LMFDB - Embedded newform 372.2.g.b.247.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(247,372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("372.247"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} - x^{13} - 2 x^{12} + 5 x^{11} + 4 x^{10} - 10 x^{9} - 20 x^{7} + 16 x^{6} + 40 x^{5} + \cdots + 256 $ x^16 - x^14 - x^13 - 2x^12 + 5x^11 + 4x^10 - 10x^9 - 20x^7 + 16x^6 + 40x^5 - 32x^4 - 32x^3 - 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			247.10
Root			$0.0932801 - 1.41113i$ of defining polynomial
Character	$\chi$	$=$	372.247
Dual form			372.2.g.b.247.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0932801 + 1.41113i) q^{2} +1.00000 q^{3} +(-1.98260 + 0.263261i) q^{4} +1.86118 q^{5} +(0.0932801 + 1.41113i) q^{6} -4.60176i q^{7} +(-0.556434 - 2.77315i) q^{8} +1.00000 q^{9} +(0.173611 + 2.62637i) q^{10} +5.40568 q^{11} +(-1.98260 + 0.263261i) q^{12} +4.47873i q^{13} +(6.49370 - 0.429252i) q^{14} +1.86118 q^{15} +(3.86139 - 1.04388i) q^{16} +2.05610i q^{17} +(0.0932801 + 1.41113i) q^{18} -1.12836i q^{19} +(-3.68997 + 0.489976i) q^{20} -4.60176i q^{21} +(0.504242 + 7.62813i) q^{22} -7.23450 q^{23} +(-0.556434 - 2.77315i) q^{24} -1.53601 q^{25} +(-6.32009 + 0.417776i) q^{26} +1.00000 q^{27} +(1.21147 + 9.12344i) q^{28} -5.24803i q^{29} +(0.173611 + 2.62637i) q^{30} +(-4.40344 + 3.40730i) q^{31} +(1.83325 + 5.35156i) q^{32} +5.40568 q^{33} +(-2.90143 + 0.191793i) q^{34} -8.56470i q^{35} +(-1.98260 + 0.263261i) q^{36} +4.62374i q^{37} +(1.59226 - 0.105253i) q^{38} +4.47873i q^{39} +(-1.03562 - 5.16133i) q^{40} +2.86966 q^{41} +(6.49370 - 0.429252i) q^{42} +8.80990 q^{43} +(-10.7173 + 1.42311i) q^{44} +1.86118 q^{45} +(-0.674834 - 10.2088i) q^{46} -0.901508i q^{47} +(3.86139 - 1.04388i) q^{48} -14.1762 q^{49} +(-0.143279 - 2.16752i) q^{50} +2.05610i q^{51} +(-1.17908 - 8.87952i) q^{52} +4.90231i q^{53} +(0.0932801 + 1.41113i) q^{54} +10.0609 q^{55} +(-12.7614 + 2.56057i) q^{56} -1.12836i q^{57} +(7.40568 - 0.489537i) q^{58} -12.4876i q^{59} +(-3.68997 + 0.489976i) q^{60} +2.48968i q^{61} +(-5.21891 - 5.89602i) q^{62} -4.60176i q^{63} +(-7.38076 + 3.08615i) q^{64} +8.33572i q^{65} +(0.504242 + 7.62813i) q^{66} +9.66081i q^{67} +(-0.541292 - 4.07642i) q^{68} -7.23450 q^{69} +(12.0859 - 0.798915i) q^{70} +2.76862i q^{71} +(-0.556434 - 2.77315i) q^{72} +4.95775i q^{73} +(-6.52472 + 0.431303i) q^{74} -1.53601 q^{75} +(0.297053 + 2.23708i) q^{76} -24.8756i q^{77} +(-6.32009 + 0.417776i) q^{78} -7.05216 q^{79} +(7.18673 - 1.94285i) q^{80} +1.00000 q^{81} +(0.267682 + 4.04948i) q^{82} -13.9898 q^{83} +(1.21147 + 9.12344i) q^{84} +3.82677i q^{85} +(0.821788 + 12.4320i) q^{86} -5.24803i q^{87} +(-3.00790 - 14.9908i) q^{88} -11.9810i q^{89} +(0.173611 + 2.62637i) q^{90} +20.6100 q^{91} +(14.3431 - 1.90456i) q^{92} +(-4.40344 + 3.40730i) q^{93} +(1.27215 - 0.0840927i) q^{94} -2.10008i q^{95} +(1.83325 + 5.35156i) q^{96} -0.960609 q^{97} +(-1.32236 - 20.0045i) q^{98} +5.40568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 2 q^{4} + 3 q^{8} + 16 q^{9} - 5 q^{10} + 4 q^{11} + 2 q^{12} + 5 q^{14} + 10 q^{16} - q^{20} - 16 q^{23} + 3 q^{24} + 12 q^{25} - 10 q^{26} + 16 q^{27} + 3 q^{28} - 5 q^{30} - 6 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) $ 16 * q + 16 * q^3 + 2 * q^4 + 3 * q^8 + 16 * q^9 - 5 * q^10 + 4 * q^11 + 2 * q^12 + 5 * q^14 + 10 * q^16 - q^20 - 16 * q^23 + 3 * q^24 + 12 * q^25 - 10 * q^26 + 16 * q^27 + 3 * q^28 - 5 * q^30 - 6 * q^31 - 20 * q^32 + 4 * q^33 + 28 * q^34 + 2 * q^36 + q^38 - 26 * q^40 + 5 * q^42 - 20 * q^43 - 14 * q^44 - 4 * q^46 + 10 * q^48 - 8 * q^49 - 11 * q^50 - 4 * q^52 + 8 * q^55 - 40 * q^56 + 36 * q^58 - q^60 - 26 * q^62 - 7 * q^64 - 6 * q^68 - 16 * q^69 + 9 * q^70 + 3 * q^72 - 52 * q^74 + 12 * q^75 - 3 * q^76 - 10 * q^78 - 12 * q^79 - 13 * q^80 + 16 * q^81 - 11 * q^82 - 28 * q^83 + 3 * q^84 + 8 * q^86 - 16 * q^88 - 5 * q^90 + 16 * q^91 - 6 * q^93 + 26 * q^94 - 20 * q^96 - 40 * q^97 - 15 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.0932801	+	1.41113i	0.0659590	+	0.997822i
$2$	0.0932801	+	1.41113i	0.0659590	+	0.997822i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.98260	+	0.263261i	−0.991299	+	0.131631i
$5$	1.86118			0.832344			0.416172	−	0.909286i	$-0.363371\pi$
$5$	1.86118			0.832344			0.416172	+	0.909286i	$0.363371\pi$
$6$	0.0932801	+	1.41113i	0.0380814	+	0.576093i
$7$		−	4.60176i		−	1.73930i	−0.493667	−	0.869651i	$-0.664344\pi$
$7$		−	4.60176i		−	1.73930i	0.493667	−	0.869651i	$-0.335656\pi$
$8$	−0.556434	−	2.77315i	−0.196729	−	0.980458i
$9$	1.00000			0.333333
$10$	0.173611	+	2.62637i	0.0549006	+	0.830532i
$11$	5.40568			1.62987			0.814936	−	0.579551i	$-0.196772\pi$
$11$	5.40568			1.62987			0.814936	+	0.579551i	$0.196772\pi$
$12$	−1.98260	+	0.263261i	−0.572327	+	0.0759970i
$13$			4.47873i			1.24218i	0.783741	+	0.621088i	$0.213309\pi$
$13$			4.47873i			1.24218i	−0.783741	+	0.621088i	$0.786691\pi$
$14$	6.49370	−	0.429252i	1.73551	−	0.114723i
$15$	1.86118			0.480554
$16$	3.86139	−	1.04388i	0.965347	−	0.260971i
$17$			2.05610i			0.498678i	0.968416	+	0.249339i	$0.0802133\pi$
$17$			2.05610i			0.498678i	−0.968416	+	0.249339i	$0.919787\pi$
$18$	0.0932801	+	1.41113i	0.0219863	+	0.332607i
$19$		−	1.12836i		−	0.258863i	−0.991588	−	0.129432i	$-0.958685\pi$
$19$		−	1.12836i		−	0.258863i	0.991588	−	0.129432i	$-0.0413153\pi$
$20$	−3.68997	+	0.489976i	−0.825102	+	0.109562i
$21$		−	4.60176i		−	1.00419i
$22$	0.504242	+	7.62813i	0.107505	+	1.62632i
$23$	−7.23450			−1.50850			−0.754249	−	0.656589i	$-0.771999\pi$
$23$	−7.23450			−1.50850			−0.754249	+	0.656589i	$0.771999\pi$
$24$	−0.556434	−	2.77315i	−0.113582	−	0.566068i
$25$	−1.53601			−0.307203
$26$	−6.32009	+	0.417776i	−1.23947	+	0.0819326i
$27$	1.00000			0.192450
$28$	1.21147	+	9.12344i	0.228945	+	1.72417i
$29$		−	5.24803i		−	0.974535i	−0.873253	−	0.487268i	$-0.837994\pi$
$29$		−	5.24803i		−	0.974535i	0.873253	−	0.487268i	$-0.162006\pi$
$30$	0.173611	+	2.62637i	0.0316969	+	0.479508i
$31$	−4.40344	+	3.40730i	−0.790882	+	0.611969i
$31$	−4.40344	+	3.40730i	−0.790882	+	0.611969i
$32$	1.83325	+	5.35156i	0.324076	+	0.946031i
$33$	5.40568			0.941007
$34$	−2.90143	+	0.191793i	−0.497592	+	0.0328923i
$35$		−	8.56470i		−	1.44770i
$36$	−1.98260	+	0.263261i	−0.330433	+	0.0438769i
$37$			4.62374i			0.760138i	0.924958	+	0.380069i	$0.124100\pi$
$37$			4.62374i			0.760138i	−0.924958	+	0.380069i	$0.875900\pi$
$38$	1.59226	−	0.105253i	0.258299	−	0.0170743i
$39$			4.47873i			0.717171i
$40$	−1.03562	−	5.16133i	−0.163746	−	0.816079i
$41$	2.86966			0.448166			0.224083	−	0.974570i	$-0.428061\pi$
$41$	2.86966			0.448166			0.224083	+	0.974570i	$0.428061\pi$
$42$	6.49370	−	0.429252i	1.00200	−	0.0662351i
$43$	8.80990			1.34350			0.671749	−	0.740779i	$-0.265543\pi$
$43$	8.80990			1.34350			0.671749	+	0.740779i	$0.265543\pi$
$44$	−10.7173	+	1.42311i	−1.61569	+	0.214541i
$45$	1.86118			0.277448
$46$	−0.674834	−	10.2088i	−0.0994989	−	1.50521i
$47$		−	0.901508i		−	0.131498i	−0.997836	−	0.0657492i	$-0.979056\pi$
$47$		−	0.901508i		−	0.131498i	0.997836	−	0.0657492i	$-0.0209437\pi$
$48$	3.86139	−	1.04388i	0.557343	−	0.150671i
$49$	−14.1762			−2.02517
$50$	−0.143279	−	2.16752i	−0.0202628	−	0.306534i
$51$			2.05610i			0.287912i
$52$	−1.17908	−	8.87952i	−0.163508	−	1.23137i
$53$			4.90231i			0.673384i	0.941615	+	0.336692i	$0.109308\pi$
$53$			4.90231i			0.673384i	−0.941615	+	0.336692i	$0.890692\pi$
$54$	0.0932801	+	1.41113i	0.0126938	+	0.192031i
$55$	10.0609			1.35662
$56$	−12.7614	+	2.56057i	−1.70531	+	0.342171i
$57$		−	1.12836i		−	0.149455i
$58$	7.40568	−	0.489537i	0.972413	−	0.0642793i
$59$		−	12.4876i		−	1.62575i	−0.582437	−	0.812876i	$-0.697901\pi$
$59$		−	12.4876i		−	1.62575i	0.582437	−	0.812876i	$-0.302099\pi$
$60$	−3.68997	+	0.489976i	−0.476373	+	0.0632557i
$61$			2.48968i			0.318770i	0.987216	+	0.159385i	$0.0509512\pi$
$61$			2.48968i			0.318770i	−0.987216	+	0.159385i	$0.949049\pi$
$62$	−5.21891	−	5.89602i	−0.662802	−	0.748795i
$63$		−	4.60176i		−	0.579767i
$64$	−7.38076	+	3.08615i	−0.922595	+	0.385769i
$65$			8.33572i			1.03392i
$66$	0.504242	+	7.62813i	0.0620679	+	0.938958i
$67$			9.66081i			1.18026i	0.807310	+	0.590128i	$0.200923\pi$
$67$			9.66081i			1.18026i	−0.807310	+	0.590128i	$0.799077\pi$
$68$	−0.541292	−	4.07642i	−0.0656413	−	0.494339i
$69$	−7.23450			−0.870931
$70$	12.0859	−	0.798915i	1.44455	−	0.0954887i
$71$			2.76862i			0.328575i	0.986412	+	0.164288i	$0.0525325\pi$
$71$			2.76862i			0.328575i	−0.986412	+	0.164288i	$0.947467\pi$
$72$	−0.556434	−	2.77315i	−0.0655763	−	0.326819i
$73$			4.95775i			0.580261i	0.956987	+	0.290130i	$0.0936987\pi$
$73$			4.95775i			0.580261i	−0.956987	+	0.290130i	$0.906301\pi$
$74$	−6.52472	+	0.431303i	−0.758483	+	0.0501379i
$75$	−1.53601			−0.177364
$76$	0.297053	+	2.23708i	0.0340743	+	0.256611i
$77$		−	24.8756i		−	2.83484i
$78$	−6.32009	+	0.417776i	−0.715609	+	0.0473038i
$79$	−7.05216			−0.793430			−0.396715	−	0.917942i	$-0.629850\pi$
$79$	−7.05216			−0.793430			−0.396715	+	0.917942i	$0.629850\pi$
$80$	7.18673	−	1.94285i	0.803501	−	0.217217i
$81$	1.00000			0.111111
$82$	0.267682	+	4.04948i	0.0295606	+	0.447190i
$83$	−13.9898			−1.53558			−0.767792	−	0.640699i	$-0.778645\pi$
$83$	−13.9898			−1.53558			−0.767792	+	0.640699i	$0.778645\pi$
$84$	1.21147	+	9.12344i	0.132182	+	0.995449i
$85$			3.82677i			0.415072i
$86$	0.821788	+	12.4320i	0.0886157	+	1.34057i
$87$		−	5.24803i		−	0.562648i
$88$	−3.00790	−	14.9908i	−0.320643	−	1.59802i
$89$		−	11.9810i		−	1.26999i	−0.772518	−	0.634993i	$-0.781003\pi$
$89$		−	11.9810i		−	1.26999i	0.772518	−	0.634993i	$-0.218997\pi$
$90$	0.173611	+	2.62637i	0.0183002	+	0.276844i
$91$	20.6100			2.16052
$92$	14.3431	−	1.90456i	1.49537	−	0.198564i
$93$	−4.40344	+	3.40730i	−0.456616	+	0.353320i
$94$	1.27215	−	0.0840927i	0.131212	−	0.00867350i
$95$		−	2.10008i		−	0.215463i
$96$	1.83325	+	5.35156i	0.187105	+	0.546191i
$97$	−0.960609			−0.0975351			−0.0487676	−	0.998810i	$-0.515529\pi$
$97$	−0.960609			−0.0975351			−0.0487676	+	0.998810i	$0.515529\pi$
$98$	−1.32236	−	20.0045i	−0.133578	−	2.02076i
$99$	5.40568			0.543291
$100$	3.04530	−	0.404373i	0.304530	−	0.0404373i
$101$	4.68761			0.466434			0.233217	−	0.972425i	$-0.425075\pi$
$101$	4.68761			0.466434			0.233217	+	0.972425i	$0.425075\pi$
$102$	−2.90143	+	0.191793i	−0.287285	+	0.0189904i
$103$		−	13.0594i		−	1.28678i	−0.765538	−	0.643390i	$-0.777527\pi$
$103$		−	13.0594i		−	1.28678i	0.765538	−	0.643390i	$-0.222473\pi$
$104$	12.4202	−	2.49212i	1.21790	−	0.244372i
$105$		−	8.56470i		−	0.835829i
$106$	−6.91782	+	0.457288i	−0.671918	+	0.0444157i
$107$			7.89615i			0.763350i	0.924297	+	0.381675i	$0.124653\pi$
$107$			7.89615i			0.763350i	−0.924297	+	0.381675i	$0.875347\pi$
$108$	−1.98260	+	0.263261i	−0.190776	+	0.0253323i
$109$	−12.4255			−1.19015			−0.595073	−	0.803672i	$-0.702877\pi$
$109$	−12.4255			−1.19015			−0.595073	+	0.803672i	$0.702877\pi$
$110$	0.938484	+	14.1973i	0.0894809	+	1.35366i
$111$			4.62374i			0.438866i
$112$	−4.80370	−	17.7692i	−0.453907	−	1.67903i
$113$	5.43385			0.511173			0.255587	−	0.966786i	$-0.417731\pi$
$113$	5.43385			0.511173			0.255587	+	0.966786i	$0.417731\pi$
$114$	1.59226	−	0.105253i	0.149129	−	0.00985788i
$115$	−13.4647			−1.25559
$116$	1.38160	+	10.4047i	0.128279	+	0.966055i
$117$			4.47873i			0.414059i
$118$	17.6217	−	1.16485i	1.62221	−	0.107233i
$119$	9.46168			0.867351
$120$	−1.03562	−	5.16133i	−0.0945390	−	0.471163i
$121$	18.2213			1.65648
$122$	−3.51327	+	0.232237i	−0.318076	+	0.0210258i
$123$	2.86966			0.258749
$124$	7.83325	−	7.91456i	0.703446	−	0.710748i
$125$	−12.1647			−1.08804
$126$	6.49370	−	0.429252i	0.578505	−	0.0382408i
$127$	−4.79137			−0.425165			−0.212583	−	0.977143i	$-0.568187\pi$
$127$	−4.79137			−0.425165			−0.212583	+	0.977143i	$0.568187\pi$
$128$	−5.04345	−	10.1274i	−0.445782	−	0.895141i
$129$	8.80990			0.775669
$130$	−11.7628	+	0.777556i	−1.03167	+	0.0681962i
$131$			8.53497i			0.745704i	0.927891	+	0.372852i	$0.121620\pi$
$131$			8.53497i			0.745704i	−0.927891	+	0.372852i	$0.878380\pi$
$132$	−10.7173	+	1.42311i	−0.932819	+	0.123865i
$133$	−5.19243			−0.450241
$134$	−13.6327	+	0.901161i	−1.17769	+	0.0778484i
$135$	1.86118			0.160185
$136$	5.70188	−	1.14408i	0.488933	−	0.0981044i
$137$		−	1.06842i		−	0.0912810i	−0.998958	−	0.0456405i	$-0.985467\pi$
$137$		−	1.06842i		−	0.0912810i	0.998958	−	0.0456405i	$-0.0145329\pi$
$138$	−0.674834	−	10.2088i	−0.0574457	−	0.869035i
$139$	−17.8201			−1.51148			−0.755741	−	0.654870i	$-0.772723\pi$
$139$	−17.8201			−1.51148			−0.755741	+	0.654870i	$0.772723\pi$
$140$	2.25475	+	16.9803i	0.190561	+	1.43510i
$141$		−	0.901508i		−	0.0759206i
$142$	−3.90690	+	0.258257i	−0.327860	+	0.0216725i
$143$			24.2106i			2.02459i
$144$	3.86139	−	1.04388i	0.321782	−	0.0869902i
$145$		−	9.76753i		−	0.811149i
$146$	−6.99605	+	0.462459i	−0.578997	+	0.0382734i
$147$	−14.1762			−1.16923
$148$	−1.21725	−	9.16701i	−0.100057	−	0.753524i
$149$	−3.47676			−0.284827			−0.142414	−	0.989807i	$-0.545486\pi$
$149$	−3.47676			−0.284827			−0.142414	+	0.989807i	$0.545486\pi$
$150$	−0.143279	−	2.16752i	−0.0116987	−	0.176977i
$151$	−19.5226			−1.58873			−0.794364	−	0.607442i	$-0.792196\pi$
$151$	−19.5226			−1.58873			−0.794364	+	0.607442i	$0.792196\pi$
$152$	−3.12911	+	0.627857i	−0.253804	+	0.0509259i
$153$			2.05610i			0.166226i
$154$	35.1028	−	2.32040i	2.82867	−	0.186983i
$155$	−8.19560	+	6.34159i	−0.658286	+	0.509369i
$156$	−1.17908	−	8.87952i	−0.0944016	−	0.710931i
$157$	−5.67916			−0.453247			−0.226623	−	0.973982i	$-0.572769\pi$
$157$	−5.67916			−0.453247			−0.226623	+	0.973982i	$0.572769\pi$
$158$	−0.657826	−	9.95155i	−0.0523338	−	0.791703i
$159$			4.90231i			0.388779i
$160$	3.41200	+	9.96021i	0.269743	+	0.787424i
$161$			33.2914i			2.62373i
$162$	0.0932801	+	1.41113i	0.00732877	+	0.110869i
$163$			14.2698i			1.11769i	0.829271	+	0.558847i	$0.188756\pi$
$163$			14.2698i			1.11769i	−0.829271	+	0.558847i	$0.811244\pi$
$164$	−5.68939	+	0.755471i	−0.444266	+	0.0589924i
$165$	10.0609			0.783242
$166$	−1.30497	−	19.7415i	−0.101286	−	1.53224i
$167$	6.22429			0.481650			0.240825	−	0.970569i	$-0.422582\pi$
$167$	6.22429			0.481650			0.240825	+	0.970569i	$0.422582\pi$
$168$	−12.7614	+	2.56057i	−0.984562	+	0.197553i
$169$	−7.05902			−0.543002
$170$	−5.40009	+	0.356961i	−0.414168	+	0.0273777i
$171$		−	1.12836i		−	0.0862877i
$172$	−17.4665	+	2.31931i	−1.33181	+	0.176845i
$173$	22.8753			1.73918			0.869588	−	0.493778i	$-0.164384\pi$
$173$	22.8753			1.73918			0.869588	+	0.493778i	$0.164384\pi$
$174$	7.40568	−	0.489537i	0.561423	−	0.0371117i
$175$			7.06836i			0.534318i
$176$	20.8734	−	5.64289i	1.57339	−	0.425349i
$177$		−	12.4876i		−	0.938628i
$178$	16.9068	−	1.11759i	1.26722	−	0.0837670i
$179$	18.2930			1.36729			0.683643	−	0.729817i	$-0.260395\pi$
$179$	18.2930			1.36729			0.683643	+	0.729817i	$0.260395\pi$
$180$	−3.68997	+	0.489976i	−0.275034	+	0.0365207i
$181$			7.07871i			0.526157i	0.964774	+	0.263078i	$0.0847378\pi$
$181$			7.07871i			0.526157i	−0.964774	+	0.263078i	$0.915262\pi$
$182$	1.92251	+	29.0835i	0.142506	+	2.15581i
$183$			2.48968i			0.184042i
$184$	4.02552	+	20.0624i	0.296765	+	1.47902i
$185$			8.60561i			0.632697i
$186$	−5.21891	−	5.89602i	−0.382669	−	0.432317i
$187$			11.1146i			0.812781i
$188$	0.237332	+	1.78733i	0.0173092	+	0.130354i
$189$		−	4.60176i		−	0.334729i
$190$	2.96349	−	0.195895i	0.214994	−	0.0142117i
$191$		−	11.7285i		−	0.848647i	−0.905511	−	0.424324i	$-0.860512\pi$
$191$		−	11.7285i		−	0.848647i	0.905511	−	0.424324i	$-0.139488\pi$
$192$	−7.38076	+	3.08615i	−0.532661	+	0.222724i
$193$	14.7229			1.05978			0.529889	−	0.848067i	$-0.322234\pi$
$193$	14.7229			1.05978			0.529889	+	0.848067i	$0.322234\pi$
$194$	−0.0896057	−	1.35555i	−0.00643331	−	0.0973227i
$195$			8.33572i			0.596933i
$196$	28.1057	−	3.73204i	2.00755	−	0.266574i
$197$		−	11.7289i		−	0.835650i	−0.908527	−	0.417825i	$-0.862792\pi$
$197$		−	11.7289i		−	0.835650i	0.908527	−	0.417825i	$-0.137208\pi$
$198$	0.504242	+	7.62813i	0.0358349	+	0.542108i
$199$	4.40807			0.312480			0.156240	−	0.987719i	$-0.450063\pi$
$199$	4.40807			0.312480			0.156240	+	0.987719i	$0.450063\pi$
$200$	0.854690	+	4.25960i	0.0604357	+	0.301199i
$201$			9.66081i			0.681421i
$202$	0.437260	+	6.61484i	0.0307655	+	0.465419i
$203$	−24.1502			−1.69501
$204$	−0.541292	−	4.07642i	−0.0378980	−	0.285407i
$205$	5.34095			0.373028
$206$	18.4286	−	1.21818i	1.28398	−	0.0848747i
$207$	−7.23450			−0.502832
$208$	4.67527	+	17.2941i	0.324171	+	1.19913i
$209$		−	6.09954i		−	0.421914i
$210$	12.0859	−	0.798915i	0.834009	−	0.0551304i
$211$		−	18.4644i		−	1.27114i	−0.772042	−	0.635572i	$-0.780764\pi$
$211$		−	18.4644i		−	1.27114i	0.772042	−	0.635572i	$-0.219236\pi$
$212$	−1.29059	−	9.71931i	−0.0886380	−	0.667525i
$213$			2.76862i			0.189703i
$214$	−11.1425	+	0.736553i	−0.761687	+	0.0503497i
$215$	16.3968			1.11825
$216$	−0.556434	−	2.77315i	−0.0378605	−	0.188689i
$217$	15.6796	+	20.2636i	1.06440	+	1.37558i
$218$	−1.15905	−	17.5340i	−0.0785008	−	1.18755i
$219$			4.95775i			0.335014i
$220$	−19.9468	+	2.64865i	−1.34481	+	0.178572i
$221$	−9.20872			−0.619446
$222$	−6.52472	+	0.431303i	−0.437910	+	0.0289471i
$223$	−11.1980			−0.749873			−0.374936	−	0.927051i	$-0.622335\pi$
$223$	−11.1980			−0.749873			−0.374936	+	0.927051i	$0.622335\pi$
$224$	24.6266	−	8.43617i	1.64543	−	0.563665i
$225$	−1.53601			−0.102401
$226$	0.506870	+	7.66789i	0.0337165	+	0.510060i
$227$			18.4616i			1.22534i	0.790339	+	0.612670i	$0.209905\pi$
$227$			18.4616i			1.22534i	−0.790339	+	0.612670i	$0.790095\pi$
$228$	0.297053	+	2.23708i	0.0196728	+	0.148154i
$229$		−	26.0983i		−	1.72462i	−0.506377	−	0.862312i	$-0.669016\pi$
$229$		−	26.0983i		−	1.72462i	0.506377	−	0.862312i	$-0.330984\pi$
$230$	−1.25599	−	19.0005i	−0.0828174	−	1.25286i
$231$		−	24.8756i		−	1.63670i
$232$	−14.5536	+	2.92018i	−0.955491	+	0.191719i
$233$	11.4479			0.749978			0.374989	−	0.927029i	$-0.377646\pi$
$233$	11.4479			0.749978			0.374989	+	0.927029i	$0.377646\pi$
$234$	−6.32009	+	0.417776i	−0.413157	+	0.0273109i
$235$		−	1.67787i		−	0.109452i
$236$	3.28751	+	24.7580i	0.213999	+	1.61161i
$237$	−7.05216			−0.458087
$238$	0.882586	+	13.3517i	0.0572096	+	0.865462i
$239$	14.5901			0.943752			0.471876	−	0.881665i	$-0.343577\pi$
$239$	14.5901			0.943752			0.471876	+	0.881665i	$0.343577\pi$
$240$	7.18673	−	1.94285i	0.463902	−	0.125411i
$241$			26.8444i			1.72920i	0.502458	+	0.864602i	$0.332429\pi$
$241$			26.8444i			1.72920i	−0.502458	+	0.864602i	$0.667571\pi$
$242$	1.69969	+	25.7127i	0.109260	+	1.65288i
$243$	1.00000			0.0641500
$244$	−0.655435	−	4.93603i	−0.0419600	−	0.315997i
$245$	−26.3844			−1.68564
$246$	0.267682	+	4.04948i	0.0170668	+	0.258185i
$247$	5.05361			0.321554
$248$	11.8992	+	10.3155i	0.755599	+	0.655034i
$249$	−13.9898			−0.886570
$250$	−1.13472	−	17.1660i	−0.0717662	−	1.08567i
$251$	−4.57814			−0.288969			−0.144485	−	0.989507i	$-0.546152\pi$
$251$	−4.57814			−0.288969			−0.144485	+	0.989507i	$0.546152\pi$
$252$	1.21147	+	9.12344i	0.0763151	+	0.574723i
$253$	−39.1074			−2.45866
$254$	−0.446939	−	6.76126i	−0.0280435	−	0.424239i
$255$			3.82677i			0.239642i
$256$	13.8206	−	8.06167i	0.863789	−	0.503854i
$257$	0.426532			0.0266063			0.0133032	−	0.999912i	$-0.495765\pi$
$257$	0.426532			0.0266063			0.0133032	+	0.999912i	$0.495765\pi$
$258$	0.821788	+	12.4320i	0.0511623	+	0.773980i
$259$	21.2773			1.32211
$260$	−2.19447	−	16.5264i	−0.136095	−	1.02492i
$261$		−	5.24803i		−	0.324845i
$262$	−12.0440	+	0.796143i	−0.744080	+	0.0491859i
$263$	1.00675			0.0620791			0.0310396	−	0.999518i	$-0.490118\pi$
$263$	1.00675			0.0620791			0.0310396	+	0.999518i	$0.490118\pi$
$264$	−3.00790	−	14.9908i	−0.185123	−	0.922618i
$265$			9.12408i			0.560488i
$266$	−0.484350	−	7.32722i	−0.0296974	−	0.449261i
$267$		−	11.9810i		−	0.733227i
$268$	−2.54332	−	19.1535i	−0.155358	−	1.16999i
$269$		−	8.04715i		−	0.490643i	−0.969442	−	0.245322i	$-0.921106\pi$
$269$		−	8.04715i		−	0.490643i	0.969442	−	0.245322i	$-0.0788936\pi$
$270$	0.173611	+	2.62637i	0.0105656	+	0.159836i
$271$	−1.75472			−0.106592			−0.0532959	−	0.998579i	$-0.516973\pi$
$271$	−1.75472			−0.106592			−0.0532959	+	0.998579i	$0.516973\pi$
$272$	2.14633	+	7.93940i	0.130140	+	0.481397i
$273$	20.6100			1.24738
$274$	1.50768	−	0.0996620i	0.0910822	−	0.00602080i
$275$	−8.30319			−0.500701
$276$	14.3431	−	1.90456i	0.863353	−	0.114641i
$277$			12.8572i			0.772517i	0.922391	+	0.386258i	$0.126233\pi$
$277$			12.8572i			0.772517i	−0.922391	+	0.386258i	$0.873767\pi$
$278$	−1.66226	−	25.1466i	−0.0996958	−	1.50819i
$279$	−4.40344	+	3.40730i	−0.263627	+	0.203990i
$280$	−23.7512	+	4.76569i	−1.41941	+	0.284804i
$281$	−12.6095			−0.752223			−0.376111	−	0.926574i	$-0.622739\pi$
$281$	−12.6095			−0.752223			−0.376111	+	0.926574i	$0.622739\pi$
$282$	1.27215	−	0.0840927i	0.0757553	−	0.00500765i
$283$		−	1.00958i		−	0.0600135i	−0.999550	−	0.0300068i	$-0.990447\pi$
$283$		−	1.00958i		−	0.0600135i	0.999550	−	0.0300068i	$-0.00955289\pi$
$284$	−0.728872	−	5.48907i	−0.0432506	−	0.325716i
$285$		−	2.10008i		−	0.124398i
$286$	−34.1643	+	2.25836i	−2.02018	+	0.133540i
$287$		−	13.2055i		−	0.779496i
$288$	1.83325	+	5.35156i	0.108025	+	0.315344i
$289$	12.7724			0.751320
$290$	13.7833	−	0.911115i	0.809382	−	0.0535025i
$291$	−0.960609			−0.0563119
$292$	−1.30518	−	9.82922i	−0.0763801	−	0.575212i
$293$	23.2804			1.36005			0.680026	−	0.733188i	$-0.261968\pi$
$293$	23.2804			1.36005			0.680026	+	0.733188i	$0.261968\pi$
$294$	−1.32236	−	20.0045i	−0.0771213	−	1.16669i
$295$		−	23.2417i		−	1.35319i
$296$	12.8223	−	2.57280i	0.745283	−	0.149541i
$297$	5.40568			0.313669
$298$	−0.324312	−	4.90617i	−0.0187869	−	0.284207i
$299$		−	32.4014i		−	1.87382i
$300$	3.04530	−	0.404373i	0.175820	−	0.0233465i
$301$		−	40.5411i		−	2.33675i
$302$	−1.82107	−	27.5490i	−0.104791	−	1.58527i
$303$	4.68761			0.269296
$304$	−1.17787	−	4.35703i	−0.0675557	−	0.249893i
$305$			4.63373i			0.265327i
$306$	−2.90143	+	0.191793i	−0.165864	+	0.0109641i
$307$			20.8616i			1.19063i	0.803491	+	0.595316i	$0.202973\pi$
$307$			20.8616i			1.19063i	−0.803491	+	0.595316i	$0.797027\pi$
$308$	6.54879	+	49.3183i	0.373152	+	2.81017i
$309$		−	13.0594i		−	0.742923i
$310$	−9.71332	−	10.9735i	−0.551679	−	0.623255i
$311$			7.18365i			0.407348i	0.979039	+	0.203674i	$0.0652882\pi$
$311$			7.18365i			0.407348i	−0.979039	+	0.203674i	$0.934712\pi$
$312$	12.4202	−	2.49212i	0.703156	−	0.141088i
$313$			7.17232i			0.405404i	0.979241	+	0.202702i	$0.0649722\pi$
$313$			7.17232i			0.405404i	−0.979241	+	0.202702i	$0.935028\pi$
$314$	−0.529753	−	8.01406i	−0.0298957	−	0.452260i
$315$		−	8.56470i		−	0.482566i
$316$	13.9816	−	1.85656i	0.786527	−	0.104440i
$317$	9.65687			0.542384			0.271192	−	0.962525i	$-0.412582\pi$
$317$	9.65687			0.542384			0.271192	+	0.962525i	$0.412582\pi$
$318$	−6.91782	+	0.457288i	−0.387932	+	0.0256434i
$319$		−	28.3692i		−	1.58837i
$320$	−13.7369	+	5.74388i	−0.767917	+	0.321093i
$321$			7.89615i			0.440720i
$322$	−46.9787	+	3.10543i	−2.61802	+	0.173059i
$323$	2.32002			0.129089
$324$	−1.98260	+	0.263261i	−0.110144	+	0.0146256i
$325$		−	6.87939i		−	0.381600i
$326$	−20.1365	+	1.33108i	−1.11526	+	0.0737219i
$327$	−12.4255			−0.687131
$328$	−1.59678	−	7.95801i	−0.0881673	−	0.439408i
$329$	−4.14852			−0.228715
$330$	0.938484	+	14.1973i	0.0516618	+	0.781537i
$331$	23.0630			1.26765			0.633827	−	0.773475i	$-0.281483\pi$
$331$	23.0630			1.26765			0.633827	+	0.773475i	$0.281483\pi$
$332$	27.7362	−	3.68298i	1.52222	−	0.202130i
$333$			4.62374i			0.253379i
$334$	0.580602	+	8.78330i	0.0317691	+	0.480601i
$335$			17.9805i			0.982379i
$336$	−4.80370	−	17.7692i	−0.262063	−	0.969388i
$337$		−	7.27230i		−	0.396147i	−0.980187	−	0.198074i	$-0.936531\pi$
$337$		−	7.27230i		−	0.396147i	0.980187	−	0.198074i	$-0.0634686\pi$
$338$	−0.658466	−	9.96123i	−0.0358158	−	0.541819i
$339$	5.43385			0.295126
$340$	−1.00744	−	7.58695i	−0.0546362	−	0.411460i
$341$	−23.8036	+	18.4187i	−1.28904	+	0.997431i
$342$	1.59226	−	0.105253i	0.0860998	−	0.00569145i
$343$			33.0231i			1.78308i
$344$	−4.90213	−	24.4312i	−0.264305	−	1.31724i
$345$	−13.4647			−0.724915
$346$	2.13381	+	32.2801i	0.114714	+	1.73539i
$347$	0.0950891			0.00510465			0.00255233	−	0.999997i	$-0.499188\pi$
$347$	0.0950891			0.00510465			0.00255233	+	0.999997i	$0.499188\pi$
$348$	1.38160	+	10.4047i	0.0740617	+	0.557752i
$349$	−17.0287			−0.911527			−0.455763	−	0.890101i	$-0.650634\pi$
$349$	−17.0287			−0.911527			−0.455763	+	0.890101i	$0.650634\pi$
$350$	−9.97441	+	0.659337i	−0.533155	+	0.0352431i
$351$			4.47873i			0.239057i
$352$	9.90995	+	28.9288i	0.528202	+	1.54191i
$353$		−	13.9266i		−	0.741236i	−0.928785	−	0.370618i	$-0.879146\pi$
$353$		−	13.9266i		−	0.741236i	0.928785	−	0.370618i	$-0.120854\pi$
$354$	17.6217	−	1.16485i	0.936584	−	0.0619110i
$355$			5.15290i			0.273488i
$356$	3.15414	+	23.7536i	0.167169	+	1.25894i
$357$	9.46168			0.500765
$358$	1.70638	+	25.8139i	0.0901847	+	1.36431i
$359$			9.26179i			0.488818i	0.969672	+	0.244409i	$0.0785940\pi$
$359$			9.26179i			0.488818i	−0.969672	+	0.244409i	$0.921406\pi$
$360$	−1.03562	−	5.16133i	−0.0545821	−	0.272026i
$361$	17.7268			0.932990
$362$	−9.98901	+	0.660303i	−0.525011	+	0.0347047i
$363$	18.2213			0.956372
$364$	−40.8614	+	5.42582i	−2.14172	+	0.284390i
$365$			9.22726i			0.482977i
$366$	−3.51327	+	0.232237i	−0.183641	+	0.0121392i
$367$	7.70696			0.402300			0.201150	−	0.979560i	$-0.435532\pi$
$367$	7.70696			0.402300			0.201150	+	0.979560i	$0.435532\pi$
$368$	−27.9352	+	7.55197i	−1.45622	+	0.393673i
$369$	2.86966			0.149389
$370$	−12.1437	+	0.802731i	−0.631319	+	0.0417320i
$371$	22.5593			1.17122
$372$	7.83325	−	7.91456i	0.406135	−	0.410351i
$373$	34.8945			1.80677			0.903384	−	0.428833i	$-0.141075\pi$
$373$	34.8945			1.80677			0.903384	+	0.428833i	$0.141075\pi$
$374$	−15.6842	+	1.03677i	−0.811011	+	0.0536102i
$375$	−12.1647			−0.628182
$376$	−2.50002	+	0.501629i	−0.128929	+	0.0258696i
$377$	23.5045			1.21054
$378$	6.49370	−	0.429252i	0.334000	−	0.0220784i
$379$		−	24.4472i		−	1.25577i	−0.778307	−	0.627883i	$-0.783921\pi$
$379$		−	24.4472i		−	1.25577i	0.778307	−	0.627883i	$-0.216079\pi$
$380$	0.552869	+	4.16361i	0.0283616	+	0.213589i
$381$	−4.79137			−0.245469
$382$	16.5505	−	1.09404i	0.846799	−	0.0559759i
$383$	15.2574			0.779614			0.389807	−	0.920897i	$-0.372542\pi$
$383$	15.2574			0.779614			0.389807	+	0.920897i	$0.372542\pi$
$384$	−5.04345	−	10.1274i	−0.257373	−	0.516810i
$385$		−	46.2980i		−	2.35956i
$386$	1.37335	+	20.7760i	0.0699019	+	1.05747i
$387$	8.80990			0.447833
$388$	1.90450	−	0.252891i	0.0966864	−	0.0128386i
$389$		−	5.57353i		−	0.282589i	−0.989968	−	0.141295i	$-0.954874\pi$
$389$		−	5.57353i		−	0.282589i	0.989968	−	0.141295i	$-0.0451265\pi$
$390$	−11.7628	+	0.777556i	−0.595633	+	0.0393731i
$391$		−	14.8749i		−	0.752254i
$392$	7.88811	+	39.3127i	0.398410	+	1.98559i
$393$			8.53497i			0.430532i
$394$	16.5511	−	1.09407i	0.833831	−	0.0551186i
$395$	−13.1253			−0.660407
$396$	−10.7173	+	1.42311i	−0.538564	+	0.0715137i
$397$	−33.7581			−1.69427			−0.847134	−	0.531379i	$-0.821674\pi$
$397$	−33.7581			−1.69427			−0.847134	+	0.531379i	$0.821674\pi$
$398$	0.411185	+	6.22038i	0.0206108	+	0.311799i
$399$	−5.19243			−0.259947
$400$	−5.93114	+	1.60342i	−0.296557	+	0.0801709i
$401$		−	14.4194i		−	0.720071i	−0.932939	−	0.360035i	$-0.882765\pi$
$401$		−	14.4194i		−	0.720071i	0.932939	−	0.360035i	$-0.117235\pi$
$402$	−13.6327	+	0.901161i	−0.679937	+	0.0449458i
$403$	−15.2604	−	19.7218i	−0.760173	−	0.982415i
$404$	−9.29364	+	1.23407i	−0.462376	+	0.0613971i
$405$	1.86118			0.0924827
$406$	−2.25273	−	34.0791i	−0.111801	−	1.69132i
$407$			24.9944i			1.23893i
$408$	5.70188	−	1.14408i	0.282285	−	0.0566406i
$409$			23.0982i			1.14213i	0.820904	+	0.571066i	$0.193470\pi$
$409$			23.0982i			1.14213i	−0.820904	+	0.571066i	$0.806530\pi$
$410$	0.498205	+	7.53680i	0.0246046	+	0.372216i
$411$		−	1.06842i		−	0.0527011i
$412$	3.43803	+	25.8915i	0.169380	+	1.27558i
$413$	−57.4651			−2.82767
$414$	−0.674834	−	10.2088i	−0.0331663	−	0.501737i
$415$	−26.0376			−1.27814
$416$	−23.9682	+	8.21062i	−1.17514	+	0.402559i
$417$	−17.8201			−0.872655
$418$	8.60727	−	0.568965i	0.420995	−	0.0278290i
$419$		−	10.0417i		−	0.490567i	−0.969451	−	0.245283i	$-0.921119\pi$
$419$		−	10.0417i		−	0.490567i	0.969451	−	0.245283i	$-0.0788810\pi$
$420$	2.25475	+	16.9803i	0.110021	+	0.828556i
$421$	−0.0877370			−0.00427604			−0.00213802	−	0.999998i	$-0.500681\pi$
$421$	−0.0877370			−0.00427604			−0.00213802	+	0.999998i	$0.500681\pi$
$422$	26.0558	−	1.72236i	1.26838	−	0.0838433i
$423$		−	0.901508i		−	0.0438328i
$424$	13.5949	−	2.72781i	0.660225	−	0.132474i
$425$		−	3.15820i		−	0.153195i
$426$	−3.90690	+	0.258257i	−0.189290	+	0.0125126i
$427$	11.4569			0.554438
$428$	−2.07875	−	15.6549i	−0.100480	−	0.756708i
$429$			24.2106i			1.16890i
$430$	1.52949	+	23.1381i	0.0737588	+	1.11582i
$431$		−	35.9640i		−	1.73232i	−0.499764	−	0.866162i	$-0.666580\pi$
$431$		−	35.9640i		−	1.73232i	0.499764	−	0.866162i	$-0.333420\pi$
$432$	3.86139	−	1.04388i	0.185781	−	0.0502238i
$433$		−	31.0804i		−	1.49363i	−0.665033	−	0.746814i	$-0.731583\pi$
$433$		−	31.0804i		−	1.49363i	0.665033	−	0.746814i	$-0.268417\pi$
$434$	−27.1320	+	24.0162i	−1.30238	+	1.15281i
$435$		−	9.76753i		−	0.468317i
$436$	24.6347	−	3.27115i	1.17979	−	0.156660i
$437$			8.16311i			0.390494i
$438$	−6.99605	+	0.462459i	−0.334284	+	0.0220971i
$439$			12.5154i			0.597328i	0.954358	+	0.298664i	$0.0965410\pi$
$439$			12.5154i			0.597328i	−0.954358	+	0.298664i	$0.903459\pi$
$440$	−5.59824	−	27.9005i	−0.266886	−	1.33010i
$441$	−14.1762			−0.675057
$442$	−0.858990	−	12.9947i	−0.0408580	−	0.618097i
$443$		−	30.0971i		−	1.42996i	−0.699146	−	0.714979i	$-0.746436\pi$
$443$		−	30.0971i		−	1.42996i	0.699146	−	0.714979i	$-0.253564\pi$
$444$	−1.21725	−	9.16701i	−0.0577682	−	0.435047i
$445$		−	22.2988i		−	1.05707i
$446$	−1.04455	−	15.8019i	−0.0494608	−	0.748240i
$447$	−3.47676			−0.164445
$448$	14.2017	+	33.9645i	0.670969	+	1.60467i
$449$			21.2101i			1.00097i	0.865746	+	0.500483i	$0.166844\pi$
$449$			21.2101i			1.00097i	−0.865746	+	0.500483i	$0.833156\pi$
$450$	−0.143279	−	2.16752i	−0.00675426	−	0.102178i
$451$	15.5125			0.730453
$452$	−10.7731	+	1.43052i	−0.506726	+	0.0672861i
$453$	−19.5226			−0.917252
$454$	−26.0518	+	1.72210i	−1.22267	+	0.0808222i
$455$	38.3590			1.79830
$456$	−3.12911	+	0.627857i	−0.146534	+	0.0294021i
$457$			11.6380i			0.544401i	0.962241	+	0.272200i	$0.0877513\pi$
$457$			11.6380i			0.544401i	−0.962241	+	0.272200i	$0.912249\pi$
$458$	36.8282	−	2.43445i	1.72087	−	0.113754i
$459$			2.05610i			0.0959706i
$460$	26.6951	−	3.54473i	1.24466	−	0.165274i
$461$		−	28.4385i		−	1.32451i	−0.749277	−	0.662256i	$-0.769599\pi$
$461$		−	28.4385i		−	1.32451i	0.749277	−	0.662256i	$-0.230401\pi$
$462$	35.1028	−	2.32040i	1.63313	−	0.107955i
$463$	−24.5199			−1.13954			−0.569768	−	0.821806i	$-0.692967\pi$
$463$	−24.5199			−1.13954			−0.569768	+	0.821806i	$0.692967\pi$
$464$	−5.47833	−	20.2647i	−0.254325	−	0.940764i
$465$	−8.19560	+	6.34159i	−0.380062	+	0.294084i
$466$	1.06786	+	16.1545i	0.0494678	+	0.748345i
$467$		−	18.0299i		−	0.834326i	−0.908832	−	0.417163i	$-0.863024\pi$
$467$		−	18.0299i		−	0.834326i	0.908832	−	0.417163i	$-0.136976\pi$
$468$	−1.17908	−	8.87952i	−0.0545028	−	0.410456i
$469$	44.4567			2.05282
$470$	2.36770	−	0.156512i	0.109214	−	0.00721934i
$471$	−5.67916			−0.261682
$472$	−34.6301	+	6.94854i	−1.59398	+	0.319833i
$473$	47.6235			2.18973
$474$	−0.657826	−	9.95155i	−0.0302150	−	0.457090i
$475$			1.73317i			0.0795234i
$476$	−18.7587	+	2.49089i	−0.859804	+	0.114170i
$477$			4.90231i			0.224461i
$478$	1.36096	+	20.5885i	0.0622489	+	0.941697i
$479$			4.50154i			0.205681i	0.994698	+	0.102840i	$0.0327931\pi$
$479$			4.50154i			0.205681i	−0.994698	+	0.102840i	$0.967207\pi$
$480$	3.41200	+	9.96021i	0.155736	+	0.454619i
$481$	−20.7085			−0.944225
$482$	−37.8811	+	2.50405i	−1.72544	+	0.114056i
$483$			33.2914i			1.51481i
$484$	−36.1256	+	4.79697i	−1.64207	+	0.218044i
$485$	−1.78787			−0.0811828
$486$	0.0932801	+	1.41113i	0.00423127	+	0.0640103i
$487$	40.6208			1.84071			0.920353	−	0.391089i	$-0.127902\pi$
$487$	40.6208			1.84071			0.920353	+	0.391089i	$0.127902\pi$
$488$	6.90426	−	1.38534i	0.312541	−	0.0627114i
$489$			14.2698i			0.645301i
$490$	−2.46114	−	37.2320i	−0.111183	−	1.68197i
$491$	−4.35303			−0.196449			−0.0982247	−	0.995164i	$-0.531316\pi$
$491$	−4.35303			−0.196449			−0.0982247	+	0.995164i	$0.531316\pi$
$492$	−5.68939	+	0.755471i	−0.256497	+	0.0340593i
$493$	10.7905			0.485979
$494$	0.471401	+	7.13132i	0.0212093	+	0.320853i
$495$	10.0609			0.452205
$496$	−13.4466	+	17.7536i	−0.603769	+	0.797159i
$497$	12.7405			0.571491
$498$	−1.30497	−	19.7415i	−0.0584773	−	0.884640i
$499$	−10.1696			−0.455255			−0.227627	−	0.973748i	$-0.573097\pi$
$499$	−10.1696			−0.455255			−0.227627	+	0.973748i	$0.573097\pi$
$500$	24.1177	−	3.20249i	1.07858	−	0.143220i
$501$	6.22429			0.278081
$502$	−0.427049	−	6.46037i	−0.0190601	−	0.288340i
$503$			17.3892i			0.775345i	0.921797	+	0.387672i	$0.126721\pi$
$503$			17.3892i			0.775345i	−0.921797	+	0.387672i	$0.873279\pi$
$504$	−12.7614	+	2.56057i	−0.568437	+	0.114057i
$505$	8.72448			0.388234
$506$	−3.64794	−	55.1857i	−0.162171	−	2.45330i
$507$	−7.05902			−0.313502
$508$	9.49936	−	1.26138i	0.421466	−	0.0559648i
$509$			3.57970i			0.158668i	0.996848	+	0.0793338i	$0.0252793\pi$
$509$			3.57970i			0.158668i	−0.996848	+	0.0793338i	$0.974721\pi$
$510$	−5.40009	+	0.356961i	−0.239120	+	0.0158065i
$511$	22.8144			1.00925
$512$	12.6653	+	18.7508i	0.559732	+	0.828674i
$513$		−	1.12836i		−	0.0498182i
$514$	0.0397869	+	0.601893i	0.00175492	+	0.0265484i
$515$		−	24.3059i		−	1.07104i
$516$	−17.4665	+	2.31931i	−0.768920	+	0.102102i
$517$		−	4.87326i		−	0.214326i
$518$	1.98475	+	30.0252i	0.0872049	+	1.31923i
$519$	22.8753			1.00411
$520$	23.1162	−	4.63827i	1.01371	−	0.203402i
$521$	4.58594			0.200914			0.100457	−	0.994941i	$-0.467970\pi$
$521$	4.58594			0.200914			0.100457	+	0.994941i	$0.467970\pi$
$522$	7.40568	−	0.489537i	0.324138	−	0.0214264i
$523$	−14.8265			−0.648320			−0.324160	−	0.946002i	$-0.605082\pi$
$523$	−14.8265			−0.648320			−0.324160	+	0.946002i	$0.605082\pi$
$524$	−2.24693	−	16.9214i	−0.0981575	−	0.739215i
$525$			7.06836i			0.308489i
$526$	0.0939101	+	1.42067i	0.00409468	+	0.0619440i
$527$	−7.00575	−	9.05393i	−0.305175	−	0.394395i
$528$	20.8734	−	5.64289i	0.908398	−	0.245575i
$529$	29.3380			1.27556
$530$	−12.8753	+	0.851094i	−0.559267	+	0.0369692i
$531$		−	12.4876i		−	0.541917i
$532$	10.2945	−	1.36697i	0.446323	−	0.0592655i
$533$			12.8524i			0.556701i
$534$	16.9068	−	1.11759i	0.731630	−	0.0483629i
$535$			14.6961i			0.635370i
$536$	26.7909	−	5.37560i	1.15719	−	0.232190i
$537$	18.2930			0.789403
$538$	11.3556	−	0.750639i	0.489575	−	0.0323623i
$539$	−76.6319			−3.30077
$540$	−3.68997	+	0.489976i	−0.158791	+	0.0210852i
$541$	25.4235			1.09304			0.546521	−	0.837445i	$-0.315952\pi$
$541$	25.4235			1.09304			0.546521	+	0.837445i	$0.315952\pi$
$542$	−0.163681	−	2.47615i	−0.00703069	−	0.106360i
$543$			7.07871i			0.303777i
$544$	−11.0033	+	3.76934i	−0.471765	+	0.161609i
$545$	−23.1260			−0.990611
$546$	1.92251	+	29.0835i	0.0822756	+	1.24466i
$547$		−	29.6160i		−	1.26629i	−0.774033	−	0.633145i	$-0.781764\pi$
$547$		−	29.6160i		−	1.26629i	0.774033	−	0.633145i	$-0.218236\pi$
$548$	0.281273	+	2.11824i	0.0120154	+	0.0904867i
$549$			2.48968i			0.106257i
$550$	−0.774522	−	11.7169i	−0.0330257	−	0.499611i
$551$	−5.92166			−0.252271
$552$	4.02552	+	20.0624i	0.171337	+	0.853912i
$553$			32.4524i			1.38001i
$554$	−18.1433	+	1.19932i	−0.770834	+	0.0509544i
$555$			8.60561i			0.365288i
$556$	35.3301	−	4.69135i	1.49833	−	0.198957i
$557$			38.9913i			1.65211i	0.563587	+	0.826057i	$0.309421\pi$
$557$			38.9913i			1.65211i	−0.563587	+	0.826057i	$0.690579\pi$
$558$	−5.21891	−	5.89602i	−0.220934	−	0.249598i
$559$			39.4572i			1.66886i
$560$	−8.94054	−	33.0716i	−0.377807	−	1.39753i
$561$			11.1146i			0.469259i
$562$	−1.17622	−	17.7938i	−0.0496158	−	0.750585i
$563$			21.7911i			0.918387i	0.888336	+	0.459193i	$0.151862\pi$
$563$			21.7911i			0.918387i	−0.888336	+	0.459193i	$0.848138\pi$
$564$	0.237332	+	1.78733i	0.00999348	+	0.0752600i
$565$	10.1134			0.425472
$566$	1.42466	−	0.0941741i	0.0598829	−	0.00395843i
$567$		−	4.60176i		−	0.193256i
$568$	7.67782	−	1.54056i	0.322154	−	0.0646403i
$569$			2.53422i			0.106240i	0.998588	+	0.0531201i	$0.0169166\pi$
$569$			2.53422i			0.106240i	−0.998588	+	0.0531201i	$0.983083\pi$
$570$	2.96349	−	0.195895i	0.124127	−	0.00820515i
$571$	−28.2369			−1.18168			−0.590838	−	0.806790i	$-0.701203\pi$
$571$	−28.2369			−1.18168			−0.590838	+	0.806790i	$0.701203\pi$
$572$	−6.37370	−	47.9998i	−0.266498	−	2.00697i
$573$		−	11.7285i		−	0.489967i
$574$	18.6347	−	1.23181i	0.777798	−	0.0514147i
$575$	11.1123			0.463414
$576$	−7.38076	+	3.08615i	−0.307532	+	0.128590i
$577$	10.9360			0.455273			0.227636	−	0.973746i	$-0.426900\pi$
$577$	10.9360			0.455273			0.227636	+	0.973746i	$0.426900\pi$
$578$	1.19141	+	18.0236i	0.0495563	+	0.749684i
$579$	14.7229			0.611863
$580$	2.57141	+	19.3651i	0.106772	+	0.804091i
$581$			64.3779i			2.67085i
$582$	−0.0896057	−	1.35555i	−0.00371428	−	0.0561893i
$583$			26.5003i			1.09753i
$584$	13.7486	−	2.75866i	0.568921	−	0.114154i
$585$			8.33572i			0.344639i
$586$	2.17159	+	32.8517i	0.0897077	+	1.35709i
$587$	−1.71705			−0.0708703			−0.0354351	−	0.999372i	$-0.511282\pi$
$587$	−1.71705			−0.0708703			−0.0354351	+	0.999372i	$0.511282\pi$
$588$	28.1057	−	3.73204i	1.15906	−	0.153907i
$589$	3.84465	+	4.96866i	0.158416	+	0.204730i
$590$	32.7972	−	2.16799i	1.35024	−	0.0892547i
$591$		−	11.7289i		−	0.482463i
$592$	4.82664	+	17.8540i	0.198374	+	0.733797i
$593$	−29.9109			−1.22829			−0.614146	−	0.789192i	$-0.710499\pi$
$593$	−29.9109			−1.22829			−0.614146	+	0.789192i	$0.710499\pi$
$594$	0.504242	+	7.62813i	0.0206893	+	0.312986i
$595$	17.6099			0.721935
$596$	6.89302	−	0.915296i	0.282349	−	0.0374920i
$597$	4.40807			0.180410
$598$	45.7227	−	3.02240i	1.86974	−	0.123595i
$599$			35.8599i			1.46519i	0.680663	+	0.732597i	$0.261692\pi$
$599$			35.8599i			1.46519i	−0.680663	+	0.732597i	$0.738308\pi$
$600$	0.854690	+	4.25960i	0.0348926	+	0.173897i
$601$		−	6.65498i		−	0.271462i	−0.990746	−	0.135731i	$-0.956662\pi$
$601$		−	6.65498i		−	0.271462i	0.990746	−	0.135731i	$-0.0433383\pi$
$602$	57.2089	−	3.78167i	2.33166	−	0.154129i
$603$			9.66081i			0.393418i
$604$	38.7055	−	5.13955i	1.57490	−	0.209125i
$605$	33.9132			1.37877
$606$	0.437260	+	6.61484i	0.0177625	+	0.268710i
$607$		−	39.8461i		−	1.61730i	−0.588287	−	0.808652i	$-0.700197\pi$
$607$		−	39.8461i		−	1.61730i	0.588287	−	0.808652i	$-0.299803\pi$
$608$	6.03848	−	2.06856i	0.244893	−	0.0838912i
$609$	−24.1502			−0.978615
$610$	−6.53882	+	0.432235i	−0.264749	+	0.0175007i
$611$	4.03761			0.163344
$612$	−0.541292	−	4.07642i	−0.0218804	−	0.164780i
$613$			18.4912i			0.746853i	0.927660	+	0.373427i	$0.121817\pi$
$613$			18.4912i			0.746853i	−0.927660	+	0.373427i	$0.878183\pi$
$614$	−29.4385	+	1.94597i	−1.18804	+	0.0785329i
$615$	5.34095			0.215368
$616$	−68.9839	+	13.8416i	−2.77944	+	0.557695i
$617$	−17.7824			−0.715893			−0.357946	−	0.933742i	$-0.616523\pi$
$617$	−17.7824			−0.715893			−0.357946	+	0.933742i	$0.616523\pi$
$618$	18.4286	−	1.21818i	0.741305	−	0.0490024i
$619$	7.76041			0.311917			0.155959	−	0.987764i	$-0.450153\pi$
$619$	7.76041			0.311917			0.155959	+	0.987764i	$0.450153\pi$
$620$	14.5791	−	14.7304i	0.585510	−	0.591587i
$621$	−7.23450			−0.290310
$622$	−10.1371	+	0.670092i	−0.406461	+	0.0268682i
$623$	−55.1338			−2.20889
$624$	4.67527	+	17.2941i	0.187160	+	0.692318i
$625$	−14.9606			−0.598424
$626$	−10.1211	+	0.669035i	−0.404521	+	0.0267400i
$627$		−	6.09954i		−	0.243592i
$628$	11.2595	−	1.49510i	0.449303	−	0.0596612i
$629$	−9.50688			−0.379064
$630$	12.0859	−	0.798915i	0.481515	−	0.0318296i
$631$	7.56577			0.301189			0.150594	−	0.988596i	$-0.451881\pi$
$631$	7.56577			0.301189			0.150594	+	0.988596i	$0.451881\pi$
$632$	3.92406	+	19.5567i	0.156091	+	0.777925i
$633$		−	18.4644i		−	0.733895i
$634$	0.900794	+	13.6271i	0.0357751	+	0.541203i
$635$	−8.91759			−0.353884
$636$	−1.29059	−	9.71931i	−0.0511752	−	0.385396i
$637$		−	63.4913i		−	2.51562i
$638$	40.0327	−	2.64628i	1.58491	−	0.104767i
$639$			2.76862i			0.109525i
$640$	−9.38677	−	18.8488i	−0.371045	−	0.745066i
$641$		−	39.4862i		−	1.55961i	−0.626021	−	0.779806i	$-0.715318\pi$
$641$		−	39.4862i		−	1.55961i	0.626021	−	0.779806i	$-0.284682\pi$
$642$	−11.1425	+	0.736553i	−0.439760	+	0.0290694i
$643$	22.3601			0.881797			0.440899	−	0.897557i	$-0.354660\pi$
$643$	22.3601			0.881797			0.440899	+	0.897557i	$0.354660\pi$
$644$	−8.76434	−	66.0035i	−0.345364	−	2.60090i
$645$	16.3968			0.645624
$646$	0.216411	+	3.27386i	0.00851459	+	0.128808i
$647$	−10.3235			−0.405858			−0.202929	−	0.979194i	$-0.565046\pi$
$647$	−10.3235			−0.405858			−0.202929	+	0.979194i	$0.565046\pi$
$648$	−0.556434	−	2.77315i	−0.0218588	−	0.108940i
$649$		−	67.5041i		−	2.64977i
$650$	9.70774	−	0.641710i	0.380769	−	0.0251699i
$651$	15.6796	+	20.2636i	0.614531	+	0.794193i
$652$	−3.75667	−	28.2912i	−0.147123	−	1.10797i
$653$	−30.8722			−1.20812			−0.604060	−	0.796938i	$-0.706451\pi$
$653$	−30.8722			−1.20812			−0.604060	+	0.796938i	$0.706451\pi$
$654$	−1.15905	−	17.5340i	−0.0453224	−	0.685635i
$655$			15.8851i			0.620683i
$656$	11.0809	−	2.99559i	0.432636	−	0.116958i
$657$			4.95775i			0.193420i
$658$	−0.386974	−	5.85412i	−0.0150858	−	0.228217i
$659$		−	3.86200i		−	0.150442i	−0.997167	−	0.0752212i	$-0.976034\pi$
$659$		−	3.86200i		−	0.150442i	0.997167	−	0.0752212i	$-0.0239663\pi$
$660$	−19.9468	+	2.64865i	−0.776427	+	0.103099i
$661$	3.60999			0.140412			0.0702062	−	0.997532i	$-0.477634\pi$
$661$	3.60999			0.140412			0.0702062	+	0.997532i	$0.477634\pi$
$662$	2.15131	+	32.5449i	0.0836132	+	1.26489i
$663$	−9.20872			−0.357637
$664$	7.78442	+	38.7960i	0.302094	+	1.50558i
$665$	−9.66405			−0.374756
$666$	−6.52472	+	0.431303i	−0.252828	+	0.0167126i
$667$			37.9669i			1.47008i
$668$	−12.3403	+	1.63861i	−0.477459	+	0.0633999i
$669$	−11.1980			−0.432939
$670$	−25.3729	+	1.67722i	−0.980240	+	0.0647967i
$671$			13.4584i			0.519555i
$672$	24.6266	−	8.43617i	0.949991	−	0.325432i
$673$			29.1976i			1.12549i	0.826632	+	0.562743i	$0.190254\pi$
$673$			29.1976i			1.12549i	−0.826632	+	0.562743i	$0.809746\pi$
$674$	10.2622	−	0.678361i	0.395285	−	0.0261295i
$675$	−1.53601			−0.0591212
$676$	13.9952	−	1.85837i	0.538277	−	0.0714757i
$677$		−	17.6108i		−	0.676837i	−0.940996	−	0.338418i	$-0.890108\pi$
$677$		−	17.6108i		−	0.676837i	0.940996	−	0.338418i	$-0.109892\pi$
$678$	0.506870	+	7.66789i	0.0194662	+	0.294483i
$679$			4.42049i			0.169643i
$680$	10.6122	−	2.12934i	0.406960	−	0.0816566i
$681$			18.4616i			0.707450i
$682$	−28.2117	−	31.8720i	−1.08028	−	1.22044i
$683$		−	23.8940i		−	0.914278i	−0.889395	−	0.457139i	$-0.848874\pi$
$683$		−	23.8940i		−	0.914278i	0.889395	−	0.457139i	$-0.151126\pi$
$684$	0.297053	+	2.23708i	0.0113581	+	0.0855369i
$685$		−	1.98851i		−	0.0759772i
$686$	−46.6000	+	3.08040i	−1.77920	+	0.117610i
$687$		−	26.0983i		−	0.995712i
$688$	34.0184	−	9.19650i	1.29694	−	0.350613i
$689$	−21.9561			−0.836462
$690$	−1.25599	−	19.0005i	−0.0478146	−	0.723336i
$691$			24.7826i			0.942775i	0.881926	+	0.471388i	$0.156247\pi$
$691$			24.7826i			0.942775i	−0.881926	+	0.471388i	$0.843753\pi$
$692$	−45.3525	+	6.02218i	−1.72404	+	0.228929i
$693$		−	24.8756i		−	0.944947i
$694$	0.00886992	+	0.134183i	0.000336697	+	0.00509353i
$695$	−33.1664			−1.25807
$696$	−14.5536	+	2.92018i	−0.551653	+	0.110689i
$697$			5.90032i			0.223490i
$698$	−1.58844	−	24.0298i	−0.0601233	−	0.909542i
$699$	11.4479			0.433000
$700$	−1.86083	−	14.0137i	−0.0703326	−	0.529669i
$701$	21.5476			0.813841			0.406921	−	0.913464i	$-0.366603\pi$
$701$	21.5476			0.813841			0.406921	+	0.913464i	$0.366603\pi$
$702$	−6.32009	+	0.417776i	−0.238536	+	0.0157679i
$703$	5.21723			0.196772
$704$	−39.8980	+	16.6827i	−1.50371	+	0.628754i
$705$		−	1.67787i		−	0.0631921i
$706$	19.6522	−	1.29907i	0.739622	−	0.0488911i
$707$		−	21.5712i		−	0.811270i
$708$	3.28751	+	24.7580i	0.123552	+	0.930461i
$709$		−	34.9369i		−	1.31208i	−0.754724	−	0.656042i	$-0.772229\pi$
$709$		−	34.9369i		−	1.31208i	0.754724	−	0.656042i	$-0.227771\pi$
$710$	−7.27144	+	0.480663i	−0.272892	+	0.0180390i
$711$	−7.05216			−0.264477
$712$	−33.2252	+	6.66665i	−1.24517	+	0.249843i
$713$	31.8567	−	24.6501i	1.19304	−	0.923153i
$714$	0.882586	+	13.3517i	0.0330300	+	0.499675i
$715$			45.0602i			1.68516i
$716$	−36.2677	+	4.81585i	−1.35539	+	0.179977i
$717$	14.5901			0.544876
$718$	−13.0696	+	0.863940i	−0.487754	+	0.0322419i
$719$	−8.11177			−0.302518			−0.151259	−	0.988494i	$-0.548333\pi$
$719$	−8.11177			−0.302518			−0.151259	+	0.988494i	$0.548333\pi$
$720$	7.18673	−	1.94285i	0.267834	−	0.0724058i
$721$	−60.0962			−2.23810
$722$	1.65356	+	25.0149i	0.0615390	+	0.930958i
$723$			26.8444i			0.998356i
$724$	−1.86355	−	14.0342i	−0.0692583	−	0.521578i
$725$			8.06105i			0.299380i
$726$	1.69969	+	25.7127i	0.0630813	+	0.954289i
$727$		−	0.657750i		−	0.0243946i	−0.999926	−	0.0121973i	$-0.996117\pi$
$727$		−	0.657750i		−	0.0243946i	0.999926	−	0.0121973i	$-0.00388262\pi$
$728$	−11.4681	−	57.1548i	−0.425037	−	2.11830i
$729$	1.00000			0.0370370
$730$	−13.0209	+	0.860719i	−0.481925	+	0.0318566i
$731$			18.1141i			0.669972i
$732$	−0.655435	−	4.93603i	−0.0242256	−	0.182441i
$733$	2.37071			0.0875640			0.0437820	−	0.999041i	$-0.486059\pi$
$733$	2.37071			0.0875640			0.0437820	+	0.999041i	$0.486059\pi$
$734$	0.718905	+	10.8756i	0.0265353	+	0.401424i
$735$	−26.3844			−0.973204
$736$	−13.2626	−	38.7159i	−0.488867	−	1.42709i
$737$			52.2232i			1.92367i
$738$	0.267682	+	4.04948i	0.00985352	+	0.149063i
$739$	−18.4019			−0.676925			−0.338462	−	0.940980i	$-0.609907\pi$
$739$	−18.4019			−0.676925			−0.338462	+	0.940980i	$0.609907\pi$
$740$	−2.26552	−	17.0615i	−0.0832823	−	0.627192i
$741$	5.05361			0.185649
$742$	2.10433	+	31.8341i	0.0772523	+	1.16867i
$743$	30.5011			1.11898			0.559489	−	0.828838i	$-0.310997\pi$
$743$	30.5011			1.11898			0.559489	+	0.828838i	$0.310997\pi$
$744$	11.8992	+	10.3155i	0.436245	+	0.378184i
$745$	−6.47087			−0.237074
$746$	3.25496	+	49.2408i	0.119173	+	1.80283i
$747$	−13.9898			−0.511862
$748$	−2.92605	−	22.0358i	−0.106987	−	0.805709i
$749$	36.3362			1.32770
$750$	−1.13472	−	17.1660i	−0.0414342	−	0.626814i
$751$		−	38.1864i		−	1.39344i	−0.717343	−	0.696721i	$-0.754642\pi$
$751$		−	38.1864i		−	1.39344i	0.717343	−	0.696721i	$-0.245358\pi$
$752$	−0.941068	−	3.48107i	−0.0343172	−	0.126942i
$753$	−4.57814			−0.166837
$754$	2.19250	+	33.1680i	0.0798462	+	1.20791i
$755$	−36.3351			−1.32237
$756$	1.21147	+	9.12344i	0.0440606	+	0.331816i
$757$			15.3976i			0.559637i	0.960053	+	0.279818i	$0.0902742\pi$
$757$			15.3976i			0.559637i	−0.960053	+	0.279818i	$0.909726\pi$
$758$	34.4982	−	2.28043i	1.25303	−	0.0828291i
$759$	−39.1074			−1.41951
$760$	−5.82383	+	1.16855i	−0.211253	+	0.0423879i
$761$		−	30.3357i		−	1.09967i	−0.835274	−	0.549833i	$-0.814691\pi$
$761$		−	30.3357i		−	1.09967i	0.835274	−	0.549833i	$-0.185309\pi$
$762$	−0.446939	−	6.76126i	−0.0161909	−	0.244935i
$763$			57.1791i			2.07002i
$764$	3.08767	+	23.2530i	0.111708	+	0.841263i
$765$			3.82677i			0.138357i
$766$	1.42321	+	21.5302i	0.0514225	+	0.777917i
$767$	55.9288			2.01947
$768$	13.8206	−	8.06167i	0.498709	−	0.290900i
$769$	2.52944			0.0912138			0.0456069	−	0.998959i	$-0.485478\pi$
$769$	2.52944			0.0912138			0.0456069	+	0.998959i	$0.485478\pi$
$770$	65.3326	−	4.31868i	2.35442	−	0.155634i
$771$	0.426532			0.0153612
$772$	−29.1896	+	3.87597i	−1.05056	+	0.139499i
$773$		−	21.6478i		−	0.778616i	−0.921108	−	0.389308i	$-0.872714\pi$
$773$		−	21.6478i		−	0.778616i	0.921108	−	0.389308i	$-0.127286\pi$
$774$	0.821788	+	12.4320i	0.0295386	+	0.446857i
$775$	6.76375	−	5.23366i	0.242961	−	0.187998i
$776$	0.534515	+	2.66392i	0.0191880	+	0.0956291i
$777$	21.2773			0.763320
$778$	7.86500	−	0.519899i	0.281974	−	0.0186393i
$779$		−	3.23801i		−	0.116014i
$780$	−2.19447	−	16.5264i	−0.0785747	−	0.591739i
$781$			14.9663i			0.535536i
$782$	20.9904	−	1.38753i	0.750616	−	0.0496179i
$783$		−	5.24803i		−	0.187549i
$784$	−54.7397	+	14.7983i	−1.95499	+	0.528510i
$785$	−10.5699			−0.377257
$786$	−12.0440	+	0.796143i	−0.429595	+	0.0283975i
$787$	−50.1436			−1.78742			−0.893712	−	0.448640i	$-0.851908\pi$
$787$	−50.1436			−1.78742			−0.893712	+	0.448640i	$0.851908\pi$
$788$	3.08777	+	23.2537i	0.109997	+	0.828379i
$789$	1.00675			0.0358414
$790$	−1.22433	−	18.5216i	−0.0435598	−	0.658969i
$791$		−	25.0053i		−	0.889085i
$792$	−3.00790	−	14.9908i	−0.106881	−	0.532674i
$793$	−11.1506			−0.395969
$794$	−3.14895	−	47.6371i	−0.111752	−	1.69058i
$795$			9.12408i			0.323598i
$796$	−8.73943	+	1.16047i	−0.309761	+	0.0411319i
$797$		−	43.4109i		−	1.53769i	−0.639433	−	0.768847i	$-0.720831\pi$
$797$		−	43.4109i		−	1.53769i	0.639433	−	0.768847i	$-0.279169\pi$
$798$	−0.484350	−	7.32722i	−0.0171458	−	0.259381i
$799$	1.85359			0.0655753
$800$	−2.81589	−	8.22007i	−0.0995569	−	0.290623i
$801$		−	11.9810i		−	0.423329i
$802$	20.3477	−	1.34504i	0.718503	−	0.0474951i
$803$			26.8000i			0.945751i
$804$	−2.54332	−	19.1535i	−0.0896958	−	0.675492i
$805$			61.9613i			2.18385i
$806$	26.4067	−	23.3741i	0.930135	−	0.823317i
$807$		−	8.04715i		−	0.283273i
$808$	−2.60834	−	12.9995i	−0.0917612	−	0.457319i
$809$			28.7942i			1.01235i	0.862430	+	0.506176i	$0.168941\pi$
$809$			28.7942i			1.01235i	−0.862430	+	0.506176i	$0.831059\pi$
$810$	0.173611	+	2.62637i	0.00610006	+	0.0922813i
$811$		−	28.5531i		−	1.00263i	−0.865264	−	0.501317i	$-0.832849\pi$
$811$		−	28.5531i		−	1.00263i	0.865264	−	0.501317i	$-0.167151\pi$
$812$	47.8801	−	6.35781i	1.68026	−	0.223115i
$813$	−1.75472			−0.0615409
$814$	−35.2705	+	2.33148i	−1.23623	+	0.0817184i
$815$			26.5586i			0.930306i
$816$	2.14633	+	7.93940i	0.0751365	+	0.277935i
$817$		−	9.94073i		−	0.347782i
$818$	−32.5946	+	2.15460i	−1.13964	+	0.0753338i
$819$	20.6100			0.720173
$820$	−10.5890	+	1.40607i	−0.369783	+	0.0491020i
$821$			1.58649i			0.0553689i	0.999617	+	0.0276845i	$0.00881336\pi$
$821$			1.58649i			0.0553689i	−0.999617	+	0.0276845i	$0.991187\pi$
$822$	1.50768	−	0.0996620i	0.0525863	−	0.00347611i
$823$	−38.7648			−1.35126			−0.675629	−	0.737242i	$-0.736128\pi$
$823$	−38.7648			−1.35126			−0.675629	+	0.737242i	$0.736128\pi$
$824$	−36.2157	+	7.26669i	−1.26163	+	0.253147i
$825$	−8.30319			−0.289080
$826$	−5.36035	−	81.0910i	−0.186510	−	2.82152i
$827$	42.9257			1.49267			0.746336	−	0.665569i	$-0.231811\pi$
$827$	42.9257			1.49267			0.746336	+	0.665569i	$0.231811\pi$
$828$	14.3431	−	1.90456i	0.498457	−	0.0661882i
$829$			45.1493i			1.56810i	0.620698	+	0.784050i	$0.286849\pi$
$829$			45.1493i			1.56810i	−0.620698	+	0.784050i	$0.713151\pi$
$830$	−2.42879	−	36.7425i	−0.0843045	−	1.27535i
$831$			12.8572i			0.446013i
$832$	−13.8220	−	33.0564i	−0.479193	−	1.14603i
$833$		−	29.1477i		−	1.00991i
$834$	−1.66226	−	25.1466i	−0.0575594	−	0.870754i
$835$	11.5845			0.400899
$836$	1.60577	+	12.0929i	0.0555368	+	0.418243i
$837$	−4.40344	+	3.40730i	−0.152205	+	0.117773i
$838$	14.1701	−	0.936686i	0.489499	−	0.0323573i
$839$		−	5.92237i		−	0.204463i	−0.994761	−	0.102231i	$-0.967402\pi$
$839$		−	5.92237i		−	0.204463i	0.994761	−	0.102231i	$-0.0325982\pi$
$840$	−23.7512	+	4.76569i	−0.819495	+	0.164432i
$841$	1.45816			0.0502814
$842$	−0.00818411	−	0.123809i	−0.000282043	−	0.00426673i
$843$	−12.6095			−0.434296
$844$	4.86097	+	36.6075i	0.167321	+	1.26008i
$845$	−13.1381			−0.451964
$846$	1.27215	−	0.0840927i	0.0437374	−	0.00289117i
$847$		−	83.8502i		−	2.88113i
$848$	5.11744	+	18.9297i	0.175733	+	0.650049i
$849$		−	1.00958i		−	0.0346488i
$850$	4.45664	−	0.294597i	0.152862	−	0.0101046i
$851$		−	33.4504i		−	1.14667i
$852$	−0.728872	−	5.48907i	−0.0249707	−	0.188052i
$853$	4.95354			0.169606			0.0848030	−	0.996398i	$-0.472974\pi$
$853$	4.95354			0.169606			0.0848030	+	0.996398i	$0.472974\pi$
$854$	1.06870	+	16.1672i	0.0365701	+	0.553231i
$855$		−	2.10008i		−	0.0718211i
$856$	21.8972	−	4.39368i	0.748432	−	0.150173i
$857$	3.47072			0.118558			0.0592788	−	0.998241i	$-0.481120\pi$
$857$	3.47072			0.118558			0.0592788	+	0.998241i	$0.481120\pi$
$858$	−34.1643	+	2.25836i	−1.16635	+	0.0770992i
$859$	19.3251			0.659364			0.329682	−	0.944092i	$-0.393058\pi$
$859$	19.3251			0.659364			0.329682	+	0.944092i	$0.393058\pi$
$860$	−32.5083	+	4.31664i	−1.10852	+	0.147196i
$861$		−	13.2055i		−	0.450042i
$862$	50.7500	−	3.35472i	1.72855	−	0.114262i
$863$	−14.9941			−0.510406			−0.255203	−	0.966887i	$-0.582142\pi$
$863$	−14.9941			−0.510406			−0.255203	+	0.966887i	$0.582142\pi$
$864$	1.83325	+	5.35156i	0.0623684	+	0.182064i
$865$	42.5750			1.44759
$866$	43.8586	−	2.89918i	1.49037	−	0.0985181i
$867$	12.7724			0.433775
$868$	−36.4209	−	36.0467i	−1.23621	−	1.22351i
$869$	−38.1217			−1.29319
$870$	13.7833	−	0.911115i	0.467297	−	0.0308897i
$871$	−43.2681			−1.46609
$872$	6.91396	+	34.4578i	0.234136	+	1.16689i
$873$	−0.960609			−0.0325117
$874$	−11.5192	+	0.761455i	−0.389644	+	0.0257566i
$875$			55.9790i			1.89243i
$876$	−1.30518	−	9.82922i	−0.0440981	−	0.332099i
$877$	−14.0223			−0.473500			−0.236750	−	0.971571i	$-0.576082\pi$
$877$	−14.0223			−0.473500			−0.236750	+	0.971571i	$0.576082\pi$
$878$	−17.6609	+	1.16744i	−0.596027	+	0.0393991i
$879$	23.2804			0.785227
$880$	38.8491	−	10.5024i	1.30960	−	0.354037i
$881$		−	15.4622i		−	0.520933i	−0.965483	−	0.260467i	$-0.916124\pi$
$881$		−	15.4622i		−	0.520933i	0.965483	−	0.260467i	$-0.0838764\pi$
$882$	−1.32236	−	20.0045i	−0.0445260	−	0.673587i
$883$	5.82313			0.195964			0.0979820	−	0.995188i	$-0.468761\pi$
$883$	5.82313			0.195964			0.0979820	+	0.995188i	$0.468761\pi$
$884$	18.2572	−	2.42430i	0.614056	−	0.0815380i
$885$		−	23.2417i		−	0.781262i
$886$	42.4711	−	2.80746i	1.42684	−	0.0943185i
$887$			4.05371i			0.136110i	0.997682	+	0.0680551i	$0.0216794\pi$
$887$			4.05371i			0.136110i	−0.997682	+	0.0680551i	$0.978321\pi$
$888$	12.8223	−	2.57280i	0.430290	−	0.0863377i
$889$			22.0487i			0.739491i
$890$	31.4666	−	2.08004i	1.05476	−	0.0697230i
$891$	5.40568			0.181097
$892$	22.2011	−	2.94800i	0.743348	−	0.0987063i
$893$	−1.01722			−0.0340401
$894$	−0.324312	−	4.90617i	−0.0108466	−	0.164087i
$895$	34.0466			1.13805
$896$	−46.6037	+	23.2088i	−1.55692	+	0.775350i
$897$		−	32.4014i		−	1.08185i
$898$	−29.9303	+	1.97848i	−0.998786	+	0.0660227i
$899$	17.8816	+	23.1094i	0.596385	+	0.770742i
$900$	3.04530	−	0.404373i	0.101510	−	0.0134791i
$901$	−10.0796			−0.335802
$902$	1.44700	+	21.8902i	0.0481799	+	0.728863i
$903$		−	40.5411i		−	1.34912i
$904$	−3.02358	−	15.0689i	−0.100563	−	0.501184i
$905$			13.1748i			0.437944i
$906$	−1.82107	−	27.5490i	−0.0605010	−	0.915255i
$907$			13.0481i			0.433255i	0.976254	+	0.216627i	$0.0695056\pi$
$907$			13.0481i			0.433255i	−0.976254	+	0.216627i	$0.930494\pi$
$908$	−4.86023	−	36.6019i	−0.161292	−	1.21468i
$909$	4.68761			0.155478
$910$	3.57813	+	54.1296i	0.118614	+	1.79438i
$911$	56.4537			1.87039			0.935197	−	0.354129i	$-0.115223\pi$
$911$	56.4537			1.87039			0.935197	+	0.354129i	$0.115223\pi$
$912$	−1.17787	−	4.35703i	−0.0390033	−	0.144276i
$913$	−75.6246			−2.50281
$914$	−16.4227	+	1.08559i	−0.543215	+	0.0359081i
$915$			4.63373i			0.153187i
$916$	6.87067	+	51.7424i	0.227013	+	1.70962i
$917$	39.2759			1.29700
$918$	−2.90143	+	0.191793i	−0.0957616	+	0.00633012i
$919$			23.4228i			0.772648i	0.922363	+	0.386324i	$0.126255\pi$
$919$			23.4228i			0.772648i	−0.922363	+	0.386324i	$0.873745\pi$
$920$	7.49221	+	37.3397i	0.247011	+	1.23105i
$921$			20.8616i			0.687412i
$922$	40.1305	−	2.65274i	1.32163	−	0.0873635i
$923$	−12.3999			−0.408148
$924$	6.54879	+	49.3183i	0.215439	+	1.62245i
$925$		−	7.10213i		−	0.233516i
$926$	−2.28722	−	34.6008i	−0.0751626	−	1.13705i
$927$		−	13.0594i		−	0.428927i
$928$	28.0852	−	9.62095i	0.921941	−	0.315823i
$929$		−	39.8933i		−	1.30886i	−0.756123	−	0.654429i	$-0.772909\pi$
$929$		−	39.8933i		−	1.30886i	0.756123	−	0.654429i	$-0.227091\pi$
$930$	−9.71332	−	10.9735i	−0.318512	−	0.359837i
$931$			15.9958i			0.524242i
$932$	−22.6966	+	3.01379i	−0.743452	+	0.0987201i
$933$			7.18365i			0.235182i
$934$	25.4427	−	1.68183i	0.832509	−	0.0550313i
$935$			20.6863i			0.676514i
$936$	12.4202	−	2.49212i	0.405967	−	0.0814574i
$937$	−28.1073			−0.918224			−0.459112	−	0.888378i	$-0.651832\pi$
$937$	−28.1073			−0.918224			−0.459112	+	0.888378i	$0.651832\pi$
$938$	4.14692	+	62.7344i	0.135402	+	2.04835i
$939$			7.17232i			0.234060i
$940$	0.441717	+	3.32654i	0.0144072	+	0.108500i
$941$		−	31.4892i		−	1.02652i	−0.858233	−	0.513260i	$-0.828438\pi$
$941$		−	31.4892i		−	1.02652i	0.858233	−	0.513260i	$-0.171562\pi$
$942$	−0.529753	−	8.01406i	−0.0172603	−	0.261112i
$943$	−20.7606			−0.676057
$944$	−13.0356	−	48.2196i	−0.424274	−	1.56941i
$945$		−	8.56470i		−	0.278610i
$946$	4.44232	+	67.2031i	0.144432	+	2.18496i
$947$	12.5383			0.407439			0.203720	−	0.979029i	$-0.434697\pi$
$947$	12.5383			0.407439			0.203720	+	0.979029i	$0.434697\pi$
$948$	13.9816	−	1.85656i	0.454101	−	0.0602983i
$949$	−22.2044			−0.720786
$950$	−2.44574	+	0.161670i	−0.0793503	+	0.00524528i
$951$	9.65687			0.313146
$952$	−5.26480	−	26.2387i	−0.170633	−	0.850401i
$953$			13.9299i			0.451235i	0.974216	+	0.225618i	$0.0724400\pi$
$953$			13.9299i			0.451235i	−0.974216	+	0.225618i	$0.927560\pi$
$954$	−6.91782	+	0.457288i	−0.223973	+	0.0148052i
$955$		−	21.8289i		−	0.706367i
$956$	−28.9262	+	3.84100i	−0.935540	+	0.124227i
$957$		−	28.3692i		−	0.917045i
$958$	−6.35228	+	0.419904i	−0.205233	+	0.0135665i
$959$	−4.91660			−0.158765
$960$	−13.7369	+	5.74388i	−0.443357	+	0.185383i
$961$	7.78064	−	30.0077i	0.250988	−	0.967990i
$962$	−1.93169	−	29.2224i	−0.0622801	−	0.942169i
$963$			7.89615i			0.254450i
$964$	−7.06710	−	53.2217i	−0.227616	−	1.71416i
$965$	27.4020			0.882100
$966$	−46.9787	+	3.10543i	−1.51151	+	0.0999154i
$967$	−17.5397			−0.564038			−0.282019	−	0.959409i	$-0.591004\pi$
$967$	−17.5397			−0.564038			−0.282019	+	0.959409i	$0.591004\pi$
$968$	−10.1390	−	50.5305i	−0.325879	−	1.62411i
$969$	2.32002			0.0745297
$970$	−0.166772	−	2.52292i	−0.00535473	−	0.0810060i
$971$		−	25.4120i		−	0.815509i	−0.913092	−	0.407755i	$-0.866312\pi$
$971$		−	25.4120i		−	0.815509i	0.913092	−	0.407755i	$-0.133688\pi$
$972$	−1.98260	+	0.263261i	−0.0635918	+	0.00844411i
$973$			82.0039i			2.62892i
$974$	3.78911	+	57.3214i	0.121411	+	1.83670i
$975$		−	6.87939i		−	0.220317i
$976$	2.59893	+	9.61361i	0.0831897	+	0.307724i
$977$	−58.3772			−1.86765			−0.933825	−	0.357729i	$-0.883551\pi$
$977$	−58.3772			−1.86765			−0.933825	+	0.357729i	$0.883551\pi$
$978$	−20.1365	+	1.33108i	−0.643895	+	0.0425633i
$979$		−	64.7655i		−	2.06992i
$980$	52.3097	−	6.94600i	1.67097	−	0.221882i
$981$	−12.4255			−0.396715
$982$	−0.406051	−	6.14270i	−0.0129576	−	0.196022i
$983$	0.225941			0.00720640			0.00360320	−	0.999994i	$-0.498853\pi$
$983$	0.225941			0.00720640			0.00360320	+	0.999994i	$0.498853\pi$
$984$	−1.59678	−	7.95801i	−0.0509034	−	0.253692i
$985$		−	21.8296i		−	0.695549i
$986$	1.00654	+	15.2268i	0.0320547	+	0.484921i
$987$	−4.14852			−0.132049
$988$	−10.0193	+	1.33042i	−0.318756	+	0.0423263i
$989$	−63.7352			−2.02666
$990$	0.938484	+	14.1973i	0.0298270	+	0.451220i
$991$	44.9992			1.42945			0.714723	−	0.699408i	$-0.246553\pi$
$991$	44.9992			1.42945			0.714723	+	0.699408i	$0.246553\pi$
$992$	−26.3070	−	17.3189i	−0.835247	−	0.549875i
$993$	23.0630			0.731881
$994$	1.18844	+	17.9786i	0.0376950	+	0.570247i
$995$	8.20421			0.260091
$996$	27.7362	−	3.68298i	0.878856	−	0.116700i
$997$	4.59144			0.145412			0.0727062	−	0.997353i	$-0.476836\pi$
$997$	4.59144			0.145412			0.0727062	+	0.997353i	$0.476836\pi$
$998$	−0.948623	−	14.3507i	−0.0300281	−	0.454263i
$999$			4.62374i			0.146289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.g.b.247.10	yes	16
3.2	odd	2		1116.2.g.i.991.7		16
4.3	odd	2		372.2.g.a.247.9	✓	16
12.11	even	2		1116.2.g.j.991.8		16
31.30	odd	2		372.2.g.a.247.10	yes	16
93.92	even	2		1116.2.g.j.991.7		16
124.123	even	2	inner	372.2.g.b.247.9	yes	16
372.371	odd	2		1116.2.g.i.991.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.g.a.247.9	✓	16	4.3	odd	2
372.2.g.a.247.10	yes	16	31.30	odd	2
372.2.g.b.247.9	yes	16	124.123	even	2	inner
372.2.g.b.247.10	yes	16	1.1	even	1	trivial
1116.2.g.i.991.7		16	3.2	odd	2
1116.2.g.i.991.8		16	372.371	odd	2
1116.2.g.j.991.7		16	93.92	even	2
1116.2.g.j.991.8		16	12.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0932801 + 1.41113i) q^{2} +1.00000 q^{3} +(-1.98260 + 0.263261i) q^{4} +1.86118 q^{5} +(0.0932801 + 1.41113i) q^{6} -4.60176i q^{7} +(-0.556434 - 2.77315i) q^{8} +1.00000 q^{9} +(0.173611 + 2.62637i) q^{10} +5.40568 q^{11} +(-1.98260 + 0.263261i) q^{12} +4.47873i q^{13} +(6.49370 - 0.429252i) q^{14} +1.86118 q^{15} +(3.86139 - 1.04388i) q^{16} +2.05610i q^{17} +(0.0932801 + 1.41113i) q^{18} -1.12836i q^{19} +(-3.68997 + 0.489976i) q^{20} -4.60176i q^{21} +(0.504242 + 7.62813i) q^{22} -7.23450 q^{23} +(-0.556434 - 2.77315i) q^{24} -1.53601 q^{25} +(-6.32009 + 0.417776i) q^{26} +1.00000 q^{27} +(1.21147 + 9.12344i) q^{28} -5.24803i q^{29} +(0.173611 + 2.62637i) q^{30} +(-4.40344 + 3.40730i) q^{31} +(1.83325 + 5.35156i) q^{32} +5.40568 q^{33} +(-2.90143 + 0.191793i) q^{34} -8.56470i q^{35} +(-1.98260 + 0.263261i) q^{36} +4.62374i q^{37} +(1.59226 - 0.105253i) q^{38} +4.47873i q^{39} +(-1.03562 - 5.16133i) q^{40} +2.86966 q^{41} +(6.49370 - 0.429252i) q^{42} +8.80990 q^{43} +(-10.7173 + 1.42311i) q^{44} +1.86118 q^{45} +(-0.674834 - 10.2088i) q^{46} -0.901508i q^{47} +(3.86139 - 1.04388i) q^{48} -14.1762 q^{49} +(-0.143279 - 2.16752i) q^{50} +2.05610i q^{51} +(-1.17908 - 8.87952i) q^{52} +4.90231i q^{53} +(0.0932801 + 1.41113i) q^{54} +10.0609 q^{55} +(-12.7614 + 2.56057i) q^{56} -1.12836i q^{57} +(7.40568 - 0.489537i) q^{58} -12.4876i q^{59} +(-3.68997 + 0.489976i) q^{60} +2.48968i q^{61} +(-5.21891 - 5.89602i) q^{62} -4.60176i q^{63} +(-7.38076 + 3.08615i) q^{64} +8.33572i q^{65} +(0.504242 + 7.62813i) q^{66} +9.66081i q^{67} +(-0.541292 - 4.07642i) q^{68} -7.23450 q^{69} +(12.0859 - 0.798915i) q^{70} +2.76862i q^{71} +(-0.556434 - 2.77315i) q^{72} +4.95775i q^{73} +(-6.52472 + 0.431303i) q^{74} -1.53601 q^{75} +(0.297053 + 2.23708i) q^{76} -24.8756i q^{77} +(-6.32009 + 0.417776i) q^{78} -7.05216 q^{79} +(7.18673 - 1.94285i) q^{80} +1.00000 q^{81} +(0.267682 + 4.04948i) q^{82} -13.9898 q^{83} +(1.21147 + 9.12344i) q^{84} +3.82677i q^{85} +(0.821788 + 12.4320i) q^{86} -5.24803i q^{87} +(-3.00790 - 14.9908i) q^{88} -11.9810i q^{89} +(0.173611 + 2.62637i) q^{90} +20.6100 q^{91} +(14.3431 - 1.90456i) q^{92} +(-4.40344 + 3.40730i) q^{93} +(1.27215 - 0.0840927i) q^{94} -2.10008i q^{95} +(1.83325 + 5.35156i) q^{96} -0.960609 q^{97} +(-1.32236 - 20.0045i) q^{98} +5.40568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 2 q^{4} + 3 q^{8} + 16 q^{9} - 5 q^{10} + 4 q^{11} + 2 q^{12} + 5 q^{14} + 10 q^{16} - q^{20} - 16 q^{23} + 3 q^{24} + 12 q^{25} - 10 q^{26} + 16 q^{27} + 3 q^{28} - 5 q^{30} - 6 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 2 * q^4 + 3 * q^8 + 16 * q^9 - 5 * q^10 + 4 * q^11 + 2 * q^12 + 5 * q^14 + 10 * q^16 - q^20 - 16 * q^23 + 3 * q^24 + 12 * q^25 - 10 * q^26 + 16 * q^27 + 3 * q^28 - 5 * q^30 - 6 * q^31 - 20 * q^32 + 4 * q^33 + 28 * q^34 + 2 * q^36 + q^38 - 26 * q^40 + 5 * q^42 - 20 * q^43 - 14 * q^44 - 4 * q^46 + 10 * q^48 - 8 * q^49 - 11 * q^50 - 4 * q^52 + 8 * q^55 - 40 * q^56 + 36 * q^58 - q^60 - 26 * q^62 - 7 * q^64 - 6 * q^68 - 16 * q^69 + 9 * q^70 + 3 * q^72 - 52 * q^74 + 12 * q^75 - 3 * q^76 - 10 * q^78 - 12 * q^79 - 13 * q^80 + 16 * q^81 - 11 * q^82 - 28 * q^83 + 3 * q^84 + 8 * q^86 - 16 * q^88 - 5 * q^90 + 16 * q^91 - 6 * q^93 + 26 * q^94 - 20 * q^96 - 40 * q^97 - 15 * q^98 + 4 * q^99

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