	−0.502537
$116$	2.92393	0.271480
$117$	0.371358	0.0343320
$118$	−8.06260	−0.742223
$119$	11.5456	1.05838
$120$	2.19404	0.200288
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	7.72555	0.696589
$124$	4.95241	0.444740
$125$	−11.3787	−1.01774
$126$	−1.89767	−0.169058
$127$	3.70014	0.328334	0.164167	−	0.986433i	$-0.447506\pi$
$127$	3.70014	0.328334	0.164167	+	0.986433i	$0.447506\pi$
$128$	−1.00000	−0.0883883
$129$	−9.98983	−0.879555
$130$	−0.814774	−0.0714604
$131$	−15.6393	−1.36641	−0.683207	−	0.730224i	$-0.739416\pi$
$131$	−15.6393	−1.36641	−0.683207	+	0.730224i	$0.739416\pi$
$132$	−1.00000	−0.0870388
$133$	0.544001	0.0471709
$134$	9.76167	0.843280
$135$	−2.19404	−0.188833
$136$	−6.08408	−0.521705
$137$	14.8897	1.27211	0.636056	−	0.771643i	$-0.280565\pi$
$137$	14.8897	1.27211	0.636056	+	0.771643i	$0.280565\pi$
$138$	−2.45625	−0.209090
$139$	8.16249	0.692333	0.346167	−	0.938173i	$-0.387483\pi$
$139$	8.16249	0.692333	0.346167	+	0.938173i	$0.387483\pi$
$140$	4.16357	0.351886
$141$	−3.88802	−0.327430
$142$	−13.1729	−1.10545
$143$	0.371358	0.0310545
$144$	1.00000	0.0833333
$145$	6.41522	0.532755
$146$	4.55463	0.376944
$147$	3.39884	0.280331
$148$	1.79170	0.147277
$149$	1.63177	0.133680	0.0668400	−	0.997764i	$-0.478708\pi$
$149$	1.63177	0.133680	0.0668400	+	0.997764i	$0.478708\pi$
$150$	−0.186181	−0.0152016
$151$	2.53234	0.206079	0.103040	−	0.994677i	$-0.467143\pi$
$151$	2.53234	0.206079	0.103040	+	0.994677i	$0.467143\pi$
$152$	−0.286668	−0.0232518
$153$	6.08408	0.491868
$154$	−1.89767	−0.152919
$155$	10.8658	0.872762
$156$	−0.371358	−0.0297324
$157$	−17.3822	−1.38725	−0.693625	−	0.720336i	$-0.743988\pi$
$157$	−17.3822	−1.38725	−0.693625	+	0.720336i	$0.743988\pi$
$158$	−8.68046	−0.690580
$159$	−3.61101	−0.286371
$160$	−2.19404	−0.173454
$161$	−4.66115	−0.367350
$162$	−1.00000	−0.0785674
$163$	−17.4219	−1.36459	−0.682296	−	0.731076i	$-0.739018\pi$
$163$	−17.4219	−1.36459	−0.682296	+	0.731076i	$0.739018\pi$
$164$	−7.72555	−0.603264
$165$	−2.19404	−0.170806
$166$	8.34840	0.647962
$167$	7.28958	0.564084	0.282042	−	0.959402i	$-0.408988\pi$
$167$	7.28958	0.564084	0.282042	+	0.959402i	$0.408988\pi$
$168$	1.89767	0.146409
$169$	−12.8621	−0.989392
$170$	−13.3487	−1.02380
$171$	0.286668	0.0219220
$172$	9.98983	0.761717
$173$	24.0574	1.82905	0.914526	−	0.404527i	$-0.132564\pi$
$173$	24.0574	1.82905	0.914526	+	0.404527i	$0.132564\pi$
$174$	2.92393	0.221662
$175$	−0.353310	−0.0267077
$176$	1.00000	0.0753778
$177$	−8.06260	−0.606022
$178$	1.14636	0.0859236
$179$	22.2002	1.65932	0.829660	−	0.558269i	$-0.188534\pi$
$179$	22.2002	1.65932	0.829660	+	0.558269i	$0.188534\pi$
$180$	2.19404	0.163534
$181$	5.16788	0.384126	0.192063	−	0.981383i	$-0.438482\pi$
$181$	5.16788	0.384126	0.192063	+	0.981383i	$0.438482\pi$
$182$	−0.704716	−0.0522370
$183$	1.00000	0.0739221
$184$	2.45625	0.181077
$185$	3.93106	0.289018
$186$	4.95241	0.363129
$187$	6.08408	0.444912
$188$	3.88802	0.283563
$189$	−1.89767	−0.138035
$190$	−0.628961	−0.0456296
$191$	−16.1316	−1.16724	−0.583619	−	0.812027i	$-0.698364\pi$
$191$	−16.1316	−1.16724	−0.583619	+	0.812027i	$0.698364\pi$
$192$	−1.00000	−0.0721688
$193$	−26.1324	−1.88105	−0.940525	−	0.339725i	$-0.889666\pi$
$193$	−26.1324	−1.88105	−0.940525	+	0.339725i	$0.889666\pi$
$194$	8.56741	0.615104
$195$	−0.814774	−0.0583472
$196$	−3.39884	−0.242774
$197$	−22.0877	−1.57368	−0.786842	−	0.617155i	$-0.788285\pi$
$197$	−22.0877	−1.57368	−0.786842	+	0.617155i	$0.788285\pi$
$198$	−1.00000	−0.0710669
$199$	2.07994	0.147443	0.0737216	−	0.997279i	$-0.476512\pi$
$199$	2.07994	0.147443	0.0737216	+	0.997279i	$0.476512\pi$
$200$	0.186181	0.0131650
$201$	9.76167	0.688535
$202$	−9.14449	−0.643404
$203$	5.54866	0.389439
$204$	−6.08408	−0.425970
$205$	−16.9502	−1.18385
$206$	−5.89973	−0.411054
$207$	−2.45625	−0.170721
$208$	0.371358	0.0257490
$209$	0.286668	0.0198292
$210$	4.16357	0.287314
$211$	−16.1297	−1.11041	−0.555206	−	0.831713i	$-0.687361\pi$
$211$	−16.1297	−1.11041	−0.555206	+	0.831713i	$0.687361\pi$
$212$	3.61101	0.248005
$213$	−13.1729	−0.902595
$214$	−5.12090	−0.350057
$215$	21.9181	1.49480
$216$	1.00000	0.0680414
$217$	9.39806	0.637982
$218$	17.0172	1.15255
$219$	4.55463	0.307773
$220$	2.19404	0.147922
$221$	2.25937	0.151982
$222$	1.79170	0.120251
$223$	22.8496	1.53012	0.765062	−	0.643957i	$-0.222708\pi$
$223$	22.8496	1.53012	0.765062	+	0.643957i	$0.222708\pi$
$224$	−1.89767	−0.126794
$225$	−0.186181	−0.0124120
$226$	5.35385	0.356133
$227$	2.98137	0.197880	0.0989402	−	0.995093i	$-0.468455\pi$
$227$	2.98137	0.197880	0.0989402	+	0.995093i	$0.468455\pi$
$228$	−0.286668	−0.0189850
$229$	−0.396149	−0.0261783	−0.0130891	−	0.999914i	$-0.504167\pi$
$229$	−0.396149	−0.0261783	−0.0130891	+	0.999914i	$0.504167\pi$
$230$	5.38911	0.355347
$231$	−1.89767	−0.124858
$232$	−2.92393	−0.191965
$233$	17.9908	1.17862	0.589308	−	0.807909i	$-0.299401\pi$
$233$	17.9908	1.17862	0.589308	+	0.807909i	$0.299401\pi$
$234$	−0.371358	−0.0242764
$235$	8.53048	0.556467
$236$	8.06260	0.524831
$237$	−8.68046	−0.563856
$238$	−11.5456	−0.748389
$239$	−13.2531	−0.857269	−0.428635	−	0.903478i	$-0.641005\pi$
$239$	−13.2531	−0.857269	−0.428635	+	0.903478i	$0.641005\pi$
$240$	−2.19404	−0.141625
$241$	−4.15809	−0.267846	−0.133923	−	0.990992i	$-0.542758\pi$
$241$	−4.15809	−0.267846	−0.133923	+	0.990992i	$0.542758\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−7.45719	−0.476422
$246$	−7.72555	−0.492563
$247$	0.106456	0.00677365
$248$	−4.95241	−0.314479
$249$	8.34840	0.529058
$250$	11.3787	0.719652
$251$	0.947287	0.0597922	0.0298961	−	0.999553i	$-0.490482\pi$
$251$	0.947287	0.0597922	0.0298961	+	0.999553i	$0.490482\pi$
$252$	1.89767	0.119542
$253$	−2.45625	−0.154423
$254$	−3.70014	−0.232167
$255$	−13.3487	−0.835929
$256$	1.00000	0.0625000
$257$	16.4809	1.02805	0.514024	−	0.857776i	$-0.328154\pi$
$257$	16.4809	1.02805	0.514024	+	0.857776i	$0.328154\pi$
$258$	9.98983	0.621939
$259$	3.40006	0.211269
$260$	0.814774	0.0505302
$261$	2.92393	0.180987
$262$	15.6393	0.966201
$263$	1.72050	0.106091	0.0530454	−	0.998592i	$-0.483107\pi$
$263$	1.72050	0.106091	0.0530454	+	0.998592i	$0.483107\pi$
$264$	1.00000	0.0615457
$265$	7.92270	0.486687
$266$	−0.544001	−0.0333549
$267$	1.14636	0.0701563
$268$	−9.76167	−0.596289
$269$	32.0556	1.95447	0.977233	−	0.212171i	$-0.0680533\pi$
$269$	32.0556	1.95447	0.977233	+	0.212171i	$0.0680533\pi$
$270$	2.19404	0.133525
$271$	5.65368	0.343436	0.171718	−	0.985146i	$-0.445068\pi$
$271$	5.65368	0.343436	0.171718	+	0.985146i	$0.445068\pi$
$272$	6.08408	0.368901
$273$	−0.704716	−0.0426513
$274$	−14.8897	−0.899519
$275$	−0.186181	−0.0112271
$276$	2.45625	0.147849
$277$	2.50520	0.150523	0.0752614	−	0.997164i	$-0.476021\pi$
$277$	2.50520	0.150523	0.0752614	+	0.997164i	$0.476021\pi$
$278$	−8.16249	−0.489554
$279$	4.95241	0.296493
$280$	−4.16357	−0.248821
$281$	−22.6348	−1.35028	−0.675138	−	0.737691i	$-0.735916\pi$
$281$	−22.6348	−1.35028	−0.675138	+	0.737691i	$0.735916\pi$
$282$	3.88802	0.231528
$283$	16.0544	0.954335	0.477167	−	0.878812i	$-0.341664\pi$
$283$	16.0544	0.954335	0.477167	+	0.878812i	$0.341664\pi$
$284$	13.1729	0.781670
$285$	−0.628961	−0.0372564
$286$	−0.371358	−0.0219588
$287$	−14.6606	−0.865386
$288$	−1.00000	−0.0589256
$289$	20.0160	1.17741
$290$	−6.41522	−0.376715
$291$	8.56741	0.502231
$292$	−4.55463	−0.266540
$293$	−2.39282	−0.139790	−0.0698950	−	0.997554i	$-0.522266\pi$
$293$	−2.39282	−0.139790	−0.0698950	+	0.997554i	$0.522266\pi$
$294$	−3.39884	−0.198224
$295$	17.6897	1.02993
$296$	−1.79170	−0.104140
$297$	−1.00000	−0.0580259
$298$	−1.63177	−0.0945260
$299$	−0.912146	−0.0527508
$300$	0.186181	0.0107491
$301$	18.9574	1.09269
$302$	−2.53234	−0.145720
$303$	−9.14449	−0.525337
$304$	0.286668	0.0164415
$305$	−2.19404	−0.125630
$306$	−6.08408	−0.347803
$307$	−1.66265	−0.0948925	−0.0474462	−	0.998874i	$-0.515108\pi$
$307$	−1.66265	−0.0948925	−0.0474462	+	0.998874i	$0.515108\pi$
$308$	1.89767	0.108130
$309$	−5.89973	−0.335624
$310$	−10.8658	−0.617136
$311$	21.9420	1.24422	0.622108	−	0.782932i	$-0.286277\pi$
$311$	21.9420	1.24422	0.622108	+	0.782932i	$0.286277\pi$
$312$	0.371358	0.0210240
$313$	1.36829	0.0773404	0.0386702	−	0.999252i	$-0.487688\pi$
$313$	1.36829	0.0773404	0.0386702	+	0.999252i	$0.487688\pi$
$314$	17.3822	0.980935
$315$	4.16357	0.234591
$316$	8.68046	0.488314
$317$	9.07521	0.509715	0.254857	−	0.966979i	$-0.417972\pi$
$317$	9.07521	0.509715	0.254857	+	0.966979i	$0.417972\pi$
$318$	3.61101	0.202495
$319$	2.92393	0.163708
$320$	2.19404	0.122651
$321$	−5.12090	−0.285821
$322$	4.66115	0.259756
$323$	1.74411	0.0970447
$324$	1.00000	0.0555556
$325$	−0.0691396	−0.00383517
$326$	17.4219	0.964912
$327$	17.0172	0.941055
$328$	7.72555	0.426572
$329$	7.37819	0.406773
$330$	2.19404	0.120778
$331$	12.3856	0.680776	0.340388	−	0.940285i	$-0.389442\pi$
$331$	12.3856	0.680776	0.340388	+	0.940285i	$0.389442\pi$
$332$	−8.34840	−0.458178
$333$	1.79170	0.0981845
$334$	−7.28958	−0.398868
$335$	−21.4175	−1.17016
$336$	−1.89767	−0.103527
$337$	20.2568	1.10346	0.551728	−	0.834024i	$-0.313969\pi$
$337$	20.2568	1.10346	0.551728	+	0.834024i	$0.313969\pi$
$338$	12.8621	0.699606
$339$	5.35385	0.290781
$340$	13.3487	0.723936
$341$	4.95241	0.268188
$342$	−0.286668	−0.0155012
$343$	−19.7336	−1.06551
$344$	−9.98983	−0.538615
$345$	5.38911	0.290140
$346$	−24.0574	−1.29334
$347$	8.93867	0.479853	0.239926	−	0.970791i	$-0.422877\pi$
$347$	8.93867	0.479853	0.239926	+	0.970791i	$0.422877\pi$
$348$	−2.92393	−0.156739
$349$	−28.5903	−1.53040	−0.765201	−	0.643792i	$-0.777360\pi$
$349$	−28.5903	−1.53040	−0.765201	+	0.643792i	$0.777360\pi$
$350$	0.353310	0.0188852
$351$	−0.371358	−0.0198216
$352$	−1.00000	−0.0533002
$353$	21.2369	1.13033	0.565164	−	0.824979i	$-0.308813\pi$
$353$	21.2369	1.13033	0.565164	+	0.824979i	$0.308813\pi$
$354$	8.06260	0.428522
$355$	28.9020	1.53396
$356$	−1.14636	−0.0607571
$357$	−11.5456	−0.611057
$358$	−22.2002	−1.17332
$359$	16.3753	0.864257	0.432129	−	0.901812i	$-0.357763\pi$
$359$	16.3753	0.864257	0.432129	+	0.901812i	$0.357763\pi$
$360$	−2.19404	−0.115636
$361$	−18.9178	−0.995675
$362$	−5.16788	−0.271618
$363$	−1.00000	−0.0524864
$364$	0.704716	0.0369371
$365$	−9.99305	−0.523060
$366$	−1.00000	−0.0522708
$367$	8.64516	0.451274	0.225637	−	0.974211i	$-0.427554\pi$
$367$	8.64516	0.451274	0.225637	+	0.974211i	$0.427554\pi$
$368$	−2.45625	−0.128041
$369$	−7.72555	−0.402176
$370$	−3.93106	−0.204366
$371$	6.85251	0.355765
$372$	−4.95241	−0.256771
$373$	35.2636	1.82588	0.912941	−	0.408092i	$-0.133806\pi$
$373$	35.2636	1.82588	0.912941	+	0.408092i	$0.133806\pi$
$374$	−6.08408	−0.314600
$375$	11.3787	0.587593
$376$	−3.88802	−0.200509
$377$	1.08582	0.0559227
$378$	1.89767	0.0976058
$379$	30.9240	1.58846	0.794229	−	0.607618i	$-0.207875\pi$
$379$	30.9240	1.58846	0.794229	+	0.607618i	$0.207875\pi$
$380$	0.628961	0.0322650
$381$	−3.70014	−0.189564
$382$	16.1316	0.825362
$383$	−19.9506	−1.01943	−0.509714	−	0.860344i	$-0.670249\pi$
$383$	−19.9506	−1.01943	−0.509714	+	0.860344i	$0.670249\pi$
$384$	1.00000	0.0510310
$385$	4.16357	0.212195
$386$	26.1324	1.33010
$387$	9.98983	0.507811
$388$	−8.56741	−0.434944
$389$	36.6497	1.85821	0.929107	−	0.369810i	$-0.120577\pi$
$389$	36.6497	1.85821	0.929107	+	0.369810i	$0.120577\pi$
$390$	0.814774	0.0412577
$391$	−14.9440	−0.755750
$392$	3.39884	0.171667
$393$	15.6393	0.788900
$394$	22.0877	1.11276
$395$	19.0453	0.958273
$396$	1.00000	0.0502519
$397$	−17.0599	−0.856210	−0.428105	−	0.903729i	$-0.640819\pi$
$397$	−17.0599	−0.856210	−0.428105	+	0.903729i	$0.640819\pi$
$398$	−2.07994	−0.104258
$399$	−0.544001	−0.0272341
$400$	−0.186181	−0.00930903
$401$	12.6058	0.629502	0.314751	−	0.949174i	$-0.398079\pi$
$401$	12.6058	0.629502	0.314751	+	0.949174i	$0.398079\pi$
$402$	−9.76167	−0.486868
$403$	1.83912	0.0916129
$404$	9.14449	0.454955
$405$	2.19404	0.109023
$406$	−5.54866	−0.275375
$407$	1.79170	0.0888112
$408$	6.08408	0.301207
$409$	36.6555	1.81250	0.906249	−	0.422744i	$-0.138933\pi$
$409$	36.6555	1.81250	0.906249	+	0.422744i	$0.138933\pi$
$410$	16.9502	0.837109
$411$	−14.8897	−0.734454
$412$	5.89973	0.290659
$413$	15.3002	0.752873
$414$	2.45625	0.120718
$415$	−18.3167	−0.899133
$416$	−0.371358	−0.0182073
$417$	−8.16249	−0.399719
$418$	−0.286668	−0.0140214
$419$	36.1510	1.76609	0.883045	−	0.469288i	$-0.155490\pi$
$419$	36.1510	1.76609	0.883045	+	0.469288i	$0.155490\pi$
$420$	−4.16357	−0.203162
$421$	28.5682	1.39233	0.696165	−	0.717882i	$-0.254888\pi$
$421$	28.5682	1.39233	0.696165	+	0.717882i	$0.254888\pi$
$422$	16.1297	0.785180
$423$	3.88802	0.189042
$424$	−3.61101	−0.175366
$425$	−1.13274	−0.0549458
$426$	13.1729	0.638231
$427$	−1.89767	−0.0918349
$428$	5.12090	0.247528
$429$	−0.371358	−0.0179293
$430$	−21.9181	−1.05698
$431$	8.45271	0.407153	0.203576	−	0.979059i	$-0.434743\pi$
$431$	8.45271	0.407153	0.203576	+	0.979059i	$0.434743\pi$
$432$	−1.00000	−0.0481125
$433$	−24.3095	−1.16824	−0.584120	−	0.811667i	$-0.698560\pi$
$433$	−24.3095	−1.16824	−0.584120	+	0.811667i	$0.698560\pi$
$434$	−9.39806	−0.451122
$435$	−6.41522	−0.307586
$436$	−17.0172	−0.814977
$437$	−0.704126	−0.0336829
$438$	−4.55463	−0.217629
$439$	−30.0394	−1.43370	−0.716851	−	0.697227i	$-0.754417\pi$
$439$	−30.0394	−1.43370	−0.716851	+	0.697227i	$0.754417\pi$
$440$	−2.19404	−0.104597
$441$	−3.39884	−0.161849
$442$	−2.25937	−0.107467
$443$	−17.8831	−0.849651	−0.424825	−	0.905275i	$-0.639665\pi$
$443$	−17.8831	−0.849651	−0.424825	+	0.905275i	$0.639665\pi$
$444$	−1.79170	−0.0850303
$445$	−2.51517	−0.119230
$446$	−22.8496	−1.08196
$447$	−1.63177	−0.0771802
$448$	1.89767	0.0896566
$449$	38.3428	1.80951	0.904755	−	0.425933i	$-0.140054\pi$
$449$	38.3428	1.80951	0.904755	+	0.425933i	$0.140054\pi$
$450$	0.186181	0.00877663
$451$	−7.72555	−0.363782
$452$	−5.35385	−0.251824
$453$	−2.53234	−0.118980
$454$	−2.98137	−0.139923
$455$	1.54618	0.0724858
$456$	0.286668	0.0134244
$457$	−27.9545	−1.30766	−0.653828	−	0.756643i	$-0.726838\pi$
$457$	−27.9545	−1.30766	−0.653828	+	0.756643i	$0.726838\pi$
$458$	0.396149	0.0185108
$459$	−6.08408	−0.283980
$460$	−5.38911	−0.251268
$461$	11.2066	0.521941	0.260971	−	0.965347i	$-0.415957\pi$
$461$	11.2066	0.521941	0.260971	+	0.965347i	$0.415957\pi$
$462$	1.89767	0.0882878
$463$	−2.18505	−0.101548	−0.0507739	−	0.998710i	$-0.516169\pi$
$463$	−2.18505	−0.101548	−0.0507739	+	0.998710i	$0.516169\pi$
$464$	2.92393	0.135740
$465$	−10.8658	−0.503890
$466$	−17.9908	−0.833407
$467$	−33.4326	−1.54708	−0.773538	−	0.633749i	$-0.781515\pi$
$467$	−33.4326	−1.54708	−0.773538	+	0.633749i	$0.781515\pi$
$468$	0.371358	0.0171660
$469$	−18.5245	−0.855380
$470$	−8.53048	−0.393482
$471$	17.3822	0.800930
$472$	−8.06260	−0.371111
$473$	9.98983	0.459333
$474$	8.68046	0.398707
$475$	−0.0533719	−0.00244887
$476$	11.5456	0.529191
$477$	3.61101	0.165337
$478$	13.2531	0.606181
$479$	7.68168	0.350985	0.175493	−	0.984481i	$-0.443848\pi$
$479$	7.68168	0.350985	0.175493	+	0.984481i	$0.443848\pi$
$480$	2.19404	0.100144
$481$	0.665361	0.0303379
$482$	4.15809	0.189396
$483$	4.66115	0.212090
$484$	1.00000	0.0454545
$485$	−18.7973	−0.853540
$486$	1.00000	0.0453609
$487$	19.6096	0.888596	0.444298	−	0.895879i	$-0.353453\pi$
$487$	19.6096	0.888596	0.444298	+	0.895879i	$0.353453\pi$
$488$	1.00000	0.0452679
$489$	17.4219	0.787847
$490$	7.45719	0.336881
$491$	−7.03025	−0.317271	−0.158635	−	0.987337i	$-0.550709\pi$
$491$	−7.03025	−0.317271	−0.158635	+	0.987337i	$0.550709\pi$
$492$	7.72555	0.348295
$493$	17.7894	0.801194
$494$	−0.106456	−0.00478969
$495$	2.19404	0.0986148
$496$	4.95241	0.222370
$497$	24.9979	1.12131
$498$	−8.34840	−0.374101
$499$	29.7633	1.33239	0.666194	−	0.745779i	$-0.267922\pi$
$499$	29.7633	1.33239	0.666194	+	0.745779i	$0.267922\pi$
$500$	−11.3787	−0.508871
$501$	−7.28958	−0.325674
$502$	−0.947287	−0.0422795
$503$	−40.8741	−1.82249	−0.911243	−	0.411869i	$-0.864876\pi$
$503$	−40.8741	−1.82249	−0.911243	+	0.411869i	$0.864876\pi$
$504$	−1.89767	−0.0845291
$505$	20.0634	0.892809
$506$	2.45625	0.109194
$507$	12.8621	0.571226
$508$	3.70014	0.164167
$509$	−11.2349	−0.497979	−0.248989	−	0.968506i	$-0.580098\pi$
$509$	−11.2349	−0.497979	−0.248989	+	0.968506i	$0.580098\pi$
$510$	13.3487	0.591091
$511$	−8.64320	−0.382353
$512$	−1.00000	−0.0441942
$513$	−0.286668	−0.0126567
$514$	−16.4809	−0.726940
$515$	12.9443	0.570392
$516$	−9.98983	−0.439778
$517$	3.88802	0.170995
$518$	−3.40006	−0.149390
$519$	−24.0574	−1.05600
$520$	−0.814774	−0.0357302
$521$	−26.1497	−1.14564	−0.572819	−	0.819682i	$-0.694150\pi$
$521$	−26.1497	−1.14564	−0.572819	+	0.819682i	$0.694150\pi$
$522$	−2.92393	−0.127977
$523$	−19.2555	−0.841983	−0.420991	−	0.907065i	$-0.638318\pi$
$523$	−19.2555	−0.841983	−0.420991	+	0.907065i	$0.638318\pi$
$524$	−15.6393	−0.683207
$525$	0.353310	0.0154197
$526$	−1.72050	−0.0750175
$527$	30.1309	1.31252
$528$	−1.00000	−0.0435194
$529$	−16.9669	−0.737689
$530$	−7.92270	−0.344140
$531$	8.06260	0.349887
$532$	0.544001	0.0235855
$533$	−2.86894	−0.124268
$534$	−1.14636	−0.0496080
$535$	11.2355	0.485751
$536$	9.76167	0.421640
$537$	−22.2002	−0.958009
$538$	−32.0556	−1.38202
$539$	−3.39884	−0.146398
$540$	−2.19404	−0.0944165
$541$	−16.9626	−0.729278	−0.364639	−	0.931149i	$-0.618808\pi$
$541$	−16.9626	−0.729278	−0.364639	+	0.931149i	$0.618808\pi$
$542$	−5.65368	−0.242846
$543$	−5.16788	−0.221775
$544$	−6.08408	−0.260853
$545$	−37.3365	−1.59932
$546$	0.704716	0.0301590
$547$	−25.7811	−1.10232	−0.551159	−	0.834400i	$-0.685814\pi$
$547$	−25.7811	−1.10232	−0.551159	+	0.834400i	$0.685814\pi$
$548$	14.8897	0.636056
$549$	−1.00000	−0.0426790
$550$	0.186181	0.00793876
$551$	0.838195	0.0357083
$552$	−2.45625	−0.104545
$553$	16.4727	0.700490
$554$	−2.50520	−0.106436
$555$	−3.93106	−0.166864
$556$	8.16249	0.346167
$557$	−34.7088	−1.47066	−0.735329	−	0.677710i	$-0.762972\pi$
$557$	−34.7088	−1.47066	−0.735329	+	0.677710i	$0.762972\pi$
$558$	−4.95241	−0.209652
$559$	3.70980	0.156908
$560$	4.16357	0.175943
$561$	−6.08408	−0.256870
$562$	22.6348	0.954790
$563$	6.66085	0.280721	0.140361	−	0.990100i	$-0.455174\pi$
$563$	6.66085	0.280721	0.140361	+	0.990100i	$0.455174\pi$
$564$	−3.88802	−0.163715
$565$	−11.7466	−0.494182
$566$	−16.0544	−0.674816
$567$	1.89767	0.0796948
$568$	−13.1729	−0.552724
$569$	26.8090	1.12389	0.561946	−	0.827174i	$-0.310053\pi$
$569$	26.8090	1.12389	0.561946	+	0.827174i	$0.310053\pi$
$570$	0.628961	0.0263443
$571$	−10.1764	−0.425870	−0.212935	−	0.977066i	$-0.568302\pi$
$571$	−10.1764	−0.425870	−0.212935	+	0.977066i	$0.568302\pi$
$572$	0.371358	0.0155272
$573$	16.1316	0.673905
$574$	14.6606	0.611920
$575$	0.457305	0.0190710
$576$	1.00000	0.0416667
$577$	−35.2055	−1.46562	−0.732812	−	0.680431i	$-0.761793\pi$
$577$	−35.2055	−1.46562	−0.732812	+	0.680431i	$0.761793\pi$
$578$	−20.0160	−0.832555
$579$	26.1324	1.08602
$580$	6.41522	0.266377
$581$	−15.8425	−0.657259
$582$	−8.56741	−0.355131
$583$	3.61101	0.149553
$584$	4.55463	0.188472
$585$	0.814774	0.0336868
$586$	2.39282	0.0988465
$587$	−5.44081	−0.224566	−0.112283	−	0.993676i	$-0.535816\pi$
$587$	−5.44081	−0.224566	−0.112283	+	0.993676i	$0.535816\pi$
$588$	3.39884	0.140166
$589$	1.41970	0.0584976
$590$	−17.6897	−0.728273
$591$	22.0877	0.908566
$592$	1.79170	0.0736384
$593$	−26.0290	−1.06888	−0.534441	−	0.845206i	$-0.679478\pi$
$593$	−26.0290	−1.06888	−0.534441	+	0.845206i	$0.679478\pi$
$594$	1.00000	0.0410305
$595$	25.3315	1.03849
$596$	1.63177	0.0668400
$597$	−2.07994	−0.0851264
$598$	0.912146	0.0373004
$599$	11.1564	0.455837	0.227919	−	0.973680i	$-0.426808\pi$
$599$	11.1564	0.455837	0.227919	+	0.973680i	$0.426808\pi$
$600$	−0.186181	−0.00760079
$601$	21.6613	0.883584	0.441792	−	0.897117i	$-0.354343\pi$
$601$	21.6613	0.883584	0.441792	+	0.897117i	$0.354343\pi$
$602$	−18.9574	−0.772647
$603$	−9.76167	−0.397526
$604$	2.53234	0.103040
$605$	2.19404	0.0892005
$606$	9.14449	0.371470
$607$	−16.5636	−0.672295	−0.336148	−	0.941809i	$-0.609124\pi$
$607$	−16.5636	−0.672295	−0.336148	+	0.941809i	$0.609124\pi$
$608$	−0.286668	−0.0116259
$609$	−5.54866	−0.224843
$610$	2.19404	0.0888342
$611$	1.44385	0.0584118
$612$	6.08408	0.245934
$613$	−24.2448	−0.979237	−0.489618	−	0.871937i	$-0.662864\pi$
$613$	−24.2448	−0.979237	−0.489618	+	0.871937i	$0.662864\pi$
$614$	1.66265	0.0670991
$615$	16.9502	0.683497
$616$	−1.89767	−0.0764594
$617$	14.8272	0.596921	0.298461	−	0.954422i	$-0.403527\pi$
$617$	14.8272	0.596921	0.298461	+	0.954422i	$0.403527\pi$
$618$	5.89973	0.237322
$619$	46.5665	1.87167	0.935833	−	0.352445i	$-0.114650\pi$
$619$	46.5665	1.87167	0.935833	+	0.352445i	$0.114650\pi$
$620$	10.8658	0.436381
$621$	2.45625	0.0985658
$622$	−21.9420	−0.879793
$623$	−2.17542	−0.0871565
$624$	−0.371358	−0.0148662
$625$	−24.0344	−0.961377
$626$	−1.36829	−0.0546880
$627$	−0.286668	−0.0114484
$628$	−17.3822	−0.693625
$629$	10.9008	0.434645
$630$	−4.16357	−0.165881
$631$	23.8610	0.949890	0.474945	−	0.880015i	$-0.342468\pi$
$631$	23.8610	0.949890	0.474945	+	0.880015i	$0.342468\pi$
$632$	−8.68046	−0.345290
$633$	16.1297	0.641097
$634$	−9.07521	−0.360423
$635$	8.11825	0.322163
$636$	−3.61101	−0.143186
$637$	−1.26218	−0.0500095
$638$	−2.92393	−0.115759
$639$	13.1729	0.521114
$640$	−2.19404	−0.0867271
$641$	−40.1331	−1.58516	−0.792581	−	0.609767i	$-0.791263\pi$
$641$	−40.1331	−1.58516	−0.792581	+	0.609767i	$0.791263\pi$
$642$	5.12090	0.202106
$643$	−9.25294	−0.364900	−0.182450	−	0.983215i	$-0.558403\pi$
$643$	−9.25294	−0.364900	−0.182450	+	0.983215i	$0.558403\pi$
$644$	−4.66115	−0.183675
$645$	−21.9181	−0.863024
$646$	−1.74411	−0.0686210
$647$	−14.6327	−0.575271	−0.287636	−	0.957740i	$-0.592869\pi$
$647$	−14.6327	−0.575271	−0.287636	+	0.957740i	$0.592869\pi$
$648$	−1.00000	−0.0392837
$649$	8.06260	0.316485
$650$	0.0691396	0.00271188
$651$	−9.39806	−0.368339
$652$	−17.4219	−0.682296
$653$	41.2023	1.61237	0.806186	−	0.591663i	$-0.201528\pi$
$653$	41.2023	1.61237	0.806186	+	0.591663i	$0.201528\pi$
$654$	−17.0172	−0.665426
$655$	−34.3133	−1.34073
$656$	−7.72555	−0.301632
$657$	−4.55463	−0.177693
$658$	−7.37819	−0.287632
$659$	42.2149	1.64446	0.822230	−	0.569155i	$-0.192730\pi$
$659$	42.2149	1.64446	0.822230	+	0.569155i	$0.192730\pi$
$660$	−2.19404	−0.0854030
$661$	−29.2941	−1.13941	−0.569704	−	0.821850i	$-0.692942\pi$
$661$	−29.2941	−1.13941	−0.569704	+	0.821850i	$0.692942\pi$
$662$	−12.3856	−0.481382
$663$	−2.25937	−0.0877466
$664$	8.34840	0.323981
$665$	1.19356	0.0462843
$666$	−1.79170	−0.0694269
$667$	−7.18189	−0.278084
$668$	7.28958	0.282042
$669$	−22.8496	−0.883417
$670$	21.4175	0.827431
$671$	−1.00000	−0.0386046
$672$	1.89767	0.0732043
$673$	−25.1282	−0.968619	−0.484310	−	0.874897i	$-0.660929\pi$
$673$	−25.1282	−0.968619	−0.484310	+	0.874897i	$0.660929\pi$
$674$	−20.2568	−0.780262
$675$	0.186181	0.00716609
$676$	−12.8621	−0.494696
$677$	12.4699	0.479259	0.239629	−	0.970864i	$-0.422974\pi$
$677$	12.4699	0.479259	0.239629	+	0.970864i	$0.422974\pi$
$678$	−5.35385	−0.205613
$679$	−16.2581	−0.623931
$680$	−13.3487	−0.511900
$681$	−2.98137	−0.114246
$682$	−4.95241	−0.189638
$683$	31.0726	1.18896	0.594480	−	0.804111i	$-0.297358\pi$
$683$	31.0726	1.18896	0.594480	+	0.804111i	$0.297358\pi$
$684$	0.286668	0.0109610
$685$	32.6686	1.24820
$686$	19.7336	0.753432
$687$	0.396149	0.0151140
$688$	9.98983	0.380859
$689$	1.34097	0.0510871
$690$	−5.38911	−0.205160
$691$	14.6001	0.555414	0.277707	−	0.960666i	$-0.410426\pi$
$691$	14.6001	0.555414	0.277707	+	0.960666i	$0.410426\pi$
$692$	24.0574	0.914526
$693$	1.89767	0.0720867
$694$	−8.93867	−0.339307
$695$	17.9088	0.679321
$696$	2.92393	0.110831
$697$	−47.0028	−1.78036
$698$	28.5903	1.08216
$699$	−17.9908	−0.680474
$700$	−0.353310	−0.0133539
$701$	30.4663	1.15070	0.575348	−	0.817909i	$-0.304867\pi$
$701$	30.4663	1.15070	0.575348	+	0.817909i	$0.304867\pi$
$702$	0.371358	0.0140160
$703$	0.513622	0.0193716
$704$	1.00000	0.0376889
$705$	−8.53048	−0.321276
$706$	−21.2369	−0.799263
$707$	17.3533	0.652636
$708$	−8.06260	−0.303011
$709$	−9.05810	−0.340184	−0.170092	−	0.985428i	$-0.554407\pi$
$709$	−9.05810	−0.340184	−0.170092	+	0.985428i	$0.554407\pi$
$710$	−28.9020	−1.08467
$711$	8.68046	0.325543
$712$	1.14636	0.0429618
$713$	−12.1644	−0.455559
$714$	11.5456	0.432083
$715$	0.814774	0.0304708
$716$	22.2002	0.829660
$717$	13.2531	0.494945
$718$	−16.3753	−0.611122
$719$	−23.5885	−0.879703	−0.439851	−	0.898071i	$-0.644969\pi$
$719$	−23.5885	−0.879703	−0.439851	+	0.898071i	$0.644969\pi$
$720$	2.19404	0.0817671
$721$	11.1958	0.416952
$722$	18.9178	0.704048
$723$	4.15809	0.154641
$724$	5.16788	0.192063
$725$	−0.544378	−0.0202177
$726$	1.00000	0.0371135
$727$	−8.90722	−0.330351	−0.165175	−	0.986264i	$-0.552819\pi$
$727$	−8.90722	−0.330351	−0.165175	+	0.986264i	$0.552819\pi$
$728$	−0.704716	−0.0261185
$729$	1.00000	0.0370370
$730$	9.99305	0.369859
$731$	60.7789	2.24799
$732$	1.00000	0.0369611
$733$	4.99807	0.184608	0.0923040	−	0.995731i	$-0.470577\pi$
$733$	4.99807	0.184608	0.0923040	+	0.995731i	$0.470577\pi$
$734$	−8.64516	−0.319099
$735$	7.45719	0.275062
$736$	2.45625	0.0905385
$737$	−9.76167	−0.359576
$738$	7.72555	0.284381
$739$	−38.9745	−1.43370	−0.716851	−	0.697227i	$-0.754417\pi$
$739$	−38.9745	−1.43370	−0.716851	+	0.697227i	$0.754417\pi$
$740$	3.93106	0.144509
$741$	−0.106456	−0.00391077
$742$	−6.85251	−0.251564
$743$	17.1457	0.629014	0.314507	−	0.949255i	$-0.398161\pi$
$743$	17.1457	0.629014	0.314507	+	0.949255i	$0.398161\pi$
$744$	4.95241	0.181564
$745$	3.58018	0.131168
$746$	−35.2636	−1.29109
$747$	−8.34840	−0.305452
$748$	6.08408	0.222456
$749$	9.71779	0.355080
$750$	−11.3787	−0.415491
$751$	19.8588	0.724657	0.362329	−	0.932050i	$-0.381982\pi$
$751$	19.8588	0.724657	0.362329	+	0.932050i	$0.381982\pi$
$752$	3.88802	0.141782
$753$	−0.947287	−0.0345211
$754$	−1.08582	−0.0395433
$755$	5.55607	0.202206
$756$	−1.89767	−0.0690177
$757$	5.67616	0.206304	0.103152	−	0.994666i	$-0.467107\pi$
$757$	5.67616	0.206304	0.103152	+	0.994666i	$0.467107\pi$
$758$	−30.9240	−1.12321
$759$	2.45625	0.0891561
$760$	−0.628961	−0.0228148
$761$	−13.8050	−0.500432	−0.250216	−	0.968190i	$-0.580502\pi$
$761$	−13.8050	−0.500432	−0.250216	+	0.968190i	$0.580502\pi$
$762$	3.70014	0.134042
$763$	−32.2931	−1.16909
$764$	−16.1316	−0.583619
$765$	13.3487	0.482624
$766$	19.9506	0.720844
$767$	2.99411	0.108111
$768$	−1.00000	−0.0360844
$769$	−27.4313	−0.989200	−0.494600	−	0.869121i	$-0.664685\pi$
$769$	−27.4313	−0.989200	−0.494600	+	0.869121i	$0.664685\pi$
$770$	−4.16357	−0.150045
$771$	−16.4809	−0.593544
$772$	−26.1324	−0.940525
$773$	−47.9739	−1.72550	−0.862751	−	0.505629i	$-0.831261\pi$
$773$	−47.9739	−1.72550	−0.862751	+	0.505629i	$0.831261\pi$
$774$	−9.98983	−0.359077
$775$	−0.922043	−0.0331208
$776$	8.56741	0.307552
$777$	−3.40006	−0.121976
$778$	−36.6497	−1.31396
$779$	−2.21466	−0.0793486
$780$	−0.814774	−0.0291736
$781$	13.1729	0.471365
$782$	14.9440	0.534396
$783$	−2.92393	−0.104493
$784$	−3.39884	−0.121387
$785$	−38.1373	−1.36118
$786$	−15.6393	−0.557837
$787$	−43.4642	−1.54933	−0.774665	−	0.632372i	$-0.782082\pi$
$787$	−43.4642	−1.54933	−0.774665	+	0.632372i	$0.782082\pi$
$788$	−22.0877	−0.786842
$789$	−1.72050	−0.0612515
$790$	−19.0453	−0.677601
$791$	−10.1599	−0.361243
$792$	−1.00000	−0.0355335
$793$	−0.371358	−0.0131873
$794$	17.0599	0.605432
$795$	−7.92270	−0.280989
$796$	2.07994	0.0737216
$797$	30.2141	1.07024	0.535119	−	0.844776i	$-0.320267\pi$
$797$	30.2141	1.07024	0.535119	+	0.844776i	$0.320267\pi$
$798$	0.544001	0.0192574
$799$	23.6550	0.836854
$800$	0.186181	0.00658248
$801$	−1.14636	−0.0405048
$802$	−12.6058	−0.445125
$803$	−4.55463	−0.160729
$804$	9.76167	0.344268
$805$	−10.2268	−0.360446
$806$	−1.83912	−0.0647801
$807$	−32.0556	−1.12841
$808$	−9.14449	−0.321702
$809$	−40.8273	−1.43541	−0.717705	−	0.696347i	$-0.754808\pi$
$809$	−40.8273	−1.43541	−0.717705	+	0.696347i	$0.754808\pi$
$810$	−2.19404	−0.0770908
$811$	38.9662	1.36829	0.684144	−	0.729347i	$-0.260176\pi$
$811$	38.9662	1.36829	0.684144	+	0.729347i	$0.260176\pi$
$812$	5.54866	0.194720
$813$	−5.65368	−0.198283
$814$	−1.79170	−0.0627990
$815$	−38.2245	−1.33894
$816$	−6.08408	−0.212985
$817$	2.86376	0.100190
$818$	−36.6555	−1.28163
$819$	0.704716	0.0246248
$820$	−16.9502	−0.591926
$821$	17.0297	0.594342	0.297171	−	0.954824i	$-0.403957\pi$
$821$	17.0297	0.594342	0.297171	+	0.954824i	$0.403957\pi$
$822$	14.8897	0.519337
$823$	30.9578	1.07912	0.539561	−	0.841946i	$-0.318590\pi$
$823$	30.9578	1.07912	0.539561	+	0.841946i	$0.318590\pi$
$824$	−5.89973	−0.205527
$825$	0.186181	0.00648197
$826$	−15.3002	−0.532362
$827$	−40.3238	−1.40220	−0.701098	−	0.713065i	$-0.747306\pi$
$827$	−40.3238	−1.40220	−0.701098	+	0.713065i	$0.747306\pi$
$828$	−2.45625	−0.0853605
$829$	1.07703	0.0374069	0.0187034	−	0.999825i	$-0.494046\pi$
$829$	1.07703	0.0374069	0.0187034	+	0.999825i	$0.494046\pi$
$830$	18.3167	0.635783
$831$	−2.50520	−0.0869044
$832$	0.371358	0.0128745
$833$	−20.6788	−0.716477
$834$	8.16249	0.282644
$835$	15.9936	0.553483
$836$	0.286668	0.00991460
$837$	−4.95241	−0.171180
$838$	−36.1510	−1.24881
$839$	−4.94121	−0.170590	−0.0852948	−	0.996356i	$-0.527183\pi$
$839$	−4.94121	−0.170590	−0.0852948	+	0.996356i	$0.527183\pi$
$840$	4.16357	0.143657
$841$	−20.4507	−0.705195
$842$	−28.5682	−0.984526
$843$	22.6348	0.779582
$844$	−16.1297	−0.555206
$845$	−28.2200	−0.970797
$846$	−3.88802	−0.133673
$847$	1.89767	0.0652048
$848$	3.61101	0.124002
$849$	−16.0544	−0.550985
$850$	1.13274	0.0388525
$851$	−4.40086	−0.150859
$852$	−13.1729	−0.451298
$853$	−10.2463	−0.350828	−0.175414	−	0.984495i	$-0.556126\pi$
$853$	−10.2463	−0.350828	−0.175414	+	0.984495i	$0.556126\pi$
$854$	1.89767	0.0649370
$855$	0.628961	0.0215100
$856$	−5.12090	−0.175029
$857$	−44.5133	−1.52055	−0.760273	−	0.649603i	$-0.774935\pi$
$857$	−44.5133	−1.52055	−0.760273	+	0.649603i	$0.774935\pi$
$858$	0.371358	0.0126779
$859$	−15.1494	−0.516889	−0.258445	−	0.966026i	$-0.583210\pi$
$859$	−15.1494	−0.516889	−0.258445	+	0.966026i	$0.583210\pi$
$860$	21.9181	0.747401
$861$	14.6606	0.499631
$862$	−8.45271	−0.287900
$863$	−11.1176	−0.378446	−0.189223	−	0.981934i	$-0.560597\pi$
$863$	−11.1176	−0.378446	−0.189223	+	0.981934i	$0.560597\pi$
$864$	1.00000	0.0340207
$865$	52.7830	1.79468
$866$	24.3095	0.826070
$867$	−20.0160	−0.679778
$868$	9.39806	0.318991
$869$	8.68046	0.294464
$870$	6.41522	0.217496
$871$	−3.62507	−0.122831
$872$	17.0172	0.576276
$873$	−8.56741	−0.289963
$874$	0.704126	0.0238174
$875$	−21.5931	−0.729978
$876$	4.55463	0.153887
$877$	−19.6570	−0.663771	−0.331885	−	0.943320i	$-0.607685\pi$
$877$	−19.6570	−0.663771	−0.331885	+	0.943320i	$0.607685\pi$
$878$	30.0394	1.01378
$879$	2.39282	0.0807078
$880$	2.19404	0.0739611
$881$	−53.7283	−1.81015	−0.905076	−	0.425250i	$-0.860186\pi$
$881$	−53.7283	−1.81015	−0.905076	+	0.425250i	$0.860186\pi$
$882$	3.39884	0.114445
$883$	6.66033	0.224138	0.112069	−	0.993700i	$-0.464252\pi$
$883$	6.66033	0.224138	0.112069	+	0.993700i	$0.464252\pi$
$884$	2.25937	0.0759908
$885$	−17.6897	−0.594632
$886$	17.8831	0.600794
$887$	−45.8203	−1.53849	−0.769247	−	0.638952i	$-0.779368\pi$
$887$	−45.8203	−1.53849	−0.769247	+	0.638952i	$0.779368\pi$
$888$	1.79170	0.0601255
$889$	7.02165	0.235499
$890$	2.51517	0.0843086
$891$	1.00000	0.0335013
$892$	22.8496	0.765062
$893$	1.11457	0.0372976
$894$	1.63177	0.0545746
$895$	48.7081	1.62813
$896$	−1.89767	−0.0633968
$897$	0.912146	0.0304557
$898$	−38.3428	−1.27952
$899$	14.4805	0.482952
$900$	−0.186181	−0.00620602
$901$	21.9696	0.731915
$902$	7.72555	0.257233
$903$	−18.9574	−0.630864
$904$	5.35385	0.178066
$905$	11.3386	0.376906
$906$	2.53234	0.0841314
$907$	−27.4283	−0.910741	−0.455371	−	0.890302i	$-0.650493\pi$
$907$	−27.4283	−0.910741	−0.455371	+	0.890302i	$0.650493\pi$
$908$	2.98137	0.0989402
$909$	9.14449	0.303304
$910$	−1.54618	−0.0512552
$911$	31.4379	1.04158	0.520792	−	0.853684i	$-0.325637\pi$
$911$	31.4379	1.04158	0.520792	+	0.853684i	$0.325637\pi$
$912$	−0.286668	−0.00949251
$913$	−8.34840	−0.276292
$914$	27.9545	0.924653
$915$	2.19404	0.0725328
$916$	−0.396149	−0.0130891
$917$	−29.6783	−0.980065
$918$	6.08408	0.200804
$919$	−18.2234	−0.601135	−0.300568	−	0.953761i	$-0.597176\pi$
$919$	−18.2234	−0.601135	−0.300568	+	0.953761i	$0.597176\pi$
$920$	5.38911	0.177674
$921$	1.66265	0.0547862
$922$	−11.2066	−0.369068
$923$	4.89187	0.161018
$924$	−1.89767	−0.0624289
$925$	−0.333579	−0.0109680
$926$	2.18505	0.0718052
$927$	5.89973	0.193773
$928$	−2.92393	−0.0959826
$929$	−34.3630	−1.12741	−0.563707	−	0.825975i	$-0.690625\pi$
$929$	−34.3630	−1.12741	−0.563707	+	0.825975i	$0.690625\pi$
$930$	10.8658	0.356304
$931$	−0.974336	−0.0319326
$932$	17.9908	0.589308
$933$	−21.9420	−0.718348
$934$	33.4326	1.09395
$935$	13.3487	0.436550
$936$	−0.371358	−0.0121382
$937$	29.1734	0.953052	0.476526	−	0.879160i	$-0.341896\pi$
$937$	29.1734	0.953052	0.476526	+	0.879160i	$0.341896\pi$
$938$	18.5245	0.604845
$939$	−1.36829	−0.0446525
$940$	8.53048	0.278234
$941$	−11.7555	−0.383219	−0.191610	−	0.981471i	$-0.561371\pi$
$941$	−11.7555	−0.383219	−0.191610	+	0.981471i	$0.561371\pi$
$942$	−17.3822	−0.566343
$943$	18.9759	0.617939
$944$	8.06260	0.262415
$945$	−4.16357	−0.135441
$946$	−9.98983	−0.324797
$947$	−1.55980	−0.0506866	−0.0253433	−	0.999679i	$-0.508068\pi$
$947$	−1.55980	−0.0506866	−0.0253433	+	0.999679i	$0.508068\pi$
$948$	−8.68046	−0.281928
$949$	−1.69140	−0.0549051
$950$	0.0533719	0.00173161
$951$	−9.07521	−0.294284
$952$	−11.5456	−0.374195
$953$	8.10178	0.262442	0.131221	−	0.991353i	$-0.458110\pi$
$953$	8.10178	0.262442	0.131221	+	0.991353i	$0.458110\pi$
$954$	−3.61101	−0.116911
$955$	−35.3933	−1.14530
$956$	−13.2531	−0.428635
$957$	−2.92393	−0.0945171
$958$	−7.68168	−0.248184
$959$	28.2558	0.912426
$960$	−2.19404	−0.0708124
$961$	−6.47359	−0.208826
$962$	−0.665361	−0.0214521
$963$	5.12090	0.165019
$964$	−4.15809	−0.133923
$965$	−57.3355	−1.84570
$966$	−4.66115	−0.149970
$967$	−11.9659	−0.384796	−0.192398	−	0.981317i	$-0.561627\pi$
$967$	−11.9659	−0.384796	−0.192398	+	0.981317i	$0.561627\pi$
$968$	−1.00000	−0.0321412
$969$	−1.74411	−0.0560288
$970$	18.7973	0.603544
$971$	21.4320	0.687786	0.343893	−	0.939009i	$-0.388254\pi$
$971$	21.4320	0.687786	0.343893	+	0.939009i	$0.388254\pi$
$972$	−1.00000	−0.0320750
$973$	15.4897	0.496578
$974$	−19.6096	−0.628332
$975$	0.0691396	0.00221424
$976$	−1.00000	−0.0320092
$977$	48.9938	1.56745	0.783725	−	0.621107i	$-0.213317\pi$
$977$	48.9938	1.56745	0.783725	+	0.621107i	$0.213317\pi$
$978$	−17.4219	−0.557092
$979$	−1.14636	−0.0366379
$980$	−7.45719	−0.238211
$981$	−17.0172	−0.543318
$982$	7.03025	0.224344
$983$	−6.88266	−0.219523	−0.109761	−	0.993958i	$-0.535009\pi$
$983$	−6.88266	−0.219523	−0.109761	+	0.993958i	$0.535009\pi$
$984$	−7.72555	−0.246281
$985$	−48.4613	−1.54411
$986$	−17.7894	−0.566530
$987$	−7.37819	−0.234851
$988$	0.106456	0.00338682
$989$	−24.5375	−0.780246
$990$	−2.19404	−0.0697312
$991$	−32.8445	−1.04334	−0.521670	−	0.853148i	$-0.674691\pi$
$991$	−32.8445	−1.04334	−0.521670	+	0.853148i	$0.674691\pi$
$992$	−4.95241	−0.157239
$993$	−12.3856	−0.393046
$994$	−24.9979	−0.792887
$995$	4.56348	0.144672
$996$	8.34840	0.264529
$997$	24.1761	0.765665	0.382833	−	0.923818i	$-0.374949\pi$
$997$	24.1761	0.765665	0.382833	+	0.923818i	$0.374949\pi$
$998$	−29.7633	−0.942140
$999$	−1.79170	−0.0566869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.z.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.z.1.5	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.19404 q^{5} +1.00000 q^{6} +1.89767 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.19404 q^{5} +1.00000 q^{6} +1.89767 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.19404 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.371358 q^{13} -1.89767 q^{14} -2.19404 q^{15} +1.00000 q^{16} +6.08408 q^{17} -1.00000 q^{18} +0.286668 q^{19} +2.19404 q^{20} -1.89767 q^{21} -1.00000 q^{22} -2.45625 q^{23} +1.00000 q^{24} -0.186181 q^{25} -0.371358 q^{26} -1.00000 q^{27} +1.89767 q^{28} +2.92393 q^{29} +2.19404 q^{30} +4.95241 q^{31} -1.00000 q^{32} -1.00000 q^{33} -6.08408 q^{34} +4.16357 q^{35} +1.00000 q^{36} +1.79170 q^{37} -0.286668 q^{38} -0.371358 q^{39} -2.19404 q^{40} -7.72555 q^{41} +1.89767 q^{42} +9.98983 q^{43} +1.00000 q^{44} +2.19404 q^{45} +2.45625 q^{46} +3.88802 q^{47} -1.00000 q^{48} -3.39884 q^{49} +0.186181 q^{50} -6.08408 q^{51} +0.371358 q^{52} +3.61101 q^{53} +1.00000 q^{54} +2.19404 q^{55} -1.89767 q^{56} -0.286668 q^{57} -2.92393 q^{58} +8.06260 q^{59} -2.19404 q^{60} -1.00000 q^{61} -4.95241 q^{62} +1.89767 q^{63} +1.00000 q^{64} +0.814774 q^{65} +1.00000 q^{66} -9.76167 q^{67} +6.08408 q^{68} +2.45625 q^{69} -4.16357 q^{70} +13.1729 q^{71} -1.00000 q^{72} -4.55463 q^{73} -1.79170 q^{74} +0.186181 q^{75} +0.286668 q^{76} +1.89767 q^{77} +0.371358 q^{78} +8.68046 q^{79} +2.19404 q^{80} +1.00000 q^{81} +7.72555 q^{82} -8.34840 q^{83} -1.89767 q^{84} +13.3487 q^{85} -9.98983 q^{86} -2.92393 q^{87} -1.00000 q^{88} -1.14636 q^{89} -2.19404 q^{90} +0.704716 q^{91} -2.45625 q^{92} -4.95241 q^{93} -3.88802 q^{94} +0.628961 q^{95} +1.00000 q^{96} -8.56741 q^{97} +3.39884 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} + 7 q^{11} - 7 q^{12} - 7 q^{13} + 4 q^{14} - 2 q^{15} + 7 q^{16} - 4 q^{17} - 7 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{21} - 7 q^{22} - q^{23} + 7 q^{24} + 5 q^{25} + 7 q^{26} - 7 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 7 q^{32} - 7 q^{33} + 4 q^{34} + 13 q^{35} + 7 q^{36} - 15 q^{37} + 4 q^{38} + 7 q^{39} - 2 q^{40} + q^{41} - 4 q^{42} - 13 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} + 11 q^{47} - 7 q^{48} + 9 q^{49} - 5 q^{50} + 4 q^{51} - 7 q^{52} + 14 q^{53} + 7 q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{57} - 6 q^{58} + 39 q^{59} - 2 q^{60} - 7 q^{61} - 7 q^{62} - 4 q^{63} + 7 q^{64} - 2 q^{65} + 7 q^{66} - 3 q^{67} - 4 q^{68} + q^{69} - 13 q^{70} + 12 q^{71} - 7 q^{72} - 21 q^{73} + 15 q^{74} - 5 q^{75} - 4 q^{76} - 4 q^{77} - 7 q^{78} + 15 q^{79} + 2 q^{80} + 7 q^{81} - q^{82} + 5 q^{83} + 4 q^{84} - 34 q^{85} + 13 q^{86} - 6 q^{87} - 7 q^{88} - 8 q^{89} - 2 q^{90} + 29 q^{91} - q^{92} - 7 q^{93} - 11 q^{94} + 13 q^{95} + 7 q^{96} - 20 q^{97} - 9 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 + 7 * q^11 - 7 * q^12 - 7 * q^13 + 4 * q^14 - 2 * q^15 + 7 * q^16 - 4 * q^17 - 7 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^21 - 7 * q^22 - q^23 + 7 * q^24 + 5 * q^25 + 7 * q^26 - 7 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 7 * q^32 - 7 * q^33 + 4 * q^34 + 13 * q^35 + 7 * q^36 - 15 * q^37 + 4 * q^38 + 7 * q^39 - 2 * q^40 + q^41 - 4 * q^42 - 13 * q^43 + 7 * q^44 + 2 * q^45 + q^46 + 11 * q^47 - 7 * q^48 + 9 * q^49 - 5 * q^50 + 4 * q^51 - 7 * q^52 + 14 * q^53 + 7 * q^54 + 2 * q^55 + 4 * q^56 + 4 * q^57 - 6 * q^58 + 39 * q^59 - 2 * q^60 - 7 * q^61 - 7 * q^62 - 4 * q^63 + 7 * q^64 - 2 * q^65 + 7 * q^66 - 3 * q^67 - 4 * q^68 + q^69 - 13 * q^70 + 12 * q^71 - 7 * q^72 - 21 * q^73 + 15 * q^74 - 5 * q^75 - 4 * q^76 - 4 * q^77 - 7 * q^78 + 15 * q^79 + 2 * q^80 + 7 * q^81 - q^82 + 5 * q^83 + 4 * q^84 - 34 * q^85 + 13 * q^86 - 6 * q^87 - 7 * q^88 - 8 * q^89 - 2 * q^90 + 29 * q^91 - q^92 - 7 * q^93 - 11 * q^94 + 13 * q^95 + 7 * q^96 - 20 * q^97 - 9 * q^98 + 7 * q^99

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