LMFDB - Embedded newform 546.2.bb.a.269.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.9
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.459307 - 1.67004i) q^{3} -1.00000 q^{4} +(-1.40279 - 2.42970i) q^{5} +(-1.67004 + 0.459307i) q^{6} +(1.21733 + 2.34907i) q^{7} +1.00000i q^{8} +(-2.57807 + 1.53412i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.459307 - 1.67004i) q^{3} -1.00000 q^{4} +(-1.40279 - 2.42970i) q^{5} +(-1.67004 + 0.459307i) q^{6} +(1.21733 + 2.34907i) q^{7} +1.00000i q^{8} +(-2.57807 + 1.53412i) q^{9} +(-2.42970 + 1.40279i) q^{10} +(-2.26401 + 1.30713i) q^{11} +(0.459307 + 1.67004i) q^{12} +(-0.591455 - 3.55671i) q^{13} +(2.34907 - 1.21733i) q^{14} +(-3.41338 + 3.45869i) q^{15} +1.00000 q^{16} -4.62784 q^{17} +(1.53412 + 2.57807i) q^{18} +(-5.90055 - 3.40668i) q^{19} +(1.40279 + 2.42970i) q^{20} +(3.36391 - 3.11193i) q^{21} +(1.30713 + 2.26401i) q^{22} +5.30862i q^{23} +(1.67004 - 0.459307i) q^{24} +(-1.43561 + 2.48656i) q^{25} +(-3.55671 + 0.591455i) q^{26} +(3.74618 + 3.60085i) q^{27} +(-1.21733 - 2.34907i) q^{28} +(5.91509 + 3.41508i) q^{29} +(3.45869 + 3.41338i) q^{30} +(5.96408 + 3.44336i) q^{31} -1.00000i q^{32} +(3.22284 + 3.18062i) q^{33} +4.62784i q^{34} +(3.99987 - 6.25297i) q^{35} +(2.57807 - 1.53412i) q^{36} -0.994157 q^{37} +(-3.40668 + 5.90055i) q^{38} +(-5.66819 + 2.62138i) q^{39} +(2.42970 - 1.40279i) q^{40} +(1.10966 - 1.92198i) q^{41} +(-3.11193 - 3.36391i) q^{42} +(-3.67020 - 6.35698i) q^{43} +(2.26401 - 1.30713i) q^{44} +(7.34394 + 4.11189i) q^{45} +5.30862 q^{46} +(-1.77046 - 3.06652i) q^{47} +(-0.459307 - 1.67004i) q^{48} +(-4.03622 + 5.71917i) q^{49} +(2.48656 + 1.43561i) q^{50} +(2.12560 + 7.72868i) q^{51} +(0.591455 + 3.55671i) q^{52} +(-9.16567 - 5.29180i) q^{53} +(3.60085 - 3.74618i) q^{54} +(6.35185 + 3.66724i) q^{55} +(-2.34907 + 1.21733i) q^{56} +(-2.97913 + 11.4189i) q^{57} +(3.41508 - 5.91509i) q^{58} -3.06017 q^{59} +(3.41338 - 3.45869i) q^{60} +(-10.3394 - 5.96948i) q^{61} +(3.44336 - 5.96408i) q^{62} +(-6.74212 - 4.18853i) q^{63} -1.00000 q^{64} +(-7.81204 + 6.42636i) q^{65} +(3.18062 - 3.22284i) q^{66} +(-4.96864 - 8.60593i) q^{67} +4.62784 q^{68} +(8.86562 - 2.43829i) q^{69} +(-6.25297 - 3.99987i) q^{70} +(4.88106 - 2.81808i) q^{71} +(-1.53412 - 2.57807i) q^{72} +(-1.76646 - 1.01987i) q^{73} +0.994157i q^{74} +(4.81204 + 1.25544i) q^{75} +(5.90055 + 3.40668i) q^{76} +(-5.82658 - 3.72712i) q^{77} +(2.62138 + 5.66819i) q^{78} +(-0.142677 - 0.247123i) q^{79} +(-1.40279 - 2.42970i) q^{80} +(4.29293 - 7.91017i) q^{81} +(-1.92198 - 1.10966i) q^{82} +0.889066 q^{83} +(-3.36391 + 3.11193i) q^{84} +(6.49186 + 11.2442i) q^{85} +(-6.35698 + 3.67020i) q^{86} +(2.98648 - 11.4470i) q^{87} +(-1.30713 - 2.26401i) q^{88} -14.4950 q^{89} +(4.11189 - 7.34394i) q^{90} +(7.63495 - 5.71905i) q^{91} -5.30862i q^{92} +(3.01121 - 11.5418i) q^{93} +(-3.06652 + 1.77046i) q^{94} +19.1154i q^{95} +(-1.67004 + 0.459307i) q^{96} +(7.06699 - 4.08013i) q^{97} +(5.71917 + 4.03622i) q^{98} +(3.83150 - 6.84316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.459307	−	1.67004i	−0.265181	−	0.964199i
$3$	−0.459307	−	1.67004i	−0.265181	−	0.964199i
$4$	−1.00000			−0.500000
$5$	−1.40279	−	2.42970i	−0.627345	−	1.08659i	−0.988082	−	0.153926i	$-0.950808\pi$
$5$	−1.40279	−	2.42970i	−0.627345	−	1.08659i	0.360738	−	0.932667i	$-0.382525\pi$
$6$	−1.67004	+	0.459307i	−0.681791	+	0.187511i
$7$	1.21733	+	2.34907i	0.460107	+	0.887864i
$7$	1.21733	+	2.34907i	0.460107	+	0.887864i
$8$			1.00000i			0.353553i
$9$	−2.57807	+	1.53412i	−0.859358	+	0.511375i
$10$	−2.42970	+	1.40279i	−0.768337	+	0.443600i
$11$	−2.26401	+	1.30713i	−0.682626	+	0.394114i	−0.800844	−	0.598873i	$-0.795615\pi$
$11$	−2.26401	+	1.30713i	−0.682626	+	0.394114i	0.118218	+	0.992988i	$0.462282\pi$
$12$	0.459307	+	1.67004i	0.132591	+	0.482099i
$13$	−0.591455	−	3.55671i	−0.164040	−	0.986454i
$13$	−0.591455	−	3.55671i	−0.164040	−	0.986454i
$14$	2.34907	−	1.21733i	0.627814	−	0.325345i
$15$	−3.41338	+	3.45869i	−0.881331	+	0.893029i
$16$	1.00000			0.250000
$17$	−4.62784			−1.12242			−0.561208	−	0.827675i	$-0.689663\pi$
$17$	−4.62784			−1.12242			−0.561208	+	0.827675i	$0.689663\pi$
$18$	1.53412	+	2.57807i	0.361596	+	0.607658i
$19$	−5.90055	−	3.40668i	−1.35368	−	0.781546i	−0.364916	−	0.931041i	$-0.618902\pi$
$19$	−5.90055	−	3.40668i	−1.35368	−	0.781546i	−0.988763	+	0.149494i	$0.952235\pi$
$20$	1.40279	+	2.42970i	0.313672	+	0.543297i
$21$	3.36391	−	3.11193i	0.734065	−	0.679079i
$22$	1.30713	+	2.26401i	0.278681	+	0.482690i
$23$			5.30862i			1.10692i	0.832874	+	0.553462i	$0.186694\pi$
$23$			5.30862i			1.10692i	−0.832874	+	0.553462i	$0.813306\pi$
$24$	1.67004	−	0.459307i	0.340896	−	0.0937557i
$25$	−1.43561	+	2.48656i	−0.287123	+	0.497311i
$26$	−3.55671	+	0.591455i	−0.697528	+	0.115994i
$27$	3.74618	+	3.60085i	0.720952	+	0.692985i
$28$	−1.21733	−	2.34907i	−0.230053	−	0.443932i
$29$	5.91509	+	3.41508i	1.09840	+	0.634164i	0.935802	−	0.352527i	$-0.114678\pi$
$29$	5.91509	+	3.41508i	1.09840	+	0.634164i	0.162603	+	0.986692i	$0.448011\pi$
$30$	3.45869	+	3.41338i	0.631467	+	0.623195i
$31$	5.96408	+	3.44336i	1.07118	+	0.618446i	0.928504	−	0.371323i	$-0.121096\pi$
$31$	5.96408	+	3.44336i	1.07118	+	0.618446i	0.142677	+	0.989769i	$0.454429\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.22284	+	3.18062i	0.561024	+	0.553675i
$34$			4.62784i			0.793667i
$35$	3.99987	−	6.25297i	0.676101	−	1.05695i
$36$	2.57807	−	1.53412i	0.429679	−	0.255687i
$37$	−0.994157			−0.163438			−0.0817192	−	0.996655i	$-0.526041\pi$
$37$	−0.994157			−0.163438			−0.0817192	+	0.996655i	$0.526041\pi$
$38$	−3.40668	+	5.90055i	−0.552637	+	0.957195i
$39$	−5.66819	+	2.62138i	−0.907637	+	0.419756i
$40$	2.42970	−	1.40279i	0.384169	−	0.221800i
$41$	1.10966	−	1.92198i	0.173299	−	0.300163i	−0.766272	−	0.642516i	$-0.777891\pi$
$41$	1.10966	−	1.92198i	0.173299	−	0.300163i	0.939571	+	0.342353i	$0.111224\pi$
$42$	−3.11193	−	3.36391i	−0.480181	−	0.519062i
$43$	−3.67020	−	6.35698i	−0.559701	−	0.969430i	−0.997521	−	0.0703677i	$-0.977583\pi$
$43$	−3.67020	−	6.35698i	−0.559701	−	0.969430i	0.437820	−	0.899062i	$-0.355751\pi$
$44$	2.26401	−	1.30713i	0.341313	−	0.197057i
$45$	7.34394	+	4.11189i	1.09477	+	0.612964i
$46$	5.30862			0.782714
$47$	−1.77046	−	3.06652i	−0.258248	−	0.447298i	0.707525	−	0.706688i	$-0.249812\pi$
$47$	−1.77046	−	3.06652i	−0.258248	−	0.447298i	−0.965773	+	0.259390i	$0.916478\pi$
$48$	−0.459307	−	1.67004i	−0.0662953	−	0.241050i
$49$	−4.03622	+	5.71917i	−0.576603	+	0.817024i
$50$	2.48656	+	1.43561i	0.351652	+	0.203027i
$51$	2.12560	+	7.72868i	0.297643	+	1.08223i
$52$	0.591455	+	3.55671i	0.0820201	+	0.493227i
$53$	−9.16567	−	5.29180i	−1.25900	−	0.726885i	−0.286121	−	0.958193i	$-0.592366\pi$
$53$	−9.16567	−	5.29180i	−1.25900	−	0.726885i	−0.972880	+	0.231308i	$0.925699\pi$
$54$	3.60085	−	3.74618i	0.490014	−	0.509790i
$55$	6.35185	+	3.66724i	0.856484	+	0.494491i
$56$	−2.34907	+	1.21733i	−0.313907	+	0.162672i
$57$	−2.97913	+	11.4189i	−0.394596	+	1.51247i
$58$	3.41508	−	5.91509i	0.448422	−	0.776689i
$59$	−3.06017			−0.398400			−0.199200	−	0.979959i	$-0.563834\pi$
$59$	−3.06017			−0.398400			−0.199200	+	0.979959i	$0.563834\pi$
$60$	3.41338	−	3.45869i	0.440666	−	0.446514i
$61$	−10.3394	−	5.96948i	−1.32383	−	0.764314i	−0.339493	−	0.940609i	$-0.610255\pi$
$61$	−10.3394	−	5.96948i	−1.32383	−	0.764314i	−0.984337	+	0.176295i	$0.943589\pi$
$62$	3.44336	−	5.96408i	0.437308	−	0.757439i
$63$	−6.74212	−	4.18853i	−0.849427	−	0.527706i
$64$	−1.00000			−0.125000
$65$	−7.81204	+	6.42636i	−0.968964	+	0.797091i
$66$	3.18062	−	3.22284i	0.391508	−	0.396704i
$67$	−4.96864	−	8.60593i	−0.607015	−	1.05138i	−0.991729	−	0.128346i	$-0.959033\pi$
$67$	−4.96864	−	8.60593i	−0.607015	−	1.05138i	0.384714	−	0.923036i	$-0.374300\pi$
$68$	4.62784			0.561208
$69$	8.86562	−	2.43829i	1.06729	−	0.293535i
$70$	−6.25297	−	3.99987i	−0.747373	−	0.478075i
$71$	4.88106	−	2.81808i	0.579276	−	0.334445i	−0.181570	−	0.983378i	$-0.558118\pi$
$71$	4.88106	−	2.81808i	0.579276	−	0.334445i	0.760845	+	0.648933i	$0.224785\pi$
$72$	−1.53412	−	2.57807i	−0.180798	−	0.303829i
$73$	−1.76646	−	1.01987i	−0.206749	−	0.119366i	0.393051	−	0.919517i	$-0.371420\pi$
$73$	−1.76646	−	1.01987i	−0.206749	−	0.119366i	−0.599799	+	0.800150i	$0.704753\pi$
$74$			0.994157i			0.115568i
$75$	4.81204	+	1.25544i	0.555647	+	0.144966i
$76$	5.90055	+	3.40668i	0.676839	+	0.390773i
$77$	−5.82658	−	3.72712i	−0.664001	−	0.424744i
$78$	2.62138	+	5.66819i	0.296812	+	0.641796i
$79$	−0.142677	−	0.247123i	−0.0160524	−	0.0278035i	0.857888	−	0.513837i	$-0.171777\pi$
$79$	−0.142677	−	0.247123i	−0.0160524	−	0.0278035i	−0.873940	+	0.486034i	$0.838443\pi$
$80$	−1.40279	−	2.42970i	−0.156836	−	0.271648i
$81$	4.29293	−	7.91017i	0.476992	−	0.878908i
$82$	−1.92198	−	1.10966i	−0.212247	−	0.122541i
$83$	0.889066			0.0975876			0.0487938	−	0.998809i	$-0.484462\pi$
$83$	0.889066			0.0975876			0.0487938	+	0.998809i	$0.484462\pi$
$84$	−3.36391	+	3.11193i	−0.367033	+	0.339540i
$85$	6.49186	+	11.2442i	0.704141	+	1.21961i
$86$	−6.35698	+	3.67020i	−0.685491	+	0.395768i
$87$	2.98648	−	11.4470i	0.320184	−	1.22725i
$88$	−1.30713	−	2.26401i	−0.139340	−	0.241345i
$89$	−14.4950			−1.53646			−0.768232	−	0.640171i	$-0.778863\pi$
$89$	−14.4950			−1.53646			−0.768232	+	0.640171i	$0.778863\pi$
$90$	4.11189	−	7.34394i	0.433431	−	0.774119i
$91$	7.63495	−	5.71905i	0.800360	−	0.599519i
$92$		−	5.30862i		−	0.553462i
$93$	3.01121	−	11.5418i	0.312248	−	1.19683i
$94$	−3.06652	+	1.77046i	−0.316288	+	0.182609i
$95$			19.1154i			1.96120i
$96$	−1.67004	+	0.459307i	−0.170448	+	0.0468779i
$97$	7.06699	−	4.08013i	0.717544	−	0.414274i	−0.0963042	−	0.995352i	$-0.530702\pi$
$97$	7.06699	−	4.08013i	0.717544	−	0.414274i	0.813848	+	0.581078i	$0.197369\pi$
$98$	5.71917	+	4.03622i	0.577723	+	0.407720i
$99$	3.83150	−	6.84316i	0.385080	−	0.687763i
$100$	1.43561	−	2.48656i	0.143561	−	0.248656i
$101$	−2.45144	−	4.24601i	−0.243927	−	0.422494i	0.717902	−	0.696144i	$-0.245102\pi$
$101$	−2.45144	−	4.24601i	−0.243927	−	0.422494i	−0.961829	+	0.273650i	$0.911769\pi$
$102$	7.72868	−	2.12560i	0.765253	−	0.210466i
$103$	2.88019	−	1.66288i	0.283794	−	0.163848i	−0.351346	−	0.936246i	$-0.614276\pi$
$103$	2.88019	−	1.66288i	0.283794	−	0.163848i	0.635140	+	0.772397i	$0.280943\pi$
$104$	3.55671	−	0.591455i	0.348764	−	0.0579969i
$105$	−12.2799	−	3.80790i	−1.19839	−	0.371613i
$106$	−5.29180	+	9.16567i	−0.513985	+	0.890249i
$107$		−	0.930416i		−	0.0899467i	−0.998988	−	0.0449734i	$-0.985680\pi$
$107$		−	0.930416i		−	0.0899467i	0.998988	−	0.0449734i	$-0.0143203\pi$
$108$	−3.74618	−	3.60085i	−0.360476	−	0.346492i
$109$	−5.59636	+	9.69317i	−0.536034	+	0.928438i	0.463079	+	0.886317i	$0.346745\pi$
$109$	−5.59636	+	9.69317i	−0.536034	+	0.928438i	−0.999113	+	0.0421205i	$0.986589\pi$
$110$	3.66724	−	6.35185i	0.349658	−	0.605626i
$111$	0.456624	+	1.66028i	0.0433408	+	0.157587i
$112$	1.21733	+	2.34907i	0.115027	+	0.221966i
$113$	−1.95091	+	1.12636i	−0.183526	+	0.105959i	−0.588948	−	0.808171i	$-0.700458\pi$
$113$	−1.95091	+	1.12636i	−0.183526	+	0.105959i	0.405422	+	0.914130i	$0.367125\pi$
$114$	11.4189	+	2.97913i	1.06947	+	0.279022i
$115$	12.8983	−	7.44686i	1.20278	−	0.694423i
$116$	−5.91509	−	3.41508i	−0.549202	−	0.317082i
$117$	6.98125	+	8.26209i	0.645417	+	0.763831i
$118$			3.06017i			0.281711i
$119$	−5.63360	−	10.8711i	−0.516431	−	0.996551i
$120$	−3.45869	−	3.41338i	−0.315733	−	0.311598i
$121$	−2.08282	+	3.60756i	−0.189348	+	0.327960i
$122$	−5.96948	+	10.3394i	−0.540451	+	0.936089i
$123$	−3.71946	−	0.970392i	−0.335373	−	0.0874973i
$124$	−5.96408	−	3.44336i	−0.535590	−	0.309223i
$125$	−5.97242			−0.534189
$126$	−4.18853	+	6.74212i	−0.373144	+	0.600636i
$127$	−9.32949	+	16.1591i	−0.827858	+	1.43389i	0.0718568	+	0.997415i	$0.477108\pi$
$127$	−9.32949	+	16.1591i	−0.827858	+	1.43389i	−0.899715	+	0.436478i	$0.856226\pi$
$128$			1.00000i			0.0883883i
$129$	−8.93066	+	9.04920i	−0.786301	+	0.796737i
$130$	6.42636	+	7.81204i	0.563629	+	0.685161i
$131$	7.60360	+	13.1698i	0.664330	+	1.15065i	0.979467	+	0.201606i	$0.0646162\pi$
$131$	7.60360	+	13.1698i	0.664330	+	1.15065i	−0.315137	+	0.949046i	$0.602050\pi$
$132$	−3.22284	−	3.18062i	−0.280512	−	0.276838i
$133$	0.819620	−	18.0078i	0.0710701	−	1.56148i
$134$	−8.60593	+	4.96864i	−0.743439	+	0.429225i
$135$	3.49390	−	14.1533i	0.300707	−	1.21812i
$136$		−	4.62784i		−	0.396834i
$137$		−	10.3994i		−	0.888481i	−0.895908	−	0.444240i	$-0.853474\pi$
$137$		−	10.3994i		−	0.888481i	0.895908	−	0.444240i	$-0.146526\pi$
$138$	−2.43829	−	8.86562i	−0.207561	−	0.754691i
$139$	8.96591	−	5.17647i	0.760478	−	0.439062i	−0.0689891	−	0.997617i	$-0.521977\pi$
$139$	8.96591	−	5.17647i	0.760478	−	0.439062i	0.829467	+	0.558555i	$0.188644\pi$
$140$	−3.99987	+	6.25297i	−0.338050	+	0.528473i
$141$	−4.30803	+	4.36521i	−0.362802	+	0.367617i
$142$	−2.81808	−	4.88106i	−0.236488	−	0.409610i
$143$	5.98814	+	7.27933i	0.500754	+	0.608729i
$144$	−2.57807	+	1.53412i	−0.214839	+	0.127844i
$145$		−	19.1625i		−	1.59136i
$146$	−1.01987	+	1.76646i	−0.0844048	+	0.146193i
$147$	11.4051	+	4.11380i	0.940678	+	0.339301i
$148$	0.994157			0.0817192
$149$	−16.2996	−	9.41056i	−1.33531	−	0.770943i	−0.349205	−	0.937046i	$-0.613548\pi$
$149$	−16.2996	−	9.41056i	−1.33531	−	0.770943i	−0.986108	+	0.166103i	$0.946882\pi$
$150$	1.25544	−	4.81204i	0.102506	−	0.392901i
$151$	10.8089	−	18.7215i	0.879612	−	1.52353i	0.0278447	−	0.999612i	$-0.491136\pi$
$151$	10.8089	−	18.7215i	0.879612	−	1.52353i	0.851767	−	0.523920i	$-0.175531\pi$
$152$	3.40668	−	5.90055i	0.276318	−	0.478597i
$153$	11.9309	−	7.09967i	0.964556	−	0.573975i
$154$	−3.72712	+	5.82658i	−0.300339	+	0.469519i
$155$		−	19.3212i		−	1.55192i
$156$	5.66819	−	2.62138i	0.453818	−	0.209878i
$157$	4.43673	+	2.56155i	0.354090	+	0.204434i	0.666485	−	0.745518i	$-0.267798\pi$
$157$	4.43673	+	2.56155i	0.354090	+	0.204434i	−0.312395	+	0.949952i	$0.601131\pi$
$158$	−0.247123	+	0.142677i	−0.0196601	+	0.0113507i
$159$	−4.62767	+	17.7376i	−0.366998	+	1.40668i
$160$	−2.42970	+	1.40279i	−0.192084	+	0.110900i
$161$	−12.4703	+	6.46234i	−0.982798	+	0.509303i
$162$	−7.91017	−	4.29293i	−0.621482	−	0.337284i
$163$	8.71655	−	15.0975i	0.682733	−	1.18253i	−0.291411	−	0.956598i	$-0.594125\pi$
$163$	8.71655	−	15.0975i	0.682733	−	1.18253i	0.974144	−	0.225930i	$-0.0725419\pi$
$164$	−1.10966	+	1.92198i	−0.0866497	+	0.150082i
$165$	3.20700	−	12.2922i	0.249664	−	0.956950i
$166$		−	0.889066i		−	0.0690049i
$167$	1.95407	−	3.38455i	0.151211	−	0.261904i	−0.780462	−	0.625203i	$-0.785016\pi$
$167$	1.95407	−	3.38455i	0.151211	−	0.261904i	0.931673	+	0.363299i	$0.118350\pi$
$168$	3.11193	+	3.36391i	0.240091	+	0.259531i
$169$	−12.3004	+	4.20727i	−0.946182	+	0.323636i
$170$	11.2442	−	6.49186i	0.862393	−	0.497903i
$171$	20.4383	−	0.269493i	1.56296	−	0.0206086i
$172$	3.67020	+	6.35698i	0.279850	+	0.484715i
$173$	3.34066	−	5.78620i	0.253986	−	0.439917i	−0.710634	−	0.703562i	$-0.751592\pi$
$173$	3.34066	−	5.78620i	0.253986	−	0.439917i	0.964620	+	0.263646i	$0.0849250\pi$
$174$	−11.4470	−	2.98648i	−0.867796	−	0.226404i
$175$	−7.58870	−	0.345397i	−0.573652	−	0.0261096i
$176$	−2.26401	+	1.30713i	−0.170657	+	0.0985286i
$177$	1.40556	+	5.11060i	0.105648	+	0.384137i
$178$			14.4950i			1.08644i
$179$	7.04886	−	4.06966i	0.526856	−	0.304181i	−0.212879	−	0.977079i	$-0.568284\pi$
$179$	7.04886	−	4.06966i	0.526856	−	0.304181i	0.739735	+	0.672898i	$0.234951\pi$
$180$	−7.34394	−	4.11189i	−0.547385	−	0.306482i
$181$			14.2577i			1.05977i	0.848070	+	0.529885i	$0.177765\pi$
$181$			14.2577i			1.05977i	−0.848070	+	0.529885i	$0.822235\pi$
$182$	−5.71905	−	7.63495i	−0.423924	−	0.565940i
$183$	−5.22029	+	20.0091i	−0.385895	+	1.47912i
$184$	−5.30862			−0.391357
$185$	1.39459	+	2.41550i	0.102532	+	0.177591i
$186$	−11.5418	−	3.01121i	−0.846287	−	0.220793i
$187$	10.4775	−	6.04918i	0.766190	−	0.442360i
$188$	1.77046	+	3.06652i	0.129124	+	0.223649i
$189$	−3.89832	+	13.1834i	−0.283561	+	0.958954i
$190$	19.1154			1.38678
$191$	1.58599	+	0.915669i	0.114758	+	0.0662555i	0.556280	−	0.830995i	$-0.312228\pi$
$191$	1.58599	+	0.915669i	0.114758	+	0.0662555i	−0.441522	+	0.897250i	$0.645561\pi$
$192$	0.459307	+	1.67004i	0.0331476	+	0.120525i
$193$	−0.833264	−	1.44326i	−0.0599797	−	0.103888i	0.834476	−	0.551044i	$-0.185770\pi$
$193$	−0.833264	−	1.44326i	−0.0599797	−	0.103888i	−0.894456	+	0.447156i	$0.852437\pi$
$194$	−4.08013	−	7.06699i	−0.292936	−	0.507380i
$195$	14.3204	+	10.0947i	1.02551	+	0.722900i
$196$	4.03622	−	5.71917i	0.288302	−	0.408512i
$197$	7.33528	+	4.23502i	0.522617	+	0.301733i	0.738005	−	0.674796i	$-0.235768\pi$
$197$	7.33528	+	4.23502i	0.522617	+	0.301733i	−0.215388	+	0.976529i	$0.569102\pi$
$198$	−6.84316	−	3.83150i	−0.486322	−	0.272293i
$199$		−	17.9221i		−	1.27046i	−0.772321	−	0.635232i	$-0.780904\pi$
$199$		−	17.9221i		−	1.27046i	0.772321	−	0.635232i	$-0.219096\pi$
$200$	−2.48656	−	1.43561i	−0.175826	−	0.101513i
$201$	−12.0901	+	12.2506i	−0.852771	+	0.864090i
$202$	−4.24601	+	2.45144i	−0.298748	+	0.172482i
$203$	−0.821640	+	18.0522i	−0.0576678	+	1.26702i
$204$	−2.12560	−	7.72868i	−0.148822	−	0.541116i
$205$	−6.22644			−0.434874
$206$	−1.66288	−	2.88019i	−0.115858	−	0.200672i
$207$	−8.14408	−	13.6860i	−0.566053	−	0.951244i
$208$	−0.591455	−	3.55671i	−0.0410100	−	0.246613i
$209$	17.8119			1.23207
$210$	−3.80790	+	12.2799i	−0.262770	+	0.847393i
$211$	−11.6075	+	20.1047i	−0.799091	+	1.38407i	0.121118	+	0.992638i	$0.461352\pi$
$211$	−11.6075	+	20.1047i	−0.799091	+	1.38407i	−0.920209	+	0.391428i	$0.871981\pi$
$212$	9.16567	+	5.29180i	0.629501	+	0.363442i
$213$	−6.94822	−	6.85721i	−0.476084	−	0.469848i
$214$	−0.930416			−0.0636019
$215$	−10.2970	+	17.8350i	−0.702251	+	1.21633i
$216$	−3.60085	+	3.74618i	−0.245007	+	0.254895i
$217$	−0.828446	+	18.2017i	−0.0562385	+	1.23561i
$218$	9.69317	+	5.59636i	0.656504	+	0.379033i
$219$	−0.891871	+	3.41849i	−0.0602670	+	0.231000i
$220$	−6.35185	−	3.66724i	−0.428242	−	0.247246i
$221$	2.73716	+	16.4599i	0.184121	+	1.10721i
$222$	1.66028	−	0.456624i	0.111431	−	0.0306466i
$223$	−8.50389	−	4.90972i	−0.569462	−	0.328779i	0.187472	−	0.982270i	$-0.439971\pi$
$223$	−8.50389	−	4.90972i	−0.569462	−	0.328779i	−0.756935	+	0.653491i	$0.773304\pi$
$224$	2.34907	−	1.21733i	0.156954	−	0.0813362i
$225$	−0.113567	−	8.61294i	−0.00757115	−	0.574196i
$226$	1.12636	+	1.95091i	0.0749243	+	0.129773i
$227$	20.0199			1.32877			0.664383	−	0.747392i	$-0.268694\pi$
$227$	20.0199			1.32877			0.664383	+	0.747392i	$0.268694\pi$
$228$	2.97913	−	11.4189i	0.197298	−	0.756233i
$229$	23.6469	−	13.6525i	1.56263	−	0.902185i	0.565641	−	0.824651i	$-0.308629\pi$
$229$	23.6469	−	13.6525i	1.56263	−	0.902185i	0.996990	−	0.0775340i	$-0.0247046\pi$
$230$	−7.44686	−	12.8983i	−0.491031	−	0.850491i
$231$	−3.54824	+	11.4425i	−0.233457	+	0.752863i
$232$	−3.41508	+	5.91509i	−0.224211	+	0.388345i
$233$	20.1926	−	11.6582i	1.32286	−	0.763754i	0.338677	−	0.940903i	$-0.390021\pi$
$233$	20.1926	−	11.6582i	1.32286	−	0.763754i	0.984184	+	0.177149i	$0.0566874\pi$
$234$	8.26209	−	6.98125i	0.540110	−	0.456378i
$235$	−4.96714	+	8.60335i	−0.324021	+	0.561220i
$236$	3.06017			0.199200
$237$	−0.347174	+	0.351781i	−0.0225513	+	0.0228507i
$238$	−10.8711	+	5.63360i	−0.704668	+	0.365172i
$239$		−	12.6283i		−	0.816854i	−0.912791	−	0.408427i	$-0.866077\pi$
$239$		−	12.6283i		−	0.816854i	0.912791	−	0.408427i	$-0.133923\pi$
$240$	−3.41338	+	3.45869i	−0.220333	+	0.223257i
$241$			10.6208i			0.684143i	0.939674	+	0.342072i	$0.111129\pi$
$241$			10.6208i			0.684143i	−0.939674	+	0.342072i	$0.888871\pi$
$242$	3.60756	+	2.08282i	0.231903	+	0.133889i
$243$	−15.1821	−	3.53617i	−0.973931	−	0.226845i
$244$	10.3394	+	5.96948i	0.661915	+	0.382157i
$245$	19.5578	+	1.78403i	1.24950	+	0.113977i
$246$	−0.970392	+	3.71946i	−0.0618699	+	0.237144i
$247$	−8.62667	+	23.0014i	−0.548902	+	1.46355i
$248$	−3.44336	+	5.96408i	−0.218654	+	0.378720i
$249$	−0.408354	−	1.48478i	−0.0258784	−	0.0940938i
$250$			5.97242i			0.377729i
$251$	10.7007	+	18.5341i	0.675421	+	1.16986i	0.976346	+	0.216216i	$0.0693716\pi$
$251$	10.7007	+	18.5341i	0.675421	+	1.16986i	−0.300924	+	0.953648i	$0.597295\pi$
$252$	6.74212	+	4.18853i	0.424714	+	0.263853i
$253$	−6.93906	−	12.0188i	−0.436255	−	0.755615i
$254$	16.1591	+	9.32949i	1.01392	+	0.585384i
$255$	15.7966	−	16.0062i	0.989220	−	1.00235i
$256$	1.00000			0.0625000
$257$	17.3366			1.08143			0.540714	−	0.841207i	$-0.318154\pi$
$257$	17.3366			1.08143			0.540714	+	0.841207i	$0.318154\pi$
$258$	9.04920	+	8.93066i	0.563378	+	0.555999i
$259$	−1.21022	−	2.33534i	−0.0751991	−	0.145111i
$260$	7.81204	−	6.42636i	0.484482	−	0.398546i
$261$	−20.4887	+	0.270157i	−1.26822	+	0.0167223i
$262$	13.1698	−	7.60360i	0.813634	−	0.469752i
$263$	19.8632	−	11.4680i	1.22482	−	0.707148i	0.258875	−	0.965911i	$-0.416648\pi$
$263$	19.8632	−	11.4680i	1.22482	−	0.707148i	0.965941	+	0.258763i	$0.0833148\pi$
$264$	−3.18062	+	3.22284i	−0.195754	+	0.198352i
$265$			29.6931i			1.82403i
$266$	−18.0078	−	0.819620i	−1.10413	−	0.0502541i
$267$	6.65765	+	24.2072i	0.407441	+	1.48146i
$268$	4.96864	+	8.60593i	0.303508	+	0.525691i
$269$	−32.1180			−1.95827			−0.979134	−	0.203215i	$-0.934861\pi$
$269$	−32.1180			−1.95827			−0.979134	+	0.203215i	$0.934861\pi$
$270$	−14.1533	−	3.49390i	−0.861342	−	0.212632i
$271$		−	9.27251i		−	0.563265i	−0.959522	−	0.281633i	$-0.909124\pi$
$271$		−	9.27251i		−	0.563265i	0.959522	−	0.281633i	$-0.0908759\pi$
$272$	−4.62784			−0.280604
$273$	−13.0578	−	10.1239i	−0.790296	−	0.612725i
$274$	−10.3994			−0.628251
$275$		−	7.50614i		−	0.452637i
$276$	−8.86562	+	2.43829i	−0.533647	+	0.146768i
$277$	−9.85253			−0.591981			−0.295991	−	0.955191i	$-0.595650\pi$
$277$	−9.85253			−0.591981			−0.295991	+	0.955191i	$0.595650\pi$
$278$	−5.17647	−	8.96591i	−0.310464	−	0.537739i
$279$	−20.6584	+	0.272395i	−1.23679	+	0.0163078i
$280$	6.25297	+	3.99987i	0.373687	+	0.239038i
$281$		−	8.70642i		−	0.519381i	−0.965692	−	0.259691i	$-0.916379\pi$
$281$		−	8.70642i		−	0.519381i	0.965692	−	0.259691i	$-0.0836206\pi$
$282$	4.36521	+	4.30803i	0.259945	+	0.256540i
$283$	−11.0728	+	6.39288i	−0.658210	+	0.380017i	−0.791594	−	0.611047i	$-0.790749\pi$
$283$	−11.0728	+	6.39288i	−0.658210	+	0.380017i	0.133385	+	0.991064i	$0.457415\pi$
$284$	−4.88106	+	2.81808i	−0.289638	+	0.167222i
$285$	31.9235	−	8.77983i	1.89098	−	0.520072i
$286$	7.27933	−	5.98814i	0.430436	−	0.354086i
$287$	5.86568	+	0.266974i	0.346240	+	0.0157590i
$288$	1.53412	+	2.57807i	0.0903991	+	0.151914i
$289$	4.41687			0.259816
$290$	−19.1625			−1.12526
$291$	−10.0599	−	9.92812i	−0.589722	−	0.581997i
$292$	1.76646	+	1.01987i	0.103374	+	0.0596832i
$293$	−6.42265	−	11.1244i	−0.375215	−	0.649892i	0.615144	−	0.788415i	$-0.289098\pi$
$293$	−6.42265	−	11.1244i	−0.375215	−	0.649892i	−0.990359	+	0.138523i	$0.955765\pi$
$294$	4.11380	−	11.4051i	0.239922	−	0.665160i
$295$	4.29276	+	7.43527i	0.249934	+	0.432898i
$296$		−	0.994157i		−	0.0577842i
$297$	−13.1882	−	3.25565i	−0.765256	−	0.188912i
$298$	−9.41056	+	16.2996i	−0.545139	+	0.944209i
$299$	18.8812	−	3.13981i	1.09193	−	0.181580i
$300$	−4.81204	−	1.25544i	−0.277823	−	0.0724829i
$301$	10.4651	−	16.3601i	0.603200	−	0.942979i
$302$	−18.7215	−	10.8089i	−1.07730	−	0.621980i
$303$	−5.96505	+	6.04422i	−0.342683	+	0.347231i
$304$	−5.90055	−	3.40668i	−0.338420	−	0.195387i
$305$			33.4956i			1.91795i
$306$	−7.09967	−	11.9309i	−0.405861	−	0.682044i
$307$		−	17.8915i		−	1.02112i	−0.859842	−	0.510561i	$-0.829438\pi$
$307$		−	17.8915i		−	1.02112i	0.859842	−	0.510561i	$-0.170562\pi$
$308$	5.82658	+	3.72712i	0.332000	+	0.212372i
$309$	−4.09997	−	4.04626i	−0.233239	−	0.230184i
$310$	−19.3212			−1.09737
$311$	12.1246	−	21.0005i	0.687524	−	1.19083i	−0.285112	−	0.958494i	$-0.592031\pi$
$311$	12.1246	−	21.0005i	0.687524	−	1.19083i	0.972636	−	0.232333i	$-0.0746359\pi$
$312$	−2.62138	−	5.66819i	−0.148406	−	0.320898i
$313$	−24.7522	+	14.2907i	−1.39908	+	0.807757i	−0.994296	−	0.106657i	$-0.965985\pi$
$313$	−24.7522	+	14.2907i	−1.39908	+	0.807757i	−0.404780	+	0.914414i	$0.632652\pi$
$314$	2.56155	−	4.43673i	0.144557	−	0.250379i
$315$	−0.719112	+	22.2569i	−0.0405174	+	1.25404i
$316$	0.142677	+	0.247123i	0.00802619	+	0.0139018i
$317$	4.70911	−	2.71880i	0.264490	−	0.152703i	−0.361891	−	0.932220i	$-0.617869\pi$
$317$	4.70911	−	2.71880i	0.264490	−	0.152703i	0.626381	+	0.779517i	$0.284535\pi$
$318$	17.7376	+	4.62767i	0.994676	+	0.259507i
$319$	−17.8558			−0.999733
$320$	1.40279	+	2.42970i	0.0784181	+	0.135824i
$321$	−1.55383	+	0.427347i	−0.0867265	+	0.0238522i
$322$	6.46234	+	12.4703i	0.360132	+	0.694943i
$323$	27.3068	+	15.7656i	1.51939	+	0.877220i
$324$	−4.29293	+	7.91017i	−0.238496	+	0.439454i
$325$	9.69306	+	3.63538i	0.537674	+	0.201654i
$326$	−15.0975	−	8.71655i	−0.836173	−	0.482765i
$327$	18.7584	+	4.89400i	1.03734	+	0.270639i
$328$	1.92198	+	1.10966i	0.106124	+	0.0612706i
$329$	5.04824	−	7.89189i	0.278318	−	0.435094i
$330$	−12.2922	−	3.20700i	−0.676666	−	0.176539i
$331$	−12.9713	+	22.4670i	−0.712969	+	1.23490i	0.250769	+	0.968047i	$0.419317\pi$
$331$	−12.9713	+	22.4670i	−0.712969	+	1.23490i	−0.963738	+	0.266851i	$0.914017\pi$
$332$	−0.889066			−0.0487938
$333$	2.56301	−	1.52516i	0.140452	−	0.0835783i
$334$	−3.38455	−	1.95407i	−0.185194	−	0.106922i
$335$	−13.9399	+	24.1445i	−0.761616	+	1.31916i
$336$	3.36391	−	3.11193i	0.183516	−	0.169770i
$337$	14.7253			0.802138			0.401069	−	0.916048i	$-0.368639\pi$
$337$	14.7253			0.802138			0.401069	+	0.916048i	$0.368639\pi$
$338$	4.20727	+	12.3004i	0.228845	+	0.669051i
$339$	2.77713	+	2.74076i	0.150833	+	0.148858i
$340$	−6.49186	−	11.2442i	−0.352071	−	0.609804i
$341$	−18.0037			−0.974955
$342$	−0.269493	−	20.4383i	−0.0145725	−	1.10518i
$343$	−18.3481	−	2.51925i	−0.990705	−	0.136027i
$344$	6.35698	−	3.67020i	0.342745	−	0.197884i
$345$	−18.3609	−	18.1204i	−0.988515	−	0.975567i
$346$	−5.78620	−	3.34066i	−0.311068	−	0.179595i
$347$			31.6862i			1.70100i	0.525974	+	0.850501i	$0.323701\pi$
$347$			31.6862i			1.70100i	−0.525974	+	0.850501i	$0.676299\pi$
$348$	−2.98648	+	11.4470i	−0.160092	+	0.613624i
$349$	6.37536	+	3.68081i	0.341265	+	0.197029i	0.660831	−	0.750534i	$-0.270204\pi$
$349$	6.37536	+	3.68081i	0.341265	+	0.197029i	−0.319566	+	0.947564i	$0.603537\pi$
$350$	−0.345397	+	7.58870i	−0.0184623	+	0.405633i
$351$	10.5915	−	15.4538i	0.565332	−	0.824863i
$352$	1.30713	+	2.26401i	0.0696702	+	0.120672i
$353$	−6.54568	−	11.3375i	−0.348391	−	0.603432i	0.637572	−	0.770390i	$-0.279939\pi$
$353$	−6.54568	−	11.3375i	−0.348391	−	0.603432i	−0.985964	+	0.166959i	$0.946605\pi$
$354$	5.11060	−	1.40556i	0.271626	−	0.0747045i
$355$	−13.6942	−	7.90633i	−0.726811	−	0.419625i
$356$	14.4950			0.768232
$357$	−15.5676	+	14.4015i	−0.823926	+	0.762209i
$358$	−4.06966	−	7.04886i	−0.215088	−	0.372544i
$359$	−4.73978	+	2.73651i	−0.250156	+	0.144428i	−0.619836	−	0.784732i	$-0.712801\pi$
$359$	−4.73978	+	2.73651i	−0.250156	+	0.144428i	0.369680	+	0.929159i	$0.379467\pi$
$360$	−4.11189	+	7.34394i	−0.216716	+	0.387060i
$361$	13.7110	+	23.7481i	0.721630	+	1.24990i
$362$	14.2577			0.749370
$363$	6.98143	+	1.82142i	0.366430	+	0.0956000i
$364$	−7.63495	+	5.71905i	−0.400180	+	0.299760i
$365$			5.72262i			0.299535i
$366$	20.0091	+	5.22029i	1.04589	+	0.272869i
$367$	−5.03630	+	2.90771i	−0.262893	+	0.151781i	−0.625654	−	0.780101i	$-0.715168\pi$
$367$	−5.03630	+	2.90771i	−0.262893	+	0.151781i	0.362761	+	0.931882i	$0.381834\pi$
$368$			5.30862i			0.276731i
$369$	0.0877818	+	6.65736i	0.00456974	+	0.346568i
$370$	2.41550	−	1.39459i	0.125576	−	0.0725012i
$371$	1.27316	−	27.9726i	0.0660994	−	1.45227i
$372$	−3.01121	+	11.5418i	−0.156124	+	0.598416i
$373$	6.30605	−	10.9224i	0.326515	−	0.565541i	−0.655303	−	0.755366i	$-0.727459\pi$
$373$	6.30605	−	10.9224i	0.326515	−	0.565541i	0.981818	+	0.189826i	$0.0607923\pi$
$374$	−6.04918	−	10.4775i	−0.312796	−	0.541778i
$375$	2.74318	+	9.97418i	0.141657	+	0.515065i
$376$	3.06652	−	1.77046i	0.158144	−	0.0913044i
$377$	8.64793	−	23.0581i	0.445391	−	1.18755i
$378$	13.1834	+	3.89832i	0.678083	+	0.200508i
$379$	5.50295	−	9.53139i	0.282668	−	0.489595i	−0.689373	−	0.724406i	$-0.742114\pi$
$379$	5.50295	−	9.53139i	0.282668	−	0.489595i	0.972041	+	0.234812i	$0.0754473\pi$
$380$		−	19.1154i		−	0.980598i
$381$	31.2715	+	8.15861i	1.60209	+	0.417978i
$382$	0.915669	−	1.58599i	0.0468497	−	0.0811461i
$383$	−11.0996	+	19.2251i	−0.567164	+	0.982356i	0.429681	+	0.902981i	$0.358626\pi$
$383$	−11.0996	+	19.2251i	−0.567164	+	0.982356i	−0.996845	+	0.0793756i	$0.974707\pi$
$384$	1.67004	−	0.459307i	0.0852239	−	0.0234389i
$385$	−0.882309	+	19.3852i	−0.0449667	+	0.987960i
$386$	−1.44326	+	0.833264i	−0.0734598	+	0.0424120i
$387$	19.2144	+	10.7582i	0.976725	+	0.546871i
$388$	−7.06699	+	4.08013i	−0.358772	+	0.207137i
$389$	8.80457	+	5.08332i	0.446409	+	0.257735i	0.706313	−	0.707900i	$-0.250357\pi$
$389$	8.80457	+	5.08332i	0.446409	+	0.257735i	−0.259903	+	0.965635i	$0.583691\pi$
$390$	10.0947	−	14.3204i	0.511168	−	0.725142i
$391$		−	24.5674i		−	1.24243i
$392$	−5.71917	−	4.03622i	−0.288862	−	0.203860i
$393$	18.5018	−	18.7473i	0.933290	−	0.945677i
$394$	4.23502	−	7.33528i	0.213357	−	0.369546i
$395$	−0.400290	+	0.693322i	−0.0201408	+	0.0348848i
$396$	−3.83150	+	6.84316i	−0.192540	+	0.343882i
$397$	23.3862	+	13.5020i	1.17372	+	0.677647i	0.954553	−	0.298041i	$-0.0963331\pi$
$397$	23.3862	+	13.5020i	1.17372	+	0.677647i	0.219166	+	0.975688i	$0.429666\pi$
$398$	−17.9221			−0.898354
$399$	−30.4503	+	6.90233i	−1.52442	+	0.345548i
$400$	−1.43561	+	2.48656i	−0.0717807	+	0.124328i
$401$			17.6521i			0.881506i	0.897628	+	0.440753i	$0.145289\pi$
$401$			17.6521i			0.881506i	−0.897628	+	0.440753i	$0.854711\pi$
$402$	12.2506	+	12.0901i	0.611004	+	0.603001i
$403$	8.71956	−	23.2491i	0.434352	−	1.15812i
$404$	2.45144	+	4.24601i	0.121963	+	0.211247i
$405$	−25.2414	+	0.665764i	−1.25425	+	0.0330821i
$406$	18.0522	+	0.821640i	0.895916	+	0.0407773i
$407$	2.25079	−	1.29949i	0.111567	−	0.0644134i
$408$	−7.72868	+	2.12560i	−0.382626	+	0.105233i
$409$		−	31.3317i		−	1.54925i	−0.632419	−	0.774626i	$-0.717938\pi$
$409$		−	31.3317i		−	1.54925i	0.632419	−	0.774626i	$-0.282062\pi$
$410$			6.22644i			0.307502i
$411$	−17.3674	+	4.77652i	−0.856672	+	0.235608i
$412$	−2.88019	+	1.66288i	−0.141897	+	0.0819242i
$413$	−3.72523	−	7.18853i	−0.183306	−	0.353725i
$414$	−13.6860	+	8.14408i	−0.672631	+	0.400260i
$415$	−1.24717	−	2.16016i	−0.0612211	−	0.106038i
$416$	−3.55671	+	0.591455i	−0.174382	+	0.0289985i
$417$	−12.7630	−	12.5958i	−0.625008	−	0.616821i
$418$		−	17.8119i		−	0.871208i
$419$	−19.9157	+	34.4951i	−0.972948	+	1.68520i	−0.286400	+	0.958110i	$0.592459\pi$
$419$	−19.9157	+	34.4951i	−0.972948	+	1.68520i	−0.686547	+	0.727085i	$0.740875\pi$
$420$	12.2799	+	3.80790i	0.599197	+	0.185807i
$421$	−15.2089			−0.741237			−0.370618	−	0.928785i	$-0.620854\pi$
$421$	−15.2089			−0.741237			−0.370618	+	0.928785i	$0.620854\pi$
$422$	20.1047	+	11.6075i	0.978683	+	0.565043i
$423$	9.26880	+	5.18962i	0.450664	+	0.252328i
$424$	5.29180	−	9.16567i	0.256993	−	0.445124i
$425$	6.64379	−	11.5074i	0.322271	−	0.558190i
$426$	−6.85721	+	6.94822i	−0.332233	+	0.336642i
$427$	1.43621	−	31.5548i	0.0695030	−	1.52705i
$428$			0.930416i			0.0449734i
$429$	9.40639	−	13.3439i	0.454145	−	0.644249i
$430$	17.8350	+	10.2970i	0.860078	+	0.496566i
$431$	−6.35131	+	3.66693i	−0.305932	+	0.176630i	−0.645105	−	0.764094i	$-0.723186\pi$
$431$	−6.35131	+	3.66693i	−0.305932	+	0.176630i	0.339173	+	0.940724i	$0.389853\pi$
$432$	3.74618	+	3.60085i	0.180238	+	0.173246i
$433$	10.9441	−	6.31856i	0.525938	−	0.303650i	−0.213423	−	0.976960i	$-0.568461\pi$
$433$	10.9441	−	6.31856i	0.525938	−	0.303650i	0.739361	+	0.673310i	$0.235128\pi$
$434$	18.2017	+	0.828446i	0.873711	+	0.0397667i
$435$	−32.0021	+	8.80147i	−1.53439	+	0.421998i
$436$	5.59636	−	9.69317i	0.268017	−	0.464219i
$437$	18.0848	−	31.3238i	0.865113	−	1.49842i
$438$	3.41849	+	0.891871i	0.163342	+	0.0426152i
$439$			8.78405i			0.419240i	0.977783	+	0.209620i	$0.0672227\pi$
$439$			8.78405i			0.419240i	−0.977783	+	0.209620i	$0.932777\pi$
$440$	−3.66724	+	6.35185i	−0.174829	+	0.302813i
$441$	1.63177	−	20.9365i	0.0777032	−	0.996977i
$442$	16.4599	−	2.73716i	0.782916	−	0.130193i
$443$	24.2732	−	14.0141i	1.15325	−	0.665831i	0.203575	−	0.979059i	$-0.434744\pi$
$443$	24.2732	−	14.0141i	1.15325	−	0.665831i	0.949678	+	0.313229i	$0.101411\pi$
$444$	−0.456624	−	1.66028i	−0.0216704	−	0.0787936i
$445$	20.3333	+	35.2184i	0.963893	+	1.66951i
$446$	−4.90972	+	8.50389i	−0.232482	+	0.402671i
$447$	−8.22951	+	31.5433i	−0.389243	+	1.49195i
$448$	−1.21733	−	2.34907i	−0.0575134	−	0.110983i
$449$	8.81604	−	5.08994i	0.416055	−	0.240209i	−0.277333	−	0.960774i	$-0.589451\pi$
$449$	8.81604	−	5.08994i	0.416055	−	0.240209i	0.693388	+	0.720565i	$0.256117\pi$
$450$	−8.61294	+	0.113567i	−0.406018	+	0.00535361i
$451$			5.80186i			0.273199i
$452$	1.95091	−	1.12636i	0.0917632	−	0.0529795i
$453$	−36.2302	−	9.45231i	−1.70224	−	0.444108i
$454$		−	20.0199i		−	0.939579i
$455$	−24.6057	−	10.5280i	−1.15354	−	0.493561i
$456$	−11.4189	−	2.97913i	−0.534737	−	0.139511i
$457$	3.23701			0.151421			0.0757105	−	0.997130i	$-0.475878\pi$
$457$	3.23701			0.151421			0.0757105	+	0.997130i	$0.475878\pi$
$458$	−13.6525	−	23.6469i	−0.637941	−	1.10495i
$459$	−17.3367	−	16.6642i	−0.809208	−	0.777817i
$460$	−12.8983	+	7.44686i	−0.601388	+	0.347212i
$461$	−10.6827	−	18.5030i	−0.497545	−	0.861773i	0.502451	−	0.864606i	$-0.332432\pi$
$461$	−10.6827	−	18.5030i	−0.497545	−	0.861773i	−0.999996	+	0.00283284i	$0.999098\pi$
$462$	11.4425	+	3.54824i	0.532354	+	0.165079i
$463$	5.12785			0.238311			0.119156	−	0.992876i	$-0.461981\pi$
$463$	5.12785			0.238311			0.119156	+	0.992876i	$0.461981\pi$
$464$	5.91509	+	3.41508i	0.274601	+	0.158541i
$465$	−32.2672	+	8.87437i	−1.49636	+	0.411539i
$466$	−11.6582	−	20.1926i	−0.540056	−	0.935404i
$467$	6.23453	+	10.7985i	0.288500	+	0.499696i	0.973452	−	0.228892i	$-0.0735102\pi$
$467$	6.23453	+	10.7985i	0.288500	+	0.499696i	−0.684952	+	0.728588i	$0.740177\pi$
$468$	−6.98125	−	8.26209i	−0.322708	−	0.381915i
$469$	14.1674	−	22.1479i	0.654191	−	1.02269i
$470$	8.60335	+	4.96714i	0.396843	+	0.229117i
$471$	2.24007	−	8.58607i	0.103217	−	0.395625i
$472$		−	3.06017i		−	0.140856i
$473$	16.6188	+	9.59486i	0.764133	+	0.441172i
$474$	0.351781	+	0.347174i	0.0161579	+	0.0159462i
$475$	16.9418	−	9.78136i	0.777344	−	0.448800i
$476$	5.63360	+	10.8711i	0.258215	+	0.498276i
$477$	31.7481	−	0.418619i	1.45364	−	0.0191673i
$478$	−12.6283			−0.577603
$479$	0.150493	+	0.260661i	0.00687619	+	0.0119099i	0.869443	−	0.494033i	$-0.164478\pi$
$479$	0.150493	+	0.260661i	0.00687619	+	0.0119099i	−0.862567	+	0.505943i	$0.831145\pi$
$480$	3.45869	+	3.41338i	0.157867	+	0.155799i
$481$	0.587999	+	3.53593i	0.0268105	+	0.161224i
$482$	10.6208			0.483762
$483$	16.5201	+	17.8577i	0.751689	+	0.812554i
$484$	2.08282	−	3.60756i	0.0946738	−	0.163980i
$485$	−19.8269	−	11.4471i	−0.900295	−	0.519785i
$486$	−3.53617	+	15.1821i	−0.160404	+	0.688673i
$487$	30.7914			1.39529			0.697646	−	0.716442i	$-0.254231\pi$
$487$	30.7914			1.39529			0.697646	+	0.716442i	$0.254231\pi$
$488$	5.96948	−	10.3394i	0.270226	−	0.468045i
$489$	−29.2170	−	7.62260i	−1.32124	−	0.344706i
$490$	1.78403	−	19.5578i	0.0805942	−	0.883531i
$491$	−3.83785	−	2.21578i	−0.173200	−	0.0999968i	0.410894	−	0.911683i	$-0.365217\pi$
$491$	−3.83785	−	2.21578i	−0.173200	−	0.0999968i	−0.584094	+	0.811686i	$0.698550\pi$
$492$	3.71946	+	0.970392i	0.167686	+	0.0437487i
$493$	−27.3741	−	15.8044i	−1.23287	−	0.711795i
$494$	23.0014	+	8.62667i	1.03488	+	0.388132i
$495$	−22.0016	+	0.290105i	−0.988896	+	0.0130393i
$496$	5.96408	+	3.44336i	0.267795	+	0.154612i
$497$	12.5617	+	8.03541i	0.563470	+	0.360437i
$498$	−1.48478	+	0.408354i	−0.0665344	+	0.0182988i
$499$	−6.28345	−	10.8833i	−0.281286	−	0.487201i	0.690416	−	0.723413i	$-0.257428\pi$
$499$	−6.28345	−	10.8833i	−0.281286	−	0.487201i	−0.971702	+	0.236211i	$0.924094\pi$
$500$	5.97242			0.267095
$501$	−6.54986	−	1.70883i	−0.292626	−	0.0763449i
$502$	18.5341	−	10.7007i	0.827219	−	0.477595i
$503$	2.69186	+	4.66244i	0.120024	+	0.207888i	0.919777	−	0.392441i	$-0.128369\pi$
$503$	2.69186	+	4.66244i	0.120024	+	0.207888i	−0.799753	+	0.600329i	$0.795036\pi$
$504$	4.18853	−	6.74212i	0.186572	−	0.300318i
$505$	−6.87768	+	11.9125i	−0.306053	+	0.530099i
$506$	−12.0188	+	6.93906i	−0.534301	+	0.308479i
$507$	12.6760	+	18.6097i	0.562959	+	0.826485i
$508$	9.32949	−	16.1591i	0.413929	−	0.716946i
$509$	−32.3642			−1.43452			−0.717258	−	0.696807i	$-0.754603\pi$
$509$	−32.3642			−1.43452			−0.717258	+	0.696807i	$0.754603\pi$
$510$	−16.0062	−	15.7966i	−0.708768	−	0.699484i
$511$	0.245372	−	5.39105i	0.0108546	−	0.238486i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.83753	−	34.0090i	−0.434338	−	1.50154i
$514$		−	17.3366i		−	0.764684i
$515$	−8.08058	−	4.66533i	−0.356073	−	0.205579i
$516$	8.93066	−	9.04920i	0.393151	−	0.398369i
$517$	8.01668	+	4.62843i	0.352573	+	0.203558i
$518$	−2.33534	+	1.21022i	−0.102609	+	0.0531738i
$519$	−11.1976	−	2.92140i	−0.491519	−	0.128235i
$520$	−6.42636	−	7.81204i	−0.281814	−	0.342580i
$521$	−20.4045	+	35.3416i	−0.893936	+	1.54834i	−0.0588209	+	0.998269i	$0.518734\pi$
$521$	−20.4045	+	35.3416i	−0.893936	+	1.54834i	−0.835115	+	0.550075i	$0.814599\pi$
$522$	0.270157	+	20.4887i	0.0118245	+	0.896766i
$523$		−	0.665987i		−	0.0291216i	−0.999894	−	0.0145608i	$-0.995365\pi$
$523$		−	0.665987i		−	0.0291216i	0.999894	−	0.0145608i	$-0.00463501\pi$
$524$	−7.60360	−	13.1698i	−0.332165	−	0.575326i
$525$	2.90872	+	12.8321i	0.126947	+	0.560038i
$526$	−11.4680	−	19.8632i	−0.500029	−	0.866076i
$527$	−27.6008	−	15.9353i	−1.20231	−	0.694154i
$528$	3.22284	+	3.18062i	0.140256	+	0.138419i
$529$	−5.18147			−0.225281
$530$	29.6931			1.28978
$531$	7.88934	−	4.69468i	0.342368	−	0.203732i
$532$	−0.819620	+	18.0078i	−0.0355350	+	0.780738i
$533$	−7.49224	−	2.80996i	−0.324525	−	0.121713i
$534$	24.2072	−	6.65765i	1.04755	−	0.288105i
$535$	−2.26063	+	1.30517i	−0.0977355	+	0.0564276i
$536$	8.60593	−	4.96864i	0.371719	−	0.214612i
$537$	−10.0341	−	9.90266i	−0.433003	−	0.427331i
$538$			32.1180i			1.38470i
$539$	1.66238	−	18.2242i	0.0716036	−	0.784970i
$540$	−3.49390	+	14.1533i	−0.150353	+	0.609061i
$541$	−8.21186	−	14.2234i	−0.353056	−	0.611510i	0.633728	−	0.773556i	$-0.281524\pi$
$541$	−8.21186	−	14.2234i	−0.353056	−	0.611510i	−0.986783	+	0.162046i	$0.948191\pi$
$542$	−9.27251			−0.398289
$543$	23.8110	−	6.54869i	1.02183	−	0.281031i
$544$			4.62784i			0.198417i
$545$	31.4019			1.34511
$546$	−10.1239	+	13.0578i	−0.433262	+	0.558824i
$547$	−1.77847			−0.0760420			−0.0380210	−	0.999277i	$-0.512105\pi$
$547$	−1.77847			−0.0760420			−0.0380210	+	0.999277i	$0.512105\pi$
$548$			10.3994i			0.444240i
$549$	35.8138	−	0.472228i	1.52849	−	0.0201542i
$550$	−7.50614			−0.320063
$551$	−23.2682	−	40.3017i	−0.991258	−	1.71691i
$552$	2.43829	+	8.86562i	0.103780	+	0.377346i
$553$	0.406825	−	0.635987i	0.0172999	−	0.0270449i
$554$			9.85253i			0.418594i
$555$	3.39344	−	3.43848i	0.144043	−	0.145955i
$556$	−8.96591	+	5.17647i	−0.380239	+	0.219531i
$557$	23.4744	−	13.5530i	0.994644	−	0.574258i	0.0879848	−	0.996122i	$-0.471957\pi$
$557$	23.4744	−	13.5530i	0.994644	−	0.574258i	0.906659	+	0.421864i	$0.138624\pi$
$558$	0.272395	+	20.6584i	0.0115314	+	0.874539i
$559$	−20.4392	+	16.8137i	−0.864485	+	0.711144i
$560$	3.99987	−	6.25297i	0.169025	−	0.264236i
$561$	−14.9148	−	14.7194i	−0.629702	−	0.621454i
$562$	−8.70642			−0.367258
$563$	−27.1947			−1.14612			−0.573060	−	0.819514i	$-0.694244\pi$
$563$	−27.1947			−1.14612			−0.573060	+	0.819514i	$0.694244\pi$
$564$	4.30803	−	4.36521i	0.181401	−	0.183809i
$565$	5.47342	+	3.16008i	0.230269	+	0.132946i
$566$	6.39288	+	11.0728i	0.268713	+	0.465424i
$567$	23.8074	+	0.455098i	0.999817	+	0.0191123i
$568$	2.81808	+	4.88106i	0.118244	+	0.204805i
$569$			17.7169i			0.742732i	0.928487	+	0.371366i	$0.121110\pi$
$569$			17.7169i			0.742732i	−0.928487	+	0.371366i	$0.878890\pi$
$570$	−8.77983	−	31.9235i	−0.367747	−	1.33713i
$571$	−8.22208	+	14.2411i	−0.344083	+	0.595970i	−0.985187	−	0.171485i	$-0.945144\pi$
$571$	−8.22208	+	14.2411i	−0.344083	+	0.595970i	0.641103	+	0.767454i	$0.278477\pi$
$572$	−5.98814	−	7.27933i	−0.250377	−	0.304364i
$573$	0.800750	−	3.06923i	0.0334518	−	0.128219i
$574$	0.266974	−	5.86568i	0.0111433	−	0.244829i
$575$	−13.2002	−	7.62113i	−0.550486	−	0.317823i
$576$	2.57807	−	1.53412i	0.107420	−	0.0639218i
$577$	5.20953	+	3.00772i	0.216876	+	0.125213i	0.604503	−	0.796603i	$-0.293372\pi$
$577$	5.20953	+	3.00772i	0.216876	+	0.125213i	−0.387627	+	0.921816i	$0.626705\pi$
$578$		−	4.41687i		−	0.183717i
$579$	−2.02757	+	2.05448i	−0.0842630	+	0.0853814i
$580$			19.1625i			0.795679i
$581$	1.08228	+	2.08847i	0.0449007	+	0.0866445i
$582$	−9.92812	+	10.0599i	−0.411534	+	0.416996i
$583$	27.6683			1.14590
$584$	1.01987	−	1.76646i	0.0422024	−	0.0730967i
$585$	10.2812	−	28.5523i	0.425074	−	1.18049i
$586$	−11.1244	+	6.42265i	−0.459543	+	0.265317i
$587$	2.25980	−	3.91408i	0.0932718	−	0.161551i	−0.815614	−	0.578596i	$-0.803601\pi$
$587$	2.25980	−	3.91408i	0.0932718	−	0.161551i	0.908886	+	0.417045i	$0.136934\pi$
$588$	−11.4051	−	4.11380i	−0.470339	−	0.169650i
$589$	−23.4609	−	40.6355i	−0.966689	−	1.67435i
$590$	7.43527	−	4.29276i	0.306105	−	0.176730i
$591$	3.70352	−	14.1954i	0.152342	−	0.583920i
$592$	−0.994157			−0.0408596
$593$	−1.70266	−	2.94909i	−0.0699198	−	0.121105i	0.828946	−	0.559329i	$-0.188941\pi$
$593$	−1.70266	−	2.94909i	−0.0699198	−	0.121105i	−0.898866	+	0.438224i	$0.855608\pi$
$594$	−3.25565	+	13.1882i	−0.133581	+	0.541118i
$595$	−18.5107	+	28.9377i	−0.758866	+	1.18633i
$596$	16.2996	+	9.41056i	0.667657	+	0.385472i
$597$	−29.9307	+	8.23176i	−1.22498	+	0.336903i
$598$	−3.13981	−	18.8812i	−0.128396	−	0.772111i
$599$	−7.92694	−	4.57662i	−0.323886	−	0.186996i	0.329237	−	0.944247i	$-0.393208\pi$
$599$	−7.92694	−	4.57662i	−0.323886	−	0.186996i	−0.653123	+	0.757252i	$0.726542\pi$
$600$	−1.25544	+	4.81204i	−0.0512532	+	0.196451i
$601$	−27.4175	−	15.8295i	−1.11838	−	0.645699i	−0.177396	−	0.984140i	$-0.556767\pi$
$601$	−27.4175	−	15.8295i	−1.11838	−	0.645699i	−0.940988	+	0.338440i	$0.890101\pi$
$602$	−16.3601	−	10.4651i	−0.666787	−	0.426526i
$603$	26.0121	+	14.5642i	1.05929	+	0.593101i
$604$	−10.8089	+	18.7215i	−0.439806	+	0.761766i
$605$	11.6870			0.475145
$606$	6.04422	+	5.96505i	0.245530	+	0.242314i
$607$	21.4426	+	12.3799i	0.870329	+	0.502485i	0.867457	−	0.497511i	$-0.165753\pi$
$607$	21.4426	+	12.3799i	0.870329	+	0.502485i	0.00287125	+	0.999996i	$0.499086\pi$
$608$	−3.40668	+	5.90055i	−0.138159	+	0.239299i
$609$	30.5253	−	6.91934i	1.23695	−	0.280386i
$610$	33.4956			1.35620
$611$	−9.85958	+	8.11071i	−0.398876	+	0.328124i
$612$	−11.9309	+	7.09967i	−0.482278	+	0.286987i
$613$	4.91597	+	8.51471i	0.198554	+	0.343906i	0.948060	−	0.318092i	$-0.103042\pi$
$613$	4.91597	+	8.51471i	0.198554	+	0.343906i	−0.749506	+	0.661998i	$0.769709\pi$
$614$	−17.8915			−0.722042
$615$	2.85985	+	10.3984i	0.115320	+	0.419305i
$616$	3.72712	−	5.82658i	0.150170	−	0.234760i
$617$	30.7175	−	17.7348i	1.23664	−	0.713975i	0.268234	−	0.963354i	$-0.413560\pi$
$617$	30.7175	−	17.7348i	1.23664	−	0.713975i	0.968406	+	0.249379i	$0.0802265\pi$
$618$	−4.04626	+	4.09997i	−0.162765	+	0.164925i
$619$	−3.76659	−	2.17464i	−0.151392	−	0.0874062i	0.422390	−	0.906414i	$-0.361191\pi$
$619$	−3.76659	−	2.17464i	−0.151392	−	0.0874062i	−0.573782	+	0.819008i	$0.694524\pi$
$620$			19.3212i			0.775958i
$621$	−19.1156	+	19.8870i	−0.767082	+	0.798040i
$622$	−21.0005	−	12.1246i	−0.842042	−	0.486153i
$623$	−17.6451	−	34.0497i	−0.706938	−	1.36417i
$624$	−5.66819	+	2.62138i	−0.226909	+	0.104939i
$625$	15.5561	+	26.9439i	0.622244	+	1.07776i
$626$	14.2907	+	24.7522i	0.571170	+	0.989296i
$627$	−8.18114	−	29.7466i	−0.326723	−	1.18796i
$628$	−4.43673	−	2.56155i	−0.177045	−	0.102217i
$629$	4.60080			0.183446
$630$	22.2569	+	0.719112i	0.886737	+	0.0286501i
$631$	−13.5641	−	23.4938i	−0.539979	−	0.935272i	−0.998904	−	0.0467969i	$-0.985099\pi$
$631$	−13.5641	−	23.4938i	−0.539979	−	0.935272i	0.458925	−	0.888475i	$-0.348235\pi$
$632$	0.247123	−	0.142677i	0.00983004	−	0.00567537i
$633$	38.9071	+	10.1507i	1.54642	+	0.403454i
$634$	−2.71880	−	4.70911i	−0.107978	−	0.187023i
$635$	52.3491			2.07741
$636$	4.62767	−	17.7376i	0.183499	−	0.703342i
$637$	22.7287	+	10.9730i	0.900543	+	0.434768i
$638$			17.8558i			0.706918i
$639$	−8.26045	+	14.7534i	−0.326778	+	0.583635i
$640$	2.42970	−	1.40279i	0.0960422	−	0.0554500i
$641$			11.4364i			0.451711i	0.974161	+	0.225855i	$0.0725176\pi$
$641$			11.4364i			0.451711i	−0.974161	+	0.225855i	$0.927482\pi$
$642$	0.427347	+	1.55383i	0.0168660	+	0.0613249i
$643$	24.5334	−	14.1644i	0.967503	−	0.558588i	0.0690290	−	0.997615i	$-0.478010\pi$
$643$	24.5334	−	14.1644i	0.967503	−	0.558588i	0.898474	+	0.439026i	$0.144677\pi$
$644$	12.4703	−	6.46234i	0.491399	−	0.254652i
$645$	34.5146	+	9.00471i	1.35901	+	0.354560i
$646$	15.7656	−	27.3068i	0.620288	−	1.07437i
$647$	−15.4825	−	26.8165i	−0.608680	−	1.05426i	−0.991458	−	0.130424i	$-0.958366\pi$
$647$	−15.4825	−	26.8165i	−0.608680	−	1.05426i	0.382778	−	0.923840i	$-0.374967\pi$
$648$	7.91017	+	4.29293i	0.310741	+	0.168642i
$649$	6.92826	−	4.00003i	0.271958	−	0.157015i
$650$	3.63538	−	9.69306i	0.142591	−	0.380193i
$651$	30.7781	−	6.97665i	1.20629	−	0.273436i
$652$	−8.71655	+	15.0975i	−0.341366	+	0.591264i
$653$			35.6088i			1.39348i	0.717324	+	0.696740i	$0.245367\pi$
$653$			35.6088i			1.39348i	−0.717324	+	0.696740i	$0.754633\pi$
$654$	4.89400	−	18.7584i	0.191370	−	0.733513i
$655$	21.3324	−	36.9489i	0.833527	−	1.44371i
$656$	1.10966	−	1.92198i	0.0433248	−	0.0750408i
$657$	6.11867	−	0.0806787i	0.238712	−	0.00314758i
$658$	−7.89189	−	5.04824i	−0.307658	−	0.196801i
$659$	15.6644	−	9.04383i	0.610197	−	0.352298i	−0.162845	−	0.986652i	$-0.552067\pi$
$659$	15.6644	−	9.04383i	0.610197	−	0.352298i	0.773043	+	0.634354i	$0.218734\pi$
$660$	−3.20700	+	12.2922i	−0.124832	+	0.478475i
$661$	−17.3239	+	10.0019i	−0.673820	+	0.389030i	−0.797522	−	0.603289i	$-0.793856\pi$
$661$	−17.3239	+	10.0019i	−0.673820	+	0.389030i	0.123703	+	0.992319i	$0.460523\pi$
$662$	22.4670	+	12.9713i	0.873205	+	0.504145i
$663$	26.2315	−	12.1313i	1.01875	−	0.471141i
$664$			0.889066i			0.0345024i
$665$	−44.9033	+	23.2697i	−1.74127	+	0.902360i
$666$	−1.52516	−	2.56301i	−0.0590988	−	0.0993146i
$667$	−18.1294	+	31.4010i	−0.701972	+	1.21585i
$668$	−1.95407	+	3.38455i	−0.0756053	+	0.130952i
$669$	−4.29354	+	16.4569i	−0.165998	+	0.636261i
$670$	24.1445	+	13.9399i	0.932785	+	0.538544i
$671$	31.2115			1.20491
$672$	−3.11193	−	3.36391i	−0.120045	−	0.129766i
$673$	13.8523	−	23.9928i	0.533966	−	0.924856i	−0.465247	−	0.885181i	$-0.654034\pi$
$673$	13.8523	−	23.9928i	0.533966	−	0.924856i	0.999213	−	0.0396751i	$-0.0126323\pi$
$674$		−	14.7253i		−	0.567197i
$675$	−14.3318	+	4.14565i	−0.551631	+	0.159566i
$676$	12.3004	−	4.20727i	0.473091	−	0.161818i
$677$	−13.8948	−	24.0666i	−0.534022	−	0.924953i	−0.999210	−	0.0397412i	$-0.987347\pi$
$677$	−13.8948	−	24.0666i	−0.534022	−	0.924953i	0.465188	−	0.885212i	$-0.345987\pi$
$678$	2.74076	−	2.77713i	0.105258	−	0.106655i
$679$	18.1873	+	11.6340i	0.697966	+	0.446471i
$680$	−11.2442	+	6.49186i	−0.431197	+	0.248952i
$681$	−9.19527	−	33.4340i	−0.352364	−	1.28119i
$682$			18.0037i			0.689397i
$683$		−	11.0755i		−	0.423792i	−0.977292	−	0.211896i	$-0.932036\pi$
$683$		−	11.0755i		−	0.423792i	0.977292	−	0.211896i	$-0.0679639\pi$
$684$	−20.4383	+	0.269493i	−0.781479	+	0.0103043i
$685$	−25.2674	+	14.5881i	−0.965417	+	0.557384i
$686$	−2.51925	+	18.3481i	−0.0961855	+	0.700534i
$687$	−33.6615	−	33.2206i	−1.28427	−	1.26744i
$688$	−3.67020	−	6.35698i	−0.139925	−	0.242358i
$689$	−13.4003	+	35.7295i	−0.510512	+	1.36119i
$690$	−18.1204	+	18.3609i	−0.689830	+	0.698986i
$691$			22.0670i			0.839468i	0.907647	+	0.419734i	$0.137877\pi$
$691$			22.0670i			0.839468i	−0.907647	+	0.419734i	$0.862123\pi$
$692$	−3.34066	+	5.78620i	−0.126993	+	0.219958i
$693$	20.7392	+	0.670076i	0.787818	+	0.0254541i
$694$	31.6862			1.20279
$695$	−25.1545	−	14.5230i	−0.954164	−	0.550887i
$696$	11.4470	+	2.98648i	0.433898	+	0.113202i
$697$	−5.13531	+	8.89462i	−0.194514	+	0.336908i
$698$	3.68081	−	6.37536i	0.139321	−	0.241311i
$699$	−28.7443	−	28.3678i	−1.08721	−	1.07297i
$700$	7.58870	+	0.345397i	0.286826	+	0.0130548i
$701$			38.0341i			1.43653i	0.695770	+	0.718264i	$0.255063\pi$
$701$			38.0341i			1.43653i	−0.695770	+	0.718264i	$0.744937\pi$
$702$	−15.4538	−	10.5915i	−0.583266	−	0.399750i
$703$	5.86607	+	3.38678i	0.221243	+	0.127735i
$704$	2.26401	−	1.30713i	0.0853283	−	0.0492643i
$705$	16.6494	+	4.34375i	0.627052	+	0.163595i
$706$	−11.3375	+	6.54568i	−0.426691	+	0.246350i
$707$	6.98996	−	10.9274i	0.262884	−	0.410966i
$708$	−1.40556	−	5.11060i	−0.0528241	−	0.192068i
$709$	−16.9219	+	29.3096i	−0.635516	+	1.10075i	0.350890	+	0.936417i	$0.385879\pi$
$709$	−16.9219	+	29.3096i	−0.635516	+	1.10075i	−0.986406	+	0.164329i	$0.947454\pi$
$710$	−7.90633	+	13.6942i	−0.296719	+	0.513933i
$711$	0.746949	+	0.418218i	0.0280128	+	0.0156844i
$712$		−	14.4950i		−	0.543222i
$713$	−18.2795	+	31.6611i	−0.684573	+	1.18572i
$714$	14.4015	+	15.5676i	0.538963	+	0.582604i
$715$	9.28649	−	24.7607i	0.347295	−	0.925998i
$716$	−7.04886	+	4.06966i	−0.263428	+	0.152090i
$717$	−21.0897	+	5.80025i	−0.787610	+	0.216614i
$718$	2.73651	+	4.73978i	0.102126	+	0.176887i
$719$	−2.09581	+	3.63004i	−0.0781603	+	0.135378i	−0.902456	−	0.430782i	$-0.858238\pi$
$719$	−2.09581	+	3.63004i	−0.0781603	+	0.135378i	0.824296	+	0.566159i	$0.191571\pi$
$720$	7.34394	+	4.11189i	0.273692	+	0.153241i
$721$	7.41235	+	4.74149i	0.276050	+	0.176582i
$722$	23.7481	−	13.7110i	0.883812	−	0.510269i
$723$	17.7371	−	4.87819i	0.659650	−	0.181422i
$724$		−	14.2577i		−	0.529885i
$725$	−16.9836	+	9.80547i	−0.630754	+	0.364166i
$726$	1.82142	−	6.98143i	0.0675994	−	0.259105i
$727$		−	5.71419i		−	0.211927i	−0.994370	−	0.105964i	$-0.966207\pi$
$727$		−	5.71419i		−	0.211927i	0.994370	−	0.105964i	$-0.0337927\pi$
$728$	5.71905	+	7.63495i	0.211962	+	0.282970i
$729$	1.06770	+	26.9789i	0.0395444	+	0.999218i
$730$	5.72262			0.211804
$731$	16.9851	+	29.4191i	0.628217	+	1.08810i
$732$	5.22029	−	20.0091i	0.192948	−	0.739558i
$733$	−33.9503	+	19.6012i	−1.25398	+	0.723988i	−0.971898	−	0.235401i	$-0.924360\pi$
$733$	−33.9503	+	19.6012i	−1.25398	+	0.723988i	−0.282086	+	0.959389i	$0.591026\pi$
$734$	2.90771	+	5.03630i	0.107326	+	0.185893i
$735$	−6.00364	−	33.4817i	−0.221448	−	1.23499i
$736$	5.30862			0.195678
$737$	22.4981	+	12.9893i	0.828729	+	0.478467i
$738$	6.65736	−	0.0877818i	0.245061	−	0.00323129i
$739$	15.5342	+	26.9060i	0.571434	+	0.989753i	0.996419	+	0.0845523i	$0.0269460\pi$
$739$	15.5342	+	26.9060i	0.571434	+	0.989753i	−0.424985	+	0.905200i	$0.639721\pi$
$740$	−1.39459	−	2.41550i	−0.0512661	−	0.0887955i
$741$	42.3756	+	3.84217i	1.55671	+	0.141146i
$742$	−27.9726	−	1.27316i	−1.02691	−	0.0467394i
$743$	−40.3395	−	23.2900i	−1.47991	−	0.854427i	−0.480170	−	0.877175i	$-0.659425\pi$
$743$	−40.3395	−	23.2900i	−1.47991	−	0.854427i	−0.999741	+	0.0227483i	$0.992758\pi$
$744$	11.5418	+	3.01121i	0.423144	+	0.110396i
$745$			52.8040i			1.93459i
$746$	−10.9224	−	6.30605i	−0.399898	−	0.230881i
$747$	−2.29208	+	1.36394i	−0.0838627	+	0.0499038i
$748$	−10.4775	+	6.04918i	−0.383095	+	0.221180i
$749$	2.18561	−	1.13262i	0.0798604	−	0.0413851i
$750$	9.97418	−	2.74318i	0.364206	−	0.100167i
$751$	35.3223			1.28893			0.644465	−	0.764633i	$-0.277080\pi$
$751$	35.3223			1.28893			0.644465	+	0.764633i	$0.277080\pi$
$752$	−1.77046	−	3.06652i	−0.0645619	−	0.111825i
$753$	26.0379	−	26.3835i	0.948872	−	0.961466i
$754$	−23.0581	−	8.64793i	−0.839727	−	0.314939i
$755$	−60.6500			−2.20728
$756$	3.89832	−	13.1834i	0.141780	−	0.479477i
$757$	−5.80540	+	10.0552i	−0.211001	+	0.365464i	−0.952028	−	0.306011i	$-0.901006\pi$
$757$	−5.80540	+	10.0552i	−0.211001	+	0.365464i	0.741027	+	0.671475i	$0.234339\pi$
$758$	−9.53139	−	5.50295i	−0.346196	−	0.199876i
$759$	−16.8847	+	17.1088i	−0.612877	+	0.621011i
$760$	−19.1154			−0.693388
$761$	−17.8853	+	30.9782i	−0.648341	+	1.12296i	0.335179	+	0.942155i	$0.391203\pi$
$761$	−17.8853	+	30.9782i	−0.648341	+	1.12296i	−0.983519	+	0.180804i	$0.942130\pi$
$762$	8.15861	−	31.2715i	0.295555	−	1.13285i
$763$	−29.5825	−	1.34644i	−1.07096	−	0.0487443i
$764$	−1.58599	−	0.915669i	−0.0573790	−	0.0331278i
$765$	−33.9865	−	19.0291i	−1.22879	−	0.688000i
$766$	19.2251	+	11.0996i	0.694631	+	0.401045i
$767$	1.80995	+	10.8841i	0.0653535	+	0.393003i
$768$	−0.459307	−	1.67004i	−0.0165738	−	0.0602624i
$769$	−42.9221	−	24.7811i	−1.54781	−	0.893629i	−0.998309	−	0.0581373i	$-0.981484\pi$
$769$	−42.9221	−	24.7811i	−1.54781	−	0.893629i	−0.549503	−	0.835492i	$-0.685183\pi$
$770$	19.3852	+	0.882309i	0.698593	+	0.0317962i
$771$	−7.96283	−	28.9528i	−0.286774	−	1.04271i
$772$	0.833264	+	1.44326i	0.0299898	+	0.0519439i
$773$	29.1769			1.04942			0.524711	−	0.851280i	$-0.324173\pi$
$773$	29.1769			1.04942			0.524711	+	0.851280i	$0.324173\pi$
$774$	10.7582	−	19.2144i	0.386696	−	0.690649i
$775$	−17.1242	+	9.88669i	−0.615121	+	0.355140i
$776$	4.08013	+	7.06699i	0.146468	+	0.253690i
$777$	−3.34425	+	3.09375i	−0.119974	+	0.110988i
$778$	5.08332	−	8.80457i	0.182246	−	0.315659i
$779$	−13.0952	+	7.56050i	−0.469183	+	0.270883i
$780$	−14.3204	−	10.0947i	−0.512753	−	0.361450i
$781$	−7.36720	+	12.7604i	−0.263619	+	0.456602i
$782$	−24.5674			−0.878530
$783$	9.86178	+	34.0929i	0.352431	+	1.21838i
$784$	−4.03622	+	5.71917i	−0.144151	+	0.204256i
$785$		−	14.3732i		−	0.513002i
$786$	−18.7473	−	18.5018i	−0.668695	−	0.659936i
$787$			29.8569i			1.06428i	0.846656	+	0.532141i	$0.178612\pi$
$787$			29.8569i			1.06428i	−0.846656	+	0.532141i	$0.821388\pi$
$788$	−7.33528	−	4.23502i	−0.261308	−	0.150866i
$789$	−28.2754	−	27.9050i	−1.00663	−	0.993444i
$790$	0.693322	+	0.400290i	0.0246673	+	0.0142417i
$791$	−5.02079	−	3.21167i	−0.178519	−	0.114194i
$792$	6.84316	+	3.83150i	0.243161	+	0.136146i
$793$	−15.1164	+	40.3051i	−0.536799	+	1.43127i
$794$	13.5020	−	23.3862i	0.479169	−	0.829945i
$795$	49.5886	−	13.6382i	1.75873	−	0.483698i
$796$			17.9221i			0.635232i
$797$	−4.28801	−	7.42705i	−0.151889	−	0.263080i	0.780033	−	0.625739i	$-0.215202\pi$
$797$	−4.28801	−	7.42705i	−0.151889	−	0.263080i	−0.931922	+	0.362659i	$0.881869\pi$
$798$	6.90233	+	30.4503i	0.244340	+	1.07793i
$799$	8.19339	+	14.1914i	0.289861	+	0.502054i
$800$	2.48656	+	1.43561i	0.0879131	+	0.0507566i
$801$	37.3691	−	22.2371i	1.32037	−	0.785709i
$802$	17.6521			0.623319
$803$	5.33239			0.188176
$804$	12.0901	−	12.2506i	0.426386	−	0.432045i
$805$	33.1947	+	21.2338i	1.16996	+	0.748392i
$806$	−23.2491	−	8.71956i	−0.818915	−	0.307133i
$807$	14.7520	+	53.6384i	0.519296	+	1.88816i
$808$	4.24601	−	2.45144i	0.149374	−	0.0862412i
$809$	6.98609	−	4.03342i	0.245618	−	0.141807i	−0.372138	−	0.928177i	$-0.621375\pi$
$809$	6.98609	−	4.03342i	0.245618	−	0.141807i	0.617756	+	0.786370i	$0.288042\pi$
$810$	0.665764	+	25.2414i	0.0233926	+	0.886891i
$811$		−	13.5376i		−	0.475370i	−0.971342	−	0.237685i	$-0.923611\pi$
$811$		−	13.5376i		−	0.475370i	0.971342	−	0.237685i	$-0.0763887\pi$
$812$	0.821640	−	18.0522i	0.0288339	−	0.633508i
$813$	−15.4855	+	4.25893i	−0.543099	+	0.149367i
$814$	−1.29949	−	2.25079i	−0.0455472	−	0.0788900i
$815$	−48.9098			−1.71323
$816$	2.12560	+	7.72868i	0.0744108	+	0.270558i
$817$			50.0129i			1.74973i
$818$	−31.3317			−1.09549
$819$	−10.9097	+	26.4571i	−0.381217	+	0.924486i
$820$	6.22644			0.217437
$821$		−	11.4413i		−	0.399305i	−0.979867	−	0.199652i	$-0.936019\pi$
$821$		−	11.4413i		−	0.399305i	0.979867	−	0.199652i	$-0.0639813\pi$
$822$	4.77652	+	17.3674i	0.166600	+	0.605759i
$823$	−38.1986			−1.33152			−0.665761	−	0.746165i	$-0.731893\pi$
$823$	−38.1986			−1.33152			−0.665761	+	0.746165i	$0.731893\pi$
$824$	1.66288	+	2.88019i	0.0579291	+	0.100336i
$825$	−12.5356	+	3.44762i	−0.436432	+	0.120031i
$826$	−7.18853	+	3.72523i	−0.250121	+	0.129617i
$827$		−	15.6707i		−	0.544923i	−0.962167	−	0.272461i	$-0.912162\pi$
$827$		−	15.6707i		−	0.544923i	0.962167	−	0.272461i	$-0.0878377\pi$
$828$	8.14408	+	13.6860i	0.283026	+	0.475622i
$829$	30.7566	−	17.7573i	1.06822	−	0.616737i	0.140525	−	0.990077i	$-0.455121\pi$
$829$	30.7566	−	17.7573i	1.06822	−	0.616737i	0.927695	+	0.373340i	$0.121788\pi$
$830$	−2.16016	+	1.24717i	−0.0749802	+	0.0432898i
$831$	4.52534	+	16.4541i	0.156982	+	0.570787i
$832$	0.591455	+	3.55671i	0.0205050	+	0.123307i
$833$	18.6790	−	26.4674i	0.647188	−	0.917040i
$834$	−12.5958	+	12.7630i	−0.436158	+	0.441947i
$835$	−10.9646			−0.379445
$836$	−17.8119			−0.616037
$837$	9.94346	+	34.3752i	0.343696	+	1.18818i
$838$	34.4951	+	19.9157i	1.19161	+	0.687978i
$839$	−5.65771	−	9.79944i	−0.195326	−	0.338314i	0.751681	−	0.659526i	$-0.229243\pi$
$839$	−5.65771	−	9.79944i	−0.195326	−	0.338314i	−0.947007	+	0.321212i	$0.895910\pi$
$840$	3.80790	−	12.2799i	0.131385	−	0.423696i
$841$	8.82553	+	15.2863i	0.304328	+	0.527112i
$842$			15.2089i			0.524134i
$843$	−14.5401	+	3.99892i	−0.500787	+	0.137730i
$844$	11.6075	−	20.1047i	0.399545	−	0.692033i
$845$	27.4771	+	23.9842i	0.945243	+	0.825083i
$846$	5.18962	−	9.26880i	0.178423	−	0.318668i
$847$	−11.0099	−	0.501111i	−0.378304	−	0.0172184i
$848$	−9.16567	−	5.29180i	−0.314750	−	0.181721i
$849$	15.7622	+	15.5557i	0.540957	+	0.533871i
$850$	−11.5074	−	6.64379i	−0.394700	−	0.227880i
$851$		−	5.27760i		−	0.180914i
$852$	6.94822	+	6.85721i	0.238042	+	0.234924i
$853$		−	1.66413i		−	0.0569786i	−0.999594	−	0.0284893i	$-0.990930\pi$
$853$		−	1.66413i		−	0.0569786i	0.999594	−	0.0284893i	$-0.00906966\pi$
$854$	−31.5548	−	1.43621i	−1.07978	−	0.0491460i
$855$	−29.3254	−	49.2808i	−1.00291	−	1.68537i
$856$	0.930416			0.0318010
$857$	8.37234	−	14.5013i	0.285994	−	0.495355i	−0.686856	−	0.726793i	$-0.741010\pi$
$857$	8.37234	−	14.5013i	0.285994	−	0.495355i	0.972850	+	0.231438i	$0.0743431\pi$
$858$	−13.3439	−	9.40639i	−0.455553	−	0.321129i
$859$	−19.5206	+	11.2702i	−0.666034	+	0.384535i	−0.794572	−	0.607170i	$-0.792305\pi$
$859$	−19.5206	+	11.2702i	−0.666034	+	0.384535i	0.128538	+	0.991705i	$0.458972\pi$
$860$	10.2970	−	17.8350i	0.351125	−	0.608167i
$861$	−2.24829	−	9.91855i	−0.0766216	−	0.338023i
$862$	3.66693	+	6.35131i	0.124896	+	0.216326i
$863$	18.0586	−	10.4261i	0.614721	−	0.354909i	−0.160090	−	0.987102i	$-0.551178\pi$
$863$	18.0586	−	10.4261i	0.614721	−	0.354909i	0.774811	+	0.632193i	$0.217845\pi$
$864$	3.60085	−	3.74618i	0.122504	−	0.127448i
$865$	−18.7449			−0.637347
$866$	−6.31856	−	10.9441i	−0.214713	−	0.371894i
$867$	−2.02870	−	7.37635i	−0.0688982	−	0.250514i
$868$	0.828446	−	18.2017i	0.0281193	−	0.617807i
$869$	0.646044	+	0.372994i	0.0219156	+	0.0126529i
$870$	8.80147	+	32.0021i	0.298398	+	1.08497i
$871$	−27.6701	+	22.7620i	−0.937564	+	0.771261i
$872$	−9.69317	−	5.59636i	−0.328252	−	0.189517i
$873$	−11.9598	+	21.3605i	−0.404778	+	0.722943i
$874$	−31.3238	−	18.0848i	−1.05954	−	0.611727i
$875$	−7.27039	−	14.0296i	−0.245784	−	0.474287i
$876$	0.891871	−	3.41849i	0.0301335	−	0.115500i
$877$	−12.4915	+	21.6358i	−0.421807	+	0.730590i	−0.996116	−	0.0880478i	$-0.971937\pi$
$877$	−12.4915	+	21.6358i	−0.421807	+	0.730590i	0.574310	+	0.818638i	$0.305271\pi$
$878$	8.78405			0.296447
$879$	−15.6282	+	15.8356i	−0.527125	+	0.534121i
$880$	6.35185	+	3.66724i	0.214121	+	0.123623i
$881$	20.4483	−	35.4175i	0.688921	−	1.19325i	−0.283266	−	0.959041i	$-0.591418\pi$
$881$	20.4483	−	35.4175i	0.688921	−	1.19325i	0.972187	−	0.234205i	$-0.0752488\pi$
$882$	−20.9365	−	1.63177i	−0.704969	−	0.0549445i
$883$	−34.1756			−1.15010			−0.575050	−	0.818118i	$-0.695017\pi$
$883$	−34.1756			−1.15010			−0.575050	+	0.818118i	$0.695017\pi$
$884$	−2.73716	−	16.4599i	−0.0920605	−	0.553605i
$885$	10.4455	−	10.5842i	0.351122	−	0.355783i
$886$	−14.0141	−	24.2732i	−0.470813	−	0.815473i
$887$	−22.9135			−0.769358			−0.384679	−	0.923050i	$-0.625688\pi$
$887$	−22.9135			−0.769358			−0.384679	+	0.923050i	$0.625688\pi$
$888$	−1.66028	+	0.456624i	−0.0557155	+	0.0153233i
$889$	−49.3160	−	2.24460i	−1.65400	−	0.0752815i
$890$	35.2184	−	20.3333i	1.18052	−	0.681575i
$891$	0.620366	+	23.5202i	0.0207830	+	0.787955i
$892$	8.50389	+	4.90972i	0.284731	+	0.164390i
$893$			24.1255i			0.807331i
$894$	31.5433	+	8.22951i	1.05497	+	0.275236i
$895$	−19.7761	−	11.4177i	−0.661041	−	0.381652i
$896$	−2.34907	+	1.21733i	−0.0784768	+	0.0406681i
$897$	−13.9159	−	30.0903i	−0.464638	−	1.00469i
$898$	−5.08994	−	8.81604i	−0.169854	−	0.294195i
$899$	23.5187	+	40.7356i	0.784393	+	1.35861i
$900$	0.113567	+	8.61294i	0.00378558	+	0.287098i
$901$	42.4172	+	24.4896i	1.41312	+	0.815867i
$902$	5.80186			0.193181
$903$	−32.1287	−	9.96288i	−1.06918	−	0.331544i
$904$	−1.12636	−	1.95091i	−0.0374622	−	0.0648864i
$905$	34.6420	−	20.0006i	1.15154	−	0.664841i
$906$	−9.45231	+	36.2302i	−0.314032	+	1.20367i
$907$	−10.9863	−	19.0289i	−0.364795	−	0.631843i	0.623949	−	0.781465i	$-0.285527\pi$
$907$	−10.9863	−	19.0289i	−0.364795	−	0.631843i	−0.988743	+	0.149623i	$0.952194\pi$
$908$	−20.0199			−0.664383
$909$	12.8339	+	7.18572i	0.425673	+	0.238335i
$910$	−10.5280	+	24.6057i	−0.349000	+	0.815673i
$911$			22.8904i			0.758392i	0.925316	+	0.379196i	$0.123799\pi$
$911$			22.8904i			0.758392i	−0.925316	+	0.379196i	$0.876201\pi$
$912$	−2.97913	+	11.4189i	−0.0986490	+	0.378116i
$913$	−2.01286	+	1.16212i	−0.0666159	+	0.0384607i
$914$		−	3.23701i		−	0.107071i
$915$	55.9390	−	15.3848i	1.84929	−	0.508605i
$916$	−23.6469	+	13.6525i	−0.781315	+	0.451093i
$917$	−21.6807	+	33.8934i	−0.715960	+	1.11926i
$918$	−16.6642	+	17.3367i	−0.549999	+	0.572196i
$919$	19.9228	−	34.5073i	0.657192	−	1.13829i	−0.324148	−	0.946007i	$-0.605077\pi$
$919$	19.9228	−	34.5073i	0.657192	−	1.13829i	0.981339	−	0.192283i	$-0.0615892\pi$
$920$	7.44686	+	12.8983i	0.245516	+	0.425246i
$921$	−29.8795	+	8.21769i	−0.984564	+	0.270782i
$922$	−18.5030	+	10.6827i	−0.609365	+	0.351817i
$923$	−12.9100	−	15.6938i	−0.424939	−	0.516566i
$924$	3.54824	−	11.4425i	0.116729	−	0.376431i
$925$	1.42723	−	2.47203i	0.0469269	−	0.0812798i
$926$		−	5.12785i		−	0.168512i
$927$	−4.87428	+	8.70559i	−0.160092	+	0.285929i
$928$	3.41508	−	5.91509i	0.112105	−	0.194172i
$929$	22.4946	−	38.9618i	0.738025	−	1.27830i	−0.215359	−	0.976535i	$-0.569092\pi$
$929$	22.4946	−	38.9618i	0.738025	−	1.27830i	0.953384	−	0.301761i	$-0.0975745\pi$
$930$	8.87437	+	32.2672i	0.291002	+	1.05808i
$931$	43.2993	−	19.9961i	1.41908	−	0.655345i
$932$	−20.1926	+	11.6582i	−0.661430	+	0.381877i
$933$	−40.6406	−	10.6030i	−1.33051	−	0.347125i
$934$	10.7985	−	6.23453i	0.353339	−	0.204000i
$935$	−29.3953	−	16.9714i	−0.961330	−	0.555024i
$936$	−8.26209	+	6.98125i	−0.270055	+	0.228189i
$937$		−	58.9592i		−	1.92611i	−0.269302	−	0.963056i	$-0.586793\pi$
$937$		−	58.9592i		−	1.92611i	0.269302	−	0.963056i	$-0.413207\pi$
$938$	−22.1479	−	14.1674i	−0.723154	−	0.462583i
$939$	35.2349	+	34.7733i	1.14985	+	1.13478i
$940$	4.96714	−	8.60335i	0.162010	−	0.280610i
$941$	−11.9470	+	20.6928i	−0.389461	+	0.674567i	−0.992377	−	0.123238i	$-0.960672\pi$
$941$	−11.9470	+	20.6928i	−0.389461	+	0.674567i	0.602916	+	0.797805i	$0.294006\pi$
$942$	−8.58607	−	2.24007i	−0.279749	−	0.0729854i
$943$	10.2031	+	5.89075i	0.332258	+	0.191829i
$944$	−3.06017			−0.0995999
$945$	37.5003	−	9.02182i	1.21988	−	0.293480i
$946$	9.59486	−	16.6188i	0.311956	−	0.540323i
$947$			16.7585i			0.544577i	0.962216	+	0.272289i	$0.0877806\pi$
$947$			16.7585i			0.544577i	−0.962216	+	0.272289i	$0.912219\pi$
$948$	0.347174	−	0.351781i	0.0112757	−	0.0114253i
$949$	−2.58259	+	6.88599i	−0.0838343	+	0.223529i
$950$	−9.78136	−	16.9418i	−0.317349	−	0.549665i
$951$	−6.70344	−	6.61563i	−0.217374	−	0.214527i
$952$	10.8711	−	5.63360i	0.352334	−	0.182586i
$953$	−0.929490	+	0.536641i	−0.0301091	+	0.0173835i	−0.514979	−	0.857203i	$-0.672200\pi$
$953$	−0.929490	+	0.536641i	−0.0301091	+	0.0173835i	0.484870	+	0.874586i	$0.338867\pi$
$954$	−0.418619	−	31.7481i	−0.0135533	−	1.02788i
$955$		−	5.13795i		−	0.166260i
$956$			12.6283i			0.408427i
$957$	8.20130	+	29.8199i	0.265110	+	0.963941i
$958$	0.260661	−	0.150493i	0.00842158	−	0.00486220i
$959$	24.4289	−	12.6595i	0.788850	−	0.408796i
$960$	3.41338	−	3.45869i	0.110166	−	0.111629i
$961$	8.21351	+	14.2262i	0.264952	+	0.458910i
$962$	3.53593	−	0.587999i	0.114003	−	0.0189579i
$963$	1.42737	+	2.39868i	0.0459965	+	0.0772964i
$964$		−	10.6208i		−	0.342072i
$965$	−2.33778	+	4.04916i	−0.0752559	+	0.130347i
$966$	17.8577	−	16.5201i	0.574563	−	0.531524i
$967$	35.2378			1.13317			0.566586	−	0.824002i	$-0.308264\pi$
$967$	35.2378			1.13317			0.566586	+	0.824002i	$0.308264\pi$
$968$	−3.60756	−	2.08282i	−0.115951	−	0.0669445i
$969$	13.7869	−	52.8446i	0.442901	−	1.69761i
$970$	−11.4471	+	19.8269i	−0.367544	+	0.636604i
$971$	5.06817	−	8.77833i	0.162645	−	0.281710i	−0.773171	−	0.634197i	$-0.781331\pi$
$971$	5.06817	−	8.77833i	0.162645	−	0.281710i	0.935817	+	0.352487i	$0.114664\pi$
$972$	15.1821	+	3.53617i	0.486965	+	0.113423i
$973$	23.0743	+	14.7600i	0.739729	+	0.473185i
$974$		−	30.7914i		−	0.986621i
$975$	1.61913	−	17.8576i	0.0518538	−	0.571900i
$976$	−10.3394	−	5.96948i	−0.330957	−	0.191078i
$977$	−11.0136	+	6.35869i	−0.352355	+	0.203432i	−0.665722	−	0.746200i	$-0.731876\pi$
$977$	−11.0136	+	6.35869i	−0.352355	+	0.203432i	0.313367	+	0.949632i	$0.398543\pi$
$978$	−7.62260	+	29.2170i	−0.243744	+	0.934257i
$979$	32.8168	−	18.9468i	1.04883	−	0.605543i
$980$	−19.5578	−	1.78403i	−0.624751	−	0.0569887i
$981$	−0.442712	−	33.5752i	−0.0141347	−	1.07197i
$982$	−2.21578	+	3.83785i	−0.0707084	+	0.122471i
$983$	−20.8104	+	36.0447i	−0.663750	+	1.14965i	0.315873	+	0.948802i	$0.397703\pi$
$983$	−20.8104	+	36.0447i	−0.663750	+	1.14965i	−0.979623	+	0.200847i	$0.935631\pi$
$984$	0.970392	−	3.71946i	0.0309350	−	0.118572i
$985$		−	23.7633i		−	0.757162i
$986$	−15.8044	+	27.3741i	−0.503315	+	0.871768i
$987$	−15.4985	−	4.80596i	−0.493322	−	0.152975i
$988$	8.62667	−	23.0014i	0.274451	−	0.731773i
$989$	33.7468	−	19.4837i	1.07309	−	0.619546i
$990$	0.290105	+	22.0016i	0.00922015	+	0.699255i
$991$	7.90381	+	13.6898i	0.251073	+	0.434871i	0.963821	−	0.266549i	$-0.0858833\pi$
$991$	7.90381	+	13.6898i	0.251073	+	0.434871i	−0.712749	+	0.701419i	$0.752550\pi$
$992$	3.44336	−	5.96408i	0.109327	−	0.189360i
$993$	43.4786	+	11.3434i	1.37975	+	0.359972i
$994$	8.03541	−	12.5617i	0.254868	−	0.398434i
$995$	−43.5453	+	25.1409i	−1.38048	+	0.797020i
$996$	0.408354	+	1.48478i	0.0129392	+	0.0470469i
$997$		−	26.5711i		−	0.841517i	−0.907173	−	0.420758i	$-0.861764\pi$
$997$		−	26.5711i		−	0.841517i	0.907173	−	0.420758i	$-0.138236\pi$
$998$	−10.8833	+	6.28345i	−0.344503	+	0.198899i
$999$	−3.72429	−	3.57982i	−0.117831	−	0.113260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.9	yes	76
3.2	odd	2	inner	546.2.bb.a.269.33	yes	76
7.5	odd	6		546.2.u.a.425.1	yes	76
13.3	even	3		546.2.u.a.185.38	yes	76
21.5	even	6		546.2.u.a.425.38	yes	76
39.29	odd	6		546.2.u.a.185.1	✓	76
91.68	odd	6	inner	546.2.bb.a.341.14	yes	76
273.68	even	6	inner	546.2.bb.a.341.28	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.1	✓	76	39.29	odd	6
546.2.u.a.185.38	yes	76	13.3	even	3
546.2.u.a.425.1	yes	76	7.5	odd	6
546.2.u.a.425.38	yes	76	21.5	even	6
546.2.bb.a.269.9	yes	76	1.1	even	1	trivial
546.2.bb.a.269.33	yes	76	3.2	odd	2	inner
546.2.bb.a.341.14	yes	76	91.68	odd	6	inner
546.2.bb.a.341.28	yes	76	273.68	even	6	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.459307 - 1.67004i) q^{3} -1.00000 q^{4} +(-1.40279 - 2.42970i) q^{5} +(-1.67004 + 0.459307i) q^{6} +(1.21733 + 2.34907i) q^{7} +1.00000i q^{8} +(-2.57807 + 1.53412i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.459307 - 1.67004i) q^{3} -1.00000 q^{4} +(-1.40279 - 2.42970i) q^{5} +(-1.67004 + 0.459307i) q^{6} +(1.21733 + 2.34907i) q^{7} +1.00000i q^{8} +(-2.57807 + 1.53412i) q^{9} +(-2.42970 + 1.40279i) q^{10} +(-2.26401 + 1.30713i) q^{11} +(0.459307 + 1.67004i) q^{12} +(-0.591455 - 3.55671i) q^{13} +(2.34907 - 1.21733i) q^{14} +(-3.41338 + 3.45869i) q^{15} +1.00000 q^{16} -4.62784 q^{17} +(1.53412 + 2.57807i) q^{18} +(-5.90055 - 3.40668i) q^{19} +(1.40279 + 2.42970i) q^{20} +(3.36391 - 3.11193i) q^{21} +(1.30713 + 2.26401i) q^{22} +5.30862i q^{23} +(1.67004 - 0.459307i) q^{24} +(-1.43561 + 2.48656i) q^{25} +(-3.55671 + 0.591455i) q^{26} +(3.74618 + 3.60085i) q^{27} +(-1.21733 - 2.34907i) q^{28} +(5.91509 + 3.41508i) q^{29} +(3.45869 + 3.41338i) q^{30} +(5.96408 + 3.44336i) q^{31} -1.00000i q^{32} +(3.22284 + 3.18062i) q^{33} +4.62784i q^{34} +(3.99987 - 6.25297i) q^{35} +(2.57807 - 1.53412i) q^{36} -0.994157 q^{37} +(-3.40668 + 5.90055i) q^{38} +(-5.66819 + 2.62138i) q^{39} +(2.42970 - 1.40279i) q^{40} +(1.10966 - 1.92198i) q^{41} +(-3.11193 - 3.36391i) q^{42} +(-3.67020 - 6.35698i) q^{43} +(2.26401 - 1.30713i) q^{44} +(7.34394 + 4.11189i) q^{45} +5.30862 q^{46} +(-1.77046 - 3.06652i) q^{47} +(-0.459307 - 1.67004i) q^{48} +(-4.03622 + 5.71917i) q^{49} +(2.48656 + 1.43561i) q^{50} +(2.12560 + 7.72868i) q^{51} +(0.591455 + 3.55671i) q^{52} +(-9.16567 - 5.29180i) q^{53} +(3.60085 - 3.74618i) q^{54} +(6.35185 + 3.66724i) q^{55} +(-2.34907 + 1.21733i) q^{56} +(-2.97913 + 11.4189i) q^{57} +(3.41508 - 5.91509i) q^{58} -3.06017 q^{59} +(3.41338 - 3.45869i) q^{60} +(-10.3394 - 5.96948i) q^{61} +(3.44336 - 5.96408i) q^{62} +(-6.74212 - 4.18853i) q^{63} -1.00000 q^{64} +(-7.81204 + 6.42636i) q^{65} +(3.18062 - 3.22284i) q^{66} +(-4.96864 - 8.60593i) q^{67} +4.62784 q^{68} +(8.86562 - 2.43829i) q^{69} +(-6.25297 - 3.99987i) q^{70} +(4.88106 - 2.81808i) q^{71} +(-1.53412 - 2.57807i) q^{72} +(-1.76646 - 1.01987i) q^{73} +0.994157i q^{74} +(4.81204 + 1.25544i) q^{75} +(5.90055 + 3.40668i) q^{76} +(-5.82658 - 3.72712i) q^{77} +(2.62138 + 5.66819i) q^{78} +(-0.142677 - 0.247123i) q^{79} +(-1.40279 - 2.42970i) q^{80} +(4.29293 - 7.91017i) q^{81} +(-1.92198 - 1.10966i) q^{82} +0.889066 q^{83} +(-3.36391 + 3.11193i) q^{84} +(6.49186 + 11.2442i) q^{85} +(-6.35698 + 3.67020i) q^{86} +(2.98648 - 11.4470i) q^{87} +(-1.30713 - 2.26401i) q^{88} -14.4950 q^{89} +(4.11189 - 7.34394i) q^{90} +(7.63495 - 5.71905i) q^{91} -5.30862i q^{92} +(3.01121 - 11.5418i) q^{93} +(-3.06652 + 1.77046i) q^{94} +19.1154i q^{95} +(-1.67004 + 0.459307i) q^{96} +(7.06699 - 4.08013i) q^{97} +(5.71917 + 4.03622i) q^{98} +(3.83150 - 6.84316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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