LMFDB - Embedded newform 308.2.d.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(43,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("308.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} - 2 x^{15} + 3 x^{14} - 3 x^{13} + 4 x^{12} - 14 x^{11} + 12 x^{10} + 16 x^{9} + \cdots + 512 $ x^18 - x^17 - 2x^15 + 3x^14 - 3x^13 + 4x^12 - 14x^11 + 12x^10 + 16x^9 + 24x^8 - 56x^7 + 32x^6 - 48x^5 + 96x^4 - 128x^3 - 256x + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.4
Root			$1.35077 + 0.418821i$ of defining polynomial
Character	$\chi$	$=$	308.43
Dual form			308.2.d.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35077 + 0.418821i) q^{2} +1.57463i q^{3} +(1.64918 - 1.13146i) q^{4} +1.58188 q^{5} +(-0.659487 - 2.12696i) q^{6} +1.00000 q^{7} +(-1.75378 + 2.21906i) q^{8} +0.520549 q^{9} +(-2.13676 + 0.662524i) q^{10} +(3.03811 - 1.33037i) q^{11} +(1.78164 + 2.59684i) q^{12} -2.62307i q^{13} +(-1.35077 + 0.418821i) q^{14} +2.49087i q^{15} +(1.43957 - 3.73197i) q^{16} -0.750224i q^{17} +(-0.703144 + 0.218017i) q^{18} +1.14137 q^{19} +(2.60880 - 1.78984i) q^{20} +1.57463i q^{21} +(-3.54662 + 3.06945i) q^{22} +3.83223i q^{23} +(-3.49420 - 2.76156i) q^{24} -2.49766 q^{25} +(1.09860 + 3.54318i) q^{26} +5.54355i q^{27} +(1.64918 - 1.13146i) q^{28} +9.02097i q^{29} +(-1.04323 - 3.36460i) q^{30} -4.41685i q^{31} +(-0.381509 + 5.64397i) q^{32} +(2.09483 + 4.78389i) q^{33} +(0.314210 + 1.01338i) q^{34} +1.58188 q^{35} +(0.858478 - 0.588983i) q^{36} -2.80558 q^{37} +(-1.54174 + 0.478031i) q^{38} +4.13036 q^{39} +(-2.77427 + 3.51029i) q^{40} +0.250697i q^{41} +(-0.659487 - 2.12696i) q^{42} +1.82459 q^{43} +(3.50512 - 5.63153i) q^{44} +0.823446 q^{45} +(-1.60502 - 5.17647i) q^{46} +4.73143i q^{47} +(5.87647 + 2.26679i) q^{48} +1.00000 q^{49} +(3.37377 - 1.04607i) q^{50} +1.18132 q^{51} +(-2.96791 - 4.32591i) q^{52} -9.11425 q^{53} +(-2.32176 - 7.48808i) q^{54} +(4.80592 - 2.10448i) q^{55} +(-1.75378 + 2.21906i) q^{56} +1.79724i q^{57} +(-3.77817 - 12.1853i) q^{58} -14.5290i q^{59} +(2.81833 + 4.10788i) q^{60} -7.65849i q^{61} +(1.84987 + 5.96616i) q^{62} +0.520549 q^{63} +(-1.84848 - 7.78352i) q^{64} -4.14938i q^{65} +(-4.83324 - 5.58460i) q^{66} -8.00407i q^{67} +(-0.848852 - 1.23725i) q^{68} -6.03433 q^{69} +(-2.13676 + 0.662524i) q^{70} +11.4380i q^{71} +(-0.912931 + 1.15513i) q^{72} +0.267868i q^{73} +(3.78970 - 1.17503i) q^{74} -3.93289i q^{75} +(1.88233 - 1.29142i) q^{76} +(3.03811 - 1.33037i) q^{77} +(-5.57918 + 1.72988i) q^{78} -6.72244 q^{79} +(2.27723 - 5.90353i) q^{80} -7.16738 q^{81} +(-0.104997 - 0.338635i) q^{82} +1.20081 q^{83} +(1.78164 + 2.59684i) q^{84} -1.18676i q^{85} +(-2.46461 + 0.764178i) q^{86} -14.2047 q^{87} +(-2.37602 + 9.07494i) q^{88} +10.6509 q^{89} +(-1.11229 + 0.344876i) q^{90} -2.62307i q^{91} +(4.33603 + 6.32002i) q^{92} +6.95489 q^{93} +(-1.98162 - 6.39109i) q^{94} +1.80551 q^{95} +(-8.88716 - 0.600735i) q^{96} -12.3457 q^{97} +(-1.35077 + 0.418821i) q^{98} +(1.58149 - 0.692521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} + q^{4} + 18 q^{7} - 7 q^{8} - 22 q^{9} + 6 q^{10} + 4 q^{11} - 8 q^{12} - q^{14} - 3 q^{16} + 5 q^{18} + 8 q^{19} - 10 q^{20} - 7 q^{22} + 28 q^{24} + 18 q^{25} - 26 q^{26} + q^{28} + 32 q^{30}+ \cdots - 4 q^{99}+O(q^{100}) $ 18 * q - q^2 + q^4 + 18 * q^7 - 7 * q^8 - 22 * q^9 + 6 * q^10 + 4 * q^11 - 8 * q^12 - q^14 - 3 * q^16 + 5 * q^18 + 8 * q^19 - 10 * q^20 - 7 * q^22 + 28 * q^24 + 18 * q^25 - 26 * q^26 + q^28 + 32 * q^30 - 11 * q^32 - 12 * q^33 + 10 * q^34 + 11 * q^36 - 8 * q^37 - 4 * q^38 - 18 * q^40 - 40 * q^43 + 15 * q^44 - 12 * q^45 - 38 * q^46 + 16 * q^48 + 18 * q^49 - 43 * q^50 - 8 * q^51 - 30 * q^52 + 4 * q^53 + 16 * q^54 - 20 * q^55 - 7 * q^56 + 36 * q^60 + 36 * q^62 - 22 * q^63 + q^64 - 48 * q^66 + 26 * q^68 - 12 * q^69 + 6 * q^70 + 67 * q^72 + 30 * q^74 - 24 * q^76 + 4 * q^77 + 52 * q^78 - 16 * q^79 - 42 * q^80 + 50 * q^81 + 2 * q^82 - 24 * q^83 - 8 * q^84 - 8 * q^86 + 72 * q^87 + 39 * q^88 + 8 * q^89 - 50 * q^90 + 18 * q^92 - 4 * q^93 - 48 * q^94 + 8 * q^95 - 80 * q^96 + 8 * q^97 - q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.35077	+	0.418821i	−0.955141	+	0.296151i
$2$	−1.35077	+	0.418821i	−0.955141	+	0.296151i
$3$			1.57463i			0.909111i	0.890718	+	0.454556i	$0.150202\pi$
$3$			1.57463i			0.909111i	−0.890718	+	0.454556i	$0.849798\pi$
$4$	1.64918	−	1.13146i	0.824589	−	0.565732i
$5$	1.58188			0.707437			0.353719	−	0.935352i	$-0.384917\pi$
$5$	1.58188			0.707437			0.353719	+	0.935352i	$0.384917\pi$
$6$	−0.659487	−	2.12696i	−0.269235	−	0.868330i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.75378	+	2.21906i	−0.620056	+	0.784557i
$9$	0.520549			0.173516
$10$	−2.13676	+	0.662524i	−0.675703	+	0.209509i
$11$	3.03811	−	1.33037i	0.916025	−	0.401121i
$11$	3.03811	−	1.33037i	0.916025	−	0.401121i
$12$	1.78164	+	2.59684i	0.514314	+	0.749643i
$13$		−	2.62307i		−	0.727509i	−0.931495	−	0.363755i	$-0.881495\pi$
$13$		−	2.62307i		−	0.727509i	0.931495	−	0.363755i	$-0.118505\pi$
$14$	−1.35077	+	0.418821i	−0.361009	+	0.111935i
$15$			2.49087i			0.643139i
$16$	1.43957	−	3.73197i	0.359894	−	0.932993i
$17$		−	0.750224i		−	0.181956i	−0.995853	−	0.0909781i	$-0.971001\pi$
$17$		−	0.750224i		−	0.181956i	0.995853	−	0.0909781i	$-0.0289993\pi$
$18$	−0.703144	+	0.218017i	−0.165733	+	0.0513871i
$19$	1.14137			0.261849			0.130924	−	0.991392i	$-0.458205\pi$
$19$	1.14137			0.261849			0.130924	+	0.991392i	$0.458205\pi$
$20$	2.60880	−	1.78984i	0.583345	−	0.400220i
$21$			1.57463i			0.343612i
$22$	−3.54662	+	3.06945i	−0.756141	+	0.654409i
$23$			3.83223i			0.799075i	0.916717	+	0.399537i	$0.130829\pi$
$23$			3.83223i			0.799075i	−0.916717	+	0.399537i	$0.869171\pi$
$24$	−3.49420	−	2.76156i	−0.713250	−	0.563700i
$25$	−2.49766			−0.499532
$26$	1.09860	+	3.54318i	0.215453	+	0.694874i
$27$			5.54355i			1.06686i
$28$	1.64918	−	1.13146i	0.311665	−	0.213827i
$29$			9.02097i			1.67515i	0.546321	+	0.837576i	$0.316028\pi$
$29$			9.02097i			1.67515i	−0.546321	+	0.837576i	$0.683972\pi$
$30$	−1.04323	−	3.36460i	−0.190467	−	0.614289i
$31$		−	4.41685i		−	0.793290i	−0.917972	−	0.396645i	$-0.870174\pi$
$31$		−	4.41685i		−	0.793290i	0.917972	−	0.396645i	$-0.129826\pi$
$32$	−0.381509	+	5.64397i	−0.0674419	+	0.997723i
$33$	2.09483	+	4.78389i	0.364663	+	0.832769i
$34$	0.314210	+	1.01338i	0.0538865	+	0.173794i
$35$	1.58188			0.267386
$36$	0.858478	−	0.588983i	0.143080	−	0.0981639i
$37$	−2.80558			−0.461234			−0.230617	−	0.973045i	$-0.574074\pi$
$37$	−2.80558			−0.461234			−0.230617	+	0.973045i	$0.574074\pi$
$38$	−1.54174	+	0.478031i	−0.250103	+	0.0775469i
$39$	4.13036			0.661387
$40$	−2.77427	+	3.51029i	−0.438651	+	0.555025i
$41$			0.250697i			0.0391523i	0.999808	+	0.0195761i	$0.00623168\pi$
$41$			0.250697i			0.0391523i	−0.999808	+	0.0195761i	$0.993768\pi$
$42$	−0.659487	−	2.12696i	−0.101761	−	0.328198i
$43$	1.82459			0.278248			0.139124	−	0.990275i	$-0.455571\pi$
$43$	1.82459			0.278248			0.139124	+	0.990275i	$0.455571\pi$
$44$	3.50512	−	5.63153i	0.528417	−	0.848985i
$45$	0.823446			0.122752
$46$	−1.60502	−	5.17647i	−0.236647	−	0.763229i
$47$			4.73143i			0.690150i	0.938575	+	0.345075i	$0.112146\pi$
$47$			4.73143i			0.690150i	−0.938575	+	0.345075i	$0.887854\pi$
$48$	5.87647	+	2.26679i	0.848195	+	0.327183i
$49$	1.00000			0.142857
$50$	3.37377	−	1.04607i	0.477124	−	0.147937i
$51$	1.18132			0.165418
$52$	−2.96791	−	4.32591i	−0.411576	−	0.599896i
$53$	−9.11425			−1.25194			−0.625969	−	0.779848i	$-0.715296\pi$
$53$	−9.11425			−1.25194			−0.625969	+	0.779848i	$0.715296\pi$
$54$	−2.32176	−	7.48808i	−0.315951	−	1.01900i
$55$	4.80592	−	2.10448i	0.648031	−	0.283768i
$56$	−1.75378	+	2.21906i	−0.234359	+	0.296535i
$57$			1.79724i			0.238050i
$58$	−3.77817	−	12.1853i	−0.496098	−	1.60001i
$59$		−	14.5290i		−	1.89152i	−0.324869	−	0.945759i	$-0.605320\pi$
$59$		−	14.5290i		−	1.89152i	0.324869	−	0.945759i	$-0.394680\pi$
$60$	2.81833	+	4.10788i	0.363845	+	0.530326i
$61$		−	7.65849i		−	0.980569i	−0.871562	−	0.490284i	$-0.836893\pi$
$61$		−	7.65849i		−	0.980569i	0.871562	−	0.490284i	$-0.163107\pi$
$62$	1.84987	+	5.96616i	0.234934	+	0.757704i
$63$	0.520549			0.0655830
$64$	−1.84848	−	7.78352i	−0.231060	−	0.972939i
$65$		−	4.14938i		−	0.514667i
$66$	−4.83324	−	5.58460i	−0.594931	−	0.687416i
$67$		−	8.00407i		−	0.977853i	−0.872325	−	0.488926i	$-0.837389\pi$
$67$		−	8.00407i		−	0.977853i	0.872325	−	0.488926i	$-0.162611\pi$
$68$	−0.848852	−	1.23725i	−0.102938	−	0.150039i
$69$	−6.03433			−0.726448
$70$	−2.13676	+	0.662524i	−0.255392	+	0.0791868i
$71$			11.4380i			1.35744i	0.734398	+	0.678719i	$0.237464\pi$
$71$			11.4380i			1.35744i	−0.734398	+	0.678719i	$0.762536\pi$
$72$	−0.912931	+	1.15513i	−0.107590	+	0.136134i
$73$			0.267868i			0.0313516i	0.999877	+	0.0156758i	$0.00498997\pi$
$73$			0.267868i			0.0313516i	−0.999877	+	0.0156758i	$0.995010\pi$
$74$	3.78970	−	1.17503i	0.440543	−	0.136595i
$75$		−	3.93289i		−	0.454130i
$76$	1.88233	−	1.29142i	0.215918	−	0.148136i
$77$	3.03811	−	1.33037i	0.346225	−	0.151609i
$78$	−5.57918	+	1.72988i	−0.631718	+	0.195871i
$79$	−6.72244			−0.756334			−0.378167	−	0.925737i	$-0.623445\pi$
$79$	−6.72244			−0.756334			−0.378167	+	0.925737i	$0.623445\pi$
$80$	2.27723	−	5.90353i	0.254602	−	0.660034i
$81$	−7.16738			−0.796376
$82$	−0.104997	−	0.338635i	−0.0115950	−	0.0373960i
$83$	1.20081			0.131806			0.0659029	−	0.997826i	$-0.479007\pi$
$83$	1.20081			0.131806			0.0659029	+	0.997826i	$0.479007\pi$
$84$	1.78164	+	2.59684i	0.194392	+	0.283338i
$85$		−	1.18676i		−	0.128723i
$86$	−2.46461	+	0.764178i	−0.265766	+	0.0824035i
$87$	−14.2047			−1.52290
$88$	−2.37602	+	9.07494i	−0.253285	+	0.967392i
$89$	10.6509			1.12899			0.564494	−	0.825437i	$-0.309071\pi$
$89$	10.6509			1.12899			0.564494	+	0.825437i	$0.309071\pi$
$90$	−1.11229	+	0.344876i	−0.117245	+	0.0363532i
$91$		−	2.62307i		−	0.274973i
$92$	4.33603	+	6.32002i	0.452063	+	0.658908i
$93$	6.95489			0.721189
$94$	−1.98162	−	6.39109i	−0.204389	−	0.659190i
$95$	1.80551			0.185242
$96$	−8.88716	−	0.600735i	−0.907042	−	0.0613122i
$97$	−12.3457			−1.25352			−0.626758	−	0.779214i	$-0.715618\pi$
$97$	−12.3457			−1.25352			−0.626758	+	0.779214i	$0.715618\pi$
$98$	−1.35077	+	0.418821i	−0.136449	+	0.0423073i
$99$	1.58149	−	0.692521i	0.158945	−	0.0696010i
$100$	−4.11909	+	2.82602i	−0.411909	+	0.282602i
$101$		−	18.5310i		−	1.84390i	−0.387307	−	0.921951i	$-0.626595\pi$
$101$		−	18.5310i		−	1.84390i	0.387307	−	0.921951i	$-0.373405\pi$
$102$	−1.59570	+	0.494763i	−0.157998	+	0.0489889i
$103$			3.44171i			0.339122i	0.985520	+	0.169561i	$0.0542349\pi$
$103$			3.44171i			0.339122i	−0.985520	+	0.169561i	$0.945765\pi$
$104$	5.82076	+	4.60030i	0.570773	+	0.451097i
$105$			2.49087i			0.243084i
$106$	12.3113	−	3.81724i	1.19578	−	0.370763i
$107$	−13.6088			−1.31561			−0.657807	−	0.753186i	$-0.728516\pi$
$107$	−13.6088			−1.31561			−0.657807	+	0.753186i	$0.728516\pi$
$108$	6.27234	+	9.14230i	0.603556	+	0.879719i
$109$		−	4.90234i		−	0.469559i	−0.972049	−	0.234779i	$-0.924563\pi$
$109$		−	4.90234i		−	0.469559i	0.972049	−	0.234779i	$-0.0754368\pi$
$110$	−5.61031	+	4.85550i	−0.534922	+	0.462953i
$111$		−	4.41773i		−	0.419313i
$112$	1.43957	−	3.73197i	0.136027	−	0.352638i
$113$	18.6980			1.75896			0.879480	−	0.475936i	$-0.157891\pi$
$113$	18.6980			1.75896			0.879480	+	0.475936i	$0.157891\pi$
$114$	−0.752721	−	2.42766i	−0.0704987	−	0.227371i
$115$			6.06212i			0.565295i
$116$	10.2069	+	14.8772i	0.947688	+	1.38131i
$117$		−	1.36544i		−	0.126235i
$118$	6.08506	+	19.6254i	0.560175	+	1.80667i
$119$		−	0.750224i		−	0.0687729i
$120$	−5.52739	−	4.36845i	−0.504580	−	0.398783i
$121$	7.46025	−	8.08361i	0.678204	−	0.734873i
$122$	3.20754	+	10.3449i	0.290397	+	0.936582i
$123$	−0.394754			−0.0355938
$124$	−4.99751	−	7.28417i	−0.448790	−	0.654138i
$125$	−11.8604			−1.06083
$126$	−0.703144	+	0.218017i	−0.0626411	+	0.0194225i
$127$	0.249900			0.0221751			0.0110875	−	0.999939i	$-0.496471\pi$
$127$	0.249900			0.0221751			0.0110875	+	0.999939i	$0.496471\pi$
$128$	5.75678	+	9.73958i	0.508833	+	0.860866i
$129$			2.87305i			0.252958i
$130$	1.73785	+	5.60487i	0.152419	+	0.491580i
$131$	−16.9727			−1.48292			−0.741458	−	0.671000i	$-0.765865\pi$
$131$	−16.9727			−1.48292			−0.741458	+	0.671000i	$0.765865\pi$
$132$	8.86756	+	5.51926i	0.771822	+	0.480390i
$133$	1.14137			0.0989696
$134$	3.35227	+	10.8117i	0.289592	+	0.933987i
$135$			8.76923i			0.754735i
$136$	1.66480	+	1.31573i	0.142755	+	0.112823i
$137$	8.45260			0.722155			0.361077	−	0.932536i	$-0.382409\pi$
$137$	8.45260			0.722155			0.361077	+	0.932536i	$0.382409\pi$
$138$	8.15101	−	2.52730i	0.693860	−	0.215138i
$139$	10.4874			0.889533			0.444766	−	0.895647i	$-0.353287\pi$
$139$	10.4874			0.889533			0.444766	+	0.895647i	$0.353287\pi$
$140$	2.60880	−	1.78984i	0.220484	−	0.151269i
$141$	−7.45024			−0.627423
$142$	−4.79046	−	15.4501i	−0.402007	−	1.29654i
$143$	−3.48965	−	7.96919i	−0.291819	−	0.666417i
$144$	0.749369	−	1.94268i	0.0624474	−	0.161890i
$145$			14.2701i			1.18506i
$146$	−0.112189	−	0.361829i	−0.00928482	−	0.0299452i
$147$			1.57463i			0.129873i
$148$	−4.62689	+	3.17441i	−0.380328	+	0.260935i
$149$			17.5806i			1.44026i	0.693841	+	0.720128i	$0.255917\pi$
$149$			17.5806i			1.44026i	−0.693841	+	0.720128i	$0.744083\pi$
$150$	1.64718	+	5.31244i	0.134491	+	0.433759i
$151$	1.11949			0.0911028			0.0455514	−	0.998962i	$-0.485496\pi$
$151$	1.11949			0.0911028			0.0455514	+	0.998962i	$0.485496\pi$
$152$	−2.00172	+	2.53278i	−0.162361	+	0.205435i
$153$		−	0.390529i		−	0.0315724i
$154$	−3.54662	+	3.06945i	−0.285794	+	0.247343i
$155$		−	6.98692i		−	0.561203i
$156$	6.81170	−	4.67336i	0.545372	−	0.374168i
$157$	8.38807			0.669441			0.334720	−	0.942318i	$-0.391358\pi$
$157$	8.38807			0.669441			0.334720	+	0.942318i	$0.391358\pi$
$158$	9.08050	−	2.81550i	0.722406	−	0.223989i
$159$		−	14.3515i		−	1.13815i
$160$	−0.603501	+	8.92808i	−0.0477110	+	0.705827i
$161$			3.83223i			0.302022i
$162$	9.68151	−	3.00185i	0.760651	−	0.235848i
$163$			4.32454i			0.338725i	0.985554	+	0.169362i	$0.0541708\pi$
$163$			4.32454i			0.338725i	−0.985554	+	0.169362i	$0.945829\pi$
$164$	0.283655	+	0.413444i	0.0221497	+	0.0322845i
$165$	3.31377	+	7.56754i	0.257977	+	0.589132i
$166$	−1.62202	+	0.502924i	−0.125893	+	0.0390345i
$167$	−21.2610			−1.64523			−0.822614	−	0.568600i	$-0.807485\pi$
$167$	−21.2610			−1.64523			−0.822614	+	0.568600i	$0.807485\pi$
$168$	−3.49420	−	2.76156i	−0.269583	−	0.213059i
$169$	6.11949			0.470730
$170$	0.497042	+	1.60305i	0.0381214	+	0.122948i
$171$	0.594141			0.0454351
$172$	3.00908	−	2.06446i	0.229440	−	0.157414i
$173$		−	2.41069i		−	0.183282i	−0.995792	−	0.0916408i	$-0.970789\pi$
$173$		−	2.41069i		−	0.183282i	0.995792	−	0.0916408i	$-0.0292112\pi$
$174$	19.1873	−	5.94921i	1.45458	−	0.451009i
$175$	−2.49766			−0.188805
$176$	−0.591305	−	13.2533i	−0.0445713	−	0.999006i
$177$	22.8778			1.71960
$178$	−14.3869	+	4.46080i	−1.07834	+	0.334351i
$179$			12.5187i			0.935689i	0.883811	+	0.467844i	$0.154969\pi$
$179$			12.5187i			0.935689i	−0.883811	+	0.467844i	$0.845031\pi$
$180$	1.35801	−	0.931700i	0.101220	−	0.0694448i
$181$	−24.6700			−1.83371			−0.916854	−	0.399223i	$-0.869280\pi$
$181$	−24.6700			−1.83371			−0.916854	+	0.399223i	$0.869280\pi$
$182$	1.09860	+	3.54318i	0.0814335	+	0.262638i
$183$	12.0593			0.891446
$184$	−8.50396	−	6.72090i	−0.626920	−	0.495471i
$185$	−4.43808			−0.326294
$186$	−9.39448	+	2.91286i	−0.688837	+	0.213581i
$187$	−0.998073	−	2.27927i	−0.0729863	−	0.166676i
$188$	5.35345	+	7.80297i	0.390440	+	0.569090i
$189$			5.54355i			0.403234i
$190$	−2.43884	+	0.756187i	−0.176932	+	0.0548596i
$191$		−	11.8677i		−	0.858720i	−0.903133	−	0.429360i	$-0.858739\pi$
$191$		−	11.8677i		−	0.858720i	0.903133	−	0.429360i	$-0.141261\pi$
$192$	12.2561	−	2.91067i	0.884510	−	0.210060i
$193$			8.28858i			0.596625i	0.954468	+	0.298312i	$0.0964237\pi$
$193$			8.28858i			0.596625i	−0.954468	+	0.298312i	$0.903576\pi$
$194$	16.6762	−	5.17064i	1.19728	−	0.371230i
$195$	6.53373			0.467890
$196$	1.64918	−	1.13146i	0.117798	−	0.0808189i
$197$		−	19.0013i		−	1.35379i	−0.736081	−	0.676893i	$-0.763326\pi$
$197$		−	19.0013i		−	1.35379i	0.736081	−	0.676893i	$-0.236674\pi$
$198$	−1.84619	+	1.59780i	−0.131203	+	0.113551i
$199$			16.0120i			1.13506i	0.823351	+	0.567532i	$0.192102\pi$
$199$			16.0120i			1.13506i	−0.823351	+	0.567532i	$0.807898\pi$
$200$	4.38036	−	5.54247i	0.309738	−	0.391912i
$201$	12.6034			0.888977
$202$	7.76117	+	25.0312i	0.546074	+	1.76119i
$203$			9.02097i			0.633148i
$204$	1.94821	−	1.33663i	0.136402	−	0.0935825i
$205$			0.396572i			0.0276978i
$206$	−1.44146	−	4.64897i	−0.100431	−	0.323909i
$207$			1.99486i			0.138653i
$208$	−9.78924	−	3.77611i	−0.678761	−	0.261826i
$209$	3.46762	−	1.51844i	0.239860	−	0.105033i
$210$	−1.04323	−	3.36460i	−0.0719896	−	0.232179i
$211$	0.980150			0.0674763			0.0337381	−	0.999431i	$-0.489259\pi$
$211$	0.980150			0.0674763			0.0337381	+	0.999431i	$0.489259\pi$
$212$	−15.0310	+	10.3125i	−1.03233	+	0.708262i
$213$	−18.0105			−1.23406
$214$	18.3824	−	5.69966i	1.25660	−	0.389621i
$215$	2.88628			0.196843
$216$	−12.3015	−	9.72219i	−0.837011	−	0.661511i
$217$		−	4.41685i		−	0.299835i
$218$	2.05320	+	6.62195i	0.139060	+	0.448495i
$219$	−0.421793			−0.0285021
$220$	5.54468	−	8.90839i	0.373822	−	0.600604i
$221$	−1.96789			−0.132375
$222$	1.85024	+	5.96736i	0.124180	+	0.400503i
$223$		−	7.90537i		−	0.529383i	−0.964333	−	0.264691i	$-0.914730\pi$
$223$		−	7.90537i		−	0.529383i	0.964333	−	0.264691i	$-0.0852700\pi$
$224$	−0.381509	+	5.64397i	−0.0254907	+	0.377104i
$225$	−1.30016			−0.0866770
$226$	−25.2568	+	7.83112i	−1.68005	+	0.520918i
$227$	−8.91322			−0.591591			−0.295796	−	0.955251i	$-0.595585\pi$
$227$	−8.91322			−0.591591			−0.295796	+	0.955251i	$0.595585\pi$
$228$	2.03351	+	2.96396i	0.134672	+	0.196293i
$229$	−20.0551			−1.32528			−0.662639	−	0.748939i	$-0.730563\pi$
$229$	−20.0551			−1.32528			−0.662639	+	0.748939i	$0.730563\pi$
$230$	−2.53894	−	8.18855i	−0.167413	−	0.539937i
$231$	2.09483	+	4.78389i	0.137830	+	0.314757i
$232$	−20.0181	−	15.8208i	−1.31425	−	1.03869i
$233$			7.48274i			0.490210i	0.969496	+	0.245105i	$0.0788225\pi$
$233$			7.48274i			0.490210i	−0.969496	+	0.245105i	$0.921177\pi$
$234$	0.571874	+	1.84440i	0.0373846	+	0.120572i
$235$			7.48454i			0.488238i
$236$	−16.4391	−	23.9609i	−1.07009	−	1.55972i
$237$		−	10.5853i		−	0.687592i
$238$	0.314210	+	1.01338i	0.0203672	+	0.0656879i
$239$	−14.2237			−0.920057			−0.460029	−	0.887904i	$-0.652161\pi$
$239$	−14.2237			−0.920057			−0.460029	+	0.887904i	$0.652161\pi$
$240$	9.29586	+	3.58579i	0.600045	+	0.231462i
$241$		−	13.7418i		−	0.885184i	−0.896723	−	0.442592i	$-0.854059\pi$
$241$		−	13.7418i		−	0.885184i	0.896723	−	0.442592i	$-0.145941\pi$
$242$	−6.69152	+	14.0436i	−0.430147	+	0.902759i
$243$			5.34471i			0.342863i
$244$	−8.66531	−	12.6302i	−0.554740	−	0.808566i
$245$	1.58188			0.101062
$246$	0.533224	−	0.165331i	0.0339971	−	0.0105411i
$247$		−	2.99390i		−	0.190498i
$248$	9.80127	+	7.74620i	0.622381	+	0.491884i
$249$			1.89083i			0.119826i
$250$	16.0207	−	4.96738i	1.01324	−	0.314165i
$251$		−	23.6620i		−	1.49353i	−0.665086	−	0.746767i	$-0.731605\pi$
$251$		−	23.6620i		−	1.49353i	0.665086	−	0.746767i	$-0.268395\pi$
$252$	0.858478	−	0.588983i	0.0540790	−	0.0371025i
$253$	5.09827	+	11.6427i	0.320525	+	0.731973i
$254$	−0.337559	+	0.104664i	−0.0211803	+	0.00656718i
$255$	1.86871			0.117023
$256$	−11.8553	−	10.7449i	−0.740953	−	0.671557i
$257$	13.6739			0.852952			0.426476	−	0.904499i	$-0.359755\pi$
$257$	13.6739			0.852952			0.426476	+	0.904499i	$0.359755\pi$
$258$	−1.20330	−	3.88085i	−0.0749139	−	0.241611i
$259$	−2.80558			−0.174330
$260$	−4.69488	−	6.84307i	−0.291164	−	0.424389i
$261$			4.69586i			0.290666i
$262$	22.9263	−	7.10854i	1.41639	−	0.439167i
$263$	−1.54709			−0.0953978			−0.0476989	−	0.998862i	$-0.515189\pi$
$263$	−1.54709			−0.0953978			−0.0476989	+	0.998862i	$0.515189\pi$
$264$	−14.2896	−	3.74135i	−0.879467	−	0.230264i
$265$	−14.4176			−0.885668
$266$	−1.54174	+	0.478031i	−0.0945299	+	0.0293100i
$267$			16.7711i			1.02638i
$268$	−9.05632	−	13.2001i	−0.553203	−	0.806326i
$269$	−11.1137			−0.677617			−0.338808	−	0.940855i	$-0.610024\pi$
$269$	−11.1137			−0.677617			−0.338808	+	0.940855i	$0.610024\pi$
$270$	−3.67274	−	11.8452i	−0.223516	−	0.720878i
$271$	12.4657			0.757235			0.378617	−	0.925553i	$-0.376400\pi$
$271$	12.4657			0.757235			0.378617	+	0.925553i	$0.376400\pi$
$272$	−2.79982	−	1.08000i	−0.169764	−	0.0654848i
$273$	4.13036			0.249981
$274$	−11.4176	+	3.54013i	−0.689760	+	0.213867i
$275$	−7.58817	+	3.32281i	−0.457584	+	0.200373i
$276$	−9.95168	+	6.82763i	−0.599021	+	0.410975i
$277$		−	21.0155i		−	1.26270i	−0.775498	−	0.631350i	$-0.782501\pi$
$277$		−	21.0155i		−	1.26270i	0.775498	−	0.631350i	$-0.217499\pi$
$278$	−14.1662	+	4.39236i	−0.849629	+	0.263436i
$279$		−	2.29919i		−	0.137649i
$280$	−2.77427	+	3.51029i	−0.165795	+	0.209780i
$281$			17.7260i			1.05744i	0.848795	+	0.528721i	$0.177328\pi$
$281$			17.7260i			1.05744i	−0.848795	+	0.528721i	$0.822672\pi$
$282$	10.0636	−	3.12032i	0.599278	−	0.185812i
$283$	32.9128			1.95646			0.978232	−	0.207513i	$-0.0665370\pi$
$283$	32.9128			1.95646			0.978232	+	0.207513i	$0.0665370\pi$
$284$	12.9417	+	18.8632i	0.767946	+	1.11933i
$285$			2.84301i			0.168405i
$286$	8.05139	+	9.30303i	0.476089	+	0.550100i
$287$			0.250697i			0.0147982i
$288$	−0.198594	+	2.93797i	−0.0117023	+	0.173121i
$289$	16.4372			0.966892
$290$	−5.97661	−	19.2756i	−0.350958	−	1.13190i
$291$		−	19.4399i		−	1.13958i
$292$	0.303084	+	0.441762i	0.0177366	+	0.0258522i
$293$		−	29.4803i		−	1.72226i	−0.508386	−	0.861130i	$-0.669757\pi$
$293$		−	29.4803i		−	1.72226i	0.508386	−	0.861130i	$-0.330243\pi$
$294$	−0.659487	−	2.12696i	−0.0384621	−	0.124047i
$295$		−	22.9831i		−	1.33813i
$296$	4.92037	−	6.22575i	0.285991	−	0.361864i
$297$	7.37496	+	16.8419i	0.427938	+	0.977268i
$298$	−7.36311	−	23.7474i	−0.426534	−	1.37565i
$299$	10.0522			0.581334
$300$	−4.44992	−	6.48603i	−0.256916	−	0.374471i
$301$	1.82459			0.105168
$302$	−1.51218	+	0.468866i	−0.0870160	+	0.0269802i
$303$	29.1794			1.67631
$304$	1.64309	−	4.25957i	0.0942377	−	0.244303i
$305$		−	12.1148i		−	0.693691i
$306$	0.163562	+	0.527516i	0.00935020	+	0.0301561i
$307$	22.5952			1.28958			0.644789	−	0.764361i	$-0.276945\pi$
$307$	22.5952			1.28958			0.644789	+	0.764361i	$0.276945\pi$
$308$	3.50512	−	5.63153i	0.199723	−	0.320886i
$309$	−5.41941			−0.308299
$310$	2.92627	+	9.43774i	0.166201	+	0.536028i
$311$		−	8.11720i		−	0.460284i	−0.973157	−	0.230142i	$-0.926081\pi$
$311$		−	8.11720i		−	0.460284i	0.973157	−	0.230142i	$-0.0739191\pi$
$312$	−7.24376	+	9.16553i	−0.410097	+	0.518896i
$313$	−22.3289			−1.26210			−0.631052	−	0.775741i	$-0.717376\pi$
$313$	−22.3289			−1.26210			−0.631052	+	0.775741i	$0.717376\pi$
$314$	−11.3304	+	3.51310i	−0.639410	+	0.198256i
$315$	0.823446			0.0463959
$316$	−11.0865	+	7.60621i	−0.623665	+	0.427883i
$317$	−4.24834			−0.238611			−0.119305	−	0.992858i	$-0.538067\pi$
$317$	−4.24834			−0.238611			−0.119305	+	0.992858i	$0.538067\pi$
$318$	6.01073	+	19.3857i	0.337065	+	1.08710i
$319$	12.0012	+	27.4067i	0.671938	+	1.53448i
$320$	−2.92408	−	12.3126i	−0.163461	−	0.688294i
$321$		−	21.4288i		−	1.19604i
$322$	−1.60502	−	5.17647i	−0.0894442	−	0.288473i
$323$		−	0.856286i		−	0.0476450i
$324$	−11.8203	+	8.10964i	−0.656682	+	0.450536i
$325$			6.55155i			0.363414i
$326$	−1.81121	−	5.84148i	−0.100314	−	0.323530i
$327$	7.71935			0.426881
$328$	−0.556313	−	0.439668i	−0.0307172	−	0.0242766i
$329$			4.73143i			0.260852i
$330$	−7.64559	−	8.83415i	−0.420876	−	0.486304i
$331$		−	0.144143i		−	0.00792284i	−0.999992	−	0.00396142i	$-0.998739\pi$
$331$		−	0.144143i		−	0.00792284i	0.999992	−	0.00396142i	$-0.00126096\pi$
$332$	1.98035	−	1.35867i	0.108686	−	0.0745669i
$333$	−1.46044			−0.0800316
$334$	28.7188	−	8.90457i	1.57142	−	0.487236i
$335$		−	12.6615i		−	0.691770i
$336$	5.87647	+	2.26679i	0.320588	+	0.123664i
$337$			28.5950i			1.55767i	0.627230	+	0.778834i	$0.284189\pi$
$337$			28.5950i			1.55767i	−0.627230	+	0.778834i	$0.715811\pi$
$338$	−8.26604	+	2.56297i	−0.449614	+	0.139407i
$339$			29.4424i			1.59909i
$340$	−1.34278	−	1.95718i	−0.0728225	−	0.106143i
$341$	−5.87603	−	13.4189i	−0.318205	−	0.726673i
$342$	−0.802549	+	0.248839i	−0.0433969	+	0.0134557i
$343$	1.00000			0.0539949
$344$	−3.19994	+	4.04889i	−0.172529	+	0.218301i
$345$	−9.54558			−0.513917
$346$	1.00965	+	3.25630i	0.0542791	+	0.175060i
$347$	−23.0033			−1.23488			−0.617442	−	0.786616i	$-0.711831\pi$
$347$	−23.0033			−1.23488			−0.617442	+	0.786616i	$0.711831\pi$
$348$	−23.4260	+	16.0721i	−1.25577	+	0.861554i
$349$			23.7790i			1.27286i	0.771334	+	0.636430i	$0.219590\pi$
$349$			23.7790i			1.27286i	−0.771334	+	0.636430i	$0.780410\pi$
$350$	3.37377	−	1.04607i	0.180336	−	0.0559150i
$351$	14.5411			0.776149
$352$	6.34949	+	17.6546i	0.338429	+	0.940992i
$353$	−1.29117			−0.0687220			−0.0343610	−	0.999409i	$-0.510940\pi$
$353$	−1.29117			−0.0687220			−0.0343610	+	0.999409i	$0.510940\pi$
$354$	−30.9027	+	9.58170i	−1.64246	+	0.509262i
$355$			18.0935i			0.960302i
$356$	17.5652	−	12.0511i	0.930951	−	0.638705i
$357$	1.18132			0.0625223
$358$	−5.24308	−	16.9099i	−0.277105	−	0.893715i
$359$	25.2115			1.33061			0.665306	−	0.746571i	$-0.268301\pi$
$359$	25.2115			1.33061			0.665306	+	0.746571i	$0.268301\pi$
$360$	−1.44415	+	1.82728i	−0.0761132	+	0.0963060i
$361$	−17.6973			−0.931435
$362$	33.3236	−	10.3323i	1.75145	−	0.543055i
$363$	12.7287	+	11.7471i	0.668082	+	0.616563i
$364$	−2.96791	−	4.32591i	−0.155561	−	0.226739i
$365$			0.423735i			0.0221793i
$366$	−16.2893	+	5.05067i	−0.851457	+	0.264003i
$367$			1.10279i			0.0575651i	0.999586	+	0.0287825i	$0.00916303\pi$
$367$			1.10279i			0.0575651i	−0.999586	+	0.0287825i	$0.990837\pi$
$368$	14.3018	+	5.51678i	0.745531	+	0.287582i
$369$			0.130500i			0.00679357i
$370$	5.99484	−	1.85876i	0.311657	−	0.0966324i
$371$	−9.11425			−0.473188
$372$	11.4699	−	7.86922i	0.594684	−	0.408000i
$373$			19.1952i			0.993888i	0.867783	+	0.496944i	$0.165545\pi$
$373$			19.1952i			0.993888i	−0.867783	+	0.496944i	$0.834455\pi$
$374$	2.30278	+	2.66076i	0.119074	+	0.137584i
$375$		−	18.6757i		−	0.964408i
$376$	−10.4993	−	8.29790i	−0.541462	−	0.427932i
$377$	23.6627			1.21869
$378$	−2.32176	−	7.48808i	−0.119418	−	0.385145i
$379$		−	7.61066i		−	0.390933i	−0.980710	−	0.195467i	$-0.937378\pi$
$379$		−	7.61066i		−	0.390933i	0.980710	−	0.195467i	$-0.0626221\pi$
$380$	2.97761	−	2.04287i	0.152748	−	0.104797i
$381$			0.393500i			0.0201596i
$382$	4.97046	+	16.0306i	0.254311	+	0.820199i
$383$			22.0885i			1.12867i	0.825546	+	0.564335i	$0.190867\pi$
$383$			22.0885i			1.12867i	−0.825546	+	0.564335i	$0.809133\pi$
$384$	−15.3362	+	9.06479i	−0.782623	+	0.462585i
$385$	4.80592	−	2.10448i	0.244933	−	0.107254i
$386$	−3.47143	−	11.1960i	−0.176691	−	0.569861i
$387$	0.949791			0.0482806
$388$	−20.3602	+	13.9687i	−1.03363	+	0.709154i
$389$	−27.1911			−1.37865			−0.689323	−	0.724454i	$-0.742092\pi$
$389$	−27.1911			−1.37865			−0.689323	+	0.724454i	$0.742092\pi$
$390$	−8.82559	+	2.73646i	−0.446901	+	0.138566i
$391$	2.87503			0.145397
$392$	−1.75378	+	2.21906i	−0.0885795	+	0.112080i
$393$		−	26.7257i		−	1.34814i
$394$	7.95814	+	25.6664i	0.400925	+	1.29306i
$395$	−10.6341			−0.535059
$396$	1.82459	−	2.93149i	0.0916891	−	0.147313i
$397$	13.6761			0.686383			0.343192	−	0.939265i	$-0.388492\pi$
$397$	13.6761			0.686383			0.343192	+	0.939265i	$0.388492\pi$
$398$	−6.70618	−	21.6286i	−0.336151	−	1.08415i
$399$			1.79724i			0.0899744i
$400$	−3.59557	+	9.32121i	−0.179778	+	0.466060i
$401$	3.77907			0.188718			0.0943588	−	0.995538i	$-0.469920\pi$
$401$	3.77907			0.188718			0.0943588	+	0.995538i	$0.469920\pi$
$402$	−17.0244	+	5.27858i	−0.849098	+	0.263272i
$403$	−11.5857			−0.577126
$404$	−20.9672	−	30.5609i	−1.04315	−	1.52046i
$405$	−11.3379			−0.563386
$406$	−3.77817	−	12.1853i	−0.187508	−	0.604745i
$407$	−8.52365	+	3.73244i	−0.422502	+	0.185010i
$408$	−2.07179	+	2.62143i	−0.102569	+	0.129780i
$409$			28.8350i			1.42580i	0.701267	+	0.712899i	$0.252618\pi$
$409$			28.8350i			1.42580i	−0.701267	+	0.712899i	$0.747382\pi$
$410$	−0.166093	−	0.535679i	−0.00820274	−	0.0264553i
$411$			13.3097i			0.656519i
$412$	3.89417	+	5.67599i	0.191852	+	0.279636i
$413$		−	14.5290i		−	0.714927i
$414$	−0.835491	−	2.69461i	−0.0410621	−	0.132433i
$415$	1.89953			0.0932444
$416$	14.8046	+	1.00073i	0.725853	+	0.0490646i
$417$			16.5138i			0.808684i
$418$	−4.04801	+	3.50339i	−0.197995	+	0.171356i
$419$			20.7473i			1.01357i	0.862072	+	0.506786i	$0.169166\pi$
$419$			20.7473i			1.01357i	−0.862072	+	0.506786i	$0.830834\pi$
$420$	2.81833	+	4.10788i	0.137520	+	0.200444i
$421$	22.2373			1.08378			0.541890	−	0.840449i	$-0.317709\pi$
$421$	22.2373			1.08378			0.541890	+	0.840449i	$0.317709\pi$
$422$	−1.32396	+	0.410507i	−0.0644494	+	0.0199832i
$423$			2.46294i			0.119752i
$424$	15.9844	−	20.2251i	0.776272	−	0.982217i
$425$			1.87381i			0.0908929i
$426$	24.3282	−	7.54319i	1.17870	−	0.365469i
$427$		−	7.65849i		−	0.370620i
$428$	−22.4434	+	15.3979i	−1.08484	+	0.744286i
$429$	12.5485	−	5.49489i	0.605847	−	0.265296i
$430$	−3.89872	+	1.20884i	−0.188013	+	0.0582953i
$431$	−12.3696			−0.595823			−0.297912	−	0.954593i	$-0.596290\pi$
$431$	−12.3696			−0.595823			−0.297912	+	0.954593i	$0.596290\pi$
$432$	20.6884	+	7.98036i	0.995371	+	0.383955i
$433$	14.3230			0.688318			0.344159	−	0.938911i	$-0.388164\pi$
$433$	14.3230			0.688318			0.344159	+	0.938911i	$0.388164\pi$
$434$	1.84987	+	5.96616i	0.0887966	+	0.286385i
$435$	−22.4700			−1.07736
$436$	−5.54682	−	8.08483i	−0.265645	−	0.387193i
$437$			4.37400i			0.209237i
$438$	0.569746	−	0.176656i	0.0272235	−	0.00844093i
$439$	−6.33190			−0.302205			−0.151103	−	0.988518i	$-0.548282\pi$
$439$	−6.33190			−0.302205			−0.151103	+	0.988518i	$0.548282\pi$
$440$	−3.75858	+	14.3554i	−0.179183	+	0.684369i
$441$	0.520549			0.0247881
$442$	2.65818	−	0.824195i	0.126437	−	0.0392030i
$443$		−	25.6345i		−	1.21793i	−0.793197	−	0.608965i	$-0.791585\pi$
$443$		−	25.6345i		−	1.21793i	0.793197	−	0.608965i	$-0.208415\pi$
$444$	−4.99851	−	7.28563i	−0.237219	−	0.345761i
$445$	16.8484			0.798689
$446$	3.31093	+	10.6784i	0.156777	+	0.505635i
$447$	−27.6828			−1.30935
$448$	−1.84848	−	7.78352i	−0.0873326	−	0.367737i
$449$	4.53508			0.214024			0.107012	−	0.994258i	$-0.465872\pi$
$449$	4.53508			0.214024			0.107012	+	0.994258i	$0.465872\pi$
$450$	1.75622	−	0.544533i	0.0827888	−	0.0256695i
$451$	0.333519	+	0.761646i	0.0157048	+	0.0358645i
$452$	30.8363	−	21.1561i	1.45042	−	0.995101i
$453$			1.76278i			0.0828226i
$454$	12.0397	−	3.73304i	0.565053	−	0.175200i
$455$		−	4.14938i		−	0.194526i
$456$	−3.98818	−	3.15196i	−0.186764	−	0.147604i
$457$		−	17.6778i		−	0.826932i	−0.910520	−	0.413466i	$-0.864318\pi$
$457$		−	17.6778i		−	0.826932i	0.910520	−	0.413466i	$-0.135682\pi$
$458$	27.0899	−	8.39949i	1.26583	−	0.392483i
$459$	4.15891			0.194121
$460$	6.85907	+	9.99751i	0.319806	+	0.466136i
$461$			33.9977i			1.58343i	0.610890	+	0.791716i	$0.290812\pi$
$461$			33.9977i			1.58343i	−0.610890	+	0.791716i	$0.709188\pi$
$462$	−4.83324	−	5.58460i	−0.224863	−	0.259819i
$463$			2.00783i			0.0933117i	0.998911	+	0.0466559i	$0.0148564\pi$
$463$			2.00783i			0.0933117i	−0.998911	+	0.0466559i	$0.985144\pi$
$464$	33.6660	+	12.9864i	1.56291	+	0.602876i
$465$	11.0018			0.510196
$466$	−3.13393	−	10.1075i	−0.145176	−	0.468220i
$467$		−	28.6605i		−	1.32625i	−0.748508	−	0.663125i	$-0.769230\pi$
$467$		−	28.6605i		−	1.32625i	0.748508	−	0.663125i	$-0.230770\pi$
$468$	−1.54495	−	2.25185i	−0.0714151	−	0.104092i
$469$		−	8.00407i		−	0.369594i
$470$	−3.13469	−	10.1099i	−0.144592	−	0.466336i
$471$			13.2081i			0.608596i
$472$	32.2408	+	25.4808i	1.48400	+	1.17285i
$473$	5.54332	−	2.42738i	0.254882	−	0.111611i
$474$	4.43336	+	14.2984i	0.203631	+	0.656747i
$475$	−2.85076			−0.130802
$476$	−0.848852	−	1.23725i	−0.0389071	−	0.0567094i
$477$	−4.74441			−0.217232
$478$	19.2131	−	5.95720i	0.878785	−	0.272476i
$479$	19.7590			0.902811			0.451405	−	0.892319i	$-0.350923\pi$
$479$	19.7590			0.902811			0.451405	+	0.892319i	$0.350923\pi$
$480$	−14.0584	−	0.950289i	−0.641675	−	0.0433746i
$481$			7.35923i			0.335552i
$482$	5.75534	+	18.5620i	0.262149	+	0.845476i
$483$	−6.03433			−0.274572
$484$	3.15696	−	21.7723i	0.143498	−	0.989651i
$485$	−19.5294			−0.886784
$486$	−2.23848	−	7.21949i	−0.101539	−	0.327483i
$487$		−	15.3754i		−	0.696727i	−0.937359	−	0.348364i	$-0.886737\pi$
$487$		−	15.3754i		−	0.696727i	0.937359	−	0.348364i	$-0.113263\pi$
$488$	16.9947	+	13.4313i	0.769313	+	0.608008i
$489$	−6.80955			−0.307938
$490$	−2.13676	+	0.662524i	−0.0965289	+	0.0299298i
$491$	−11.0024			−0.496532			−0.248266	−	0.968692i	$-0.579861\pi$
$491$	−11.0024			−0.496532			−0.248266	+	0.968692i	$0.579861\pi$
$492$	−0.651020	+	0.446651i	−0.0293502	+	0.0201366i
$493$	6.76775			0.304804
$494$	1.25391	+	4.04409i	0.0564161	+	0.181952i
$495$	2.50172	−	1.09548i	0.112444	−	0.0492384i
$496$	−16.4836	−	6.35838i	−0.740134	−	0.285500i
$497$			11.4380i			0.513063i
$498$	−0.791918	−	2.55408i	−0.0354867	−	0.114451i
$499$		−	2.31056i		−	0.103435i	−0.998662	−	0.0517175i	$-0.983530\pi$
$499$		−	2.31056i		−	0.103435i	0.998662	−	0.0517175i	$-0.0164695\pi$
$500$	−19.5599	+	13.4196i	−0.874745	+	0.600143i
$501$		−	33.4782i		−	1.49570i
$502$	9.91016	+	31.9620i	0.442312	+	1.42654i
$503$	−25.2485			−1.12578			−0.562888	−	0.826533i	$-0.690310\pi$
$503$	−25.2485			−1.12578			−0.562888	+	0.826533i	$0.690310\pi$
$504$	−0.912931	+	1.15513i	−0.0406652	+	0.0514537i
$505$		−	29.3138i		−	1.30444i
$506$	−11.7628	−	13.5914i	−0.522922	−	0.604213i
$507$			9.63592i			0.427946i
$508$	0.412130	−	0.282754i	0.0182853	−	0.0125452i
$509$	33.9007			1.50262			0.751310	−	0.659949i	$-0.229422\pi$
$509$	33.9007			1.50262			0.751310	+	0.659949i	$0.229422\pi$
$510$	−2.52420	+	0.782655i	−0.111774	+	0.0346566i
$511$			0.267868i			0.0118498i
$512$	20.5140	+	9.54870i	0.906597	+	0.421997i
$513$			6.32726i			0.279355i
$514$	−18.4703	+	5.72690i	−0.814690	+	0.252603i
$515$			5.44437i			0.239907i
$516$	3.25076	+	4.73818i	0.143107	+	0.208587i
$517$	6.29453	+	14.3746i	0.276833	+	0.632195i
$518$	3.78970	−	1.17503i	0.166510	−	0.0516280i
$519$	3.79594			0.166623
$520$	9.20774	+	7.27712i	0.403786	+	0.319123i
$521$	−39.3095			−1.72218			−0.861090	−	0.508453i	$-0.830217\pi$
$521$	−39.3095			−1.72218			−0.861090	+	0.508453i	$0.830217\pi$
$522$	−1.96672	−	6.34304i	−0.0860812	−	0.277627i
$523$	−21.6105			−0.944962			−0.472481	−	0.881341i	$-0.656641\pi$
$523$	−21.6105			−0.944962			−0.472481	+	0.881341i	$0.656641\pi$
$524$	−27.9911	+	19.2041i	−1.22280	+	0.838933i
$525$		−	3.93289i		−	0.171645i
$526$	2.08977	−	0.647955i	0.0911184	−	0.0282522i
$527$	−3.31363			−0.144344
$528$	20.8690	−	0.931085i	0.908208	−	0.0405203i
$529$	8.31403			0.361480
$530$	19.4750	−	6.03841i	0.845938	−	0.262292i
$531$		−	7.56307i		−	0.328209i
$532$	1.88233	−	1.29142i	0.0816092	−	0.0559903i
$533$	0.657596			0.0284837
$534$	−7.02410	−	22.6540i	−0.303963	−	0.980334i
$535$	−21.5275			−0.930715
$536$	17.7615	+	14.0374i	0.767181	+	0.606324i
$537$	−19.7122			−0.850645
$538$	15.0121	−	4.65467i	0.647220	−	0.200677i
$539$	3.03811	−	1.33037i	0.130861	−	0.0573029i
$540$	9.92207	+	14.4620i	0.426978	+	0.622346i
$541$			14.4449i			0.621036i	0.950568	+	0.310518i	$0.100502\pi$
$541$			14.4449i			0.621036i	−0.950568	+	0.310518i	$0.899498\pi$
$542$	−16.8383	+	5.22088i	−0.723266	+	0.224256i
$543$		−	38.8461i		−	1.66704i
$544$	4.23425	+	0.286217i	0.181542	+	0.0122715i
$545$		−	7.75490i		−	0.332183i
$546$	−5.57918	+	1.72988i	−0.238767	+	0.0740321i
$547$	−39.5985			−1.69311			−0.846555	−	0.532301i	$-0.821327\pi$
$547$	−39.5985			−1.69311			−0.846555	+	0.532301i	$0.821327\pi$
$548$	13.9398	−	9.56382i	0.595481	−	0.408546i
$549$		−	3.98662i		−	0.170145i
$550$	8.85824	−	7.66644i	0.377717	−	0.326898i
$551$			10.2963i			0.438637i
$552$	10.5829	−	13.3906i	0.450439	−	0.569940i
$553$	−6.72244			−0.285867
$554$	8.80174	+	28.3872i	0.373950	+	1.20606i
$555$		−	6.98832i		−	0.296638i
$556$	17.2956	−	11.8662i	0.733499	−	0.503238i
$557$		−	1.26393i		−	0.0535543i	−0.999641	−	0.0267771i	$-0.991476\pi$
$557$		−	1.26393i		−	0.0535543i	0.999641	−	0.0267771i	$-0.00852445\pi$
$558$	0.962949	+	3.10568i	0.0407649	+	0.131474i
$559$		−	4.78604i		−	0.202428i
$560$	2.27723	−	5.90353i	0.0962306	−	0.249470i
$561$	3.58899	−	1.57159i	0.151527	−	0.0663527i
$562$	−7.42401	−	23.9438i	−0.313163	−	1.01001i
$563$	38.8614			1.63781			0.818906	−	0.573928i	$-0.194581\pi$
$563$	38.8614			1.63781			0.818906	+	0.573928i	$0.194581\pi$
$564$	−12.2868	+	8.42968i	−0.517366	+	0.354954i
$565$	29.5780			1.24435
$566$	−44.4578	+	13.7846i	−1.86870	+	0.579409i
$567$	−7.16738			−0.301002
$568$	−25.3816	−	20.0597i	−1.06499	−	0.841688i
$569$		−	21.3750i		−	0.896085i	−0.894012	−	0.448042i	$-0.852121\pi$
$569$		−	21.3750i		−	0.896085i	0.894012	−	0.448042i	$-0.147879\pi$
$570$	−1.19071	−	3.84026i	−0.0498735	−	0.160851i
$571$	26.0093			1.08846			0.544228	−	0.838937i	$-0.316823\pi$
$571$	26.0093			1.08846			0.544228	+	0.838937i	$0.316823\pi$
$572$	−14.7719	−	9.19419i	−0.617644	−	0.384429i
$573$	18.6873			0.780672
$574$	−0.104997	−	0.338635i	−0.00438250	−	0.0141343i
$575$		−	9.57161i		−	0.399164i
$576$	−0.962227	−	4.05170i	−0.0400928	−	0.168821i
$577$	11.9433			0.497206			0.248603	−	0.968605i	$-0.420029\pi$
$577$	11.9433			0.497206			0.248603	+	0.968605i	$0.420029\pi$
$578$	−22.2029	+	6.88423i	−0.923518	+	0.286346i
$579$	−13.0514			−0.542399
$580$	16.1461	+	23.5339i	0.670430	+	0.977191i
$581$	1.20081			0.0498179
$582$	8.14183	+	26.2588i	0.337490	+	1.08846i
$583$	−27.6901	+	12.1253i	−1.14681	+	0.502178i
$584$	−0.594417	−	0.469783i	−0.0245971	−	0.0194398i
$585$		−	2.15996i		−	0.0893032i
$586$	12.3470	+	39.8212i	0.510049	+	1.64500i
$587$			16.6576i			0.687533i	0.939055	+	0.343767i	$0.111703\pi$
$587$			16.6576i			0.687533i	−0.939055	+	0.343767i	$0.888297\pi$
$588$	1.78164	+	2.59684i	0.0734734	+	0.107092i
$589$		−	5.04127i		−	0.207722i
$590$	9.62583	+	31.0450i	0.396289	+	1.27810i
$591$	29.9200			1.23074
$592$	−4.03883	+	10.4703i	−0.165995	+	0.430328i
$593$			25.5783i			1.05037i	0.850987	+	0.525187i	$0.176005\pi$
$593$			25.5783i			1.05037i	−0.850987	+	0.525187i	$0.823995\pi$
$594$	−17.0157	−	19.6608i	−0.698161	−	0.806694i
$595$		−	1.18676i		−	0.0486526i
$596$	19.8918	+	28.9935i	0.814800	+	1.18762i
$597$	−25.2130			−1.03190
$598$	−13.5783	+	4.21008i	−0.555256	+	0.172163i
$599$			9.69854i			0.396272i	0.980175	+	0.198136i	$0.0634887\pi$
$599$			9.69854i			0.396272i	−0.980175	+	0.198136i	$0.936511\pi$
$600$	8.72732	+	6.89743i	0.356291	+	0.281586i
$601$		−	23.1097i		−	0.942664i	−0.881956	−	0.471332i	$-0.843773\pi$
$601$		−	23.1097i		−	0.942664i	0.881956	−	0.471332i	$-0.156227\pi$
$602$	−2.46461	+	0.764178i	−0.100450	+	0.0311456i
$603$		−	4.16651i		−	0.169673i
$604$	1.84624	−	1.26666i	0.0751224	−	0.0515398i
$605$	11.8012	−	12.7873i	0.479787	−	0.519877i
$606$	−39.4147	+	12.2209i	−1.60111	+	0.496442i
$607$	3.90145			0.158355			0.0791775	−	0.996861i	$-0.474771\pi$
$607$	3.90145			0.158355			0.0791775	+	0.996861i	$0.474771\pi$
$608$	−0.435444	+	6.44188i	−0.0176596	+	0.261253i
$609$	−14.2047			−0.575602
$610$	5.07393	+	16.3643i	0.205438	+	0.662573i
$611$	12.4109			0.502090
$612$	−0.441869	−	0.644051i	−0.0178615	−	0.0260342i
$613$			26.4674i			1.06901i	0.845165	+	0.534505i	$0.179502\pi$
$613$			26.4674i			1.06901i	−0.845165	+	0.534505i	$0.820498\pi$
$614$	−30.5210	+	9.46336i	−1.23173	+	0.381910i
$615$	−0.624453			−0.0251804
$616$	−2.37602	+	9.07494i	−0.0957328	+	0.365640i
$617$	3.74920			0.150937			0.0754685	−	0.997148i	$-0.475955\pi$
$617$	3.74920			0.150937			0.0754685	+	0.997148i	$0.475955\pi$
$618$	7.32040	−	2.26976i	0.294469	−	0.0913033i
$619$			1.06345i			0.0427436i	0.999772	+	0.0213718i	$0.00680338\pi$
$619$			1.06345i			0.0427436i	−0.999772	+	0.0213718i	$0.993197\pi$
$620$	−7.90545	−	11.5227i	−0.317491	−	0.462762i
$621$	−21.2442			−0.852499
$622$	3.39966	+	10.9645i	0.136314	+	0.439636i
$623$	10.6509			0.426717
$624$	5.94596	−	15.4144i	0.238029	−	0.617070i
$625$	−6.27338			−0.250935
$626$	30.1613	−	9.35181i	1.20549	−	0.373773i
$627$	2.39098	+	5.46021i	0.0954867	+	0.218060i
$628$	13.8334	−	9.49080i	0.552013	−	0.378724i
$629$			2.10481i			0.0839243i
$630$	−1.11229	+	0.344876i	−0.0443146	+	0.0137402i
$631$			45.3102i			1.80377i	0.431975	+	0.901885i	$0.357817\pi$
$631$			45.3102i			1.80377i	−0.431975	+	0.901885i	$0.642183\pi$
$632$	11.7897	−	14.9175i	0.468970	−	0.593387i
$633$			1.54337i			0.0613435i
$634$	5.73855	−	1.77930i	0.227907	−	0.0706649i
$635$	0.395312			0.0156875
$636$	−16.2383	−	23.6682i	−0.643889	−	0.938507i
$637$		−	2.62307i		−	0.103930i
$638$	−27.6894	−	31.9939i	−1.09623	−	1.26665i
$639$			5.95403i			0.235538i
$640$	9.10653	+	15.4068i	0.359967	+	0.609009i
$641$	−11.3560			−0.448535			−0.224268	−	0.974528i	$-0.571999\pi$
$641$	−11.3560			−0.448535			−0.224268	+	0.974528i	$0.571999\pi$
$642$	8.97484	+	28.9455i	0.354209	+	1.14239i
$643$			24.4202i			0.963040i	0.876435	+	0.481520i	$0.159915\pi$
$643$			24.4202i			0.963040i	−0.876435	+	0.481520i	$0.840085\pi$
$644$	4.33603	+	6.32002i	0.170864	+	0.249044i
$645$			4.54482i			0.178952i
$646$	0.358630	+	1.15665i	0.0141101	+	0.0455077i
$647$		−	41.2607i		−	1.62213i	−0.584959	−	0.811063i	$-0.698890\pi$
$647$		−	41.2607i		−	1.62213i	0.584959	−	0.811063i	$-0.301110\pi$
$648$	12.5700	−	15.9049i	0.493798	−	0.624802i
$649$	−19.3289	−	44.1408i	−0.758727	−	1.73268i
$650$	−2.74393	−	8.84965i	−0.107626	−	0.347112i
$651$	6.95489			0.272584
$652$	4.89307	+	7.13194i	0.191627	+	0.279308i
$653$	−39.0128			−1.52669			−0.763345	−	0.645991i	$-0.776444\pi$
$653$	−39.0128			−1.52669			−0.763345	+	0.645991i	$0.776444\pi$
$654$	−10.4271	+	3.23303i	−0.407732	+	0.126421i
$655$	−26.8488			−1.04907
$656$	0.935595	+	0.360897i	0.0365288	+	0.0140907i
$657$			0.139439i			0.00544002i
$658$	−1.98162	−	6.39109i	−0.0772517	−	0.249151i
$659$	19.6952			0.767217			0.383609	−	0.923496i	$-0.374681\pi$
$659$	19.6952			0.767217			0.383609	+	0.923496i	$0.374681\pi$
$660$	14.0274	+	8.73080i	0.546016	+	0.339846i
$661$	2.52788			0.0983233			0.0491616	−	0.998791i	$-0.484345\pi$
$661$	2.52788			0.0983233			0.0491616	+	0.998791i	$0.484345\pi$
$662$	0.0603703	+	0.194705i	0.00234636	+	0.00756743i
$663$		−	3.09870i		−	0.120343i
$664$	−2.10596	+	2.66467i	−0.0817271	+	0.103409i
$665$	1.80551			0.0700148
$666$	1.97272	−	0.611663i	0.0764415	−	0.0237015i
$667$	−34.5704			−1.33857
$668$	−35.0632	+	24.0561i	−1.35664	+	0.930759i
$669$	12.4480			0.481268
$670$	5.30289	+	17.1028i	0.204868	+	0.660737i
$671$	−10.1886	−	23.2673i	−0.393326	−	0.898226i
$672$	−8.88716	−	0.600735i	−0.342829	−	0.0231738i
$673$		−	46.2104i		−	1.78128i	−0.454708	−	0.890640i	$-0.650256\pi$
$673$		−	46.2104i		−	1.78128i	0.454708	−	0.890640i	$-0.349744\pi$
$674$	−11.9762	−	38.6253i	−0.461305	−	1.48779i
$675$		−	13.8459i		−	0.532930i
$676$	10.0921	−	6.92399i	0.388159	−	0.266307i
$677$			21.2646i			0.817263i	0.912699	+	0.408632i	$0.133994\pi$
$677$			21.2646i			0.817263i	−0.912699	+	0.408632i	$0.866006\pi$
$678$	−12.3311	−	39.7700i	−0.473573	−	1.52736i
$679$	−12.3457			−0.473784
$680$	2.63350	+	2.08133i	0.100990	+	0.0798152i
$681$		−	14.0350i		−	0.537822i
$682$	13.5573	+	15.6649i	0.519136	+	0.599839i
$683$			5.77734i			0.221064i	0.993873	+	0.110532i	$0.0352555\pi$
$683$			5.77734i			0.221064i	−0.993873	+	0.110532i	$0.964745\pi$
$684$	0.979844	−	0.672249i	0.0374653	−	0.0257041i
$685$	13.3710			0.510879
$686$	−1.35077	+	0.418821i	−0.0515728	+	0.0159907i
$687$		−	31.5793i		−	1.20482i
$688$	2.62664	−	6.80933i	0.100140	−	0.259603i
$689$			23.9073i			0.910797i
$690$	12.8939	−	3.99789i	0.490863	−	0.152197i
$691$		−	45.1630i		−	1.71808i	−0.511907	−	0.859041i	$-0.671061\pi$
$691$		−	45.1630i		−	1.71808i	0.511907	−	0.859041i	$-0.328939\pi$
$692$	−2.72762	−	3.97566i	−0.103688	−	0.151132i
$693$	1.58149	−	0.692521i	0.0600757	−	0.0263067i
$694$	31.0723	−	9.63429i	1.17949	−	0.365713i
$695$	16.5899			0.629289
$696$	24.9119	−	31.5210i	0.944283	−	1.19480i
$697$	0.188079			0.00712400
$698$	−9.95914	−	32.1200i	−0.376959	−	1.21576i
$699$	−11.7825			−0.445656
$700$	−4.11909	+	2.82602i	−0.155687	+	0.106813i
$701$			4.89016i			0.184699i	0.995727	+	0.0923494i	$0.0294377\pi$
$701$			4.89016i			0.184699i	−0.995727	+	0.0923494i	$0.970562\pi$
$702$	−19.6418	+	6.09014i	−0.741331	+	0.229857i
$703$	−3.20221			−0.120774
$704$	−15.9708	−	21.1880i	−0.601923	−	0.798554i
$705$	−11.7854			−0.443863
$706$	1.74408	−	0.540769i	0.0656392	−	0.0203521i
$707$		−	18.5310i		−	0.696929i
$708$	37.7296	−	25.8854i	1.41796	−	0.972834i
$709$	15.6950			0.589436			0.294718	−	0.955584i	$-0.404774\pi$
$709$	15.6950			0.589436			0.294718	+	0.955584i	$0.404774\pi$
$710$	−7.57793	−	24.4402i	−0.284395	−	0.917224i
$711$	−3.49936			−0.131236
$712$	−18.6793	+	23.6349i	−0.700036	+	0.885756i
$713$	16.9264			0.633898
$714$	−1.59570	+	0.494763i	−0.0597176	+	0.0185160i
$715$	−5.52020	−	12.6063i	−0.206444	−	0.471448i
$716$	14.1644	+	20.6455i	0.529349	+	0.771558i
$717$		−	22.3971i		−	0.836435i
$718$	−34.0550	+	10.5591i	−1.27092	+	0.394062i
$719$			11.7761i			0.439176i	0.975593	+	0.219588i	$0.0704713\pi$
$719$			11.7761i			0.439176i	−0.975593	+	0.219588i	$0.929529\pi$
$720$	1.18541	−	3.07308i	0.0441777	−	0.114527i
$721$			3.44171i			0.128176i
$722$	23.9050	−	7.41199i	0.889652	−	0.275846i
$723$	21.6381			0.804731
$724$	−40.6852	+	27.9133i	−1.51206	+	1.03739i
$725$		−	22.5313i		−	0.836792i
$726$	−22.1135	−	10.5367i	−0.820708	−	0.391052i
$727$		−	10.6509i		−	0.395019i	−0.980301	−	0.197509i	$-0.936715\pi$
$727$		−	10.6509i		−	0.395019i	0.980301	−	0.197509i	$-0.0632853\pi$
$728$	5.82076	+	4.60030i	0.215732	+	0.170499i
$729$	−29.9181			−1.10808
$730$	−0.177469	−	0.572370i	−0.00656843	−	0.0211844i
$731$		−	1.36885i		−	0.0506289i
$732$	19.8879	−	13.6446i	0.735077	−	0.504320i
$733$		−	27.9850i		−	1.03365i	−0.856091	−	0.516824i	$-0.827114\pi$
$733$		−	27.9850i		−	1.03365i	0.856091	−	0.516824i	$-0.172886\pi$
$734$	−0.461871	−	1.48962i	−0.0170480	−	0.0549828i
$735$			2.49087i			0.0918771i
$736$	−21.6290	−	1.46203i	−0.797255	−	0.0538911i
$737$	−10.6483	−	24.3173i	−0.392237	−	0.895738i
$738$	−0.0546562	−	0.176276i	−0.00201192	−	0.00648881i
$739$	25.9409			0.954252			0.477126	−	0.878835i	$-0.341679\pi$
$739$	25.9409			0.954252			0.477126	+	0.878835i	$0.341679\pi$
$740$	−7.31918	+	5.02153i	−0.269058	+	0.184595i
$741$	4.71428			0.173183
$742$	12.3113	−	3.81724i	0.451961	−	0.140135i
$743$	12.3792			0.454147			0.227074	−	0.973878i	$-0.427084\pi$
$743$	12.3792			0.454147			0.227074	+	0.973878i	$0.427084\pi$
$744$	−12.1974	+	15.4333i	−0.447178	+	0.565814i
$745$			27.8103i			1.01889i
$746$	−8.03934	−	25.9283i	−0.294341	−	0.949304i
$747$	0.625080			0.0228705
$748$	−4.22491	−	2.62963i	−0.154478	−	0.0961487i
$749$	−13.6088			−0.497255
$750$	7.82177	+	25.2266i	0.285611	+	0.921146i
$751$			11.2531i			0.410632i	0.978696	+	0.205316i	$0.0658223\pi$
$751$			11.2531i			0.410632i	−0.978696	+	0.205316i	$0.934178\pi$
$752$	17.6576	+	6.81124i	0.643905	+	0.248380i
$753$	37.2589			1.35779
$754$	−31.9629	+	9.91042i	−1.16402	+	0.360916i
$755$	1.77090			0.0644495
$756$	6.27234	+	9.14230i	0.228123	+	0.332502i
$757$	−23.9144			−0.869184			−0.434592	−	0.900627i	$-0.643107\pi$
$757$	−23.9144			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$758$	3.18750	+	10.2803i	0.115775	+	0.373396i
$759$	−18.3330	+	8.02787i	−0.665445	+	0.291393i
$760$	−3.16648	+	4.00655i	−0.114860	+	0.145333i
$761$			43.0293i			1.55981i	0.625897	+	0.779905i	$0.284733\pi$
$761$			43.0293i			1.55981i	−0.625897	+	0.779905i	$0.715267\pi$
$762$	−0.164806	−	0.531529i	−0.00597029	−	0.0192553i
$763$		−	4.90234i		−	0.177477i
$764$	−13.4279	−	19.5720i	−0.485806	−	0.708091i
$765$		−	0.617769i		−	0.0223355i
$766$	−9.25114	−	29.8366i	−0.334257	−	1.07804i
$767$	−38.1107			−1.37610
$768$	16.9192	−	18.6676i	0.610520	−	0.673609i
$769$			43.5881i			1.57183i	0.618337	+	0.785913i	$0.287807\pi$
$769$			43.5881i			1.57183i	−0.618337	+	0.785913i	$0.712193\pi$
$770$	−5.61031	+	4.85550i	−0.202182	+	0.174980i
$771$			21.5312i			0.775429i
$772$	9.37824	+	13.6693i	0.337530	+	0.491970i
$773$	−34.7584			−1.25017			−0.625087	−	0.780555i	$-0.714937\pi$
$773$	−34.7584			−1.25017			−0.625087	+	0.780555i	$0.714937\pi$
$774$	−1.28295	+	0.397792i	−0.0461148	+	0.0142984i
$775$			11.0318i			0.396274i
$776$	21.6517	−	27.3959i	0.777250	−	0.983454i
$777$		−	4.41773i		−	0.158485i
$778$	36.7291	−	11.3882i	1.31680	−	0.408288i
$779$			0.286139i			0.0102520i
$780$	10.7753	−	7.39269i	0.385817	−	0.264701i
$781$	15.2167	+	34.7498i	0.544496	+	1.24345i
$782$	−3.88351	+	1.20412i	−0.138874	+	0.0430594i
$783$	−50.0082			−1.78715
$784$	1.43957	−	3.73197i	0.0514134	−	0.133285i
$785$	13.2689			0.473587
$786$	11.1933	+	36.1004i	0.399252	+	1.28766i
$787$	2.81410			0.100312			0.0501560	−	0.998741i	$-0.484028\pi$
$787$	2.81410			0.100312			0.0501560	+	0.998741i	$0.484028\pi$
$788$	−21.4993	−	31.3365i	−0.765881	−	1.11632i
$789$		−	2.43609i		−	0.0867273i
$790$	14.3642	−	4.45378i	0.511057	−	0.158458i
$791$	18.6980			0.664824
$792$	−1.23684	+	4.72395i	−0.0439491	+	0.167858i
$793$	−20.0888			−0.713373
$794$	−18.4733	+	5.72784i	−0.655593	+	0.203273i
$795$		−	22.7024i		−	0.805171i
$796$	18.1171	+	26.4067i	0.642142	+	0.935961i
$797$	43.2960			1.53362			0.766811	−	0.641872i	$-0.221842\pi$
$797$	43.2960			1.53362			0.766811	+	0.641872i	$0.221842\pi$
$798$	−0.752721	−	2.42766i	−0.0266460	−	0.0859382i
$799$	3.54963			0.125577
$800$	0.952881	−	14.0967i	0.0336894	−	0.498395i
$801$	5.54429			0.195898
$802$	−5.10467	+	1.58275i	−0.180252	+	0.0558890i
$803$	0.356363	+	0.813814i	0.0125758	+	0.0287189i
$804$	20.7853	−	14.2603i	0.733040	−	0.502923i
$805$			6.06212i			0.213662i
$806$	15.6497	−	4.85234i	0.551236	−	0.170917i
$807$		−	17.5000i		−	0.616029i
$808$	41.1214	+	32.4993i	1.44665	+	1.14332i
$809$		−	3.65797i		−	0.128607i	−0.997930	−	0.0643037i	$-0.979517\pi$
$809$		−	3.65797i		−	0.128607i	0.997930	−	0.0643037i	$-0.0204826\pi$
$810$	15.3150	−	4.74856i	0.538113	−	0.166847i
$811$	43.8841			1.54098			0.770489	−	0.637453i	$-0.220012\pi$
$811$	43.8841			1.54098			0.770489	+	0.637453i	$0.220012\pi$
$812$	10.2069	+	14.8772i	0.358192	+	0.522087i
$813$			19.6288i			0.688411i
$814$	9.95030	−	8.61157i	0.348758	−	0.301835i
$815$			6.84090i			0.239626i
$816$	1.70060	−	4.40867i	0.0595330	−	0.154334i
$817$	2.08254			0.0728589
$818$	−12.0767	−	38.9495i	−0.422252	−	1.36184i
$819$		−	1.36544i		−	0.0477123i
$820$	0.448707	+	0.654018i	0.0156695	+	0.0228393i
$821$		−	4.70257i		−	0.164121i	−0.996627	−	0.0820604i	$-0.973850\pi$
$821$		−	4.70257i		−	0.164121i	0.996627	−	0.0820604i	$-0.0261500\pi$
$822$	−5.57438	−	17.9784i	−0.194429	−	0.627068i
$823$			27.6445i			0.963627i	0.876274	+	0.481814i	$0.160022\pi$
$823$			27.6445i			0.963627i	−0.876274	+	0.481814i	$0.839978\pi$
$824$	−7.63737	−	6.03602i	−0.266060	−	0.210275i
$825$	−5.23218	−	11.9485i	−0.182161	−	0.415995i
$826$	6.08506	+	19.6254i	0.211726	+	0.682856i
$827$	38.9620			1.35484			0.677422	−	0.735595i	$-0.263097\pi$
$827$	38.9620			1.35484			0.677422	+	0.735595i	$0.263097\pi$
$828$	2.25712	+	3.28988i	0.0784403	+	0.114331i
$829$	45.2248			1.57072			0.785361	−	0.619038i	$-0.212478\pi$
$829$	45.2248			1.57072			0.785361	+	0.619038i	$0.212478\pi$
$830$	−2.56584	+	0.795565i	−0.0890616	+	0.0276145i
$831$	33.0916			1.14793
$832$	−20.4167	+	4.84871i	−0.707823	+	0.168099i
$833$		−	0.750224i		−	0.0259937i
$834$	−6.91633	−	22.3064i	−0.239493	−	0.772408i
$835$	−33.6324			−1.16390
$836$	4.00065	−	6.42767i	0.138365	−	0.222306i
$837$	24.4850			0.846327
$838$	−8.68940	−	28.0249i	−0.300170	−	0.968104i
$839$			49.5274i			1.70987i	0.518732	+	0.854937i	$0.326404\pi$
$839$			49.5274i			1.70987i	−0.518732	+	0.854937i	$0.673596\pi$
$840$	−5.52739	−	4.36845i	−0.190713	−	0.150726i
$841$	−52.3778			−1.80613
$842$	−30.0376	+	9.31345i	−1.03516	+	0.320963i
$843$	−27.9118			−0.961333
$844$	1.61644	−	1.10901i	0.0556402	−	0.0381735i
$845$	9.68029			0.333012
$846$	−1.03153	−	3.32688i	−0.0354648	−	0.114380i
$847$	7.46025	−	8.08361i	0.256337	−	0.277756i
$848$	−13.1206	+	34.0141i	−0.450565	+	1.16805i
$849$			51.8254i			1.77864i
$850$	−0.784790	−	2.53109i	−0.0269181	−	0.0868156i
$851$		−	10.7516i		−	0.368560i
$852$	−29.7026	+	20.3783i	−1.01759	+	0.698149i
$853$			6.05040i			0.207162i	0.994621	+	0.103581i	$0.0330301\pi$
$853$			6.05040i			0.207162i	−0.994621	+	0.103581i	$0.966970\pi$
$854$	3.20754	+	10.3449i	0.109760	+	0.353995i
$855$	0.939858			0.0321425
$856$	23.8669	−	30.1988i	0.815755	−	1.03217i
$857$		−	54.7756i		−	1.87110i	−0.353198	−	0.935549i	$-0.614906\pi$
$857$		−	54.7756i		−	1.87110i	0.353198	−	0.935549i	$-0.385094\pi$
$858$	−14.6488	+	12.6779i	−0.500102	+	0.432818i
$859$		−	13.9017i		−	0.474318i	−0.971471	−	0.237159i	$-0.923784\pi$
$859$		−	13.9017i		−	0.474318i	0.971471	−	0.237159i	$-0.0762163\pi$
$860$	4.76000	−	3.26573i	0.162315	−	0.111360i
$861$	−0.394754			−0.0134532
$862$	16.7085	−	5.18065i	0.569095	−	0.176454i
$863$			55.7602i			1.89810i	0.315128	+	0.949049i	$0.397953\pi$
$863$			55.7602i			1.89810i	−0.315128	+	0.949049i	$0.602047\pi$
$864$	−31.2877	−	2.11492i	−1.06443	−	0.0719509i
$865$		−	3.81342i		−	0.129660i
$866$	−19.3471	+	5.99876i	−0.657441	+	0.203846i
$867$			25.8824i			0.879013i
$868$	−4.99751	−	7.28417i	−0.169627	−	0.247241i
$869$	−20.4235	+	8.94331i	−0.692821	+	0.303381i
$870$	30.3519	−	9.41093i	1.02903	−	0.319060i
$871$	−20.9953			−0.711397
$872$	10.8786	+	8.59764i	0.368396	+	0.291153i
$873$	−6.42654			−0.217505
$874$	−1.83192	−	5.90828i	−0.0619657	−	0.199851i
$875$	−11.8604			−0.400954
$876$	−0.695611	+	0.477244i	−0.0235025	+	0.0161246i
$877$		−	11.2468i		−	0.379777i	−0.981806	−	0.189888i	$-0.939187\pi$
$877$		−	11.2468i		−	0.379777i	0.981806	−	0.189888i	$-0.0608126\pi$
$878$	8.55297	−	2.65193i	0.288649	−	0.0894985i
$879$	46.4205			1.56573
$880$	−0.935373	−	20.9651i	−0.0315314	−	0.706734i
$881$	15.3650			0.517662			0.258831	−	0.965923i	$-0.416663\pi$
$881$	15.3650			0.517662			0.258831	+	0.965923i	$0.416663\pi$
$882$	−0.703144	+	0.218017i	−0.0236761	+	0.00734102i
$883$		−	20.8359i		−	0.701183i	−0.936528	−	0.350592i	$-0.885981\pi$
$883$		−	20.8359i		−	0.701183i	0.936528	−	0.350592i	$-0.114019\pi$
$884$	−3.24540	+	2.22660i	−0.109155	+	0.0748887i
$885$	36.1899			1.21651
$886$	10.7363	+	34.6264i	0.360692	+	1.16330i
$887$	14.5362			0.488079			0.244039	−	0.969765i	$-0.421527\pi$
$887$	14.5362			0.488079			0.244039	+	0.969765i	$0.421527\pi$
$888$	9.80323	+	7.74775i	0.328975	+	0.259998i
$889$	0.249900			0.00838139
$890$	−22.7583	+	7.05645i	−0.762860	+	0.236533i
$891$	−21.7753	+	9.53524i	−0.729500	+	0.319443i
$892$	−8.94465	−	13.0374i	−0.299489	−	0.436523i
$893$			5.40032i			0.180715i
$894$	37.3932	−	11.5942i	1.25062	−	0.387767i
$895$			19.8030i			0.661941i
$896$	5.75678	+	9.73958i	0.192321	+	0.325377i
$897$			15.8285i			0.528498i
$898$	−6.12586	+	1.89939i	−0.204423	+	0.0633834i
$899$	39.8443			1.32888
$900$	−2.14419	+	1.47108i	−0.0714729	+	0.0490360i
$901$			6.83773i			0.227798i
$902$	−0.769502	−	0.889126i	−0.0256216	−	0.0296047i
$903$			2.87305i			0.0956093i
$904$	−32.7923	+	41.4920i	−1.09065	+	1.38000i
$905$	−39.0250			−1.29723
$906$	−0.738289	−	2.38112i	−0.0245280	−	0.0791073i
$907$			53.5839i			1.77922i	0.456718	+	0.889611i	$0.349025\pi$
$907$			53.5839i			1.77922i	−0.456718	+	0.889611i	$0.650975\pi$
$908$	−14.6995	+	10.0850i	−0.487819	+	0.334682i
$909$		−	9.64629i		−	0.319947i
$910$	1.73785	+	5.60487i	0.0576091	+	0.185800i
$911$			31.4308i			1.04135i	0.853755	+	0.520675i	$0.174320\pi$
$911$			31.4308i			1.04135i	−0.853755	+	0.520675i	$0.825680\pi$
$912$	6.70724	+	2.58726i	0.222099	+	0.0856726i
$913$	3.64819	−	1.59752i	0.120738	−	0.0528701i
$914$	7.40383	+	23.8787i	0.244897	+	0.789837i
$915$	19.0763			0.630643
$916$	−33.0744	+	22.6916i	−1.09281	+	0.749752i
$917$	−16.9727			−0.560489
$918$	−5.61774	+	1.74184i	−0.185413	+	0.0574892i
$919$	40.2618			1.32811			0.664057	−	0.747682i	$-0.268833\pi$
$919$	40.2618			1.32811			0.664057	+	0.747682i	$0.268833\pi$
$920$	−13.4522	−	10.6316i	−0.443507	−	0.350515i
$921$			35.5791i			1.17237i
$922$	−14.2390	−	45.9232i	−0.468935	−	1.51240i
$923$	30.0026			0.987549
$924$	8.86756	+	5.51926i	0.291721	+	0.181570i
$925$	7.00738			0.230401
$926$	−0.840921	−	2.71212i	−0.0276344	−	0.0891258i
$927$			1.79158i			0.0588432i
$928$	−50.9141	−	3.44158i	−1.67134	−	0.112975i
$929$	−7.61834			−0.249950			−0.124975	−	0.992160i	$-0.539885\pi$
$929$	−7.61834			−0.249950			−0.124975	+	0.992160i	$0.539885\pi$
$930$	−14.8609	+	4.60778i	−0.487309	+	0.151095i
$931$	1.14137			0.0374070
$932$	8.46646	+	12.3404i	0.277328	+	0.404222i
$933$	12.7816			0.418450
$934$	12.0036	+	38.7139i	0.392771	+	1.26676i
$935$	−1.57883	−	3.60552i	−0.0516333	−	0.117913i
$936$	3.02999	+	2.39468i	0.0990385	+	0.0782727i
$937$			2.79736i			0.0913858i	0.998956	+	0.0456929i	$0.0145496\pi$
$937$			2.79736i			0.0913858i	−0.998956	+	0.0456929i	$0.985450\pi$
$938$	3.35227	+	10.8117i	0.109456	+	0.353014i
$939$		−	35.1597i		−	1.14739i
$940$	8.46850	+	12.3433i	0.276212	+	0.402595i
$941$			32.7923i			1.06900i	0.845169	+	0.534499i	$0.179500\pi$
$941$			32.7923i			1.06900i	−0.845169	+	0.534499i	$0.820500\pi$
$942$	−5.53182	−	17.8411i	−0.180236	−	0.581295i
$943$	−0.960728			−0.0312856
$944$	−54.2219	−	20.9156i	−1.76477	−	0.680745i
$945$			8.76923i			0.285263i
$946$	−6.47113	+	5.60050i	−0.210395	+	0.182088i
$947$		−	7.15816i		−	0.232609i	−0.993214	−	0.116305i	$-0.962895\pi$
$947$		−	7.15816i		−	0.232609i	0.993214	−	0.116305i	$-0.0371049\pi$
$948$	−11.9769	−	17.4571i	−0.388993	−	0.566981i
$949$	0.702638			0.0228086
$950$	3.85073	−	1.19396i	0.124934	−	0.0387372i
$951$		−	6.68956i		−	0.216924i
$952$	1.66480	+	1.31573i	0.0539563	+	0.0426431i
$953$			38.2832i			1.24011i	0.784557	+	0.620057i	$0.212891\pi$
$953$			38.2832i			1.24011i	−0.784557	+	0.620057i	$0.787109\pi$
$954$	6.40863	−	1.98706i	0.207487	−	0.0643335i
$955$		−	18.7733i		−	0.607491i
$956$	−23.4575	+	16.0937i	−0.758669	+	0.520506i
$957$	−43.1553	+	18.8974i	−1.39501	+	0.610866i
$958$	−26.6899	+	8.27548i	−0.862312	+	0.267369i
$959$	8.45260			0.272949
$960$	19.3877	−	4.60433i	0.625736	−	0.148604i
$961$	11.4914			0.370691
$962$	−3.08220	−	9.94065i	−0.0993741	−	0.320499i
$963$	−7.08406			−0.228281
$964$	−15.5483	−	22.6626i	−0.500778	−	0.729913i
$965$			13.1115i			0.422075i
$966$	8.15101	−	2.52730i	0.262255	−	0.0813147i
$967$	60.3137			1.93956			0.969778	−	0.243988i	$-0.0784559\pi$
$967$	60.3137			1.93956			0.969778	+	0.243988i	$0.0784559\pi$
$968$	4.85437	+	30.7317i	0.156025	+	0.987753i
$969$	1.34833			0.0433146
$970$	26.3798	−	8.17932i	0.847003	−	0.262622i
$971$			7.52865i			0.241606i	0.992676	+	0.120803i	$0.0385469\pi$
$971$			7.52865i			0.241606i	−0.992676	+	0.120803i	$0.961453\pi$
$972$	6.04735	+	8.81437i	0.193969	+	0.282721i
$973$	10.4874			0.336212
$974$	6.43955	+	20.7687i	0.206337	+	0.665473i
$975$	−10.3162			−0.330384
$976$	−28.5813	−	11.0250i	−0.914864	−	0.352900i
$977$	36.8738			1.17970			0.589849	−	0.807513i	$-0.299187\pi$
$977$	36.8738			1.17970			0.589849	+	0.807513i	$0.299187\pi$
$978$	9.19815	−	2.85198i	0.294125	−	0.0911963i
$979$	32.3585	−	14.1695i	1.03418	−	0.452861i
$980$	2.60880	−	1.78984i	0.0833350	−	0.0571743i
$981$		−	2.55191i		−	0.0814762i
$982$	14.8618	−	4.60805i	0.474258	−	0.147049i
$983$			5.97352i			0.190526i	0.995452	+	0.0952628i	$0.0303691\pi$
$983$			5.97352i			0.190526i	−0.995452	+	0.0952628i	$0.969631\pi$
$984$	0.692314	−	0.875985i	0.0220702	−	0.0279254i
$985$		−	30.0577i		−	0.957719i
$986$	−9.14169	+	2.83448i	−0.291131	+	0.0902681i
$987$	−7.45024			−0.237144
$988$	−3.38750	−	4.93748i	−0.107771	−	0.157082i
$989$			6.99226i			0.222341i
$990$	−2.92044	+	2.52752i	−0.0928178	+	0.0803300i
$991$			17.3869i			0.552312i	0.961113	+	0.276156i	$0.0890606\pi$
$991$			17.3869i			0.552312i	−0.961113	+	0.276156i	$0.910939\pi$
$992$	24.9286	+	1.68507i	0.791484	+	0.0535010i
$993$	0.226972			0.00720274
$994$	−4.79046	−	15.4501i	−0.151944	−	0.490048i
$995$			25.3291i			0.802987i
$996$	2.13940	+	3.11831i	0.0677896	+	0.0988074i
$997$		−	39.6637i		−	1.25616i	−0.778148	−	0.628081i	$-0.783841\pi$
$997$		−	39.6637i		−	1.25616i	0.778148	−	0.628081i	$-0.216159\pi$
$998$	0.967713	+	3.12105i	0.0306324	+	0.0987950i
$999$		−	15.5529i		−	0.492071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.d.a.43.4	yes	18
4.3	odd	2		308.2.d.b.43.16	yes	18
11.10	odd	2		308.2.d.b.43.15	yes	18
44.43	even	2	inner	308.2.d.a.43.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.d.a.43.3	✓	18	44.43	even	2	inner
308.2.d.a.43.4	yes	18	1.1	even	1	trivial
308.2.d.b.43.15	yes	18	11.10	odd	2
308.2.d.b.43.16	yes	18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35077 + 0.418821i) q^{2} +1.57463i q^{3} +(1.64918 - 1.13146i) q^{4} +1.58188 q^{5} +(-0.659487 - 2.12696i) q^{6} +1.00000 q^{7} +(-1.75378 + 2.21906i) q^{8} +0.520549 q^{9} +(-2.13676 + 0.662524i) q^{10} +(3.03811 - 1.33037i) q^{11} +(1.78164 + 2.59684i) q^{12} -2.62307i q^{13} +(-1.35077 + 0.418821i) q^{14} +2.49087i q^{15} +(1.43957 - 3.73197i) q^{16} -0.750224i q^{17} +(-0.703144 + 0.218017i) q^{18} +1.14137 q^{19} +(2.60880 - 1.78984i) q^{20} +1.57463i q^{21} +(-3.54662 + 3.06945i) q^{22} +3.83223i q^{23} +(-3.49420 - 2.76156i) q^{24} -2.49766 q^{25} +(1.09860 + 3.54318i) q^{26} +5.54355i q^{27} +(1.64918 - 1.13146i) q^{28} +9.02097i q^{29} +(-1.04323 - 3.36460i) q^{30} -4.41685i q^{31} +(-0.381509 + 5.64397i) q^{32} +(2.09483 + 4.78389i) q^{33} +(0.314210 + 1.01338i) q^{34} +1.58188 q^{35} +(0.858478 - 0.588983i) q^{36} -2.80558 q^{37} +(-1.54174 + 0.478031i) q^{38} +4.13036 q^{39} +(-2.77427 + 3.51029i) q^{40} +0.250697i q^{41} +(-0.659487 - 2.12696i) q^{42} +1.82459 q^{43} +(3.50512 - 5.63153i) q^{44} +0.823446 q^{45} +(-1.60502 - 5.17647i) q^{46} +4.73143i q^{47} +(5.87647 + 2.26679i) q^{48} +1.00000 q^{49} +(3.37377 - 1.04607i) q^{50} +1.18132 q^{51} +(-2.96791 - 4.32591i) q^{52} -9.11425 q^{53} +(-2.32176 - 7.48808i) q^{54} +(4.80592 - 2.10448i) q^{55} +(-1.75378 + 2.21906i) q^{56} +1.79724i q^{57} +(-3.77817 - 12.1853i) q^{58} -14.5290i q^{59} +(2.81833 + 4.10788i) q^{60} -7.65849i q^{61} +(1.84987 + 5.96616i) q^{62} +0.520549 q^{63} +(-1.84848 - 7.78352i) q^{64} -4.14938i q^{65} +(-4.83324 - 5.58460i) q^{66} -8.00407i q^{67} +(-0.848852 - 1.23725i) q^{68} -6.03433 q^{69} +(-2.13676 + 0.662524i) q^{70} +11.4380i q^{71} +(-0.912931 + 1.15513i) q^{72} +0.267868i q^{73} +(3.78970 - 1.17503i) q^{74} -3.93289i q^{75} +(1.88233 - 1.29142i) q^{76} +(3.03811 - 1.33037i) q^{77} +(-5.57918 + 1.72988i) q^{78} -6.72244 q^{79} +(2.27723 - 5.90353i) q^{80} -7.16738 q^{81} +(-0.104997 - 0.338635i) q^{82} +1.20081 q^{83} +(1.78164 + 2.59684i) q^{84} -1.18676i q^{85} +(-2.46461 + 0.764178i) q^{86} -14.2047 q^{87} +(-2.37602 + 9.07494i) q^{88} +10.6509 q^{89} +(-1.11229 + 0.344876i) q^{90} -2.62307i q^{91} +(4.33603 + 6.32002i) q^{92} +6.95489 q^{93} +(-1.98162 - 6.39109i) q^{94} +1.80551 q^{95} +(-8.88716 - 0.600735i) q^{96} -12.3457 q^{97} +(-1.35077 + 0.418821i) q^{98} +(1.58149 - 0.692521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} + q^{4} + 18 q^{7} - 7 q^{8} - 22 q^{9} + 6 q^{10} + 4 q^{11} - 8 q^{12} - q^{14} - 3 q^{16} + 5 q^{18} + 8 q^{19} - 10 q^{20} - 7 q^{22} + 28 q^{24} + 18 q^{25} - 26 q^{26} + q^{28} + 32 q^{30}+ \cdots - 4 q^{99}+O(q^{100}) \) 18 * q - q^2 + q^4 + 18 * q^7 - 7 * q^8 - 22 * q^9 + 6 * q^10 + 4 * q^11 - 8 * q^12 - q^14 - 3 * q^16 + 5 * q^18 + 8 * q^19 - 10 * q^20 - 7 * q^22 + 28 * q^24 + 18 * q^25 - 26 * q^26 + q^28 + 32 * q^30 - 11 * q^32 - 12 * q^33 + 10 * q^34 + 11 * q^36 - 8 * q^37 - 4 * q^38 - 18 * q^40 - 40 * q^43 + 15 * q^44 - 12 * q^45 - 38 * q^46 + 16 * q^48 + 18 * q^49 - 43 * q^50 - 8 * q^51 - 30 * q^52 + 4 * q^53 + 16 * q^54 - 20 * q^55 - 7 * q^56 + 36 * q^60 + 36 * q^62 - 22 * q^63 + q^64 - 48 * q^66 + 26 * q^68 - 12 * q^69 + 6 * q^70 + 67 * q^72 + 30 * q^74 - 24 * q^76 + 4 * q^77 + 52 * q^78 - 16 * q^79 - 42 * q^80 + 50 * q^81 + 2 * q^82 - 24 * q^83 - 8 * q^84 - 8 * q^86 + 72 * q^87 + 39 * q^88 + 8 * q^89 - 50 * q^90 + 18 * q^92 - 4 * q^93 - 48 * q^94 + 8 * q^95 - 80 * q^96 + 8 * q^97 - q^98 - 4 * q^99

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