LMFDB - Embedded newform 483.2.q.d.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	483.64
Dual form			483.2.q.d.400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35051 - 0.690173i) q^{2} +(0.654861 - 0.755750i) q^{3} +(3.36607 + 2.16324i) q^{4} +(-0.0495443 + 0.344588i) q^{5} +(-2.06086 + 1.32443i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-3.21050 - 3.70511i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-2.35051 - 0.690173i) q^{2} +(0.654861 - 0.755750i) q^{3} +(3.36607 + 2.16324i) q^{4} +(-0.0495443 + 0.344588i) q^{5} +(-2.06086 + 1.32443i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-3.21050 - 3.70511i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.354280 - 0.775765i) q^{10} +(-4.70164 + 1.38053i) q^{11} +(3.83917 - 1.12728i) q^{12} +(2.21545 - 4.85115i) q^{13} +(-0.348635 - 2.42481i) q^{14} +(0.227978 + 0.263100i) q^{15} +(1.66478 + 3.64537i) q^{16} +(1.38235 - 0.888385i) q^{17} +(-0.348635 + 2.42481i) q^{18} +(0.574197 + 0.369014i) q^{19} +(-0.912196 + 1.05273i) q^{20} +(0.959493 + 0.281733i) q^{21} +12.0041 q^{22} +(2.27209 - 4.22346i) q^{23} -4.90256 q^{24} +(4.68118 + 1.37452i) q^{25} +(-8.55557 + 9.87366i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.569438 + 3.96053i) q^{28} +(8.41969 - 5.41101i) q^{29} +(-0.354280 - 0.775765i) q^{30} +(-2.95343 - 3.40844i) q^{31} +(-0.00174857 - 0.0121615i) q^{32} +(-2.03559 + 4.45732i) q^{33} +(-3.86238 + 1.13410i) q^{34} +(-0.334030 + 0.0980800i) q^{35} +(1.66218 - 3.63967i) q^{36} +(0.852979 + 5.93260i) q^{37} +(-1.09497 - 1.26367i) q^{38} +(-2.21545 - 4.85115i) q^{39} +(1.43580 - 0.922731i) q^{40} +(0.712237 - 4.95372i) q^{41} +(-2.06086 - 1.32443i) q^{42} +(4.58010 - 5.28572i) q^{43} +(-18.8125 - 5.52384i) q^{44} +0.348131 q^{45} +(-8.25550 + 8.35916i) q^{46} -0.771067 q^{47} +(3.84519 + 1.12905i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-10.0545 - 6.46165i) q^{50} +(0.233853 - 1.62648i) q^{51} +(17.9516 - 11.5368i) q^{52} +(-1.31115 - 2.87102i) q^{53} +(1.60424 + 1.85139i) q^{54} +(-0.242773 - 1.68853i) q^{55} +(2.03660 - 4.45953i) q^{56} +(0.654901 - 0.192296i) q^{57} +(-23.5251 + 6.90760i) q^{58} +(5.03154 - 11.0175i) q^{59} +(0.198239 + 1.37878i) q^{60} +(-8.11392 - 9.36396i) q^{61} +(4.58967 + 10.0500i) q^{62} +(0.841254 - 0.540641i) q^{63} +(1.13638 - 7.90367i) q^{64} +(1.56189 + 1.00376i) q^{65} +(7.86100 - 9.07208i) q^{66} +(-5.56349 - 1.63359i) q^{67} +6.57489 q^{68} +(-1.70397 - 4.48291i) q^{69} +0.852833 q^{70} +(-2.94627 - 0.865103i) q^{71} +(-3.21050 + 3.70511i) q^{72} +(3.35777 + 2.15791i) q^{73} +(2.08958 - 14.5334i) q^{74} +(4.10431 - 2.63768i) q^{75} +(1.13452 + 2.48425i) q^{76} +(-3.20890 - 3.70327i) q^{77} +(1.85930 + 12.9317i) q^{78} +(-3.86639 + 8.46622i) q^{79} +(-1.33863 + 0.393058i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-5.09305 + 11.1522i) q^{82} +(2.15493 + 14.9879i) q^{83} +(2.62026 + 3.02395i) q^{84} +(0.237639 + 0.520357i) q^{85} +(-14.4136 + 9.26309i) q^{86} +(1.42436 - 9.90664i) q^{87} +(20.2096 + 12.9879i) q^{88} +(-2.48290 + 2.86542i) q^{89} +(-0.818288 - 0.240271i) q^{90} +5.33309 q^{91} +(16.7844 - 9.30136i) q^{92} -4.51002 q^{93} +(1.81240 + 0.532170i) q^{94} +(-0.155606 + 0.179579i) q^{95} +(-0.0103362 - 0.00664264i) q^{96} +(1.58090 - 10.9954i) q^{97} +(2.06086 - 1.32443i) q^{98} +(2.03559 + 4.45732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−2.35051	−	0.690173i	−1.66206	−	0.488026i	−0.690210	−	0.723609i	$-0.742482\pi$
$2$	−2.35051	−	0.690173i	−1.66206	−	0.488026i	−0.971854	+	0.235583i	$0.924300\pi$
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	3.36607	+	2.16324i	1.68303	+	1.08162i
$5$	−0.0495443	+	0.344588i	−0.0221569	+	0.154104i	−0.997896	−	0.0648308i	$-0.979349\pi$
$5$	−0.0495443	+	0.344588i	−0.0221569	+	0.154104i	0.975739	+	0.218935i	$0.0702583\pi$
$6$	−2.06086	+	1.32443i	−0.841341	+	0.540697i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$8$	−3.21050	−	3.70511i	−1.13508	−	1.30995i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.354280	−	0.775765i	0.112033	−	0.245318i
$11$	−4.70164	+	1.38053i	−1.41760	+	0.416244i	−0.898690	−	0.438585i	$-0.855480\pi$
$11$	−4.70164	+	1.38053i	−1.41760	+	0.416244i	−0.518909	+	0.854830i	$0.673662\pi$
$12$	3.83917	−	1.12728i	1.10827	−	0.325419i
$13$	2.21545	−	4.85115i	0.614455	−	1.34547i	−0.305030	−	0.952343i	$-0.598667\pi$
$13$	2.21545	−	4.85115i	0.614455	−	1.34547i	0.919485	−	0.393125i	$-0.128606\pi$
$14$	−0.348635	−	2.42481i	−0.0931767	−	0.648058i
$15$	0.227978	+	0.263100i	0.0588636	+	0.0679322i
$16$	1.66478	+	3.64537i	0.416196	+	0.911343i
$17$	1.38235	−	0.888385i	0.335270	−	0.215465i	−0.362163	−	0.932115i	$-0.617962\pi$
$17$	1.38235	−	0.888385i	0.335270	−	0.215465i	0.697433	+	0.716650i	$0.254325\pi$
$18$	−0.348635	+	2.42481i	−0.0821741	+	0.571533i
$19$	0.574197	+	0.369014i	0.131730	+	0.0846576i	0.604846	−	0.796342i	$-0.293235\pi$
$19$	0.574197	+	0.369014i	0.131730	+	0.0846576i	−0.473116	+	0.881000i	$0.656871\pi$
$20$	−0.912196	+	1.05273i	−0.203973	+	0.235398i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	12.0041			2.55928
$23$	2.27209	−	4.22346i	0.473764	−	0.880652i
$23$	2.27209	−	4.22346i	0.473764	−	0.880652i
$24$	−4.90256			−1.00073
$25$	4.68118	+	1.37452i	0.936236	+	0.274904i
$26$	−8.55557	+	9.87366i	−1.67789	+	1.93638i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.569438	+	3.96053i	−0.107614	+	0.748469i
$29$	8.41969	−	5.41101i	1.56350	−	1.00480i	0.582031	−	0.813166i	$-0.302258\pi$
$29$	8.41969	−	5.41101i	1.56350	−	1.00480i	0.981467	−	0.191633i	$-0.0613782\pi$
$30$	−0.354280	−	0.775765i	−0.0646824	−	0.141635i
$31$	−2.95343	−	3.40844i	−0.530452	−	0.612174i	0.425765	−	0.904834i	$-0.360005\pi$
$31$	−2.95343	−	3.40844i	−0.530452	−	0.612174i	−0.956217	+	0.292660i	$0.905460\pi$
$32$	−0.00174857	−	0.0121615i	−0.000309106	−	0.00214988i
$33$	−2.03559	+	4.45732i	−0.354350	+	0.775919i
$34$	−3.86238	+	1.13410i	−0.662393	+	0.194496i
$35$	−0.334030	+	0.0980800i	−0.0564613	+	0.0165785i
$36$	1.66218	−	3.63967i	0.277030	−	0.606611i
$37$	0.852979	+	5.93260i	0.140229	+	0.975314i	0.931472	+	0.363812i	$0.118525\pi$
$37$	0.852979	+	5.93260i	0.140229	+	0.975314i	−0.791243	+	0.611501i	$0.790566\pi$
$38$	−1.09497	−	1.26367i	−0.177628	−	0.204994i
$39$	−2.21545	−	4.85115i	−0.354756	−	0.776806i
$40$	1.43580	−	0.922731i	0.227020	−	0.145897i
$41$	0.712237	−	4.95372i	0.111233	−	0.773641i	−0.855491	−	0.517818i	$-0.826745\pi$
$41$	0.712237	−	4.95372i	0.111233	−	0.773641i	0.966724	−	0.255823i	$-0.0823464\pi$
$42$	−2.06086	−	1.32443i	−0.317997	−	0.204364i
$43$	4.58010	−	5.28572i	0.698459	−	0.806064i	−0.290085	−	0.957001i	$-0.593683\pi$
$43$	4.58010	−	5.28572i	0.698459	−	0.806064i	0.988543	+	0.150937i	$0.0482289\pi$
$44$	−18.8125	−	5.52384i	−2.83609	−	0.832750i
$45$	0.348131			0.0518964
$46$	−8.25550	+	8.35916i	−1.21721	+	1.23249i
$47$	−0.771067			−0.112472			−0.0562359	−	0.998418i	$-0.517910\pi$
$47$	−0.771067			−0.112472			−0.0562359	+	0.998418i	$0.517910\pi$
$48$	3.84519	+	1.12905i	0.555005	+	0.162964i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	−10.0545	−	6.46165i	−1.42192	−	0.913815i
$51$	0.233853	−	1.62648i	0.0327459	−	0.227753i
$52$	17.9516	−	11.5368i	2.48943	−	1.59986i
$53$	−1.31115	−	2.87102i	−0.180101	−	0.394366i	0.797953	−	0.602720i	$-0.205916\pi$
$53$	−1.31115	−	2.87102i	−0.180101	−	0.394366i	−0.978053	+	0.208355i	$0.933189\pi$
$54$	1.60424	+	1.85139i	0.218310	+	0.251943i
$55$	−0.242773	−	1.68853i	−0.0327356	−	0.227681i
$56$	2.03660	−	4.45953i	0.272152	−	0.595929i
$57$	0.654901	−	0.192296i	0.0867437	−	0.0254703i
$58$	−23.5251	+	6.90760i	−3.08900	+	0.907013i
$59$	5.03154	−	11.0175i	0.655051	−	1.43436i	−0.232013	−	0.972713i	$-0.574531\pi$
$59$	5.03154	−	11.0175i	0.655051	−	1.43436i	0.887063	−	0.461648i	$-0.152742\pi$
$60$	0.198239	+	1.37878i	0.0255926	+	0.178000i
$61$	−8.11392	−	9.36396i	−1.03888	−	1.19893i	−0.979655	−	0.200688i	$-0.935682\pi$
$61$	−8.11392	−	9.36396i	−1.03888	−	1.19893i	−0.0592258	−	0.998245i	$-0.518863\pi$
$62$	4.58967	+	10.0500i	0.582888	+	1.27635i
$63$	0.841254	−	0.540641i	0.105988	−	0.0681143i
$64$	1.13638	−	7.90367i	0.142047	−	0.987959i
$65$	1.56189	+	1.00376i	0.193728	+	0.124502i
$66$	7.86100	−	9.07208i	0.967622	−	1.11670i
$67$	−5.56349	−	1.63359i	−0.679688	−	0.199574i	−0.0763755	−	0.997079i	$-0.524335\pi$
$67$	−5.56349	−	1.63359i	−0.679688	−	0.199574i	−0.603313	+	0.797505i	$0.706153\pi$
$68$	6.57489			0.797322
$69$	−1.70397	−	4.48291i	−0.205134	−	0.539679i
$70$	0.852833			0.101933
$71$	−2.94627	−	0.865103i	−0.349658	−	0.102669i	0.102187	−	0.994765i	$-0.467416\pi$
$71$	−2.94627	−	0.865103i	−0.349658	−	0.102669i	−0.451845	+	0.892096i	$0.649234\pi$
$72$	−3.21050	+	3.70511i	−0.378360	+	0.436651i
$73$	3.35777	+	2.15791i	0.392998	+	0.252564i	0.722184	−	0.691701i	$-0.243138\pi$
$73$	3.35777	+	2.15791i	0.392998	+	0.252564i	−0.329187	+	0.944265i	$0.606775\pi$
$74$	2.08958	−	14.5334i	0.242909	−	1.68947i
$75$	4.10431	−	2.63768i	0.473925	−	0.304573i
$76$	1.13452	+	2.48425i	0.130138	+	0.284963i
$77$	−3.20890	−	3.70327i	−0.365689	−	0.422027i
$78$	1.85930	+	12.9317i	0.210525	+	1.46423i
$79$	−3.86639	+	8.46622i	−0.435003	+	0.952524i	0.557486	+	0.830187i	$0.311766\pi$
$79$	−3.86639	+	8.46622i	−0.435003	+	0.952524i	−0.992489	+	0.122337i	$0.960961\pi$
$80$	−1.33863	+	0.393058i	−0.149664	+	0.0439452i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−5.09305	+	11.1522i	−0.562433	+	1.23156i
$83$	2.15493	+	14.9879i	0.236535	+	1.64513i	0.668840	+	0.743407i	$0.266791\pi$
$83$	2.15493	+	14.9879i	0.236535	+	1.64513i	−0.432305	+	0.901727i	$0.642300\pi$
$84$	2.62026	+	3.02395i	0.285894	+	0.329940i
$85$	0.237639	+	0.520357i	0.0257756	+	0.0564406i
$86$	−14.4136	+	9.26309i	−1.55426	+	0.998865i
$87$	1.42436	−	9.90664i	0.152707	−	1.06210i
$88$	20.2096	+	12.9879i	2.15435	+	1.38452i
$89$	−2.48290	+	2.86542i	−0.263187	+	0.303733i	−0.871927	−	0.489636i	$-0.837130\pi$
$89$	−2.48290	+	2.86542i	−0.263187	+	0.303733i	0.608740	+	0.793369i	$0.291675\pi$
$90$	−0.818288	−	0.240271i	−0.0862551	−	0.0253268i
$91$	5.33309			0.559060
$92$	16.7844	−	9.30136i	1.74989	−	0.969734i
$93$	−4.51002			−0.467667
$94$	1.81240	+	0.532170i	0.186935	+	0.0548891i
$95$	−0.155606	+	0.179579i	−0.0159648	+	0.0184244i
$96$	−0.0103362	−	0.00664264i	−0.00105493	−	0.000677962i
$97$	1.58090	−	10.9954i	0.160516	−	1.11641i	−0.737148	−	0.675731i	$-0.763828\pi$
$97$	1.58090	−	10.9954i	0.160516	−	1.11641i	0.897664	−	0.440681i	$-0.145263\pi$
$98$	2.06086	−	1.32443i	0.208178	−	0.133788i
$99$	2.03559	+	4.45732i	0.204584	+	0.447977i
$100$	12.7838	+	14.7532i	1.27838	+	1.47532i
$101$	1.20822	+	8.40333i	0.120222	+	0.836162i	0.957304	+	0.289084i	$0.0933508\pi$
$101$	1.20822	+	8.40333i	0.120222	+	0.836162i	−0.837082	+	0.547078i	$0.815740\pi$
$102$	−1.67223	+	3.66167i	−0.165575	+	0.362559i
$103$	−0.163914	+	0.0481295i	−0.0161509	+	0.00474234i	−0.289798	−	0.957088i	$-0.593588\pi$
$103$	−0.163914	+	0.0481295i	−0.0161509	+	0.00474234i	0.273647	+	0.961830i	$0.411770\pi$
$104$	−25.0867	+	7.36613i	−2.45996	+	0.722308i
$105$	−0.144619	+	0.316672i	−0.0141134	+	0.0309040i
$106$	1.10038	+	7.65330i	0.106878	+	0.743355i
$107$	13.0400	+	15.0489i	1.26062	+	1.45483i	0.835304	+	0.549788i	$0.185292\pi$
$107$	13.0400	+	15.0489i	1.26062	+	1.45483i	0.425316	+	0.905045i	$0.360163\pi$
$108$	−1.66218	−	3.63967i	−0.159943	−	0.350227i
$109$	4.93130	−	3.16915i	0.472333	−	0.303550i	−0.282733	−	0.959199i	$-0.591241\pi$
$109$	4.93130	−	3.16915i	0.472333	−	0.303550i	0.755066	+	0.655649i	$0.227605\pi$
$110$	−0.594733	+	4.13646i	−0.0567056	+	0.394396i
$111$	5.04214	+	3.24039i	0.478579	+	0.307564i
$112$	−2.62437	+	3.02868i	−0.247980	+	0.286184i
$113$	3.81091	+	1.11898i	0.358500	+	0.105265i	0.456023	−	0.889968i	$-0.349274\pi$
$113$	3.81091	+	1.11898i	0.358500	+	0.105265i	−0.0975225	+	0.995233i	$0.531092\pi$
$114$	−1.67207			−0.156604
$115$	1.34278	+	0.992184i	0.125215	+	0.0925216i
$116$	40.0466			3.71823
$117$	−5.11707	−	1.50251i	−0.473073	−	0.138907i
$118$	−19.4307	+	22.4242i	−1.78874	+	2.06432i
$119$	1.38235	+	0.888385i	0.126720	+	0.0814381i
$120$	0.242894	−	1.68936i	0.0221731	−	0.154217i
$121$	10.9458	−	7.03444i	0.995073	−	0.639494i
$122$	12.6091	+	27.6101i	1.14158	+	2.49970i
$123$	−3.27735	−	3.78227i	−0.295509	−	0.341036i
$124$	−2.56817	−	17.8620i	−0.230629	−	1.60406i
$125$	−1.42866	+	3.12834i	−0.127784	+	0.279807i
$126$	−2.35051	+	0.690173i	−0.209400	+	0.0614855i
$127$	−12.5736	+	3.69193i	−1.11572	+	0.327606i	−0.787082	−	0.616848i	$-0.788409\pi$
$127$	−12.5736	+	3.69193i	−1.11572	+	0.327606i	−0.328642	+	0.944455i	$0.606591\pi$
$128$	−8.13618	+	17.8157i	−0.719143	+	1.57470i
$129$	−0.995351	−	6.92282i	−0.0876358	−	0.609520i
$130$	−2.97846	−	3.43733i	−0.261229	−	0.301474i
$131$	0.877908	+	1.92235i	0.0767032	+	0.167957i	0.944099	−	0.329663i	$-0.106935\pi$
$131$	0.877908	+	1.92235i	0.0767032	+	0.167957i	−0.867396	+	0.497619i	$0.834208\pi$
$132$	−16.4942	+	10.6002i	−1.43563	+	0.922626i
$133$	−0.0971368	+	0.675602i	−0.00842283	+	0.0585821i
$134$	11.9496	+	7.67954i	1.03229	+	0.663411i
$135$	0.227978	−	0.263100i	0.0196212	−	0.0226441i
$136$	−7.72960	−	2.26962i	−0.662808	−	0.194618i
$137$	−21.1245			−1.80479			−0.902393	−	0.430914i	$-0.858191\pi$
$137$	−21.1245			−1.80479			−0.902393	+	0.430914i	$0.858191\pi$
$138$	0.911225	+	11.7132i	0.0775686	+	0.997092i
$139$	−6.54046			−0.554755			−0.277377	−	0.960761i	$-0.589465\pi$
$139$	−6.54046			−0.554755			−0.277377	+	0.960761i	$0.589465\pi$
$140$	−1.33654	−	0.392443i	−0.112958	−	0.0331675i
$141$	−0.504942	+	0.582734i	−0.0425238	+	0.0490750i
$142$	6.32818	+	4.06687i	0.531049	+	0.341284i
$143$	−3.71909	+	25.8669i	−0.311006	+	2.16310i
$144$	3.37134	−	2.16663i	0.280945	−	0.180553i
$145$	1.44742	+	3.16941i	0.120202	+	0.263205i
$146$	−6.40316	−	7.38964i	−0.529930	−	0.611571i
$147$	0.142315	+	0.989821i	0.0117379	+	0.0816391i
$148$	−9.96246	+	21.8147i	−0.818909	+	1.79316i
$149$	1.97886	−	0.581046i	0.162115	−	0.0476011i	−0.199668	−	0.979864i	$-0.563986\pi$
$149$	1.97886	−	0.581046i	0.162115	−	0.0476011i	0.361783	+	0.932262i	$0.382168\pi$
$150$	−11.4677	+	3.36722i	−0.936334	+	0.274932i
$151$	−0.0748164	+	0.163825i	−0.00608848	+	0.0133319i	−0.912652	−	0.408738i	$-0.865969\pi$
$151$	−0.0748164	+	0.163825i	−0.00608848	+	0.0133319i	0.906563	+	0.422070i	$0.138696\pi$
$152$	−0.476219	−	3.31218i	−0.0386265	−	0.268653i
$153$	−1.07607	−	1.24185i	−0.0869952	−	0.100398i
$154$	4.98667	+	10.9193i	0.401838	+	0.879902i
$155$	1.32083	−	0.848848i	0.106092	−	0.0681811i
$156$	3.03687	−	21.1219i	0.243144	−	1.69110i
$157$	4.04769	+	2.60130i	0.323041	+	0.207606i	0.692103	−	0.721799i	$-0.256684\pi$
$157$	4.04769	+	2.60130i	0.323041	+	0.207606i	−0.369062	+	0.929405i	$0.620321\pi$
$158$	14.9312	−	17.2315i	1.18786	−	1.37086i
$159$	−3.02840	−	0.889218i	−0.240168	−	0.0705196i
$160$	0.00427736			0.000338155
$161$	4.78565	+	0.312281i	0.377162	+	0.0246112i
$162$	2.44975			0.192470
$163$	−0.271247	−	0.0796453i	−0.0212457	−	0.00623830i	0.271092	−	0.962553i	$-0.412615\pi$
$163$	−0.271247	−	0.0796453i	−0.0212457	−	0.00623830i	−0.292338	+	0.956315i	$0.594433\pi$
$164$	13.1135	−	15.1338i	1.02399	−	1.18175i
$165$	−1.43509	−	0.922274i	−0.111721	−	0.0717989i
$166$	5.27904	−	36.7165i	0.409733	−	2.84975i
$167$	15.8394	−	10.1793i	1.22569	−	0.787701i	0.242473	−	0.970158i	$-0.422041\pi$
$167$	15.8394	−	10.1793i	1.22569	−	0.787701i	0.983214	+	0.182457i	$0.0584051\pi$
$168$	−2.03660	−	4.45953i	−0.157127	−	0.344060i
$169$	−10.1123	−	11.6702i	−0.777868	−	0.897708i
$170$	−0.199437	−	1.38712i	−0.0152961	−	0.106387i
$171$	0.283541	−	0.620868i	0.0216829	−	0.0474790i
$172$	26.8512	−	7.88423i	2.04739	−	0.601167i
$173$	22.6176	−	6.64112i	1.71958	−	0.504915i	0.734738	−	0.678351i	$-0.237305\pi$
$173$	22.6176	−	6.64112i	1.71958	−	0.504915i	0.984845	+	0.173436i	$0.0554871\pi$
$174$	−10.1853	+	22.3026i	−0.772143	+	1.69076i
$175$	0.694326	+	4.82915i	0.0524861	+	0.365049i
$176$	−12.8598	−	14.8409i	−0.969341	−	1.11868i
$177$	−5.03154	−	11.0175i	−0.378194	−	0.828128i
$178$	7.81372	−	5.02157i	0.585663	−	0.376383i
$179$	0.553907	−	3.85251i	0.0414009	−	0.287950i	−0.958594	−	0.284776i	$-0.908081\pi$
$179$	0.553907	−	3.85251i	0.0414009	−	0.287950i	0.999995	−	0.00317358i	$-0.00101018\pi$
$180$	1.17183	+	0.753092i	0.0873434	+	0.0561322i
$181$	−1.79316	+	2.06941i	−0.133284	+	0.153818i	−0.818468	−	0.574552i	$-0.805176\pi$
$181$	−1.79316	+	2.06941i	−0.133284	+	0.153818i	0.685184	+	0.728370i	$0.259722\pi$
$182$	−12.5355	−	3.68076i	−0.929194	−	0.272836i
$183$	−12.3903			−0.915917
$184$	−22.9429	+	5.14104i	−1.69137	+	0.379002i
$185$	−2.08656			−0.153407
$186$	10.6009	+	3.11269i	0.777292	+	0.228234i
$187$	−5.27289	+	6.08524i	−0.385592	+	0.444997i
$188$	−2.59547	−	1.66800i	−0.189294	−	0.121652i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	0.489694	−	0.314707i	0.0355261	−	0.0228313i
$191$	−4.46369	−	9.77413i	−0.322982	−	0.707231i	0.676594	−	0.736356i	$-0.263455\pi$
$191$	−4.46369	−	9.77413i	−0.322982	−	0.707231i	−0.999576	+	0.0291251i	$0.990728\pi$
$192$	−5.22903	−	6.03462i	−0.377373	−	0.435511i
$193$	2.99885	+	20.8575i	0.215862	+	1.50135i	0.753090	+	0.657917i	$0.228562\pi$
$193$	2.99885	+	20.8575i	0.215862	+	1.50135i	−0.537228	+	0.843437i	$0.680529\pi$
$194$	−11.3046	+	24.7537i	−0.811626	+	1.77721i
$195$	1.78141	−	0.523070i	0.127570	−	0.0374578i
$196$	−3.83917	+	1.12728i	−0.274227	+	0.0805202i
$197$	6.58210	−	14.4128i	0.468955	−	1.02687i	−0.516399	−	0.856348i	$-0.672728\pi$
$197$	6.58210	−	14.4128i	0.468955	−	1.02687i	0.985354	−	0.170521i	$-0.0545450\pi$
$198$	−1.70836	−	11.8819i	−0.121408	−	0.844409i
$199$	−2.95251	−	3.40738i	−0.209298	−	0.241542i	0.641388	−	0.767216i	$-0.278359\pi$
$199$	−2.95251	−	3.40738i	−0.209298	−	0.241542i	−0.850686	+	0.525674i	$0.823813\pi$
$200$	−9.93616	−	21.7572i	−0.702593	−	1.53846i
$201$	−4.87789	+	3.13483i	−0.344060	+	0.221114i
$202$	2.95982	−	20.5860i	0.208252	−	1.44843i
$203$	8.41969	+	5.41101i	0.590947	+	0.379778i
$204$	4.30563	−	4.96897i	0.301455	−	0.347897i
$205$	1.67170	+	0.490857i	0.116757	+	0.0342829i
$206$	0.418500			0.0291583
$207$	−4.50382	−	1.64791i	−0.313037	−	0.114537i
$208$	21.3725			1.48192
$209$	−3.20910	−	0.942277i	−0.221978	−	0.0651787i
$210$	0.558487	−	0.644529i	0.0385393	−	0.0444767i
$211$	−3.59280	−	2.30895i	−0.247339	−	0.158955i	0.411098	−	0.911591i	$-0.365145\pi$
$211$	−3.59280	−	2.30895i	−0.247339	−	0.158955i	−0.658436	+	0.752636i	$0.728782\pi$
$212$	1.79729	−	12.5004i	0.123438	−	0.858531i
$213$	−2.58320	+	1.66012i	−0.176998	+	0.113750i
$214$	−20.2642	−	44.3725i	−1.38523	−	3.03324i
$215$	1.59448	+	1.84012i	0.108742	+	0.125495i
$216$	0.697707	+	4.85266i	0.0474730	+	0.330182i
$217$	1.87353	−	4.10245i	0.127183	−	0.278493i
$218$	−13.7784	+	4.04569i	−0.933188	+	0.274009i
$219$	3.82971	−	1.12451i	0.258788	−	0.0759871i
$220$	2.83550	−	6.20887i	0.191169	−	0.418602i
$221$	−1.24716	−	8.67418i	−0.0838929	−	0.583488i
$222$	−9.61520	−	11.0965i	−0.645330	−	0.744750i
$223$	10.3987	+	22.7701i	0.696351	+	1.52480i	0.844341	+	0.535807i	$0.179992\pi$
$223$	10.3987	+	22.7701i	0.696351	+	1.52480i	−0.147990	+	0.988989i	$0.547280\pi$
$224$	0.0103362	−	0.00664264i	0.000690613	−	0.000443830i
$225$	0.694326	−	4.82915i	0.0462884	−	0.321943i
$226$	−8.18530	−	5.26037i	−0.544478	−	0.349915i
$227$	4.59208	−	5.29954i	0.304787	−	0.351743i	−0.582608	−	0.812754i	$-0.697968\pi$
$227$	4.59208	−	5.29954i	0.304787	−	0.351743i	0.887395	+	0.461011i	$0.152513\pi$
$228$	2.62042	+	0.769426i	0.173542	+	0.0509565i
$229$	8.13004			0.537248			0.268624	−	0.963245i	$-0.413431\pi$
$229$	8.13004			0.537248			0.268624	+	0.963245i	$0.413431\pi$
$230$	−2.47145	−	3.25890i	−0.162963	−	0.214885i
$231$	−4.90013			−0.322405
$232$	−47.0798	−	13.8239i	−3.09094	−	0.907581i
$233$	−12.1033	+	13.9680i	−0.792916	+	0.915074i	−0.997971	−	0.0636765i	$-0.979717\pi$
$233$	−12.1033	+	13.9680i	−0.792916	+	0.915074i	0.205054	+	0.978751i	$0.434263\pi$
$234$	10.9907	+	7.06332i	0.718487	+	0.461744i
$235$	0.0382020	−	0.265701i	0.00249202	−	0.0173324i
$236$	40.7701	−	26.2013i	2.65391	−	1.70556i
$237$	3.86639	+	8.46622i	0.251149	+	0.549940i
$238$	−2.63610	−	3.04222i	−0.170873	−	0.197198i
$239$	−0.955123	−	6.64303i	−0.0617818	−	0.429702i	−0.997113	−	0.0759291i	$-0.975808\pi$
$239$	−0.955123	−	6.64303i	−0.0617818	−	0.429702i	0.935331	−	0.353773i	$-0.115101\pi$
$240$	−0.579564	+	1.26907i	−0.0374107	+	0.0819180i
$241$	−7.38739	+	2.16913i	−0.475863	+	0.139726i	−0.510865	−	0.859661i	$-0.670675\pi$
$241$	−7.38739	+	2.16913i	−0.475863	+	0.139726i	0.0350013	+	0.999387i	$0.488856\pi$
$242$	−30.5832	+	8.98005i	−1.96596	+	0.577259i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	−7.05550	−	49.0721i	−0.451682	−	3.14152i
$245$	−0.227978	−	0.263100i	−0.0145650	−	0.0168089i
$246$	5.09305	+	11.1522i	0.324721	+	0.711039i
$247$	3.06224	−	1.96799i	0.194846	−	0.125220i
$248$	−3.14667	+	21.8856i	−0.199814	+	1.38974i
$249$	12.7383	+	8.18639i	0.807255	+	0.518791i
$250$	5.51719	−	6.36717i	0.348937	−	0.402695i
$251$	−11.5682	−	3.39672i	−0.730177	−	0.214399i	−0.104548	−	0.994520i	$-0.533339\pi$
$251$	−11.5682	−	3.39672i	−0.730177	−	0.214399i	−0.625629	+	0.780121i	$0.715158\pi$
$252$	4.00125			0.252055
$253$	−4.85197	+	22.9939i	−0.305041	+	1.44561i
$254$	32.1024			2.01429
$255$	0.548880	+	0.161166i	0.0343722	+	0.0100926i
$256$	20.9621	−	24.1915i	1.31013	−	1.51197i
$257$	−3.65152	−	2.34669i	−0.227776	−	0.146383i	0.421776	−	0.906700i	$-0.361407\pi$
$257$	−3.65152	−	2.34669i	−0.227776	−	0.146383i	−0.649551	+	0.760318i	$0.725043\pi$
$258$	−2.43836	+	16.9591i	−0.151805	+	1.05583i
$259$	−5.04214	+	3.24039i	−0.313304	+	0.201348i
$260$	3.08603	+	6.75747i	0.191388	+	0.419081i
$261$	−6.55418	−	7.56393i	−0.405694	−	0.468195i
$262$	−0.736781	−	5.12442i	−0.0455185	−	0.316588i
$263$	−9.76913	+	21.3914i	−0.602390	+	1.31905i	0.325268	+	0.945622i	$0.394545\pi$
$263$	−9.76913	+	21.3914i	−0.602390	+	1.31905i	−0.927659	+	0.373429i	$0.878182\pi$
$264$	23.0501	−	6.76812i	1.41864	−	0.416549i
$265$	1.05428	−	0.309565i	0.0647639	−	0.0190164i
$266$	0.694603	−	1.52097i	0.0425889	−	0.0932566i
$267$	0.539585	+	3.75290i	0.0330221	+	0.229674i
$268$	−15.1932	−	17.5339i	−0.928075	−	1.07106i
$269$	9.64491	+	21.1194i	0.588060	+	1.28767i	0.936607	+	0.350381i	$0.113948\pi$
$269$	9.64491	+	21.1194i	0.588060	+	1.28767i	−0.348547	+	0.937291i	$0.613325\pi$
$270$	−0.717449	+	0.461077i	−0.0436626	+	0.0280602i
$271$	−3.27046	+	22.7466i	−0.198667	+	1.38176i	0.609493	+	0.792792i	$0.291373\pi$
$271$	−3.27046	+	22.7466i	−0.198667	+	1.38176i	−0.808159	+	0.588964i	$0.799536\pi$
$272$	5.53981	+	3.56022i	0.335900	+	0.215870i
$273$	3.49243	−	4.03048i	0.211372	−	0.243936i
$274$	49.6534	+	14.5795i	2.99967	+	0.880783i
$275$	−23.9068			−1.44163
$276$	3.96193	−	18.7759i	0.238480	−	1.13018i
$277$	−4.34057			−0.260800			−0.130400	−	0.991461i	$-0.541626\pi$
$277$	−4.34057			−0.260800			−0.130400	+	0.991461i	$0.541626\pi$
$278$	15.3734	+	4.51405i	0.922038	+	0.270735i
$279$	−2.95343	+	3.40844i	−0.176817	+	0.204058i
$280$	1.43580	+	0.922731i	0.0858053	+	0.0551437i
$281$	−1.97316	+	13.7236i	−0.117709	+	0.818683i	0.842359	+	0.538916i	$0.181166\pi$
$281$	−1.97316	+	13.7236i	−0.117709	+	0.818683i	−0.960068	+	0.279766i	$0.909743\pi$
$282$	1.58906	−	1.02123i	0.0946271	−	0.0608132i
$283$	−3.61787	−	7.92203i	−0.215060	−	0.470916i	0.771100	−	0.636715i	$-0.219707\pi$
$283$	−3.61787	−	7.92203i	−0.215060	−	0.470916i	−0.986160	+	0.165799i	$0.946980\pi$
$284$	−8.04592	−	9.28549i	−0.477438	−	0.550992i
$285$	0.0338164	+	0.235198i	0.00200311	+	0.0139319i
$286$	26.5944	−	58.2336i	1.57256	−	3.44343i
$287$	4.80193	−	1.40998i	0.283449	−	0.0832282i
$288$	−0.0117889	+	0.00346154i	−0.000694668	+	0.000203973i
$289$	−5.94038	+	13.0076i	−0.349434	+	0.765154i
$290$	−1.21474	−	8.44871i	−0.0713321	−	0.496125i
$291$	−7.27449	−	8.39521i	−0.426438	−	0.492136i
$292$	6.63442	+	14.5274i	0.388250	+	0.850149i
$293$	12.4066	−	7.97322i	0.724800	−	0.465801i	−0.125504	−	0.992093i	$-0.540055\pi$
$293$	12.4066	−	7.97322i	0.724800	−	0.465801i	0.850304	+	0.526292i	$0.176418\pi$
$294$	0.348635	−	2.42481i	0.0203328	−	0.141418i
$295$	3.54723	+	2.27966i	0.206527	+	0.132727i
$296$	19.2425	−	22.2070i	1.11844	−	1.29075i
$297$	4.70164	+	1.38053i	0.272817	+	0.0801063i
$298$	−5.05236			−0.292676
$299$	−15.4549	−	20.3791i	−0.893782	−	1.17855i
$300$	19.5213			1.12706
$301$	6.71070	+	1.97044i	0.386798	+	0.113574i
$302$	0.288925	−	0.333437i	0.0166258	−	0.0191871i
$303$	7.14203	+	4.58990i	0.410299	+	0.263683i
$304$	−0.389278	+	2.70749i	−0.0223266	+	0.155285i
$305$	3.62871	−	2.33203i	0.207779	−	0.133532i
$306$	1.67223	+	3.66167i	0.0955949	+	0.209324i
$307$	19.4650	+	22.4638i	1.11092	+	1.28207i	0.955748	+	0.294188i	$0.0950491\pi$
$307$	19.4650	+	22.4638i	1.11092	+	1.28207i	0.155176	+	0.987887i	$0.450405\pi$
$308$	−2.79032	−	19.4071i	−0.158993	−	1.10582i
$309$	−0.0709670	+	0.155396i	−0.00403717	+	0.00884017i
$310$	−3.69049	+	1.08363i	−0.209606	+	0.0615458i
$311$	−25.0316	+	7.34993i	−1.41941	+	0.416776i	−0.899304	−	0.437325i	$-0.855926\pi$
$311$	−25.0316	+	7.34993i	−1.41941	+	0.416776i	−0.520107	+	0.854101i	$0.674108\pi$
$312$	−10.8614	+	23.7831i	−0.614904	+	1.34645i
$313$	−4.57056	−	31.7890i	−0.258343	−	1.79682i	−0.544633	−	0.838675i	$-0.683331\pi$
$313$	−4.57056	−	31.7890i	−0.258343	−	1.79682i	0.286289	−	0.958143i	$-0.407578\pi$
$314$	−7.71882	−	8.90799i	−0.435598	−	0.502707i
$315$	0.144619	+	0.316672i	0.00814836	+	0.0178424i
$316$	−31.3290	+	20.1339i	−1.76239	+	1.13262i
$317$	−1.38434	+	9.62831i	−0.0777524	+	0.540779i	0.913298	+	0.407292i	$0.133527\pi$
$317$	−1.38434	+	9.62831i	−0.0777524	+	0.540779i	−0.991050	+	0.133488i	$0.957382\pi$
$318$	6.50458	+	4.18024i	0.364759	+	0.234416i
$319$	−32.1163	+	37.0642i	−1.79817	+	2.07520i
$320$	2.66721	+	0.783163i	0.149102	+	0.0437802i
$321$	19.9126			1.11141
$322$	−11.0332	−	4.03695i	−0.614857	−	0.224970i
$323$	1.12157			0.0624058
$324$	−3.83917	−	1.12728i	−0.213287	−	0.0626269i
$325$	17.0389	−	19.6639i	0.945148	−	1.09076i
$326$	0.582601	+	0.374415i	0.0322673	+	0.0207369i
$327$	0.834228	−	5.80218i	0.0461329	−	0.320861i
$328$	−20.6407	+	13.2650i	−1.13969	+	0.732436i
$329$	−0.320313	−	0.701388i	−0.0176594	−	0.0386687i
$330$	2.73666	+	3.15828i	0.150648	+	0.173857i
$331$	−4.66082	−	32.4167i	−0.256182	−	1.78178i	−0.559436	−	0.828873i	$-0.688982\pi$
$331$	−4.66082	−	32.4167i	−0.256182	−	1.78178i	0.303255	−	0.952910i	$-0.401927\pi$
$332$	−25.1688	+	55.1119i	−1.38131	+	3.02466i
$333$	5.75083	−	1.68859i	0.315143	−	0.0925344i
$334$	−44.2561	+	12.9948i	−2.42159	+	0.711043i
$335$	0.838554	−	1.83618i	0.0458151	−	0.100321i
$336$	0.570330	+	3.96673i	0.0311140	+	0.216403i
$337$	13.3217	+	15.3741i	0.725680	+	0.837480i	0.991978	−	0.126411i	$-0.0403459\pi$
$337$	13.3217	+	15.3741i	0.725680	+	0.837480i	−0.266298	+	0.963891i	$0.585800\pi$
$338$	15.7146	+	34.4102i	0.854762	+	1.87167i
$339$	3.34129	−	2.14731i	0.181474	−	0.116626i
$340$	−0.325748	+	2.26563i	−0.0176662	+	0.122871i
$341$	18.5914	+	11.9480i	1.00678	+	0.647020i
$342$	−1.09497	+	1.26367i	−0.0592094	+	0.0683313i
$343$	−0.959493	−	0.281733i	−0.0518078	−	0.0152121i
$344$	−34.2885			−1.84871
$345$	1.62918	−	0.365066i	0.0877120	−	0.0196545i
$346$	−57.7464			−3.10447
$347$	−10.0983	−	2.96513i	−0.542105	−	0.159176i	−0.000795415	−	1.00000i	$-0.500253\pi$
$347$	−10.0983	−	2.96513i	−0.542105	−	0.159176i	−0.541310	+	0.840823i	$0.682071\pi$
$348$	26.2249	−	30.2652i	1.40580	−	1.62238i
$349$	9.42070	+	6.05432i	0.504278	+	0.324080i	0.767926	−	0.640539i	$-0.221289\pi$
$349$	9.42070	+	6.05432i	0.504278	+	0.324080i	−0.263647	+	0.964619i	$0.584925\pi$
$350$	1.70092	−	11.8302i	0.0909181	−	0.632350i
$351$	−4.48648	+	2.88329i	−0.239471	+	0.153899i
$352$	0.0250105	+	0.0547653i	0.00133306	+	0.00291900i
$353$	10.3269	+	11.9179i	0.549645	+	0.634324i	0.960800	−	0.277241i	$-0.0894201\pi$
$353$	10.3269	+	11.9179i	0.549645	+	0.634324i	−0.411156	+	0.911565i	$0.634875\pi$
$354$	4.22270	+	29.3695i	0.224434	+	1.56097i
$355$	0.444075	−	0.972389i	0.0235691	−	0.0516090i
$356$	−14.5562	+	4.27408i	−0.771476	+	0.226526i
$357$	1.57665	−	0.462945i	0.0834449	−	0.0245016i
$358$	−3.96086	+	8.67307i	−0.209338	+	0.458386i
$359$	0.817284	+	5.68434i	0.0431346	+	0.300008i	0.999956	+	0.00933279i	$0.00297076\pi$
$359$	0.817284	+	5.68434i	0.0431346	+	0.300008i	−0.956822	+	0.290675i	$0.906120\pi$
$360$	−1.11767	−	1.28986i	−0.0589066	−	0.0679819i
$361$	−7.69935	−	16.8592i	−0.405229	−	0.887328i
$362$	5.64309	−	3.62660i	0.296594	−	0.190610i
$363$	1.85170	−	12.8789i	0.0971891	−	0.675965i
$364$	17.9516	+	11.5368i	0.940917	+	0.604691i
$365$	−0.909949	+	1.05014i	−0.0476289	+	0.0549667i
$366$	29.1236	+	8.55145i	1.52231	+	0.446991i
$367$	31.7372			1.65667			0.828334	−	0.560235i	$-0.189289\pi$
$367$	31.7372			1.65667			0.828334	+	0.560235i	$0.189289\pi$
$368$	19.1786	+	1.25147i	0.999754	+	0.0652375i
$369$	−5.00466			−0.260532
$370$	4.90450	+	1.44009i	0.254973	+	0.0748667i
$371$	2.06690	−	2.38533i	0.107308	−	0.123840i
$372$	−15.1810	−	9.75625i	−0.787099	−	0.505838i
$373$	−0.945521	+	6.57625i	−0.0489572	+	0.340505i	0.950591	+	0.310446i	$0.100479\pi$
$373$	−0.945521	+	6.57625i	−0.0489572	+	0.340505i	−0.999548	+	0.0300587i	$0.990431\pi$
$374$	16.5939	−	10.6642i	0.858049	−	0.551435i
$375$	1.42866	+	3.12834i	0.0737758	+	0.161547i
$376$	2.47551	+	2.85689i	0.127665	+	0.147333i
$377$	−7.59624	−	52.8330i	−0.391226	−	2.72104i
$378$	−1.01766	+	2.22837i	−0.0523428	+	0.114615i
$379$	−29.2855	+	8.59901i	−1.50430	+	0.441702i	−0.927072	−	0.374883i	$-0.877683\pi$
$379$	−29.2855	+	8.59901i	−1.50430	+	0.441702i	−0.577225	+	0.816585i	$0.695865\pi$
$380$	−0.912252	+	0.267861i	−0.0467975	+	0.0137410i
$381$	−5.44376	+	11.9202i	−0.278892	+	0.610689i
$382$	3.74613	+	26.0549i	0.191669	+	1.33309i
$383$	−9.40355	−	10.8523i	−0.480499	−	0.554525i	0.462803	−	0.886461i	$-0.346844\pi$
$383$	−9.40355	−	10.8523i	−0.480499	−	0.554525i	−0.943302	+	0.331936i	$0.892298\pi$
$384$	8.13618	+	17.8157i	0.415198	+	0.909156i
$385$	1.43509	−	0.922274i	0.0731388	−	0.0470034i
$386$	7.34643	−	51.0955i	0.373923	−	2.60069i
$387$	−5.88373	−	3.78125i	−0.299087	−	0.192212i
$388$	29.1071	−	33.5914i	1.47769	−	1.70534i
$389$	15.2100	+	4.46605i	0.771175	+	0.226438i	0.643570	−	0.765387i	$-0.277453\pi$
$389$	15.2100	+	4.46605i	0.771175	+	0.226438i	0.127606	+	0.991825i	$0.459271\pi$
$390$	−4.54824			−0.230309
$391$	−0.611219	−	7.85680i	−0.0309107	−	0.397336i
$392$	4.90256			0.247617
$393$	2.02772	+	0.595394i	0.102285	+	0.0300336i
$394$	−25.4186	+	29.3347i	−1.28057	+	1.47786i
$395$	−2.72580	−	1.75176i	−0.137150	−	0.0881408i
$396$	−2.79032	+	19.4071i	−0.140219	+	0.975244i
$397$	−12.1423	+	7.80340i	−0.609406	+	0.391642i	−0.808634	−	0.588311i	$-0.799793\pi$
$397$	−12.1423	+	7.80340i	−0.609406	+	0.391642i	0.199228	+	0.979953i	$0.436157\pi$
$398$	4.58823	+	10.0468i	0.229987	+	0.503602i
$399$	0.446974	+	0.515836i	0.0223767	+	0.0258241i
$400$	2.78253	+	19.3529i	0.139126	+	0.967645i
$401$	−1.49097	+	3.26477i	−0.0744556	+	0.163035i	−0.943200	−	0.332226i	$-0.892200\pi$
$401$	−1.49097	+	3.26477i	−0.0744556	+	0.163035i	0.868744	+	0.495261i	$0.164928\pi$
$402$	13.6291	−	4.00187i	0.679759	−	0.199595i
$403$	−23.0780	+	6.77633i	−1.14960	+	0.337553i
$404$	−14.1115	+	30.8998i	−0.702073	+	1.53732i
$405$	−0.0495443	−	0.344588i	−0.00246187	−	0.0171227i
$406$	−16.0561	−	18.5297i	−0.796850	−	0.919613i
$407$	−12.2005	−	26.7154i	−0.604757	−	1.32423i
$408$	−6.77707	+	4.35536i	−0.335515	+	0.215622i
$409$	3.70623	−	25.7774i	0.183261	−	1.27461i	−0.665726	−	0.746197i	$-0.731878\pi$
$409$	3.70623	−	25.7774i	0.183261	−	1.27461i	0.848987	−	0.528414i	$-0.177213\pi$
$410$	−3.59059	−	2.30753i	−0.177326	−	0.113961i
$411$	−13.8336	+	15.9648i	−0.682361	+	0.787486i
$412$	−0.655861	−	0.192578i	−0.0323120	−	0.00948765i
$413$	12.1121			0.595996
$414$	9.44895	+	6.98184i	0.464391	+	0.343139i
$415$	−5.27141			−0.258763
$416$	−0.0628714	−	0.0184607i	−0.00308252	−	0.000905111i
$417$	−4.28309	+	4.94295i	−0.209744	+	0.242057i
$418$	6.89270	+	4.42967i	0.337133	+	0.216662i
$419$	−3.91552	+	27.2331i	−0.191286	+	1.33042i	0.637324	+	0.770596i	$0.280041\pi$
$419$	−3.91552	+	27.2331i	−0.191286	+	1.33042i	−0.828610	+	0.559826i	$0.810868\pi$
$420$	−1.17183	+	0.753092i	−0.0571797	+	0.0367471i
$421$	−2.74589	−	6.01266i	−0.133827	−	0.293039i	0.830841	−	0.556510i	$-0.187860\pi$
$421$	−2.74589	−	6.01266i	−0.133827	−	0.293039i	−0.964667	+	0.263471i	$0.915133\pi$
$422$	6.85135	+	7.90688i	0.333518	+	0.384901i
$423$	0.109734	+	0.763219i	0.00533547	+	0.0371090i
$424$	−6.42801	+	14.0754i	−0.312172	+	0.683561i
$425$	7.69214	−	2.25862i	0.373124	−	0.109559i
$426$	7.21761	−	2.11928i	0.349695	−	0.102680i
$427$	5.14712	−	11.2706i	0.249086	−	0.545423i
$428$	11.3390	+	78.8642i	0.548090	+	3.81205i
$429$	17.1134	+	19.7499i	0.826242	+	0.953534i
$430$	−2.47784	−	5.42570i	−0.119492	−	0.261651i
$431$	−4.74268	+	3.04794i	−0.228447	+	0.146814i	−0.649858	−	0.760056i	$-0.725171\pi$
$431$	−4.74268	+	3.04794i	−0.228447	+	0.146814i	0.421411	+	0.906870i	$0.361535\pi$
$432$	0.570330	−	3.96673i	0.0274400	−	0.190849i
$433$	23.0395	+	14.8066i	1.10721	+	0.711558i	0.960682	−	0.277649i	$-0.0895554\pi$
$433$	23.0395	+	14.8066i	1.10721	+	0.711558i	0.146523	+	0.989207i	$0.453192\pi$
$434$	−7.23516	+	8.34982i	−0.347299	+	0.400804i
$435$	3.34314	+	0.981634i	0.160291	+	0.0470658i
$436$	23.4547			1.12328
$437$	2.86314	−	1.58666i	0.136963	−	0.0759003i
$438$	−9.77790			−0.467206
$439$	36.5201	+	10.7233i	1.74301	+	0.511794i	0.989361	−	0.145483i	$-0.0464736\pi$
$439$	36.5201	+	10.7233i	1.74301	+	0.511794i	0.753649	+	0.657277i	$0.228292\pi$
$440$	−5.47675	+	6.32051i	−0.261094	+	0.301318i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	−3.05522	+	21.2495i	−0.145322	+	1.01074i
$443$	−4.28044	+	2.75087i	−0.203370	+	0.130698i	−0.638362	−	0.769737i	$-0.720388\pi$
$443$	−4.28044	+	2.75087i	−0.203370	+	0.130698i	0.434992	+	0.900434i	$0.356751\pi$
$444$	9.96246	+	21.8147i	0.472797	+	1.03528i
$445$	−0.864374	−	0.997541i	−0.0409753	−	0.0472880i
$446$	−8.72709	−	60.6982i	−0.413240	−	2.87415i
$447$	0.856753	−	1.87603i	0.0405230	−	0.0887331i
$448$	7.66150	−	2.24962i	0.361972	−	0.106285i
$449$	−11.3138	+	3.32203i	−0.533931	+	0.156776i	−0.537573	−	0.843217i	$-0.680659\pi$
$449$	−11.3138	+	3.32203i	−0.533931	+	0.156776i	0.00364201	+	0.999993i	$0.498841\pi$
$450$	−4.96497	+	10.8718i	−0.234051	+	0.512500i
$451$	3.49006	+	24.2739i	0.164340	+	1.14301i
$452$	10.4072	+	12.0105i	0.489511	+	0.564926i
$453$	0.0748164	+	0.163825i	0.00351518	+	0.00769718i
$454$	−14.4514	+	9.28732i	−0.678236	+	0.435876i
$455$	−0.264224	+	1.83772i	−0.0123870	+	0.0861536i
$456$	−2.81503	−	1.80911i	−0.131826	−	0.0847195i
$457$	15.5417	−	17.9360i	0.727008	−	0.839012i	−0.265123	−	0.964215i	$-0.585413\pi$
$457$	15.5417	−	17.9360i	0.727008	−	0.839012i	0.992131	+	0.125202i	$0.0399580\pi$
$458$	−19.1098	−	5.61114i	−0.892941	−	0.262191i
$459$	−1.64321			−0.0766983
$460$	2.37357	+	6.24452i	0.110668	+	0.291152i
$461$	1.60568			0.0747839			0.0373920	−	0.999301i	$-0.488095\pi$
$461$	1.60568			0.0747839			0.0373920	+	0.999301i	$0.488095\pi$
$462$	11.5178	+	3.38194i	0.535858	+	0.157342i
$463$	−0.543077	+	0.626744i	−0.0252389	+	0.0291273i	−0.768229	−	0.640175i	$-0.778862\pi$
$463$	−0.543077	+	0.626744i	−0.0252389	+	0.0291273i	0.742990	+	0.669303i	$0.233407\pi$
$464$	33.7421	+	21.6847i	1.56644	+	1.00669i
$465$	0.223445	−	1.55410i	0.0103620	−	0.0720695i
$466$	38.0894	−	24.4786i	1.76446	−	1.13395i
$467$	−13.5686	−	29.7110i	−0.627878	−	1.37486i	−0.909648	−	0.415380i	$-0.863649\pi$
$467$	−13.5686	−	29.7110i	−0.627878	−	1.37486i	0.281770	−	0.959482i	$-0.409079\pi$
$468$	−13.9741	−	16.1270i	−0.645954	−	0.745470i
$469$	−0.825193	−	5.73934i	−0.0381039	−	0.265018i
$470$	−0.273174	+	0.598167i	−0.0126006	+	0.0275914i
$471$	4.61660	−	1.35556i	0.212722	−	0.0624608i
$472$	−56.9749	+	16.7293i	−2.62248	+	0.770030i
$473$	−14.2369	+	31.1745i	−0.654614	+	1.43341i
$474$	−3.24485	−	22.5684i	−0.149041	−	1.03660i
$475$	2.18070	+	2.51666i	0.100057	+	0.115472i
$476$	2.73131	+	5.98073i	0.125189	+	0.274126i
$477$	−2.65521	+	1.70640i	−0.121573	+	0.0781305i
$478$	−2.33981	+	16.2737i	−0.107020	+	0.744343i
$479$	−8.37381	−	5.38152i	−0.382609	−	0.245888i	0.335172	−	0.942157i	$-0.391206\pi$
$479$	−8.37381	−	5.38152i	−0.382609	−	0.245888i	−0.717781	+	0.696269i	$0.754842\pi$
$480$	0.00280107	−	0.00323261i	0.000127851	−	0.000147548i
$481$	30.6697	+	9.00543i	1.39842	+	0.410612i
$482$	18.8612			0.859105
$483$	3.36994	−	3.41226i	0.153338	−	0.155263i
$484$	52.0615			2.36643
$485$	3.71055	+	1.08952i	0.168488	+	0.0494724i
$486$	1.60424	−	1.85139i	0.0727699	−	0.0839809i
$487$	13.7801	+	8.85596i	0.624438	+	0.401302i	0.814247	−	0.580519i	$-0.197150\pi$
$487$	13.7801	+	8.85596i	0.624438	+	0.401302i	−0.189809	+	0.981821i	$0.560787\pi$
$488$	−8.64480	+	60.1259i	−0.391332	+	2.72177i
$489$	−0.237821	+	0.152838i	−0.0107546	+	0.00691158i
$490$	0.354280	+	0.775765i	0.0160047	+	0.0350455i
$491$	−8.94619	−	10.3245i	−0.403736	−	0.465936i	0.517078	−	0.855938i	$-0.327020\pi$
$491$	−8.94619	−	10.3245i	−0.403736	−	0.465936i	−0.920814	+	0.390002i	$0.872474\pi$
$492$	−2.84984	−	19.8211i	−0.128481	−	0.893603i
$493$	6.83194	−	14.9599i	0.307695	−	0.673758i
$494$	−8.55610	+	2.51230i	−0.384957	+	0.113034i
$495$	−1.63679	+	0.480605i	−0.0735682	+	0.0216016i
$496$	7.50821	−	16.4407i	0.337128	−	0.738208i
$497$	−0.437000	−	3.03940i	−0.0196021	−	0.136336i
$498$	−24.2914	−	28.0338i	−1.08853	−	1.25623i
$499$	4.75256	+	10.4066i	0.212754	+	0.465866i	0.985679	−	0.168631i	$-0.0539347\pi$
$499$	4.75256	+	10.4066i	0.212754	+	0.465866i	−0.772926	+	0.634497i	$0.781207\pi$
$500$	−11.5763	+	7.43965i	−0.517709	+	0.332711i
$501$	2.67954	−	18.6366i	0.119713	−	0.832624i
$502$	24.8468	+	15.9681i	1.10897	+	0.712690i
$503$	22.4704	−	25.9322i	1.00190	−	1.15626i	0.0142039	−	0.999899i	$-0.495479\pi$
$503$	22.4704	−	25.9322i	1.00190	−	1.15626i	0.987700	−	0.156360i	$-0.0499759\pi$
$504$	−4.70397	−	1.38121i	−0.209532	−	0.0615240i
$505$	−2.95555			−0.131520
$506$	27.2744	−	50.6987i	1.21249	−	2.25383i
$507$	−15.4419			−0.685799
$508$	−50.3100	−	14.7724i	−2.23215	−	0.655418i
$509$	−10.5452	+	12.1698i	−0.467408	+	0.539417i	−0.939689	−	0.342031i	$-0.888885\pi$
$509$	−10.5452	+	12.1698i	−0.467408	+	0.539417i	0.472281	+	0.881448i	$0.343431\pi$
$510$	−1.17892	−	0.757644i	−0.0522033	−	0.0335490i
$511$	−0.568035	+	3.95077i	−0.0251284	+	0.174772i
$512$	−33.0150	+	21.2175i	−1.45907	+	0.937688i
$513$	−0.283541	−	0.620868i	−0.0125186	−	0.0274120i
$514$	6.96333	+	8.03611i	0.307139	+	0.354458i
$515$	−0.00846384	−	0.0588673i	−0.000372961	−	0.00259400i
$516$	11.6253	−	25.4559i	0.511775	−	1.12063i
$517$	3.62528	−	1.06448i	0.159440	−	0.0468157i
$518$	14.0881	−	4.13663i	0.618994	−	0.181753i
$519$	9.79234	−	21.4422i	0.429836	−	0.941210i
$520$	−1.29538	−	9.00954i	−0.0568060	−	0.395094i
$521$	−20.5320	−	23.6951i	−0.899521	−	1.03810i	−0.999072	−	0.0430704i	$-0.986286\pi$
$521$	−20.5320	−	23.6951i	−0.899521	−	1.03810i	0.0995508	−	0.995032i	$-0.468259\pi$
$522$	10.1853	+	22.3026i	0.445797	+	0.976160i
$523$	−36.1634	+	23.2408i	−1.58131	+	1.01625i	−0.605990	+	0.795472i	$0.707223\pi$
$523$	−36.1634	+	23.2408i	−1.58131	+	1.01625i	−0.975324	+	0.220777i	$0.929141\pi$
$524$	−1.20341	+	8.36989i	−0.0525712	+	0.365641i
$525$	4.10431	+	2.63768i	0.179127	+	0.115118i
$526$	37.7263	−	43.5384i	1.64494	−	1.89837i
$527$	−7.11069	−	2.08789i	−0.309747	−	0.0909498i
$528$	−19.6374			−0.854608
$529$	−12.6752	−	19.1922i	−0.551095	−	0.834442i
$530$	−2.69175			−0.116922
$531$	−11.6215	−	3.41237i	−0.504328	−	0.148084i
$532$	−1.78846	+	2.06399i	−0.0775395	+	0.0894853i
$533$	−22.4533	−	14.4299i	−0.972561	−	0.625027i
$534$	1.32185	−	9.19364i	0.0572019	−	0.397848i
$535$	−5.83173	+	3.74782i	−0.252128	+	0.162033i
$536$	11.8089	+	25.8580i	0.510068	+	1.11689i
$537$	−2.54880	−	2.94147i	−0.109989	−	0.126934i
$538$	−8.09444	−	56.2981i	−0.348976	−	2.42718i
$539$	2.03559	−	4.45732i	0.0876790	−	0.191990i
$540$	1.33654	−	0.392443i	0.0575154	−	0.0168880i
$541$	31.5904	−	9.27579i	1.35818	−	0.398797i	0.480058	−	0.877237i	$-0.340616\pi$
$541$	31.5904	−	9.27579i	1.35818	−	0.398797i	0.878120	+	0.478440i	$0.158797\pi$
$542$	23.3863	−	51.2089i	1.00453	−	2.19961i
$543$	0.389690	+	2.71036i	0.0167232	+	0.116312i
$544$	−0.0132213	−	0.0152582i	−0.000566857	−	0.000654188i
$545$	0.847735	+	1.85628i	0.0363130	+	0.0795143i
$546$	−10.9907	+	7.06332i	−0.470360	+	0.302282i
$547$	−0.559867	+	3.89396i	−0.0239382	+	0.166494i	−0.998284	−	0.0585637i	$-0.981348\pi$
$547$	−0.559867	+	3.89396i	−0.0239382	+	0.166494i	0.974345	+	0.225058i	$0.0722570\pi$
$548$	−71.1065	−	45.6973i	−3.03752	−	1.95209i
$549$	−8.11392	+	9.36396i	−0.346294	+	0.399644i
$550$	56.1932	+	16.4998i	2.39609	+	0.703555i
$551$	6.83130			0.291023
$552$	−11.1391	+	20.7058i	−0.474111	+	0.881296i
$553$	−9.30730			−0.395787
$554$	10.2026	+	2.99574i	0.433466	+	0.127277i
$555$	−1.36641	+	1.57692i	−0.0580008	+	0.0669365i
$556$	−22.0156	−	14.1486i	−0.933671	−	0.600034i
$557$	−0.488565	+	3.39805i	−0.0207012	+	0.143980i	−0.997551	−	0.0699480i	$-0.977717\pi$
$557$	−0.488565	+	3.39805i	−0.0207012	+	0.143980i	0.976849	+	0.213928i	$0.0686258\pi$
$558$	9.29450	−	5.97321i	0.393467	−	0.252866i
$559$	−15.4949	−	33.9290i	−0.655362	−	1.43504i
$560$	−0.913625	−	1.05438i	−0.0386077	−	0.0445557i
$561$	1.14591	+	7.96997i	0.0483803	+	0.336492i
$562$	14.1096	−	30.8957i	0.595178	−	1.30326i
$563$	8.22947	−	2.41639i	0.346831	−	0.101839i	−0.103677	−	0.994611i	$-0.533061\pi$
$563$	8.22947	−	2.41639i	0.346831	−	0.101839i	0.450508	+	0.892772i	$0.351243\pi$
$564$	−2.96026	+	0.869211i	−0.124650	+	0.0366004i
$565$	−0.574397	+	1.25775i	−0.0241651	+	0.0529141i
$566$	3.03628	+	21.1178i	0.127624	+	0.887647i
$567$	−0.654861	−	0.755750i	−0.0275016	−	0.0317385i
$568$	6.25369	+	13.6937i	0.262399	+	0.574573i
$569$	−1.77119	+	1.13828i	−0.0742522	+	0.0477190i	−0.577240	−	0.816574i	$-0.695870\pi$
$569$	−1.77119	+	1.13828i	−0.0742522	+	0.0477190i	0.502988	+	0.864293i	$0.332234\pi$
$570$	0.0828415	−	0.576176i	0.00346985	−	0.0241333i
$571$	−7.54648	−	4.84983i	−0.315810	−	0.202959i	0.373126	−	0.927781i	$-0.378286\pi$
$571$	−7.54648	−	4.84983i	−0.315810	−	0.202959i	−0.688937	+	0.724822i	$0.741922\pi$
$572$	−68.4750	+	79.0244i	−2.86308	+	3.30417i
$573$	−10.3099	−	3.02726i	−0.430702	−	0.126465i
$574$	−12.2601			−0.511728
$575$	16.4413	−	16.6477i	0.685649	−	0.694258i
$576$	−7.98495			−0.332706
$577$	−28.1441	−	8.26386i	−1.17165	−	0.344029i	−0.362704	−	0.931905i	$-0.618146\pi$
$577$	−28.1441	−	8.26386i	−1.17165	−	0.344029i	−0.808951	+	0.587876i	$0.799964\pi$
$578$	22.9405	−	26.4747i	0.954197	−	1.10120i
$579$	17.7269	+	11.3924i	0.736703	+	0.473450i
$580$	−1.98408	+	13.7996i	−0.0823844	+	0.572996i
$581$	−12.7383	+	8.18639i	−0.528472	+	0.339629i
$582$	11.3046	+	24.7537i	0.468592	+	1.02607i
$583$	10.1281	+	11.6884i	0.419463	+	0.484086i
$584$	−2.78482	−	19.3689i	−0.115237	−	0.801490i
$585$	0.771267	−	1.68884i	0.0318880	−	0.0698249i
$586$	−34.6647	+	10.1785i	−1.43199	+	0.420469i
$587$	44.4026	−	13.0378i	1.83269	−	0.538126i	0.832809	−	0.553561i	$-0.186731\pi$
$587$	44.4026	−	13.0378i	1.83269	−	0.538126i	0.999881	+	0.0154343i	$0.00491309\pi$
$588$	−1.66218	+	3.63967i	−0.0685472	+	0.150097i
$589$	−0.438089	−	3.04697i	−0.0180511	−	0.125548i
$590$	−6.76444	−	7.80658i	−0.278488	−	0.321392i
$591$	−6.58210	−	14.4128i	−0.270751	−	0.592863i
$592$	−20.2065	+	12.9859i	−0.830482	+	0.533719i
$593$	3.71317	−	25.8256i	0.152481	−	1.06053i	−0.759561	−	0.650436i	$-0.774586\pi$
$593$	3.71317	−	25.8256i	0.152481	−	1.06053i	0.912042	−	0.410096i	$-0.134505\pi$
$594$	−10.0985	−	6.48989i	−0.414345	−	0.266284i
$595$	−0.374614	+	0.432328i	−0.0153577	+	0.0177237i
$596$	7.91793	+	2.32491i	0.324331	+	0.0952321i
$597$	−4.50860			−0.184525
$598$	22.2619	+	58.5680i	0.910358	+	2.39502i
$599$	−9.05898			−0.370140			−0.185070	−	0.982725i	$-0.559251\pi$
$599$	−9.05898			−0.370140			−0.185070	+	0.982725i	$0.559251\pi$
$600$	−22.9498	−	6.73866i	−0.936920	−	0.275105i
$601$	7.12503	−	8.22272i	0.290636	−	0.335412i	−0.591589	−	0.806240i	$-0.701499\pi$
$601$	7.12503	−	8.22272i	0.290636	−	0.335412i	0.882225	+	0.470828i	$0.156045\pi$
$602$	−14.4136	−	9.26309i	−0.587456	−	0.377535i
$603$	−0.825193	+	5.73934i	−0.0336045	+	0.233724i
$604$	−0.606231	+	0.389601i	−0.0246672	+	0.0158526i
$605$	1.88168	+	4.12031i	0.0765012	+	0.167514i
$606$	−13.6196	−	15.7179i	−0.553258	−	0.638494i
$607$	1.68510	+	11.7201i	0.0683962	+	0.475706i	0.995017	+	0.0997080i	$0.0317909\pi$
$607$	1.68510	+	11.7201i	0.0683962	+	0.475706i	−0.926621	+	0.375998i	$0.877300\pi$
$608$	0.00348376	−	0.00762837i	0.000141285	−	0.000309371i
$609$	9.60309	−	2.81972i	0.389137	−	0.114261i
$610$	−10.1388	+	2.97703i	−0.410509	+	0.120536i
$611$	−1.70826	+	3.74057i	−0.0691088	+	0.151327i
$612$	−0.935704	−	6.50796i	−0.0378236	−	0.263069i
$613$	−21.5933	−	24.9200i	−0.872146	−	1.00651i	−0.999892	−	0.0147032i	$-0.995320\pi$
$613$	−21.5933	−	24.9200i	−0.872146	−	1.00651i	0.127746	−	0.991807i	$-0.459226\pi$
$614$	−30.2488	−	66.2356i	−1.22074	−	2.67305i
$615$	1.46570	−	0.941947i	0.0591027	−	0.0379830i
$616$	−3.41886	+	23.7787i	−0.137750	+	0.958070i
$617$	−27.9863	−	17.9857i	−1.12668	−	0.724076i	−0.161819	−	0.986820i	$-0.551736\pi$
$617$	−27.9863	−	17.9857i	−1.12668	−	0.724076i	−0.964866	+	0.262744i	$0.915373\pi$
$618$	0.274059	−	0.316281i	0.0110243	−	0.0127227i
$619$	27.5734	+	8.09628i	1.10827	+	0.325417i	0.784133	−	0.620593i	$-0.213108\pi$
$619$	27.5734	+	8.09628i	1.10827	+	0.325417i	0.324136	+	0.946010i	$0.394926\pi$
$620$	6.28228			0.252302
$621$	−4.19478	+	2.32461i	−0.168331	+	0.0932835i
$622$	63.9098			2.56255
$623$	−3.63791	−	1.06819i	−0.145750	−	0.0427960i
$624$	13.9960	−	16.1523i	0.560289	−	0.646608i
$625$	19.5144	+	12.5411i	0.780574	+	0.501645i
$626$	−11.1967	+	77.8748i	−0.447511	+	3.11250i
$627$	−2.81364	+	1.80822i	−0.112366	+	0.0722132i
$628$	7.99759	+	17.5123i	0.319139	+	0.698816i
$629$	6.44955	+	7.44318i	0.257160	+	0.296779i
$630$	−0.121371	−	0.844153i	−0.00483553	−	0.0336319i
$631$	−19.0599	+	41.7354i	−0.758764	+	1.66146i	−0.00881828	+	0.999961i	$0.502807\pi$
$631$	−19.0599	+	41.7354i	−0.758764	+	1.66146i	−0.749945	+	0.661500i	$0.769920\pi$
$632$	43.7813	−	12.8553i	1.74153	−	0.511358i
$633$	−4.09777	+	1.20321i	−0.162872	+	0.0478235i
$634$	9.89911	−	21.6760i	0.393144	−	0.860865i
$635$	−0.649247	−	4.51562i	−0.0257646	−	0.179197i
$636$	−8.27020	−	9.54432i	−0.327935	−	0.378457i
$637$	2.21545	+	4.85115i	0.0877792	+	0.192210i
$638$	101.071	−	64.9542i	4.00143	−	2.57156i
$639$	−0.437000	+	3.03940i	−0.0172874	+	0.120237i
$640$	−5.73599	−	3.68630i	−0.226735	−	0.145714i
$641$	−28.3677	+	32.7381i	−1.12046	+	1.29308i	−0.168891	+	0.985635i	$0.554019\pi$
$641$	−28.3677	+	32.7381i	−1.12046	+	1.29308i	−0.951567	+	0.307443i	$0.900527\pi$
$642$	−46.8047	−	13.7431i	−1.84724	−	0.542397i
$643$	−7.50867			−0.296113			−0.148056	−	0.988979i	$-0.547302\pi$
$643$	−7.50867			−0.296113			−0.148056	+	0.988979i	$0.547302\pi$
$644$	15.4333	+	11.4037i	0.608157	+	0.449368i
$645$	2.43483			0.0958715
$646$	−2.63626	−	0.774077i	−0.103722	−	0.0304556i
$647$	−26.0854	+	30.1042i	−1.02552	+	1.18352i	−0.0426776	+	0.999089i	$0.513589\pi$
$647$	−26.0854	+	30.1042i	−1.02552	+	1.18352i	−0.982846	+	0.184428i	$0.940957\pi$
$648$	4.12430	+	2.65053i	0.162018	+	0.104122i
$649$	−8.44650	+	58.7467i	−0.331554	+	2.30601i
$650$	−53.6217	+	34.4606i	−2.10322	+	1.35165i
$651$	−1.87353	−	4.10245i	−0.0734294	−	0.160788i
$652$	−0.740744	−	0.854864i	−0.0290098	−	0.0334791i
$653$	0.833027	+	5.79383i	0.0325989	+	0.226730i	0.999608	−	0.0280133i	$-0.00891808\pi$
$653$	0.833027	+	5.79383i	0.0325989	+	0.226730i	−0.967009	+	0.254743i	$0.918009\pi$
$654$	−5.96537	+	13.0623i	−0.233265	+	0.510778i
$655$	−0.705915	+	0.207275i	−0.0275824	+	0.00809891i
$656$	19.2439	−	5.65051i	0.751346	−	0.220615i
$657$	1.65809	−	3.63070i	0.0646881	−	0.141647i
$658$	0.268821	+	1.86969i	0.0104797	+	0.0728882i
$659$	3.70449	+	4.27521i	0.144306	+	0.166538i	0.823301	−	0.567604i	$-0.192130\pi$
$659$	3.70449	+	4.27521i	0.144306	+	0.166538i	−0.678995	+	0.734143i	$0.737584\pi$
$660$	−2.83550	−	6.20887i	−0.110372	−	0.241680i
$661$	16.2466	−	10.4411i	0.631919	−	0.406110i	−0.185100	−	0.982720i	$-0.559261\pi$
$661$	16.2466	−	10.4411i	0.631919	−	0.406110i	0.817020	+	0.576610i	$0.195625\pi$
$662$	−11.4178	+	79.4127i	−0.443766	+	3.08646i
$663$	−7.37222	−	4.73784i	−0.286313	−	0.184002i
$664$	48.6133	−	56.1028i	1.88656	−	2.17721i
$665$	−0.227992	−	0.0669444i	−0.00884113	−	0.00259599i
$666$	−14.6828			−0.568948
$667$	−3.72284	−	47.8545i	−0.144149	−	1.85294i
$668$	75.3368			2.91487
$669$	24.0182	+	7.05237i	0.928596	+	0.272661i
$670$	−3.23831	+	3.73721i	−0.125107	+	0.144381i
$671$	51.0760	+	32.8245i	1.97177	+	1.26718i
$672$	0.00174857	−	0.0121615i	6.74524e−5	−	0.000469142i
$673$	−38.9488	+	25.0309i	−1.50137	+	0.964870i	−0.506656	+	0.862148i	$0.669119\pi$
$673$	−38.9488	+	25.0309i	−1.50137	+	0.964870i	−0.994710	+	0.102721i	$0.967245\pi$
$674$	−20.7021	−	45.3313i	−0.797415	−	1.74610i
$675$	−3.19494	−	3.68715i	−0.122973	−	0.141919i
$676$	−8.79320	−	61.1580i	−0.338200	−	2.35223i
$677$	8.27038	−	18.1096i	0.317856	−	0.696009i	−0.681502	−	0.731816i	$-0.738673\pi$
$677$	8.27038	−	18.1096i	0.317856	−	0.696009i	0.999359	+	0.0358074i	$0.0114003\pi$
$678$	−9.33576	+	2.74123i	−0.358538	+	0.105276i
$679$	10.6585	−	3.12961i	0.409035	−	0.120104i
$680$	1.16504	−	2.55108i	0.0446772	−	0.0978295i
$681$	−0.997955	−	6.94093i	−0.0382417	−	0.265977i
$682$	−35.4532	−	40.9152i	−1.35757	−	1.56672i
$683$	−8.89624	−	19.4801i	−0.340405	−	0.745384i	0.659575	−	0.751639i	$-0.270736\pi$
$683$	−8.89624	−	19.4801i	−0.340405	−	0.745384i	−0.999980	+	0.00625504i	$0.998009\pi$
$684$	2.29751	−	1.47652i	0.0878474	−	0.0564561i
$685$	1.04660	−	7.27924i	0.0399884	−	0.278126i
$686$	2.06086	+	1.32443i	0.0786839	+	0.0505671i
$687$	5.32405	−	6.14428i	0.203125	−	0.234419i
$688$	26.8933	+	7.89658i	1.02530	+	0.301054i
$689$	−16.8326			−0.641270
$690$	−4.08137	−	0.266324i	−0.155375	−	0.0101388i
$691$	−34.8381			−1.32530			−0.662652	−	0.748927i	$-0.730569\pi$
$691$	−34.8381			−1.32530			−0.662652	+	0.748927i	$0.730569\pi$
$692$	90.4987	+	26.5728i	3.44024	+	1.01015i
$693$	−3.20890	+	3.70327i	−0.121896	+	0.140676i
$694$	21.6897	+	13.9392i	0.823331	+	0.529123i
$695$	0.324042	−	2.25376i	0.0122916	−	0.0854902i
$696$	−41.2781	+	26.5278i	−1.56464	+	1.00553i
$697$	−3.41624	−	7.48053i	−0.129399	−	0.283345i
$698$	−17.9650	−	20.7327i	−0.679984	−	0.784743i
$699$	2.63031	+	18.2942i	0.0994874	+	0.691950i
$700$	−8.10945	+	17.7572i	−0.306509	+	0.671160i
$701$	−4.46271	+	1.31037i	−0.168554	+	0.0494920i	−0.364921	−	0.931039i	$-0.618904\pi$
$701$	−4.46271	+	1.31037i	−0.168554	+	0.0494920i	0.196367	+	0.980531i	$0.437086\pi$
$702$	12.5355	−	3.68076i	0.473122	−	0.138921i
$703$	−1.69943	+	3.72124i	−0.0640954	+	0.140349i
$704$	5.56839	+	38.7290i	0.209867	+	1.45966i
$705$	−0.175786	−	0.202868i	−0.00662049	−	0.00764045i
$706$	−16.0481	−	35.1404i	−0.603978	−	1.32253i
$707$	−7.14203	+	4.58990i	−0.268603	+	0.172621i
$708$	6.89707	−	47.9702i	0.259208	−	1.80283i
$709$	−1.19987	−	0.771108i	−0.0450620	−	0.0289596i	0.517916	−	0.855432i	$-0.326708\pi$
$709$	−1.19987	−	0.771108i	−0.0450620	−	0.0289596i	−0.562978	+	0.826472i	$0.690344\pi$
$710$	−1.71492	+	1.97912i	−0.0643598	+	0.0742752i
$711$	8.93029	+	2.62217i	0.334912	+	0.0983390i
$712$	18.5880			0.696615
$713$	−21.1059	+	4.72940i	−0.790421	+	0.177117i
$714$	−4.02544			−0.150648
$715$	−8.72915	−	2.56311i	−0.326452	−	0.0958549i
$716$	10.1984	−	11.7696i	0.381132	−	0.439849i
$717$	−5.64594	−	3.62842i	−0.210851	−	0.135506i
$718$	2.00214	−	13.9252i	0.0747191	−	0.519683i
$719$	34.0161	−	21.8608i	1.26859	−	0.815271i	0.279152	−	0.960247i	$-0.409947\pi$
$719$	34.0161	−	21.8608i	1.26859	−	0.815271i	0.989435	+	0.144976i	$0.0463104\pi$
$720$	0.579564	+	1.26907i	0.0215991	+	0.0472954i
$721$	−0.111872	−	0.129108i	−0.00416635	−	0.00480822i
$722$	6.46165	+	44.9417i	0.240478	+	1.67256i
$723$	−3.19839	+	7.00349i	−0.118949	+	0.260463i
$724$	−10.5125	+	3.08676i	−0.390695	+	0.114718i
$725$	46.8516	−	13.7569i	1.74003	−	0.510918i
$726$	−13.2411	+	28.9939i	−0.491423	+	1.07607i
$727$	7.22903	+	50.2790i	0.268110	+	1.86475i	0.466361	+	0.884594i	$0.345565\pi$
$727$	7.22903	+	50.2790i	0.268110	+	1.86475i	−0.198251	+	0.980151i	$0.563526\pi$
$728$	−17.1219	−	19.7597i	−0.634579	−	0.732343i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	2.86362	−	1.84034i	0.105987	−	0.0681140i
$731$	1.63557	−	11.3756i	0.0604936	−	0.420742i
$732$	−41.7066	−	26.8032i	−1.54152	−	0.990675i
$733$	28.0976	−	32.4264i	1.03781	−	1.19770i	0.0578851	−	0.998323i	$-0.481564\pi$
$733$	28.0976	−	32.4264i	1.03781	−	1.19770i	0.979924	−	0.199372i	$-0.0638903\pi$
$734$	−74.5987	−	21.9041i	−2.75349	−	0.808497i
$735$	−0.348131			−0.0128410
$736$	−0.0553367	−	0.0202472i	−0.00203974	−	0.000746321i
$737$	28.4127			1.04660
$738$	11.7635	+	3.45408i	0.433021	+	0.127146i
$739$	9.41391	−	10.8642i	0.346296	−	0.399647i	−0.555706	−	0.831379i	$-0.687552\pi$
$739$	9.41391	−	10.8642i	0.346296	−	0.399647i	0.902002	+	0.431732i	$0.142097\pi$
$740$	−7.02352	−	4.51374i	−0.258190	−	0.165928i
$741$	0.518040	−	3.60305i	0.0190307	−	0.132361i
$742$	−6.50458	+	4.18024i	−0.238791	+	0.153461i
$743$	0.553765	+	1.21258i	0.0203157	+	0.0444851i	0.919518	−	0.393048i	$-0.128579\pi$
$743$	0.553765	+	1.21258i	0.0203157	+	0.0444851i	−0.899202	+	0.437533i	$0.855852\pi$
$744$	14.4794	+	16.7101i	0.530840	+	0.612622i
$745$	0.102180	+	0.710679i	0.00374359	+	0.0260373i
$746$	6.76121	−	14.8050i	0.247545	−	0.542049i
$747$	14.5286	−	4.26600i	0.531575	−	0.156085i
$748$	−30.9128	+	9.07681i	−1.13028	+	0.331881i
$749$	−8.27198	+	18.1131i	−0.302251	+	0.661838i
$750$	−1.19900	−	8.33922i	−0.0437813	−	0.304505i
$751$	−7.54740	−	8.71016i	−0.275408	−	0.317838i	0.601148	−	0.799138i	$-0.294710\pi$
$751$	−7.54740	−	8.71016i	−0.275408	−	0.317838i	−0.876556	+	0.481300i	$0.840165\pi$
$752$	−1.28366	−	2.81083i	−0.0468103	−	0.102500i
$753$	−10.1426	+	6.51826i	−0.369617	+	0.237539i
$754$	−18.6089	+	129.427i	−0.677695	+	4.71347i
$755$	−0.0527455	−	0.0338974i	−0.00191960	−	0.00123365i
$756$	2.62026	−	3.02395i	0.0952981	−	0.109980i
$757$	45.4899	+	13.3570i	1.65336	+	0.485470i	0.969693	−	0.244325i	$-0.0785664\pi$
$757$	45.4899	+	13.3570i	1.65336	+	0.485470i	0.683666	+	0.729795i	$0.260385\pi$
$758$	74.7709			2.71580
$759$	14.2002	+	18.7247i	0.515436	+	0.679662i
$760$	1.16493			0.0422565
$761$	43.4441	+	12.7563i	1.57485	+	0.462417i	0.948408	−	0.317053i	$-0.102693\pi$
$761$	43.4441	+	12.7563i	1.57485	+	0.462417i	0.626439	+	0.779470i	$0.284512\pi$
$762$	21.0226	−	24.2614i	0.761569	−	0.878898i
$763$	4.93130	+	3.16915i	0.178525	+	0.114731i
$764$	6.11869	−	42.5564i	0.221366	−	1.53964i
$765$	0.481241	−	0.309275i	0.0173993	−	0.0111818i
$766$	14.6132	+	31.9985i	0.527997	+	1.15615i
$767$	−42.3006	−	48.8175i	−1.52739	−	1.76270i
$768$	−4.55550	−	31.6842i	−0.164382	−	1.14330i
$769$	−4.01079	+	8.78240i	−0.144633	+	0.316701i	−0.968059	−	0.250721i	$-0.919332\pi$
$769$	−4.01079	+	8.78240i	−0.144633	+	0.316701i	0.823427	+	0.567423i	$0.192059\pi$
$770$	−4.00972	+	1.17736i	−0.144500	+	0.0424291i
$771$	−4.16475	+	1.22288i	−0.149990	+	0.0440410i
$772$	−35.0254	+	76.6949i	−1.26059	+	2.76031i
$773$	−1.96725	−	13.6825i	−0.0707570	−	0.492125i	−0.994127	−	0.108215i	$-0.965486\pi$
$773$	−1.96725	−	13.6825i	−0.0707570	−	0.492125i	0.923371	−	0.383910i	$-0.125423\pi$
$774$	11.2201	+	12.9487i	0.403297	+	0.465430i
$775$	−9.14058	−	20.0151i	−0.328339	−	0.718963i
$776$	−45.8146	+	29.4432i	−1.64465	+	1.05695i
$777$	−0.852979	+	5.93260i	−0.0306005	+	0.212831i
$778$	−32.6689	−	20.9950i	−1.17124	−	0.752707i
$779$	2.23695	−	2.58158i	0.0801472	−	0.0924948i
$780$	7.12788	+	2.09293i	0.255219	+	0.0749391i
$781$	15.0466			0.538410
$782$	−3.98588	+	18.8894i	−0.142535	+	0.675482i
$783$	−10.0085			−0.357675
$784$	−3.84519	−	1.12905i	−0.137328	−	0.0403232i
$785$	−1.09692	+	1.26591i	−0.0391506	+	0.0451822i
$786$	−4.35527	−	2.79896i	−0.155347	−	0.0998356i
$787$	1.58260	−	11.0072i	0.0564136	−	0.392365i	−0.941978	−	0.335674i	$-0.891036\pi$
$787$	1.58260	−	11.0072i	0.0564136	−	0.392365i	0.998392	−	0.0566910i	$-0.0180550\pi$
$788$	53.3341	−	34.2758i	1.89995	−	1.22102i
$789$	9.76913	+	21.3914i	0.347790	+	0.761554i
$790$	5.19801	+	5.99882i	0.184937	+	0.213428i
$791$	0.565245	+	3.93137i	0.0200978	+	0.139783i
$792$	9.97960	−	21.8523i	0.354610	−	0.776487i
$793$	−63.4020	+	18.6165i	−2.25147	+	0.661091i
$794$	33.9264	−	9.96170i	1.20400	−	0.353527i
$795$	0.456454	−	0.999494i	0.0161887	−	0.0354484i
$796$	−2.56737	−	17.8564i	−0.0909980	−	0.632905i
$797$	24.3442	+	28.0948i	0.862318	+	0.995167i	0.999989	+	0.00468952i	$0.00149272\pi$
$797$	24.3442	+	28.0948i	0.862318	+	0.995167i	−0.137671	+	0.990478i	$0.543962\pi$
$798$	−0.694603	−	1.52097i	−0.0245887	−	0.0538417i
$799$	−1.06589	+	0.685004i	−0.0377084	+	0.0242337i
$800$	0.00853092	−	0.0593338i	0.000301613	−	0.00209777i
$801$	3.18960	+	2.04983i	0.112699	+	0.0724273i
$802$	5.75781	−	6.64487i	0.203315	−	0.234638i
$803$	−18.7661	−	5.51023i	−0.662242	−	0.194452i
$804$	−23.2007			−0.818226
$805$	−0.344710	+	1.63361i	−0.0121494	+	0.0575771i
$806$	58.9221			2.07544
$807$	22.2770	+	6.54113i	0.784189	+	0.230259i
$808$	27.2563	−	31.4554i	0.958872	−	1.10660i
$809$	16.9780	+	10.9111i	0.596914	+	0.383614i	0.803930	−	0.594724i	$-0.202739\pi$
$809$	16.9780	+	10.9111i	0.596914	+	0.383614i	−0.207016	+	0.978338i	$0.566375\pi$
$810$	−0.121371	+	0.844153i	−0.00426454	+	0.0296605i
$811$	−46.4277	+	29.8373i	−1.63030	+	1.04773i	−0.681512	+	0.731807i	$0.738677\pi$
$811$	−46.4277	+	29.8373i	−1.63030	+	1.04773i	−0.948785	+	0.315921i	$0.897686\pi$
$812$	16.6360	+	36.4277i	0.583807	+	1.27836i
$813$	15.0490	+	17.3675i	0.527792	+	0.609104i
$814$	10.2392	+	71.2154i	0.358885	+	2.49610i
$815$	0.0408836	−	0.0895225i	0.00143209	−	0.00313584i
$816$	6.31844	−	1.85526i	0.221190	−	0.0649471i
$817$	4.58038	−	1.34492i	0.160247	−	0.0470528i
$818$	−26.5024	+	58.0322i	−0.926635	+	2.02905i
$819$	−0.758978	−	5.27881i	−0.0265209	−	0.184457i
$820$	4.56523	+	5.26856i	0.159425	+	0.183986i
$821$	2.74362	+	6.00770i	0.0957531	+	0.209670i	0.951447	−	0.307812i	$-0.0995967\pi$
$821$	2.74362	+	6.00770i	0.0957531	+	0.209670i	−0.855694	+	0.517482i	$0.826869\pi$
$822$	43.5345	−	27.9779i	1.51844	−	0.975843i
$823$	3.35547	−	23.3378i	0.116964	−	0.813504i	−0.843903	−	0.536495i	$-0.819748\pi$
$823$	3.35547	−	23.3378i	0.116964	−	0.813504i	0.960867	−	0.277008i	$-0.0893430\pi$
$824$	0.704570	+	0.452800i	0.0245449	+	0.0157740i
$825$	−15.6556	+	18.0675i	−0.545059	+	0.629031i
$826$	−28.4696	−	8.35943i	−0.990584	−	0.290862i
$827$	18.4185			0.640473			0.320236	−	0.947338i	$-0.396238\pi$
$827$	18.4185			0.640473			0.320236	+	0.947338i	$0.396238\pi$
$828$	−11.5954	−	15.2898i	−0.402966	−	0.531358i
$829$	−24.8739			−0.863907			−0.431953	−	0.901896i	$-0.642176\pi$
$829$	−24.8739			−0.863907			−0.431953	+	0.901896i	$0.642176\pi$
$830$	12.3905	+	3.63818i	0.430081	+	0.126283i
$831$	−2.84247	+	3.28038i	−0.0986041	+	0.113795i
$832$	−35.8243	−	23.0229i	−1.24199	−	0.798175i
$833$	−0.233853	+	1.62648i	−0.00810251	+	0.0563542i
$834$	13.4790	−	8.66240i	0.466738	−	0.299954i
$835$	2.72293	+	5.96238i	0.0942308	+	0.206337i
$836$	−8.76368	−	10.1138i	−0.303098	−	0.349794i
$837$	0.641842	+	4.46411i	0.0221853	+	0.154302i
$838$	27.9990	−	61.3093i	0.967210	−	2.11789i
$839$	−44.2807	+	13.0020i	−1.52874	+	0.448878i	−0.934664	−	0.355531i	$-0.884300\pi$
$839$	−44.2807	+	13.0020i	−1.52874	+	0.448878i	−0.594075	+	0.804410i	$0.702482\pi$
$840$	1.63760	−	0.480843i	0.0565026	−	0.0165907i
$841$	29.5652	−	64.7388i	1.01949	−	2.23237i
$842$	2.30448	+	16.0280i	0.0794175	+	0.552361i
$843$	9.07948	+	10.4783i	0.312714	+	0.360891i
$844$	−7.09879	−	15.5442i	−0.244350	−	0.535053i
$845$	4.52242	−	2.90638i	0.155576	−	0.0999826i
$846$	0.268821	−	1.86969i	0.00924226	−	0.0642813i
$847$	10.9458	+	7.03444i	0.376102	+	0.241706i
$848$	8.28316	−	9.55928i	0.284445	−	0.328267i
$849$	−8.35627	−	2.45362i	−0.286787	−	0.0842081i
$850$	−19.6393			−0.673623
$851$	26.9941	+	9.87690i	0.925347	+	0.338576i
$852$	−12.2865			−0.420927
$853$	3.51076	+	1.03085i	0.120206	+	0.0352957i	0.341282	−	0.939961i	$-0.389139\pi$
$853$	3.51076	+	1.03085i	0.120206	+	0.0352957i	−0.221076	+	0.975257i	$0.570957\pi$
$854$	−19.8770	+	22.9393i	−0.680178	+	0.784968i
$855$	0.199896	+	0.128465i	0.00683630	+	0.00439342i
$856$	13.8931	−	96.6289i	0.474858	−	3.30271i
$857$	1.19909	−	0.770608i	0.0409601	−	0.0263235i	−0.520001	−	0.854166i	$-0.674068\pi$
$857$	1.19909	−	0.770608i	0.0409601	−	0.0263235i	0.560961	+	0.827842i	$0.310432\pi$
$858$	−26.5944	−	58.2336i	−0.907918	−	1.98806i
$859$	16.6808	+	19.2506i	0.569141	+	0.656824i	0.965234	−	0.261387i	$-0.0841798\pi$
$859$	16.6808	+	19.2506i	0.569141	+	0.656824i	−0.396093	+	0.918210i	$0.629634\pi$
$860$	1.38649	+	9.64322i	0.0472788	+	0.328831i
$861$	2.07901	−	4.55240i	0.0708525	−	0.155145i
$862$	13.2513	−	3.89094i	0.451342	−	0.132526i
$863$	−33.1458	+	9.73247i	−1.12829	+	0.331297i	−0.792037	−	0.610473i	$-0.790979\pi$
$863$	−33.1458	+	9.73247i	−1.12829	+	0.331297i	−0.336258	+	0.941770i	$0.609161\pi$
$864$	−0.00510404	+	0.0111763i	−0.000173643	+	0.000380225i
$865$	1.16788	+	8.12277i	0.0397091	+	0.276183i
$866$	−43.9355	−	50.7042i	−1.49299	−	1.72300i
$867$	5.94038	+	13.0076i	0.201746	+	0.441762i
$868$	15.1810	−	9.75625i	0.515277	−	0.331149i
$869$	6.49055	−	45.1428i	0.220177	−	1.53136i
$870$	−7.18060	−	4.61469i	−0.243445	−	0.156453i
$871$	−20.2504	+	23.3702i	−0.686159	+	0.791869i
$872$	−27.5740	−	8.09645i	−0.933773	−	0.274180i
$873$	−11.1085			−0.375964
$874$	−7.82493	+	1.75341i	−0.264682	+	0.0593098i
$875$	−3.43912			−0.116264
$876$	15.3237	+	4.49943i	0.517738	+	0.152022i
$877$	4.52642	−	5.22376i	0.152846	−	0.176394i	−0.674162	−	0.738583i	$-0.735495\pi$
$877$	4.52642	−	5.22376i	0.152846	−	0.176394i	0.827009	+	0.562189i	$0.190041\pi$
$878$	−78.4401	−	50.4104i	−2.64723	−	1.70127i
$879$	2.09882	−	14.5976i	0.0707915	−	0.492365i
$880$	5.75114	−	3.69603i	0.193871	−	0.124593i
$881$	−6.31819	−	13.8349i	−0.212865	−	0.466110i	0.772837	−	0.634604i	$-0.218837\pi$
$881$	−6.31819	−	13.8349i	−0.212865	−	0.466110i	−0.985703	+	0.168494i	$0.946110\pi$
$882$	−1.60424	−	1.85139i	−0.0540176	−	0.0623397i
$883$	1.86253	+	12.9542i	0.0626791	+	0.435942i	0.996863	+	0.0791500i	$0.0252206\pi$
$883$	1.86253	+	12.9542i	0.0626791	+	0.435942i	−0.934184	+	0.356793i	$0.883870\pi$
$884$	14.5663	−	31.8958i	0.489918	−	1.07277i
$885$	4.04579	−	1.18795i	0.135998	−	0.0399326i
$886$	11.9598	−	3.51171i	0.401797	−	0.117978i
$887$	9.91224	−	21.7048i	0.332821	−	0.728775i	−0.667048	−	0.745015i	$-0.732442\pi$
$887$	9.91224	−	21.7048i	0.332821	−	0.728775i	0.999868	+	0.0162397i	$0.00516949\pi$
$888$	−4.18178	−	29.0850i	−0.140332	−	0.976027i
$889$	−8.58155	−	9.90364i	−0.287816	−	0.332157i
$890$	1.34325	+	2.94130i	0.0450258	+	0.0985927i
$891$	4.12225	−	2.64921i	0.138101	−	0.0887519i
$892$	−14.2543	+	99.1405i	−0.477268	+	3.31947i
$893$	−0.442744	−	0.284534i	−0.0148159	−	0.00952158i
$894$	−3.30859	+	3.81832i	−0.110656	+	0.127704i
$895$	1.30008	+	0.381739i	0.0434570	+	0.0127601i
$896$	−19.5857			−0.654311
$897$	−25.5223	−	1.66542i	−0.852166	−	0.0556069i
$898$	28.8860			0.963939
$899$	−43.3101	−	12.7170i	−1.44447	−	0.424135i
$900$	12.7838	−	14.7532i	0.426125	−	0.491775i
$901$	−4.36305	−	2.80396i	−0.145354	−	0.0934135i
$902$	8.54975	−	59.4648i	0.284675	−	1.97996i
$903$	5.88373	−	3.78125i	0.195798	−	0.125832i
$904$	−8.08895	−	17.7123i	−0.269034	−	0.589103i
$905$	−0.624254	−	0.720428i	−0.0207509	−	0.0239478i
$906$	−0.0627894	−	0.436710i	−0.00208604	−	0.0145087i
$907$	12.2642	−	26.8548i	0.407225	−	0.891698i	−0.589261	−	0.807943i	$-0.700581\pi$
$907$	12.2642	−	26.8548i	0.407225	−	0.891698i	0.996486	−	0.0837559i	$-0.0266916\pi$
$908$	26.9214	−	7.90485i	0.893420	−	0.262332i
$909$	8.14585	−	2.39184i	0.270181	−	0.0793322i
$910$	1.88941	−	4.13723i	0.0626333	−	0.137148i
$911$	5.14742	+	35.8011i	0.170542	+	1.18614i	0.877743	+	0.479132i	$0.159048\pi$
$911$	5.14742	+	35.8011i	0.170542	+	1.18614i	−0.707201	+	0.707012i	$0.750043\pi$
$912$	1.79126	+	2.06722i	0.0593146	+	0.0684526i
$913$	−30.8229	−	67.4927i	−1.02009	−	2.23368i
$914$	−48.9098	+	31.4325i	−1.61779	+	1.03969i
$915$	0.613868	−	4.26955i	0.0202939	−	0.141147i
$916$	27.3663	+	17.5872i	0.904207	+	0.581099i
$917$	−1.38394	+	1.59715i	−0.0457016	+	0.0527425i
$918$	3.86238	+	1.13410i	0.127478	+	0.0374308i
$919$	35.1961			1.16101			0.580506	−	0.814256i	$-0.302855\pi$
$919$	35.1961			1.16101			0.580506	+	0.814256i	$0.302855\pi$
$920$	−0.634850	−	8.16056i	−0.0209304	−	0.269046i
$921$	29.7238			0.979433
$922$	−3.77417	−	1.10820i	−0.124296	−	0.0364965i
$923$	−10.7241	+	12.3762i	−0.352987	+	0.407368i
$924$	−16.4942	−	10.6002i	−0.542619	−	0.348720i
$925$	−4.16152	+	28.9440i	−0.136830	+	0.951673i
$926$	1.70907	−	1.09835i	0.0561636	−	0.0360941i
$927$	0.0709670	+	0.155396i	0.00233086	+	0.00510387i
$928$	−0.0805287	−	0.0929350i	−0.00264348	−	0.00305074i
$929$	1.62445	+	11.2983i	0.0532964	+	0.370685i	0.998962	+	0.0455448i	$0.0145024\pi$
$929$	1.62445	+	11.2983i	0.0532964	+	0.370685i	−0.945666	+	0.325140i	$0.894589\pi$
$930$	−1.59781	+	3.49871i	−0.0523942	+	0.114727i
$931$	−0.654901	+	0.192296i	−0.0214635	+	0.00630226i
$932$	−70.9568	+	20.8348i	−2.32427	+	0.682467i
$933$	−10.8375	+	23.7308i	−0.354803	+	0.776911i
$934$	11.3874	+	79.2008i	0.372606	+	2.59153i
$935$	−1.83566	−	2.11846i	−0.0600325	−	0.0692812i
$936$	10.8614	+	23.7831i	0.355015	+	0.777374i
$937$	−7.14670	+	4.59290i	−0.233472	+	0.150044i	−0.652147	−	0.758093i	$-0.726131\pi$
$937$	−7.14670	+	4.59290i	−0.233472	+	0.150044i	0.418674	+	0.908137i	$0.362495\pi$
$938$	−2.02151	+	14.0599i	−0.0660047	+	0.459073i
$939$	−27.0176	−	17.3631i	−0.881685	−	0.566625i
$940$	0.703365	−	0.811726i	0.0229412	−	0.0264756i
$941$	14.0577	+	4.12771i	0.458268	+	0.134560i	0.502715	−	0.864452i	$-0.332335\pi$
$941$	14.0577	+	4.12771i	0.458268	+	0.134560i	−0.0444474	+	0.999012i	$0.514153\pi$
$942$	−11.7870			−0.384040
$943$	−19.3035	−	14.2634i	−0.628610	−	0.464481i
$944$	48.5394			1.57982
$945$	0.334030	+	0.0980800i	0.0108660	+	0.00319054i
$946$	54.9799	−	63.4502i	1.78755	−	2.06294i
$947$	−27.4666	−	17.6517i	−0.892545	−	0.573604i	0.0120256	−	0.999928i	$-0.496172\pi$
$947$	−27.4666	−	17.6517i	−0.892545	−	0.573604i	−0.904571	+	0.426324i	$0.859808\pi$
$948$	−5.29993	+	36.8618i	−0.172134	+	1.19722i
$949$	17.9073	−	11.5083i	0.581296	−	0.373577i
$950$	−3.38883	−	7.42051i	−0.109948	−	0.240753i
$951$	6.37004	+	7.35141i	0.206563	+	0.238386i
$952$	−1.14648	−	7.97392i	−0.0371575	−	0.258436i
$953$	−19.0476	+	41.7085i	−0.617014	+	1.35107i	0.300658	+	0.953732i	$0.402794\pi$
$953$	−19.0476	+	41.7085i	−0.617014	+	1.35107i	−0.917672	+	0.397339i	$0.869934\pi$
$954$	7.41880	−	2.17836i	0.240193	−	0.0705269i
$955$	3.58920	−	1.05388i	0.116144	−	0.0341029i
$956$	11.1555	−	24.4270i	0.360793	−	0.790027i
$957$	6.97955	+	48.5438i	0.225617	+	1.56920i
$958$	15.9686	+	18.4287i	0.515921	+	0.595405i
$959$	−8.77543	−	19.2155i	−0.283373	−	0.620501i
$960$	2.33853	−	1.50288i	0.0754756	−	0.0485052i
$961$	1.51704	−	10.5513i	0.0489369	−	0.340363i
$962$	−65.8742	−	42.3348i	−2.12387	−	1.36493i
$963$	13.0400	−	15.0489i	0.420207	−	0.484944i
$964$	−29.5588	−	8.67925i	−0.952025	−	0.279540i
$965$	−7.33581			−0.236148
$966$	−10.2761	+	5.69471i	−0.330629	+	0.183224i
$967$	13.8978			0.446923			0.223462	−	0.974713i	$-0.428264\pi$
$967$	13.8978			0.446923			0.223462	+	0.974713i	$0.428264\pi$
$968$	−61.2048	−	17.9713i	−1.96720	−	0.577621i
$969$	0.734471	−	0.847625i	0.0235946	−	0.0272296i
$970$	−7.96975	−	5.12185i	−0.255893	−	0.164453i
$971$	−1.75793	+	12.2267i	−0.0564147	+	0.392373i	0.941977	+	0.335678i	$0.108965\pi$
$971$	−1.75793	+	12.2267i	−0.0564147	+	0.392373i	−0.998392	+	0.0566950i	$0.981944\pi$
$972$	−3.36607	+	2.16324i	−0.107967	+	0.0693860i
$973$	−2.71701	−	5.94941i	−0.0871032	−	0.190729i
$974$	−26.2783	−	30.3267i	−0.842010	−	0.971732i
$975$	−3.70291	−	25.7543i	−0.118588	−	0.824797i
$976$	20.6272	−	45.1672i	0.660260	−	1.44577i
$977$	3.22826	−	0.947904i	0.103281	−	0.0303261i	−0.229684	−	0.973265i	$-0.573769\pi$
$977$	3.22826	−	0.947904i	0.103281	−	0.0303261i	0.332965	+	0.942939i	$0.391951\pi$
$978$	0.664486	−	0.195111i	0.0212479	−	0.00623895i
$979$	7.71791	−	16.8999i	0.246665	−	0.540122i
$980$	−0.198239	−	1.37878i	−0.00633252	−	0.0440436i
$981$	−3.83869	−	4.43009i	−0.122560	−	0.141442i
$982$	13.9025	+	30.4422i	0.443646	+	0.971449i
$983$	31.8051	−	20.4399i	1.01443	−	0.651932i	0.0758905	−	0.997116i	$-0.475820\pi$
$983$	31.8051	−	20.4399i	1.01443	−	0.651932i	0.938535	+	0.345185i	$0.112184\pi$
$984$	−3.49179	+	24.2859i	−0.111314	+	0.774206i
$985$	4.64037	+	2.98218i	0.147854	+	0.0950203i
$986$	−26.3834	+	30.4481i	−0.840220	+	0.969666i
$987$	−0.739834	−	0.217235i	−0.0235492	−	0.00691466i
$988$	14.5650			0.463373
$989$	−11.9176	−	31.3535i	−0.378957	−	0.996983i
$990$	4.17900			0.132817
$991$	−28.6876	−	8.42345i	−0.911293	−	0.267580i	−0.207708	−	0.978191i	$-0.566600\pi$
$991$	−28.6876	−	8.42345i	−0.911293	−	0.267580i	−0.703585	+	0.710611i	$0.748419\pi$
$992$	−0.0362877	+	0.0418782i	−0.00115213	+	0.00132963i
$993$	−27.5511	−	17.7060i	−0.874307	−	0.561883i
$994$	−1.07054	+	7.44575i	−0.0339554	+	0.236165i
$995$	1.32042	−	0.848583i	0.0418601	−	0.0269019i
$996$	25.1688	+	55.1119i	0.797502	+	1.74629i
$997$	7.09601	+	8.18923i	0.224733	+	0.259356i	0.856907	−	0.515470i	$-0.172383\pi$
$997$	7.09601	+	8.18923i	0.224733	+	0.259356i	−0.632174	+	0.774826i	$0.717837\pi$
$998$	−3.98856	−	27.7411i	−0.126256	−	0.878128i
$999$	2.48984	−	5.45198i	0.0787749	−	0.172493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.64.1	✓	60
23.9	even	11	inner	483.2.q.d.400.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.64.1	✓	60	1.1	even	1	trivial
483.2.q.d.400.1	yes	60	23.9	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35051 - 0.690173i) q^{2} +(0.654861 - 0.755750i) q^{3} +(3.36607 + 2.16324i) q^{4} +(-0.0495443 + 0.344588i) q^{5} +(-2.06086 + 1.32443i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-3.21050 - 3.70511i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-2.35051 - 0.690173i) q^{2} +(0.654861 - 0.755750i) q^{3} +(3.36607 + 2.16324i) q^{4} +(-0.0495443 + 0.344588i) q^{5} +(-2.06086 + 1.32443i) q^{6} +(0.415415 + 0.909632i) q^{7} +(-3.21050 - 3.70511i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.354280 - 0.775765i) q^{10} +(-4.70164 + 1.38053i) q^{11} +(3.83917 - 1.12728i) q^{12} +(2.21545 - 4.85115i) q^{13} +(-0.348635 - 2.42481i) q^{14} +(0.227978 + 0.263100i) q^{15} +(1.66478 + 3.64537i) q^{16} +(1.38235 - 0.888385i) q^{17} +(-0.348635 + 2.42481i) q^{18} +(0.574197 + 0.369014i) q^{19} +(-0.912196 + 1.05273i) q^{20} +(0.959493 + 0.281733i) q^{21} +12.0041 q^{22} +(2.27209 - 4.22346i) q^{23} -4.90256 q^{24} +(4.68118 + 1.37452i) q^{25} +(-8.55557 + 9.87366i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.569438 + 3.96053i) q^{28} +(8.41969 - 5.41101i) q^{29} +(-0.354280 - 0.775765i) q^{30} +(-2.95343 - 3.40844i) q^{31} +(-0.00174857 - 0.0121615i) q^{32} +(-2.03559 + 4.45732i) q^{33} +(-3.86238 + 1.13410i) q^{34} +(-0.334030 + 0.0980800i) q^{35} +(1.66218 - 3.63967i) q^{36} +(0.852979 + 5.93260i) q^{37} +(-1.09497 - 1.26367i) q^{38} +(-2.21545 - 4.85115i) q^{39} +(1.43580 - 0.922731i) q^{40} +(0.712237 - 4.95372i) q^{41} +(-2.06086 - 1.32443i) q^{42} +(4.58010 - 5.28572i) q^{43} +(-18.8125 - 5.52384i) q^{44} +0.348131 q^{45} +(-8.25550 + 8.35916i) q^{46} -0.771067 q^{47} +(3.84519 + 1.12905i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-10.0545 - 6.46165i) q^{50} +(0.233853 - 1.62648i) q^{51} +(17.9516 - 11.5368i) q^{52} +(-1.31115 - 2.87102i) q^{53} +(1.60424 + 1.85139i) q^{54} +(-0.242773 - 1.68853i) q^{55} +(2.03660 - 4.45953i) q^{56} +(0.654901 - 0.192296i) q^{57} +(-23.5251 + 6.90760i) q^{58} +(5.03154 - 11.0175i) q^{59} +(0.198239 + 1.37878i) q^{60} +(-8.11392 - 9.36396i) q^{61} +(4.58967 + 10.0500i) q^{62} +(0.841254 - 0.540641i) q^{63} +(1.13638 - 7.90367i) q^{64} +(1.56189 + 1.00376i) q^{65} +(7.86100 - 9.07208i) q^{66} +(-5.56349 - 1.63359i) q^{67} +6.57489 q^{68} +(-1.70397 - 4.48291i) q^{69} +0.852833 q^{70} +(-2.94627 - 0.865103i) q^{71} +(-3.21050 + 3.70511i) q^{72} +(3.35777 + 2.15791i) q^{73} +(2.08958 - 14.5334i) q^{74} +(4.10431 - 2.63768i) q^{75} +(1.13452 + 2.48425i) q^{76} +(-3.20890 - 3.70327i) q^{77} +(1.85930 + 12.9317i) q^{78} +(-3.86639 + 8.46622i) q^{79} +(-1.33863 + 0.393058i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-5.09305 + 11.1522i) q^{82} +(2.15493 + 14.9879i) q^{83} +(2.62026 + 3.02395i) q^{84} +(0.237639 + 0.520357i) q^{85} +(-14.4136 + 9.26309i) q^{86} +(1.42436 - 9.90664i) q^{87} +(20.2096 + 12.9879i) q^{88} +(-2.48290 + 2.86542i) q^{89} +(-0.818288 - 0.240271i) q^{90} +5.33309 q^{91} +(16.7844 - 9.30136i) q^{92} -4.51002 q^{93} +(1.81240 + 0.532170i) q^{94} +(-0.155606 + 0.179579i) q^{95} +(-0.0103362 - 0.00664264i) q^{96} +(1.58090 - 10.9954i) q^{97} +(2.06086 - 1.32443i) q^{98} +(2.03559 + 4.45732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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