LMFDB - Embedded newform 630.2.r.b.59.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(59,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	630.59
Dual form			630.2.r.b.299.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50744 - 0.853008i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20770 + 0.355056i) q^{5} +(-1.49245 + 0.878978i) q^{6} +(-0.692019 + 2.55365i) q^{7} -1.00000 q^{8} +(1.54476 + 2.57172i) q^{9} +(1.41134 - 1.73440i) q^{10} +2.84121i q^{11} +(0.0149941 + 1.73199i) q^{12} +(-2.51471 + 4.35560i) q^{13} +(1.86551 + 1.87613i) q^{14} +(-3.02511 - 2.41841i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.91852 + 2.26236i) q^{17} +(2.99955 - 0.0519390i) q^{18} +(-3.40172 + 1.96399i) q^{19} +(-0.796362 - 2.08945i) q^{20} +(3.22146 - 3.25917i) q^{21} +(2.46056 + 1.42061i) q^{22} -6.42150 q^{23} +(1.50744 + 0.853008i) q^{24} +(4.74787 + 1.56771i) q^{25} +(2.51471 + 4.35560i) q^{26} +(-0.134933 - 5.19440i) q^{27} +(2.55753 - 0.677517i) q^{28} +(3.16363 - 1.82652i) q^{29} +(-3.60696 + 1.41062i) q^{30} +(1.76921 - 1.02145i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.42358 - 4.28296i) q^{33} +(3.91852 - 2.26236i) q^{34} +(-2.43446 + 5.39198i) q^{35} +(1.45479 - 2.62366i) q^{36} +(0.925584 - 0.534386i) q^{37} +3.92797i q^{38} +(7.50614 - 4.42075i) q^{39} +(-2.20770 - 0.355056i) q^{40} +(-2.85368 + 4.94272i) q^{41} +(-1.21180 - 4.41945i) q^{42} +(6.76731 - 3.90711i) q^{43} +(2.46056 - 1.42061i) q^{44} +(2.49725 + 6.22605i) q^{45} +(-3.21075 + 5.56118i) q^{46} +(1.93936 + 1.11969i) q^{47} +(1.49245 - 0.878978i) q^{48} +(-6.04222 - 3.53434i) q^{49} +(3.73162 - 3.32792i) q^{50} +(-3.97713 - 6.75290i) q^{51} +5.02942 q^{52} +(2.88164 - 4.99115i) q^{53} +(-4.56595 - 2.48034i) q^{54} +(-1.00879 + 6.27254i) q^{55} +(0.692019 - 2.55365i) q^{56} +(6.80319 - 0.0588963i) q^{57} -3.65305i q^{58} +(6.40511 + 11.0940i) q^{59} +(-0.581850 + 3.82903i) q^{60} +(-9.03596 - 5.21692i) q^{61} -2.04291i q^{62} +(-7.63626 + 2.16508i) q^{63} +1.00000 q^{64} +(-7.09820 + 8.72300i) q^{65} +(-2.49736 - 4.24036i) q^{66} +(5.19591 - 2.99986i) q^{67} -4.52472i q^{68} +(9.68003 + 5.47759i) q^{69} +(3.45236 + 4.80429i) q^{70} -7.81664i q^{71} +(-1.54476 - 2.57172i) q^{72} +(7.04158 - 12.1964i) q^{73} -1.06877i q^{74} +(-5.81986 - 6.41321i) q^{75} +(3.40172 + 1.96399i) q^{76} +(-7.25545 - 1.96617i) q^{77} +(-0.0754114 - 8.71088i) q^{78} +(-2.25537 + 3.90642i) q^{79} +(-1.41134 + 1.73440i) q^{80} +(-4.22746 + 7.94535i) q^{81} +(2.85368 + 4.94272i) q^{82} +(-10.9918 + 6.34613i) q^{83} +(-4.43326 - 1.16028i) q^{84} +(7.84765 + 6.38590i) q^{85} -7.81422i q^{86} +(-6.32703 + 0.0547740i) q^{87} -2.84121i q^{88} +(5.33519 + 9.24081i) q^{89} +(6.64055 + 0.950343i) q^{90} +(-9.38244 - 9.43583i) q^{91} +(3.21075 + 5.56118i) q^{92} +(-3.53829 + 0.0306315i) q^{93} +(1.93936 - 1.11969i) q^{94} +(-8.20731 + 3.12809i) q^{95} +(-0.0149941 - 1.73199i) q^{96} +(8.91744 + 15.4455i) q^{97} +(-6.08194 + 3.46554i) q^{98} +(-7.30680 + 4.38898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.50744	−	0.853008i	−0.870321	−	0.492484i
$3$	−1.50744	−	0.853008i	−0.870321	−	0.492484i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.20770	+	0.355056i	0.987313	+	0.158786i
$5$	2.20770	+	0.355056i	0.987313	+	0.158786i
$6$	−1.49245	+	0.878978i	−0.609289	+	0.358841i
$7$	−0.692019	+	2.55365i	−0.261559	+	0.965188i
$7$	−0.692019	+	2.55365i	−0.261559	+	0.965188i
$8$	−1.00000			−0.353553
$9$	1.54476	+	2.57172i	0.514919	+	0.857239i
$10$	1.41134	−	1.73440i	0.446304	−	0.548464i
$11$			2.84121i			0.856658i	0.903623	+	0.428329i	$0.140898\pi$
$11$			2.84121i			0.856658i	−0.903623	+	0.428329i	$0.859102\pi$
$12$	0.0149941	+	1.73199i	0.00432841	+	0.499981i
$13$	−2.51471	+	4.35560i	−0.697455	+	1.20803i	0.271892	+	0.962328i	$0.412351\pi$
$13$	−2.51471	+	4.35560i	−0.697455	+	1.20803i	−0.969346	+	0.245699i	$0.920983\pi$
$14$	1.86551	+	1.87613i	0.498579	+	0.501417i
$15$	−3.02511	−	2.41841i	−0.781080	−	0.624431i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.91852	+	2.26236i	0.950381	+	0.548703i	0.893199	−	0.449661i	$-0.148455\pi$
$17$	3.91852	+	2.26236i	0.950381	+	0.548703i	0.0571816	+	0.998364i	$0.481789\pi$
$18$	2.99955	−	0.0519390i	0.707001	−	0.0122421i
$19$	−3.40172	+	1.96399i	−0.780409	+	0.450569i	−0.836575	−	0.547852i	$-0.815446\pi$
$19$	−3.40172	+	1.96399i	−0.780409	+	0.450569i	0.0561661	+	0.998421i	$0.482112\pi$
$20$	−0.796362	−	2.08945i	−0.178072	−	0.467216i
$21$	3.22146	−	3.25917i	0.702980	−	0.711210i
$22$	2.46056	+	1.42061i	0.524594	+	0.302874i
$23$	−6.42150			−1.33897			−0.669487	−	0.742824i	$-0.733486\pi$
$23$	−6.42150			−1.33897			−0.669487	+	0.742824i	$0.733486\pi$
$24$	1.50744	+	0.853008i	0.307705	+	0.174119i
$25$	4.74787	+	1.56771i	0.949574	+	0.313543i
$26$	2.51471	+	4.35560i	0.493175	+	0.854204i
$27$	−0.134933	−	5.19440i	−0.0259679	−	0.999663i
$28$	2.55753	−	0.677517i	0.483328	−	0.128039i
$29$	3.16363	−	1.82652i	0.587472	−	0.339177i	−0.176626	−	0.984278i	$-0.556518\pi$
$29$	3.16363	−	1.82652i	0.587472	−	0.339177i	0.764097	+	0.645101i	$0.223185\pi$
$30$	−3.60696	+	1.41062i	−0.658538	+	0.257542i
$31$	1.76921	−	1.02145i	0.317760	−	0.183459i	−0.332634	−	0.943056i	$-0.607937\pi$
$31$	1.76921	−	1.02145i	0.317760	−	0.183459i	0.650394	+	0.759597i	$0.274604\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.42358	−	4.28296i	0.421890	−	0.745568i
$34$	3.91852	−	2.26236i	0.672021	−	0.387991i
$35$	−2.43446	+	5.39198i	−0.411498	+	0.911411i
$36$	1.45479	−	2.62366i	0.242466	−	0.437276i
$37$	0.925584	−	0.534386i	0.152165	−	0.0878526i	−0.421984	−	0.906603i	$-0.638666\pi$
$37$	0.925584	−	0.534386i	0.152165	−	0.0878526i	0.574149	+	0.818751i	$0.305333\pi$
$38$			3.92797i			0.637201i
$39$	7.50614	−	4.42075i	1.20194	−	0.707886i
$40$	−2.20770	−	0.355056i	−0.349068	−	0.0561393i
$41$	−2.85368	+	4.94272i	−0.445670	+	0.771923i	−0.998099	−	0.0616375i	$-0.980368\pi$
$41$	−2.85368	+	4.94272i	−0.445670	+	0.771923i	0.552429	+	0.833560i	$0.313701\pi$
$42$	−1.21180	−	4.41945i	−0.186985	−	0.681936i
$43$	6.76731	−	3.90711i	1.03201	−	0.595829i	0.114447	−	0.993429i	$-0.463490\pi$
$43$	6.76731	−	3.90711i	1.03201	−	0.595829i	0.917559	+	0.397601i	$0.130157\pi$
$44$	2.46056	−	1.42061i	0.370944	−	0.214164i
$45$	2.49725	+	6.22605i	0.372268	+	0.928125i
$46$	−3.21075	+	5.56118i	−0.473399	+	0.819951i
$47$	1.93936	+	1.11969i	0.282884	+	0.163323i	0.634728	−	0.772735i	$-0.281112\pi$
$47$	1.93936	+	1.11969i	0.282884	+	0.163323i	−0.351844	+	0.936059i	$0.614445\pi$
$48$	1.49245	−	0.878978i	0.215416	−	0.126870i
$49$	−6.04222	−	3.53434i	−0.863174	−	0.504906i
$50$	3.73162	−	3.32792i	0.527730	−	0.470639i
$51$	−3.97713	−	6.75290i	−0.556909	−	0.945595i
$52$	5.02942			0.697455
$53$	2.88164	−	4.99115i	0.395824	−	0.685587i	−0.597382	−	0.801957i	$-0.703792\pi$
$53$	2.88164	−	4.99115i	0.395824	−	0.685587i	0.993206	+	0.116370i	$0.0371258\pi$
$54$	−4.56595	−	2.48034i	−0.621347	−	0.337532i
$55$	−1.00879	+	6.27254i	−0.136025	+	0.845789i
$56$	0.692019	−	2.55365i	0.0924749	−	0.341245i
$57$	6.80319	−	0.0588963i	0.901105	−	0.00780100i
$58$		−	3.65305i		−	0.479669i
$59$	6.40511	+	11.0940i	0.833875	+	1.44431i	0.894943	+	0.446180i	$0.147216\pi$
$59$	6.40511	+	11.0940i	0.833875	+	1.44431i	−0.0610683	+	0.998134i	$0.519451\pi$
$60$	−0.581850	+	3.82903i	−0.0751165	+	0.494325i
$61$	−9.03596	−	5.21692i	−1.15694	−	0.667958i	−0.206369	−	0.978474i	$-0.566165\pi$
$61$	−9.03596	−	5.21692i	−1.15694	−	0.667958i	−0.950568	+	0.310517i	$0.899498\pi$
$62$		−	2.04291i		−	0.259450i
$63$	−7.63626	+	2.16508i	−0.962078	+	0.272775i
$64$	1.00000			0.125000
$65$	−7.09820	+	8.72300i	−0.880424	+	1.08195i
$66$	−2.49736	−	4.24036i	−0.307404	−	0.521952i
$67$	5.19591	−	2.99986i	0.634781	−	0.366491i	−0.147820	−	0.989014i	$-0.547226\pi$
$67$	5.19591	−	2.99986i	0.634781	−	0.366491i	0.782601	+	0.622523i	$0.213892\pi$
$68$		−	4.52472i		−	0.548703i
$69$	9.68003	+	5.47759i	1.16534	+	0.659424i
$70$	3.45236	+	4.80429i	0.412636	+	0.574223i
$71$		−	7.81664i		−	0.927664i	−0.885923	−	0.463832i	$-0.846474\pi$
$71$		−	7.81664i		−	0.927664i	0.885923	−	0.463832i	$-0.153526\pi$
$72$	−1.54476	−	2.57172i	−0.182051	−	0.303080i
$73$	7.04158	−	12.1964i	0.824154	−	1.42748i	−0.0784100	−	0.996921i	$-0.524984\pi$
$73$	7.04158	−	12.1964i	0.824154	−	1.42748i	0.902564	−	0.430556i	$-0.141682\pi$
$74$		−	1.06877i		−	0.124242i
$75$	−5.81986	−	6.41321i	−0.672020	−	0.740533i
$76$	3.40172	+	1.96399i	0.390205	+	0.225285i
$77$	−7.25545	−	1.96617i	−0.826836	−	0.224066i
$78$	−0.0754114	−	8.71088i	−0.00853865	−	0.986313i
$79$	−2.25537	+	3.90642i	−0.253749	+	0.439506i	−0.964555	−	0.263882i	$-0.914997\pi$
$79$	−2.25537	+	3.90642i	−0.253749	+	0.439506i	0.710806	+	0.703388i	$0.248330\pi$
$80$	−1.41134	+	1.73440i	−0.157792	+	0.193911i
$81$	−4.22746	+	7.94535i	−0.469718	+	0.882817i
$82$	2.85368	+	4.94272i	0.315136	+	0.545832i
$83$	−10.9918	+	6.34613i	−1.20651	+	0.696578i	−0.961995	−	0.273068i	$-0.911962\pi$
$83$	−10.9918	+	6.34613i	−1.20651	+	0.696578i	−0.244513	+	0.969646i	$0.578628\pi$
$84$	−4.43326	−	1.16028i	−0.483708	−	0.126597i
$85$	7.84765	+	6.38590i	0.851197	+	0.692648i
$86$		−	7.81422i		−	0.842629i
$87$	−6.32703	+	0.0547740i	−0.678328	+	0.00587239i
$88$		−	2.84121i		−	0.302874i
$89$	5.33519	+	9.24081i	0.565529	+	0.979524i	0.997000	+	0.0773979i	$0.0246612\pi$
$89$	5.33519	+	9.24081i	0.565529	+	0.979524i	−0.431472	+	0.902127i	$0.642005\pi$
$90$	6.64055	+	0.950343i	0.699975	+	0.100175i
$91$	−9.38244	−	9.43583i	−0.983547	−	0.989144i
$92$	3.21075	+	5.56118i	0.334744	+	0.579793i
$93$	−3.53829	+	0.0306315i	−0.366904	+	0.00317634i
$94$	1.93936	−	1.11969i	0.200029	−	0.115487i
$95$	−8.20731	+	3.12809i	−0.842052	+	0.320935i
$96$	−0.0149941	−	1.73199i	−0.00153032	−	0.176770i
$97$	8.91744	+	15.4455i	0.905429	+	1.56825i	0.820341	+	0.571875i	$0.193784\pi$
$97$	8.91744	+	15.4455i	0.905429	+	1.56825i	0.0850876	+	0.996373i	$0.472883\pi$
$98$	−6.08194	+	3.46554i	−0.614369	+	0.350073i
$99$	−7.30680	+	4.38898i	−0.734361	+	0.441109i
$100$	−1.01626	−	4.89563i	−0.101626	−	0.489563i
$101$	−10.0818			−1.00318			−0.501590	−	0.865106i	$-0.667251\pi$
$101$	−10.0818			−1.00318			−0.501590	+	0.865106i	$0.667251\pi$
$102$	−7.83675	+	0.0678439i	−0.775954	+	0.00671754i
$103$	−2.06967			−0.203931			−0.101965	−	0.994788i	$-0.532513\pi$
$103$	−2.06967			−0.203931			−0.101965	+	0.994788i	$0.532513\pi$
$104$	2.51471	−	4.35560i	0.246587	−	0.427102i
$105$	8.26920	−	6.05148i	0.806991	−	0.590564i
$106$	−2.88164	−	4.99115i	−0.279890	−	0.484783i
$107$	1.27205	+	2.20325i	0.122973	+	0.212996i	0.920939	−	0.389707i	$-0.127424\pi$
$107$	1.27205	+	2.20325i	0.122973	+	0.212996i	−0.797966	+	0.602703i	$0.794090\pi$
$108$	−4.43102	+	2.71406i	−0.426375	+	0.261160i
$109$	5.96532	−	10.3322i	0.571374	−	0.989649i	−0.425051	−	0.905170i	$-0.639744\pi$
$109$	5.96532	−	10.3322i	0.571374	−	0.989649i	0.996425	−	0.0844800i	$-0.0269229\pi$
$110$	4.92779	+	4.00991i	0.469846	+	0.382330i
$111$	−1.85110	+	0.0160252i	−0.175699	+	0.00152105i
$112$	−1.86551	−	1.87613i	−0.176274	−	0.177278i
$113$	−4.09453	+	7.09194i	−0.385181	+	0.667153i	−0.991794	−	0.127844i	$-0.959194\pi$
$113$	−4.09453	+	7.09194i	−0.385181	+	0.667153i	0.606613	+	0.794997i	$0.292528\pi$
$114$	3.35059	−	5.92119i	0.313812	−	0.554570i
$115$	−14.1767	−	2.27999i	−1.32199	−	0.212610i
$116$	−3.16363	−	1.82652i	−0.293736	−	0.169588i
$117$	−15.0860	+	0.261223i	−1.39470	+	0.0241501i
$118$	12.8102			1.17928
$119$	−8.48895	+	8.44092i	−0.778181	+	0.773778i
$120$	3.02511	+	2.41841i	0.276154	+	0.220770i
$121$	2.92751			0.266137
$122$	−9.03596	+	5.21692i	−0.818078	+	0.472317i
$123$	8.51793	−	5.01664i	0.768036	−	0.452335i
$124$	−1.76921	−	1.02145i	−0.158880	−	0.0917294i
$125$	9.92524	+	5.14680i	0.887741	+	0.460344i
$126$	−1.94311	+	7.69573i	−0.173106	+	0.685590i
$127$		−	18.1709i		−	1.61240i	−0.591641	−	0.806202i	$-0.701520\pi$
$127$		−	18.1709i		−	1.61240i	0.591641	−	0.806202i	$-0.298480\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−13.5341	+	0.117167i	−1.19161	+	0.0103160i
$130$	4.00524	+	10.5087i	0.351282	+	0.921676i
$131$	−17.1088			−1.49481			−0.747403	−	0.664371i	$-0.768700\pi$
$131$	−17.1088			−1.49481			−0.747403	+	0.664371i	$0.768700\pi$
$132$	−4.92094	+	0.0426013i	−0.428313	+	0.00370797i
$133$	−2.66127	−	10.0459i	−0.230761	−	0.871092i
$134$		−	5.99972i		−	0.518296i
$135$	1.54641	−	11.5156i	0.133094	−	0.991103i
$136$	−3.91852	−	2.26236i	−0.336010	−	0.193996i
$137$	−6.20017			−0.529716			−0.264858	−	0.964287i	$-0.585325\pi$
$137$	−6.20017			−0.529716			−0.264858	+	0.964287i	$0.585325\pi$
$138$	9.58374	−	5.64436i	0.815822	−	0.480479i
$139$	−13.0131	−	7.51311i	−1.10376	−	0.637253i	−0.166550	−	0.986033i	$-0.553263\pi$
$139$	−13.0131	−	7.51311i	−1.10376	−	0.637253i	−0.937205	+	0.348780i	$0.886596\pi$
$140$	5.88682	−	0.587687i	0.497527	−	0.0496686i
$141$	−1.96836	−	3.34215i	−0.165766	−	0.281460i
$142$	−6.76941	−	3.90832i	−0.568076	−	0.327979i
$143$	−12.3752	−	7.14482i	−1.03487	−	0.597480i
$144$	−2.99955	+	0.0519390i	−0.249963	+	0.00432825i
$145$	7.63286	−	2.90915i	0.633875	−	0.241592i
$146$	−7.04158	−	12.1964i	−0.582765	−	1.00938i
$147$	6.09347	+	10.4819i	0.502581	+	0.864530i
$148$	−0.925584	−	0.534386i	−0.0760826	−	0.0439263i
$149$		−	2.28339i		−	0.187063i	−0.995616	−	0.0935314i	$-0.970184\pi$
$149$		−	2.28339i		−	0.187063i	0.995616	−	0.0935314i	$-0.0298155\pi$
$150$	−8.46393	+	1.83355i	−0.691077	+	0.149708i
$151$	13.1905			1.07343			0.536714	−	0.843764i	$-0.319666\pi$
$151$	13.1905			1.07343			0.536714	+	0.843764i	$0.319666\pi$
$152$	3.40172	−	1.96399i	0.275916	−	0.159300i
$153$	0.235009	+	13.5721i	0.0189994	+	1.09724i
$154$	−5.33048	+	5.30032i	−0.429542	+	0.427112i
$155$	4.26856	−	1.62690i	0.342859	−	0.130675i
$156$	−7.58155	−	4.29013i	−0.607010	−	0.343485i
$157$	8.96306	+	15.5245i	0.715330	+	1.23899i	0.962832	+	0.270101i	$0.0870571\pi$
$157$	8.96306	+	15.5245i	0.715330	+	1.23899i	−0.247502	+	0.968887i	$0.579610\pi$
$158$	2.25537	+	3.90642i	0.179428	+	0.310778i
$159$	−8.60139	+	5.06580i	−0.682134	+	0.401744i
$160$	0.796362	+	2.08945i	0.0629579	+	0.165186i
$161$	4.44380	−	16.3982i	0.350220	−	1.29236i
$162$	4.76714	+	7.63376i	0.374542	+	0.599765i
$163$	−3.27021	+	1.88806i	−0.256143	+	0.147884i	−0.622574	−	0.782561i	$-0.713913\pi$
$163$	−3.27021	+	1.88806i	−0.256143	+	0.147884i	0.366431	+	0.930445i	$0.380580\pi$
$164$	5.70736			0.445670
$165$	6.87122	−	8.59498i	0.534924	−	0.669118i
$166$			12.6923i			0.985110i
$167$	20.8655	+	12.0467i	1.61462	+	0.932201i	0.988280	+	0.152651i	$0.0487811\pi$
$167$	20.8655	+	12.0467i	1.61462	+	0.932201i	0.626340	+	0.779550i	$0.284552\pi$
$168$	−3.22146	+	3.25917i	−0.248541	+	0.251451i
$169$	−6.14752	−	10.6478i	−0.472886	−	0.819062i
$170$	9.45418	−	3.60331i	0.725102	−	0.276361i
$171$	−10.3057	−	5.71439i	−0.788093	−	0.436991i
$172$	−6.76731	−	3.90711i	−0.516003	−	0.297914i
$173$	10.5424	+	6.08668i	0.801527	+	0.462762i	0.844005	−	0.536336i	$-0.180192\pi$
$173$	10.5424	+	6.08668i	0.801527	+	0.462762i	−0.0424779	+	0.999097i	$0.513525\pi$
$174$	−3.11608	+	5.50675i	−0.236229	+	0.417466i
$175$	−7.28900	+	11.0395i	−0.550997	+	0.834507i
$176$	−2.46056	−	1.42061i	−0.185472	−	0.107082i
$177$	−0.192077	−	22.1871i	−0.0144374	−	1.66769i
$178$	10.6704			0.799778
$179$	3.16979	+	1.83008i	0.236921	+	0.136786i	0.613761	−	0.789492i	$-0.289656\pi$
$179$	3.16979	+	1.83008i	0.236921	+	0.136786i	−0.376840	+	0.926278i	$0.622989\pi$
$180$	4.14329	−	5.27571i	0.308823	−	0.393228i
$181$		−	11.5653i		−	0.859645i	−0.902914	−	0.429822i	$-0.858576\pi$
$181$		−	11.5653i		−	0.859645i	0.902914	−	0.429822i	$-0.141424\pi$
$182$	−12.8629	+	3.40752i	−0.953461	+	0.252582i
$183$	9.17111	+	15.5719i	0.677948	+	1.15111i
$184$	6.42150			0.473399
$185$	2.23315	−	0.851130i	0.164184	−	0.0625763i
$186$	−1.74262	+	3.07957i	−0.127775	+	0.225805i
$187$	−6.42784	+	11.1333i	−0.470050	+	0.814151i
$188$		−	2.23938i		−	0.163323i
$189$	13.3580	+	3.25005i	0.971654	+	0.236406i
$190$	−1.39465	+	8.67178i	−0.101179	+	0.629117i
$191$	8.16751	+	4.71552i	0.590980	+	0.341203i	0.765485	−	0.643454i	$-0.222499\pi$
$191$	8.16751	+	4.71552i	0.590980	+	0.341203i	−0.174505	+	0.984656i	$0.555832\pi$
$192$	−1.50744	−	0.853008i	−0.108790	−	0.0615605i
$193$	1.28623	−	0.742606i	0.0925850	−	0.0534540i	−0.452993	−	0.891514i	$-0.649644\pi$
$193$	1.28623	−	0.742606i	0.0925850	−	0.0534540i	0.545578	+	0.838060i	$0.316310\pi$
$194$	17.8349			1.28047
$195$	18.1409	−	7.09458i	1.29910	−	0.508053i
$196$	−0.0397207	+	6.99989i	−0.00283719	+	0.499992i
$197$	17.6493			1.25746			0.628729	−	0.777624i	$-0.283575\pi$
$197$	17.6493			1.25746			0.628729	+	0.777624i	$0.283575\pi$
$198$	0.147570	+	8.52236i	0.0104873	+	0.605658i
$199$	17.8938	+	10.3310i	1.26846	+	0.732344i	0.974696	−	0.223534i	$-0.0717595\pi$
$199$	17.8938	+	10.3310i	1.26846	+	0.732344i	0.293762	+	0.955879i	$0.405093\pi$
$200$	−4.74787	−	1.56771i	−0.335725	−	0.110854i
$201$	−10.3914	+	0.0899601i	−0.732954	+	0.00634529i
$202$	−5.04091	+	8.73112i	−0.354677	+	0.614319i
$203$	2.47500	+	9.34278i	0.173711	+	0.655735i
$204$	−3.85962	+	6.82074i	−0.270227	+	0.477548i
$205$	−8.05500	+	9.89881i	−0.562586	+	0.691363i
$206$	−1.03484	+	1.79239i	−0.0721004	+	0.124882i
$207$	−9.91964	−	16.5143i	−0.689463	−	1.14782i
$208$	−2.51471	−	4.35560i	−0.174364	−	0.302007i
$209$	−5.58010	−	9.66502i	−0.385984	−	0.668544i
$210$	−1.10613	−	10.1871i	−0.0763304	−	0.702975i
$211$	5.63953	−	9.76796i	0.388241	−	0.672454i	−0.603972	−	0.797006i	$-0.706416\pi$
$211$	5.63953	−	9.76796i	0.388241	−	0.672454i	0.992213	+	0.124552i	$0.0397493\pi$
$212$	−5.76328			−0.395824
$213$	−6.66765	+	11.7831i	−0.456860	+	0.807366i
$214$	2.54409			0.173911
$215$	16.3274	−	6.22295i	1.11352	−	0.424402i
$216$	0.134933	+	5.19440i	0.00918103	+	0.353434i
$217$	1.38411	+	5.22481i	0.0939593	+	0.354683i
$218$	−5.96532	−	10.3322i	−0.404023	−	0.699788i
$219$	−21.0184	+	12.3788i	−1.42029	+	0.836481i
$220$	5.93658	−	2.26263i	0.400244	−	0.152547i
$221$	−19.7079	+	11.3783i	−1.32569	+	0.765390i
$222$	−0.911672	+	1.61111i	−0.0611874	+	0.108131i
$223$	6.07248	+	10.5178i	0.406643	+	0.704327i	0.994511	−	0.104630i	$-0.0333658\pi$
$223$	6.07248	+	10.5178i	0.406643	+	0.704327i	−0.587868	+	0.808957i	$0.700032\pi$
$224$	−2.55753	+	0.677517i	−0.170882	+	0.0452685i
$225$	3.30258	+	14.6319i	0.220172	+	0.975461i
$226$	4.09453	+	7.09194i	0.272364	+	0.471749i
$227$		−	23.7710i		−	1.57774i	−0.614563	−	0.788868i	$-0.710668\pi$
$227$		−	23.7710i		−	1.57774i	0.614563	−	0.788868i	$-0.289332\pi$
$228$	−3.45260	−	5.86229i	−0.228654	−	0.388240i
$229$		−	11.4143i		−	0.754279i	−0.926156	−	0.377139i	$-0.876908\pi$
$229$		−	11.4143i		−	0.754279i	0.926156	−	0.377139i	$-0.123092\pi$
$230$	−9.06290	+	11.1374i	−0.597590	+	0.734379i
$231$	9.26000	+	9.15285i	0.609264	+	0.602213i
$232$	−3.16363	+	1.82652i	−0.207703	+	0.119917i
$233$	−4.16132	−	7.20762i	−0.272617	−	0.472187i	0.696914	−	0.717155i	$-0.254556\pi$
$233$	−4.16132	−	7.20762i	−0.272617	−	0.472187i	−0.969531	+	0.244968i	$0.921223\pi$
$234$	−7.31677	+	13.1955i	−0.478312	+	0.862614i
$235$	3.88396	+	3.16051i	0.253362	+	0.206169i
$236$	6.40511	−	11.0940i	0.416937	−	0.722157i
$237$	6.73204	−	3.96484i	0.437293	−	0.257544i
$238$	3.06557	+	11.5721i	0.198712	+	0.750108i
$239$	−6.41684	−	3.70476i	−0.415071	−	0.239641i	0.277895	−	0.960611i	$-0.410363\pi$
$239$	−6.41684	−	3.70476i	−0.415071	−	0.239641i	−0.692966	+	0.720970i	$0.743696\pi$
$240$	3.60696	−	1.41062i	0.232828	−	0.0910549i
$241$		−	8.66889i		−	0.558412i	−0.960231	−	0.279206i	$-0.909929\pi$
$241$		−	8.66889i		−	0.558412i	0.960231	−	0.279206i	$-0.0900713\pi$
$242$	1.46376	−	2.53530i	0.0940937	−	0.162975i
$243$	13.1501	−	8.37109i	0.843579	−	0.537006i
$244$			10.4338i			0.667958i
$245$	−12.0845	−	9.94809i	−0.772051	−	0.635560i
$246$	−0.0855764	−	9.88506i	−0.00545615	−	0.630249i
$247$		−	19.7554i		−	1.25701i
$248$	−1.76921	+	1.02145i	−0.112345	+	0.0648624i
$249$	21.9828	−	0.190308i	1.39310	−	0.0120603i
$250$	9.41988	−	6.02211i	0.595766	−	0.380872i
$251$	15.4449			0.974871			0.487436	−	0.873159i	$-0.337932\pi$
$251$	15.4449			0.974871			0.487436	+	0.873159i	$0.337932\pi$
$252$	5.69315	+	5.53065i	0.358634	+	0.348398i
$253$		−	18.2448i		−	1.14704i
$254$	−15.7364	−	9.08543i	−0.987391	−	0.570071i
$255$	−6.38264	−	16.3205i	−0.399697	−	1.02203i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	5.81756i		−	0.362890i	−0.983401	−	0.181445i	$-0.941923\pi$
$257$		−	5.81756i		−	0.362890i	0.983401	−	0.181445i	$-0.0580774\pi$
$258$	−6.66559	+	11.7795i	−0.414982	+	0.733358i
$259$	0.724112	+	2.73342i	0.0449941	+	0.169847i
$260$	11.1034	+	1.78572i	0.688606	+	0.110746i
$261$	9.58434	+	5.31443i	0.593256	+	0.328955i
$262$	−8.55442	+	14.8167i	−0.528494	+	0.915378i
$263$	2.17568			0.134158			0.0670790	−	0.997748i	$-0.478632\pi$
$263$	2.17568			0.134158			0.0670790	+	0.997748i	$0.478632\pi$
$264$	−2.42358	+	4.28296i	−0.149161	+	0.263598i
$265$	8.13393	−	9.99581i	0.499663	−	0.614037i
$266$	−10.0307	−	2.71823i	−0.615019	−	0.166665i
$267$	−0.159992	−	18.4809i	−0.00979136	−	1.13101i
$268$	−5.19591	−	2.99986i	−0.317390	−	0.183245i
$269$	−1.75606	+	3.04158i	−0.107069	+	0.185449i	−0.914582	−	0.404401i	$-0.867480\pi$
$269$	−1.75606	+	3.04158i	−0.107069	+	0.185449i	0.807513	+	0.589850i	$0.200813\pi$
$270$	−9.19958	−	7.09702i	−0.559869	−	0.431911i
$271$	1.39309	−	0.804303i	0.0846244	−	0.0488579i	−0.457091	−	0.889420i	$-0.651109\pi$
$271$	1.39309	−	0.804303i	0.0846244	−	0.0488579i	0.541715	+	0.840562i	$0.317775\pi$
$272$	−3.91852	+	2.26236i	−0.237595	+	0.137176i
$273$	6.09464	+	22.2273i	0.368864	+	1.34525i
$274$	−3.10008	+	5.36950i	−0.187283	+	0.324383i
$275$	−4.45421	+	13.4897i	−0.268599	+	0.813460i
$276$	−0.0962843	−	11.1219i	−0.00579563	−	0.669462i
$277$		−	4.47810i		−	0.269063i	−0.990909	−	0.134531i	$-0.957047\pi$
$277$		−	4.47810i		−	0.269063i	0.990909	−	0.134531i	$-0.0429529\pi$
$278$	−13.0131	+	7.51311i	−0.780473	+	0.450606i
$279$	5.35989	+	2.97201i	0.320888	+	0.177930i
$280$	2.43446	−	5.39198i	0.145487	−	0.322232i
$281$	−9.04334	+	5.22117i	−0.539480	+	0.311469i	−0.744868	−	0.667211i	$-0.767488\pi$
$281$	−9.04334	+	5.22117i	−0.539480	+	0.311469i	0.205388	+	0.978681i	$0.434154\pi$
$282$	−3.87857	+	0.0335773i	−0.230965	+	0.00199950i
$283$	−9.25191	−	16.0248i	−0.549969	−	0.952574i	−0.998276	−	0.0586944i	$-0.981306\pi$
$283$	−9.25191	−	16.0248i	−0.549969	−	0.952574i	0.448307	−	0.893880i	$-0.352027\pi$
$284$	−6.76941	+	3.90832i	−0.401690	+	0.231916i
$285$	15.0403	+	2.28549i	0.890911	+	0.135381i
$286$	−12.3752	+	7.14482i	−0.731761	+	0.422482i
$287$	−10.6471	−	10.7077i	−0.628481	−	0.632058i
$288$	−1.45479	+	2.62366i	−0.0857246	+	0.154600i
$289$	1.73653	+	3.00776i	0.102149	+	0.176927i
$290$	1.29704	−	8.06483i	0.0761646	−	0.473583i
$291$	−0.267417	−	30.8897i	−0.0156763	−	1.81079i
$292$	−14.0832			−0.824154
$293$	0.317382	+	0.183240i	0.0185416	+	0.0107050i	0.509242	−	0.860623i	$-0.329926\pi$
$293$	0.317382	+	0.183240i	0.0185416	+	0.0107050i	−0.490701	+	0.871328i	$0.663259\pi$
$294$	12.1243	−	0.0361611i	0.707104	−	0.00210896i
$295$	10.2016	+	26.7664i	0.593959	+	1.55840i
$296$	−0.925584	+	0.534386i	−0.0537985	+	0.0310606i
$297$	14.7584	−	0.383373i	0.856369	−	0.0222456i
$298$	−1.97748	−	1.14170i	−0.114552	−	0.0661367i
$299$	16.1482	−	27.9695i	0.933874	−	1.61752i
$300$	−2.64407	+	8.24675i	−0.152655	+	0.476126i
$301$	5.29427	+	19.9851i	0.305157	+	1.15192i
$302$	6.59525	−	11.4233i	0.379514	−	0.657337i
$303$	15.1978	+	8.59987i	0.873088	+	0.494050i
$304$		−	3.92797i		−	0.225285i
$305$	−18.0964	−	14.7257i	−1.03620	−	0.843189i
$306$	11.8713	+	6.58253i	0.678637	+	0.376298i
$307$	−24.9894			−1.42622			−0.713110	−	0.701053i	$-0.752714\pi$
$307$	−24.9894			−1.42622			−0.713110	+	0.701053i	$0.752714\pi$
$308$	1.92497	+	7.26649i	0.109685	+	0.414047i
$309$	3.11991	+	1.76545i	0.177485	+	0.100433i
$310$	0.725347	−	4.51013i	0.0411970	−	0.256158i
$311$	12.0159	+	20.8121i	0.681358	+	1.18015i	0.974567	+	0.224098i	$0.0719436\pi$
$311$	12.0159	+	20.8121i	0.681358	+	1.18015i	−0.293209	+	0.956049i	$0.594723\pi$
$312$	−7.50614	+	4.42075i	−0.424951	+	0.250276i
$313$	−3.25239	+	5.63330i	−0.183836	+	0.318413i	−0.943184	−	0.332272i	$-0.892185\pi$
$313$	−3.25239	+	5.63330i	−0.183836	+	0.318413i	0.759348	+	0.650685i	$0.225518\pi$
$314$	17.9261			1.01163
$315$	−17.6273	+	2.06855i	−0.993185	+	0.116550i
$316$	4.51074			0.253749
$317$	3.69441	−	6.39890i	0.207499	−	0.359398i	−0.743427	−	0.668817i	$-0.766801\pi$
$317$	3.69441	−	6.39890i	0.207499	−	0.359398i	0.950926	+	0.309419i	$0.100134\pi$
$318$	0.0864149	+	9.98192i	0.00484591	+	0.559758i
$319$	5.18954	+	8.98855i	0.290559	+	0.503262i
$320$	2.20770	+	0.355056i	0.123414	+	0.0198482i
$321$	−0.0381463	−	4.40633i	−0.00212912	−	0.245938i
$322$	−11.9794	−	12.0476i	−0.667585	−	0.671384i
$323$	−17.7730			−0.988914
$324$	8.99460	−	0.311587i	0.499700	−	0.0173104i
$325$	−18.7678	+	16.7375i	−1.04105	+	0.928429i
$326$			3.77612i			0.209140i
$327$	−17.8059	+	10.4868i	−0.984666	+	0.579920i
$328$	2.85368	−	4.94272i	0.157568	−	0.272916i
$329$	−4.20136	+	4.17758i	−0.231628	+	0.230318i
$330$	−4.00786	−	10.2481i	−0.220626	−	0.564142i
$331$	−13.1569	+	22.7885i	−0.723171	+	1.25257i	0.236552	+	0.971619i	$0.423983\pi$
$331$	−13.1569	+	22.7885i	−0.723171	+	1.25257i	−0.959723	+	0.280949i	$0.909351\pi$
$332$	10.9918	+	6.34613i	0.603254	+	0.348289i
$333$	2.80409	+	1.55485i	0.153663	+	0.0852050i
$334$	20.8655	−	12.0467i	1.14171	−	0.659166i
$335$	12.5361	−	4.77795i	0.684921	−	0.261047i
$336$	1.21180	+	4.41945i	0.0661090	+	0.241101i
$337$	5.78970	+	3.34269i	0.315385	+	0.182088i	0.649334	−	0.760504i	$-0.275048\pi$
$337$	5.78970	+	3.34269i	0.315385	+	0.182088i	−0.333949	+	0.942591i	$0.608381\pi$
$338$	−12.2950			−0.668761
$339$	12.2217	−	7.19801i	0.663794	−	0.390942i
$340$	1.60653	−	9.98921i	0.0871262	−	0.541741i
$341$	2.90217	+	5.02671i	0.157161	+	0.272211i
$342$	−10.1016	+	6.06776i	−0.546234	+	0.328107i
$343$	13.2068	−	12.9839i	0.713100	−	0.701063i
$344$	−6.76731	+	3.90711i	−0.364869	+	0.210657i
$345$	19.4257	+	15.5298i	1.04585	+	0.836097i
$346$	10.5424	−	6.08668i	0.566765	−	0.327222i
$347$	1.20698	+	2.09055i	0.0647940	+	0.112226i	0.896603	−	0.442836i	$-0.146028\pi$
$347$	1.20698	+	2.09055i	0.0647940	+	0.112226i	−0.831809	+	0.555063i	$0.812694\pi$
$348$	3.21095	+	5.45198i	0.172125	+	0.292257i
$349$	0.654664	−	0.377971i	0.0350434	−	0.0202323i	−0.482376	−	0.875964i	$-0.660226\pi$
$349$	0.654664	−	0.377971i	0.0350434	−	0.0202323i	0.517419	+	0.855732i	$0.326893\pi$
$350$	5.91598	+	11.8322i	0.316223	+	0.632458i
$351$	22.9641	+	12.4747i	1.22573	+	0.665849i
$352$	−2.46056	+	1.42061i	−0.131148	+	0.0757186i
$353$		−	9.36256i		−	0.498319i	−0.968462	−	0.249159i	$-0.919846\pi$
$353$		−	9.36256i		−	0.498319i	0.968462	−	0.249159i	$-0.0801543\pi$
$354$	−19.3107	−	10.9272i	−1.02635	−	0.580775i
$355$	2.77534	−	17.2568i	0.147300	−	0.915895i
$356$	5.33519	−	9.24081i	0.282764	−	0.489762i
$357$	19.9968	−	5.48304i	1.05834	−	0.290193i
$358$	3.16979	−	1.83008i	0.167529	−	0.0967227i
$359$	20.7136	−	11.9590i	1.09322	−	0.631172i	0.158790	−	0.987312i	$-0.449241\pi$
$359$	20.7136	−	11.9590i	1.09322	−	0.631172i	0.934433	+	0.356140i	$0.115907\pi$
$360$	−2.49725	−	6.22605i	−0.131617	−	0.328142i
$361$	−1.78551	+	3.09260i	−0.0939744	+	0.162768i
$362$	−10.0159	−	5.78267i	−0.526423	−	0.303930i
$363$	−4.41305	−	2.49719i	−0.231625	−	0.131068i
$364$	−3.48045	+	12.8434i	−0.182425	+	0.673175i
$365$	19.8761	−	24.4258i	1.04036	−	1.27850i
$366$	18.0712	−	0.156445i	0.944599	−	0.00817754i
$367$	−5.27255			−0.275225			−0.137612	−	0.990486i	$-0.543943\pi$
$367$	−5.27255			−0.275225			−0.137612	+	0.990486i	$0.543943\pi$
$368$	3.21075	−	5.56118i	0.167372	−	0.289896i
$369$	−17.1195	+	0.296434i	−0.891206	+	0.0154318i
$370$	0.379474	−	2.35953i	0.0197279	−	0.122666i
$371$	10.7515	+	10.8127i	0.558189	+	0.561365i
$372$	1.79567	+	3.04893i	0.0931013	+	0.158080i
$373$		−	7.35577i		−	0.380867i	−0.981700	−	0.190434i	$-0.939011\pi$
$373$		−	7.35577i		−	0.380867i	0.981700	−	0.190434i	$-0.0609894\pi$
$374$	6.42784	+	11.1333i	0.332376	+	0.575692i
$375$	−10.5715	−	16.2248i	−0.545908	−	0.837845i
$376$	−1.93936	−	1.11969i	−0.100015	−	0.0577435i
$377$			18.3727i			0.946242i
$378$	9.49365	−	9.94337i	0.488300	−	0.511432i
$379$	−6.48462			−0.333092			−0.166546	−	0.986034i	$-0.553261\pi$
$379$	−6.48462			−0.333092			−0.166546	+	0.986034i	$0.553261\pi$
$380$	6.81266	+	5.54369i	0.349482	+	0.284386i
$381$	−15.4999	+	27.3915i	−0.794083	+	1.40331i
$382$	8.16751	−	4.71552i	0.417886	−	0.241267i
$383$		−	9.82502i		−	0.502035i	−0.967983	−	0.251018i	$-0.919235\pi$
$383$		−	9.82502i		−	0.502035i	0.967983	−	0.251018i	$-0.0807652\pi$
$384$	−1.49245	+	0.878978i	−0.0761611	+	0.0448552i
$385$	−15.3198	−	6.91681i	−0.780767	−	0.352513i
$386$		−	1.48521i		−	0.0755953i
$387$	20.5018	+	11.3681i	1.04217	+	0.577872i
$388$	8.91744	−	15.4455i	0.452714	−	0.784124i
$389$		−	8.29709i		−	0.420679i	−0.977628	−	0.210340i	$-0.932543\pi$
$389$		−	8.29709i		−	0.420679i	0.977628	−	0.210340i	$-0.0674570\pi$
$390$	2.92636	−	19.2578i	0.148182	−	0.975155i
$391$	−25.1628	−	14.5277i	−1.27254	−	0.734699i
$392$	6.04222	+	3.53434i	0.305178	+	0.178511i
$393$	25.7906	+	14.5940i	1.30096	+	0.736168i
$394$	8.82464	−	15.2847i	0.444579	−	0.770033i
$395$	−6.36618	+	7.82341i	−0.320317	+	0.393639i
$396$	7.45437	+	4.13338i	0.374596	+	0.207710i
$397$	6.65037	+	11.5188i	0.333772	+	0.578111i	0.983248	−	0.182272i	$-0.0583450\pi$
$397$	6.65037	+	11.5188i	0.333772	+	0.578111i	−0.649476	+	0.760382i	$0.725012\pi$
$398$	17.8938	−	10.3310i	0.896935	−	0.517846i
$399$	−4.55754	+	17.4137i	−0.228162	+	0.871776i
$400$	−3.73162	+	3.32792i	−0.186581	+	0.166396i
$401$			20.8884i			1.04312i	0.853215	+	0.521559i	$0.174649\pi$
$401$			20.8884i			1.04312i	−0.853215	+	0.521559i	$0.825351\pi$
$402$	−5.11780	+	9.04422i	−0.255253	+	0.451085i
$403$			10.2746i			0.511816i
$404$	5.04091	+	8.73112i	0.250795	+	0.434389i
$405$	−12.1540	+	16.0400i	−0.603937	+	0.797032i
$406$	9.32859	+	2.52798i	0.462970	+	0.125461i
$407$	1.51831	+	2.62978i	0.0752596	+	0.130353i
$408$	3.97713	+	6.75290i	0.196897	+	0.334318i
$409$	24.5197	−	14.1565i	1.21242	−	0.699992i	0.249136	−	0.968469i	$-0.419854\pi$
$409$	24.5197	−	14.1565i	1.21242	−	0.699992i	0.963286	+	0.268477i	$0.0865202\pi$
$410$	4.54512	+	11.9252i	0.224468	+	0.588946i
$411$	9.34638	+	5.28879i	0.461023	+	0.260877i
$412$	1.03484	+	1.79239i	0.0509827	+	0.0883046i
$413$	−32.7626	+	8.67915i	−1.61214	+	0.427073i
$414$	−19.2616	+	0.333526i	−0.946656	+	0.0163919i
$415$	−26.5198	+	10.1076i	−1.30181	+	0.496164i
$416$	−5.02942			−0.246587
$417$	13.2077	+	22.4258i	0.646784	+	1.09820i
$418$	−11.1602			−0.545864
$419$	7.85403	−	13.6036i	0.383695	−	0.664578i	−0.607893	−	0.794019i	$-0.707985\pi$
$419$	7.85403	−	13.6036i	0.383695	−	0.664578i	0.991587	+	0.129441i	$0.0413182\pi$
$420$	−9.37533	−	4.13560i	−0.457469	−	0.201796i
$421$	−13.2658	−	22.9771i	−0.646537	−	1.11983i	−0.983944	−	0.178476i	$-0.942883\pi$
$421$	−13.2658	−	22.9771i	−0.646537	−	1.11983i	0.337408	−	0.941359i	$-0.390450\pi$
$422$	−5.63953	−	9.76796i	−0.274528	−	0.475497i
$423$	0.116311	+	6.71712i	0.00565523	+	0.326598i
$424$	−2.88164	+	4.99115i	−0.139945	+	0.242391i
$425$	15.0579	+	16.8845i	0.730415	+	0.819019i
$426$	6.87065	+	11.6659i	0.332884	+	0.565216i
$427$	19.5752	−	19.4645i	0.947311	−	0.941951i
$428$	1.27205	−	2.20325i	0.0614867	−	0.106498i
$429$	12.5603	+	21.3265i	0.606416	+	1.02965i
$430$	2.77449	−	17.2514i	0.133798	−	0.831939i
$431$	14.0479	+	8.11059i	0.676666	+	0.390673i	0.798598	−	0.601865i	$-0.205576\pi$
$431$	14.0479	+	8.11059i	0.676666	+	0.390673i	−0.121932	+	0.992538i	$0.538909\pi$
$432$	4.56595	+	2.48034i	0.219679	+	0.119336i
$433$	−19.7268			−0.948010			−0.474005	−	0.880522i	$-0.657192\pi$
$433$	−19.7268			−0.948010			−0.474005	+	0.880522i	$0.657192\pi$
$434$	5.21687	+	1.41373i	0.250418	+	0.0678613i
$435$	−13.9876	−	2.12552i	−0.670655	−	0.101911i
$436$	−11.9306			−0.571374
$437$	21.8442	−	12.6117i	1.04495	−	0.603301i
$438$	0.211164	+	24.3918i	0.0100898	+	1.16549i
$439$	−11.3678	−	6.56319i	−0.542555	−	0.313244i	0.203559	−	0.979063i	$-0.434749\pi$
$439$	−11.3678	−	6.56319i	−0.542555	−	0.313244i	−0.746114	+	0.665819i	$0.768083\pi$
$440$	1.00879	−	6.27254i	0.0480922	−	0.299032i
$441$	−0.244423	−	20.9986i	−0.0116392	−	0.999932i
$442$			22.7567i			1.08243i
$443$	4.31000	−	7.46514i	0.204774	−	0.354679i	−0.745287	−	0.666744i	$-0.767687\pi$
$443$	4.31000	−	7.46514i	0.204774	−	0.354679i	0.950061	+	0.312065i	$0.101021\pi$
$444$	0.939428	+	1.59509i	0.0445833	+	0.0756995i
$445$	8.49748	+	22.2952i	0.402819	+	1.05690i
$446$	12.1450			0.575081
$447$	−1.94775	+	3.44208i	−0.0921254	+	0.162805i
$448$	−0.692019	+	2.55365i	−0.0326948	+	0.120648i
$449$			37.2222i			1.75663i	0.478086	+	0.878313i	$0.341331\pi$
$449$			37.2222i			1.75663i	−0.478086	+	0.878313i	$0.658669\pi$
$450$	14.3229	+	4.45584i	0.675188	+	0.210050i
$451$	−14.0433	−	8.10791i	−0.661274	−	0.381786i
$452$	8.18907			0.385181
$453$	−19.8839	−	11.2516i	−0.934227	−	0.528646i
$454$	−20.5863	−	11.8855i	−0.966162	−	0.557814i
$455$	−17.3634	−	24.1628i	−0.814007	−	1.13277i
$456$	−6.80319	+	0.0588963i	−0.318589	+	0.00275807i
$457$	−35.0771	−	20.2518i	−1.64084	−	0.947337i	−0.980537	−	0.196334i	$-0.937096\pi$
$457$	−35.0771	−	20.2518i	−1.64084	−	0.947337i	−0.660299	−	0.751003i	$-0.729570\pi$
$458$	−9.88508	−	5.70716i	−0.461900	−	0.266678i
$459$	11.2229	−	20.6596i	0.523838	−	0.964309i
$460$	5.11384	+	13.4174i	0.238434	+	0.625590i
$461$	−16.8755	−	29.2292i	−0.785971	−	1.36134i	−0.928417	−	0.371539i	$-0.878830\pi$
$461$	−16.8755	−	29.2292i	−0.785971	−	1.36134i	0.142446	−	0.989803i	$-0.454503\pi$
$462$	12.5566	−	3.44298i	0.584186	−	0.160182i
$463$	23.0998	+	13.3367i	1.07354	+	0.619809i	0.929147	−	0.369712i	$-0.120543\pi$
$463$	23.0998	+	13.3367i	1.07354	+	0.619809i	0.144394	+	0.989520i	$0.453877\pi$
$464$			3.65305i			0.169588i
$465$	−7.82236	−	1.18867i	−0.362753	−	0.0551231i
$466$	−8.32264			−0.385539
$467$	4.89263	−	2.82476i	0.226404	−	0.130714i	−0.382508	−	0.923952i	$-0.624940\pi$
$467$	4.89263	−	2.82476i	0.226404	−	0.130714i	0.608912	+	0.793238i	$0.291606\pi$
$468$	7.76922	+	12.9342i	0.359132	+	0.597885i
$469$	4.06491	+	15.3445i	0.187700	+	0.708542i
$470$	4.67907	−	1.78335i	0.215829	−	0.0822600i
$471$	−0.268785	−	31.0478i	−0.0123850	−	1.43061i
$472$	−6.40511	−	11.0940i	−0.294819	−	0.510642i
$473$	11.1009	+	19.2274i	0.510421	+	0.884076i
$474$	−0.0676343	−	7.81254i	−0.00310655	−	0.358842i
$475$	−19.2299	+	3.99182i	−0.882329	+	0.183157i
$476$	11.5545	+	3.13119i	0.529601	+	0.143518i
$477$	17.2872	−	0.299339i	0.791529	−	0.0137058i
$478$	−6.41684	+	3.70476i	−0.293499	+	0.169452i
$479$	0.273858			0.0125129			0.00625644	−	0.999980i	$-0.498009\pi$
$479$	0.273858			0.0125129			0.00625644	+	0.999980i	$0.498009\pi$
$480$	0.581850	−	3.82903i	0.0265577	−	0.174770i
$481$			5.37530i			0.245093i
$482$	−7.50748	−	4.33445i	−0.341956	−	0.197429i
$483$	−20.6866	+	20.9288i	−0.941272	+	0.952292i
$484$	−1.46376	−	2.53530i	−0.0665343	−	0.115241i
$485$	14.2030	+	37.2651i	0.644926	+	1.69212i
$486$	−0.674530	−	15.5739i	−0.0305973	−	0.706444i
$487$	12.4072	+	7.16329i	0.562223	+	0.324600i	0.754037	−	0.656832i	$-0.228104\pi$
$487$	12.4072	+	7.16329i	0.562223	+	0.324600i	−0.191814	+	0.981431i	$0.561437\pi$
$488$	9.03596	+	5.21692i	0.409039	+	0.236159i
$489$	6.54018	−	0.0566193i	0.295757	−	0.00256041i
$490$	−14.6576	+	5.49145i	−0.662161	+	0.248078i
$491$	31.8165	+	18.3692i	1.43586	+	0.828992i	0.997558	−	0.0698374i	$-0.0222480\pi$
$491$	31.8165	+	18.3692i	1.43586	+	0.828992i	0.438298	+	0.898830i	$0.355581\pi$
$492$	−8.60350	−	4.86842i	−0.387876	−	0.219485i
$493$	16.5290			0.744429
$494$	−17.1087	−	9.87771i	−0.769756	−	0.444419i
$495$	−17.6895	+	7.09522i	−0.795086	+	0.318907i
$496$			2.04291i			0.0917294i
$497$	19.9609	+	5.40926i	0.895370	+	0.242639i
$498$	10.8266	−	19.1328i	0.485151	−	0.857362i
$499$	−32.0792			−1.43606			−0.718032	−	0.696010i	$-0.754957\pi$
$499$	−32.0792			−1.43606			−0.718032	+	0.696010i	$0.754957\pi$
$500$	−0.505361	−	11.1689i	−0.0226004	−	0.499489i
$501$	−21.1776	−	35.9581i	−0.946144	−	1.60649i
$502$	7.72243	−	13.3756i	0.344669	−	0.596984i
$503$		−	35.1778i		−	1.56850i	−0.620445	−	0.784250i	$-0.713048\pi$
$503$		−	35.1778i		−	1.56850i	0.620445	−	0.784250i	$-0.286952\pi$
$504$	7.63626	−	2.16508i	0.340146	−	0.0964405i
$505$	−22.2576	−	3.57961i	−0.990452	−	0.159291i
$506$	−15.8005	−	9.12242i	−0.702418	−	0.405541i
$507$	0.184352	+	21.2948i	0.00818738	+	0.945736i
$508$	−15.7364	+	9.08543i	−0.698191	+	0.403101i
$509$	−23.4941			−1.04136			−0.520679	−	0.853752i	$-0.674321\pi$
$509$	−23.4941			−1.04136			−0.520679	+	0.853752i	$0.674321\pi$
$510$	−17.3253	−	2.63271i	−0.767176	−	0.116578i
$511$	26.2723	+	26.4218i	1.16222	+	1.16883i
$512$	−1.00000			−0.0441942
$513$	10.6607	+	17.4049i	0.470683	+	0.768446i
$514$	−5.03816	−	2.90878i	−0.222224	−	0.128301i
$515$	−4.56921	−	0.734849i	−0.201344	−	0.0323813i
$516$	6.86853	+	11.6623i	0.302370	+	0.513404i
$517$	−3.18127	+	5.51012i	−0.139912	+	0.242335i
$518$	2.72927	+	0.739611i	0.119917	+	0.0324966i
$519$	−10.7001	−	18.1681i	−0.469683	−	0.797491i
$520$	7.09820	−	8.72300i	0.311277	−	0.382529i
$521$	0.581200	−	1.00667i	0.0254628	−	0.0441029i	−0.853013	−	0.521889i	$-0.825227\pi$
$521$	0.581200	−	1.00667i	0.0254628	−	0.0441029i	0.878476	+	0.477786i	$0.158561\pi$
$522$	9.39460	−	5.64306i	0.411191	−	0.246990i
$523$	1.24452	+	2.15558i	0.0544191	+	0.0942567i	0.891952	−	0.452131i	$-0.149336\pi$
$523$	1.24452	+	2.15558i	0.0544191	+	0.0942567i	−0.837533	+	0.546387i	$0.816003\pi$
$524$	8.55442	+	14.8167i	0.373701	+	0.647270i
$525$	20.4045	−	10.4238i	0.890526	−	0.454932i
$526$	1.08784	−	1.88419i	0.0474320	−	0.0821547i
$527$	9.24359			0.402657
$528$	2.49736	+	4.24036i	0.108684	+	0.184538i
$529$	18.2356			0.792853
$530$	−4.58966	−	12.0421i	−0.199362	−	0.523075i
$531$	−18.6363	+	33.6096i	−0.808745	+	1.45853i
$532$	−7.36938	+	7.32769i	−0.319503	+	0.317695i
$533$	−14.3523	−	24.8590i	−0.621669	−	1.07676i
$534$	−16.0850	−	9.10191i	−0.696064	−	0.393878i
$535$	2.02602	+	5.31576i	0.0875925	+	0.229820i
$536$	−5.19591	+	2.99986i	−0.224429	+	0.129574i
$537$	−3.21720	−	5.46259i	−0.138832	−	0.235728i
$538$	1.75606	+	3.04158i	0.0757091	+	0.131132i
$539$	10.0418	−	17.1672i	0.432532	−	0.739445i
$540$	−10.7460	+	4.41856i	−0.462434	+	0.190144i
$541$	−10.4582	−	18.1142i	−0.449634	−	0.778789i	0.548728	−	0.836001i	$-0.315112\pi$
$541$	−10.4582	−	18.1142i	−0.449634	−	0.778789i	−0.998362	+	0.0572120i	$0.981779\pi$
$542$		−	1.60861i		−	0.0690956i
$543$	−9.86532	+	17.4341i	−0.423361	+	0.748167i
$544$			4.52472i			0.193996i
$545$	16.8382	−	20.6925i	0.721268	−	0.886368i
$546$	22.2967	+	5.83552i	0.954210	+	0.249737i
$547$	0.150888	−	0.0871155i	0.00645152	−	0.00372479i	−0.496771	−	0.867882i	$-0.665481\pi$
$547$	0.150888	−	0.0871155i	0.00645152	−	0.00372479i	0.503222	+	0.864157i	$0.332148\pi$
$548$	3.10008	+	5.36950i	0.132429	+	0.229374i
$549$	−0.541923	−	31.2968i	−0.0231287	−	1.33572i
$550$	9.45533	+	10.6023i	0.403176	+	0.452084i
$551$	−7.17453	+	12.4267i	−0.305645	+	0.529393i
$552$	−9.68003	−	5.47759i	−0.412009	−	0.233142i
$553$	−8.41485	−	8.46273i	−0.357836	−	0.359872i
$554$	−3.87815	−	2.23905i	−0.164767	−	0.0951281i
$555$	−4.09236	−	0.621865i	−0.173711	−	0.0263967i
$556$			15.0262i			0.637253i
$557$	10.1509	−	17.5819i	0.430109	−	0.744971i	−0.566773	−	0.823874i	$-0.691808\pi$
$557$	10.1509	−	17.5819i	0.430109	−	0.744971i	0.996882	+	0.0789031i	$0.0251418\pi$
$558$	5.25379	−	3.15580i	0.222411	−	0.133596i
$559$			39.3010i			1.66225i
$560$	−3.45236	−	4.80429i	−0.145889	−	0.203018i
$561$	19.1864	−	11.2999i	0.810051	−	0.477081i
$562$			10.4423i			0.440484i
$563$	−10.3964	+	6.00235i	−0.438155	+	0.252969i	−0.702815	−	0.711373i	$-0.748074\pi$
$563$	−10.3964	+	6.00235i	−0.438155	+	0.252969i	0.264660	+	0.964342i	$0.414740\pi$
$564$	−1.91020	+	3.37573i	−0.0804341	+	0.142144i
$565$	−11.5575	+	14.2031i	−0.486229	+	0.597528i
$566$	−18.5038			−0.777773
$567$	−17.3641	−	16.2938i	−0.729225	−	0.684274i
$568$			7.81664i			0.327979i
$569$	−27.9918	−	16.1611i	−1.17348	−	0.677509i	−0.218982	−	0.975729i	$-0.570274\pi$
$569$	−27.9918	−	16.1611i	−1.17348	−	0.677509i	−0.954497	+	0.298220i	$0.903607\pi$
$570$	9.49945	−	11.8826i	0.397888	−	0.497705i
$571$	19.8939	+	34.4573i	0.832535	+	1.44199i	0.896022	+	0.444009i	$0.146444\pi$
$571$	19.8939	+	34.4573i	0.832535	+	1.44199i	−0.0634876	+	0.997983i	$0.520222\pi$
$572$			14.2896i			0.597480i
$573$	−8.28967	−	14.0753i	−0.346306	−	0.588005i
$574$	−14.5967	+	3.86683i	−0.609256	+	0.161398i
$575$	−30.4884	−	10.0671i	−1.27146	−	0.419826i
$576$	1.54476	+	2.57172i	0.0643648	+	0.107155i
$577$	−5.59098	+	9.68386i	−0.232756	+	0.403144i	−0.958618	−	0.284695i	$-0.908108\pi$
$577$	−5.59098	+	9.68386i	−0.232756	+	0.403144i	0.725862	+	0.687840i	$0.241441\pi$
$578$	3.47307			0.144461
$579$	−2.57237	+	0.0222694i	−0.106904	+	0.000925483i
$580$	−6.33583	−	5.15568i	−0.263081	−	0.214078i
$581$	−8.59922	−	32.4608i	−0.356756	−	1.34670i
$582$	−26.8850	−	15.2133i	−1.11442	−	0.630611i
$583$	14.1809	+	8.18735i	0.587313	+	0.339085i
$584$	−7.04158	+	12.1964i	−0.291382	+	0.504689i
$585$	−33.3981	−	4.77967i	−1.38084	−	0.197615i
$586$	0.317382	−	0.183240i	0.0131109	−	0.00756959i
$587$	−2.92497	+	1.68873i	−0.120726	+	0.0697015i	−0.559147	−	0.829068i	$-0.688871\pi$
$587$	−2.92497	+	1.68873i	−0.120726	+	0.0697015i	0.438421	+	0.898770i	$0.355538\pi$
$588$	6.03083	−	10.5180i	0.248707	−	0.433756i
$589$	−4.01225	+	6.94942i	−0.165322	+	0.286346i
$590$	28.2811	+	4.54835i	1.16432	+	0.187253i
$591$	−26.6052	−	15.0550i	−1.09439	−	0.619279i
$592$			1.06877i			0.0439263i
$593$	−28.6406	+	16.5357i	−1.17613	+	0.679039i	−0.955116	−	0.296232i	$-0.904270\pi$
$593$	−28.6406	+	16.5357i	−1.17613	+	0.679039i	−0.221014	+	0.975271i	$0.570937\pi$
$594$	7.04719	−	12.9728i	0.289150	−	0.532282i
$595$	−21.7381	+	15.6210i	−0.891173	+	0.640397i
$596$	−1.97748	+	1.14170i	−0.0810005	+	0.0467657i
$597$	−18.1614	−	30.8369i	−0.743298	−	1.26207i
$598$	−16.1482	−	27.9695i	−0.660349	−	1.14376i
$599$	−13.0450	+	7.53154i	−0.533005	+	0.307730i	−0.742239	−	0.670135i	$-0.766236\pi$
$599$	−13.0450	+	7.53154i	−0.533005	+	0.307730i	0.209234	+	0.977866i	$0.432903\pi$
$600$	5.81986	+	6.41321i	0.237595	+	0.261818i
$601$	38.2212	−	22.0670i	1.55908	−	0.900133i	0.561730	−	0.827321i	$-0.310136\pi$
$601$	38.2212	−	22.0670i	1.55908	−	0.900133i	0.997346	−	0.0728123i	$-0.0231974\pi$
$602$	19.9548	+	5.40759i	0.813295	+	0.220397i
$603$	15.7412	+	8.72835i	0.641031	+	0.355446i
$604$	−6.59525	−	11.4233i	−0.268357	−	0.464808i
$605$	6.46306	+	1.03943i	0.262761	+	0.0422589i
$606$	15.0466	−	8.86170i	0.611226	−	0.359982i
$607$	−19.4623			−0.789952			−0.394976	−	0.918692i	$-0.629247\pi$
$607$	−19.4623			−0.789952			−0.394976	+	0.918692i	$0.629247\pi$
$608$	−3.40172	−	1.96399i	−0.137958	−	0.0796502i
$609$	4.23855	−	16.1949i	0.171755	−	0.656250i
$610$	−21.8010	+	8.30911i	−0.882696	+	0.336426i
$611$	−9.75383	+	5.63138i	−0.394598	+	0.227821i
$612$	11.6363	−	6.98958i	0.470369	−	0.282537i
$613$	−26.5030	−	15.3015i	−1.07045	−	0.618023i	−0.142144	−	0.989846i	$-0.545400\pi$
$613$	−26.5030	−	15.3015i	−1.07045	−	0.618023i	−0.928304	+	0.371823i	$0.878733\pi$
$614$	−12.4947	+	21.6414i	−0.504245	+	0.873377i
$615$	20.5862	−	8.05089i	0.830116	−	0.324643i
$616$	7.25545	+	1.96617i	0.292331	+	0.0792194i
$617$	−18.9195	+	32.7695i	−0.761671	+	1.31925i	0.180318	+	0.983608i	$0.442287\pi$
$617$	−18.9195	+	32.7695i	−0.761671	+	1.31925i	−0.941989	+	0.335644i	$0.891046\pi$
$618$	3.08887	−	1.81920i	0.124253	−	0.0731788i
$619$		−	48.6701i		−	1.95621i	−0.208101	−	0.978107i	$-0.566728\pi$
$619$		−	48.6701i		−	1.95621i	0.208101	−	0.978107i	$-0.433272\pi$
$620$	−3.54321	−	2.88323i	−0.142299	−	0.115793i
$621$	0.866472	+	33.3558i	0.0347703	+	1.33852i
$622$	24.0318			0.963586
$623$	−27.2898	+	7.22936i	−1.09334	+	0.289638i
$624$	0.0754114	+	8.71088i	0.00301887	+	0.348714i
$625$	20.0845	+	14.8866i	0.803382	+	0.595464i
$626$	3.25239	+	5.63330i	0.129991	+	0.225152i
$627$	0.167337	+	19.3293i	0.00668279	+	0.771939i
$628$	8.96306	−	15.5245i	0.357665	−	0.619494i
$629$	4.83590			0.192820
$630$	−7.02222	+	16.3000i	−0.279772	+	0.649406i
$631$	40.7671			1.62291			0.811456	−	0.584414i	$-0.198675\pi$
$631$	40.7671			1.62291			0.811456	+	0.584414i	$0.198675\pi$
$632$	2.25537	−	3.90642i	0.0897138	−	0.155389i
$633$	−16.8334	+	9.91405i	−0.669068	+	0.394048i
$634$	−3.69441	−	6.39890i	−0.146724	−	0.254133i
$635$	6.45168	−	40.1158i	0.256027	−	1.59195i
$636$	8.68780	+	4.91612i	0.344494	+	0.194937i
$637$	30.5886	−	17.4297i	1.21196	−	0.690589i
$638$	10.3791			0.410912
$639$	20.1022	−	12.0748i	0.795230	−	0.477672i
$640$	1.41134	−	1.73440i	0.0557880	−	0.0685580i
$641$			19.4398i			0.767826i	0.923369	+	0.383913i	$0.125424\pi$
$641$			19.4398i			0.767826i	−0.923369	+	0.383913i	$0.874576\pi$
$642$	−3.83507	−	2.17013i	−0.151358	−	0.0856483i
$643$	3.29651	−	5.70972i	0.130002	−	0.225169i	−0.793675	−	0.608342i	$-0.791835\pi$
$643$	3.29651	−	5.70972i	0.130002	−	0.225169i	0.923677	+	0.383172i	$0.125168\pi$
$644$	−16.4232	+	4.35068i	−0.647164	+	0.171441i
$645$	−29.9209	−	4.54670i	−1.17813	−	0.179026i
$646$	−8.88648	+	15.3918i	−0.349634	+	0.605584i
$647$	34.2506	+	19.7746i	1.34653	+	0.777419i	0.987756	−	0.156006i	$-0.0498620\pi$
$647$	34.2506	+	19.7746i	1.34653	+	0.777419i	0.358773	+	0.933425i	$0.383195\pi$
$648$	4.22746	−	7.94535i	0.166070	−	0.312123i
$649$	−31.5204	+	18.1983i	−1.23728	+	0.714346i
$650$	5.11117	+	24.6222i	0.200477	+	0.965761i
$651$	2.37034	−	9.05674i	0.0929010	−	0.354962i
$652$	3.27021	+	1.88806i	0.128071	+	0.0739421i
$653$	−20.7618			−0.812472			−0.406236	−	0.913768i	$-0.633159\pi$
$653$	−20.7618			−0.812472			−0.406236	+	0.913768i	$0.633159\pi$
$654$	0.178889	+	20.6637i	0.00699511	+	0.808015i
$655$	−37.7712	−	6.07460i	−1.47584	−	0.237354i
$656$	−2.85368	−	4.94272i	−0.111417	−	0.192981i
$657$	42.2431	−	0.731465i	1.64806	−	0.0285372i
$658$	1.51722	+	5.72727i	0.0591472	+	0.223272i
$659$	4.81761	−	2.78145i	0.187667	−	0.108350i	−0.403223	−	0.915102i	$-0.632110\pi$
$659$	4.81761	−	2.78145i	0.187667	−	0.108350i	0.590890	+	0.806752i	$0.298777\pi$
$660$	−10.8791	−	1.65316i	−0.423468	−	0.0643491i
$661$	37.4454	−	21.6191i	1.45646	−	0.840885i	0.457621	−	0.889147i	$-0.348702\pi$
$661$	37.4454	−	21.6191i	1.45646	−	0.840885i	0.998835	+	0.0482622i	$0.0153683\pi$
$662$	13.1569	+	22.7885i	0.511359	+	0.885699i
$663$	39.4143	−	0.341215i	1.53072	−	0.0132517i
$664$	10.9918	−	6.34613i	0.426565	−	0.246277i
$665$	−2.30842	−	23.1233i	−0.0895167	−	0.896682i
$666$	2.74858	−	1.65099i	0.106505	−	0.0639747i
$667$	−20.3152	+	11.7290i	−0.786609	+	0.454149i
$668$		−	24.0934i		−	0.932201i
$669$	−0.182102	−	21.0349i	−0.00704048	−	0.813256i
$670$	2.13024	−	13.2456i	0.0822982	−	0.511721i
$671$	14.8224	−	25.6731i	0.572211	−	0.991099i
$672$	4.43326	+	1.16028i	0.171017	+	0.0447587i
$673$	−11.8398	+	6.83568i	−0.456389	+	0.263496i	−0.710525	−	0.703672i	$-0.751542\pi$
$673$	−11.8398	+	6.83568i	−0.456389	+	0.263496i	0.254136	+	0.967169i	$0.418209\pi$
$674$	5.78970	−	3.34269i	0.223011	−	0.128755i
$675$	7.50269	−	24.8739i	0.288779	−	0.957396i
$676$	−6.14752	+	10.6478i	−0.236443	+	0.409531i
$677$	−7.18335	−	4.14731i	−0.276078	−	0.159394i	0.355568	−	0.934650i	$-0.384287\pi$
$677$	−7.18335	−	4.14731i	−0.276078	−	0.159394i	−0.631647	+	0.775256i	$0.717621\pi$
$678$	−0.122787	−	14.1833i	−0.00471562	−	0.544708i
$679$	−45.6133	+	12.0834i	−1.75048	+	0.463720i
$680$	−7.84765	−	6.38590i	−0.300944	−	0.244888i
$681$	−20.2768	+	35.8333i	−0.777010	+	1.37314i
$682$	5.80434			0.222260
$683$	20.1186	−	34.8465i	0.769817	−	1.33336i	−0.167845	−	0.985813i	$-0.553681\pi$
$683$	20.1186	−	34.8465i	0.769817	−	1.33336i	0.937662	−	0.347549i	$-0.112986\pi$
$684$	0.204015	+	11.7822i	0.00780071	+	0.450502i
$685$	−13.6881	−	2.20141i	−0.522995	−	0.0841114i
$686$	−4.64096	−	17.9293i	−0.177193	−	0.684546i
$687$	−9.73650	+	17.2064i	−0.371470	+	0.656465i
$688$			7.81422i			0.297914i
$689$	14.4930	+	25.1026i	0.552138	+	0.956331i
$690$	23.1621	−	9.05827i	0.881765	−	0.344843i
$691$	6.60595	+	3.81395i	0.251302	+	0.145089i	0.620360	−	0.784317i	$-0.286986\pi$
$691$	6.60595	+	3.81395i	0.251302	+	0.145089i	−0.369058	+	0.929406i	$0.620320\pi$
$692$		−	12.1734i		−	0.462762i
$693$	−6.15146	−	21.6962i	−0.233675	−	0.824172i
$694$	2.41396			0.0916325
$695$	−26.0614	−	21.2070i	−0.988565	−	0.804429i
$696$	6.32703	−	0.0547740i	0.239825	−	0.00207620i
$697$	−22.3644	+	12.9121i	−0.847112	+	0.489080i
$698$		−	0.755941i		−	0.0286128i
$699$	0.124790	+	14.4147i	0.00471999	+	0.545214i
$700$	13.2050	+	0.792714i	0.499101	+	0.0299618i
$701$			31.4440i			1.18762i	0.804604	+	0.593812i	$0.202378\pi$
$701$			31.4440i			1.18762i	−0.804604	+	0.593812i	$0.797622\pi$
$702$	22.2854	−	13.6501i	0.841109	−	0.515190i
$703$	−2.09906	+	3.63567i	−0.0791674	+	0.137122i
$704$			2.84121i			0.107082i
$705$	−3.15890	−	8.07734i	−0.118971	−	0.304210i
$706$	−8.10821	−	4.68128i	−0.305157	−	0.176182i
$707$	6.97681	−	25.7454i	0.262390	−	0.968256i
$708$	−19.1186	+	11.2599i	−0.718520	+	0.423173i
$709$	10.0658	−	17.4345i	0.378030	−	0.654768i	−0.612745	−	0.790280i	$-0.709935\pi$
$709$	10.0658	−	17.4345i	0.378030	−	0.654768i	0.990776	+	0.135513i	$0.0432682\pi$
$710$	−13.5571	−	11.0319i	−0.508790	−	0.414020i
$711$	−13.5302	+	0.234283i	−0.507422	+	0.00878631i
$712$	−5.33519	−	9.24081i	−0.199945	−	0.346314i
$713$	−11.3610	+	6.55927i	−0.425472	+	0.245647i
$714$	5.24993	−	20.0592i	0.196474	−	0.750698i
$715$	−24.7839	−	20.1675i	−0.926865	−	0.754222i
$716$		−	3.66016i		−	0.136786i
$717$	6.51281	+	11.0583i	0.243225	+	0.412981i
$718$		−	23.9180i		−	0.892612i
$719$	−12.4736	−	21.6049i	−0.465187	−	0.805728i	0.534023	−	0.845470i	$-0.320680\pi$
$719$	−12.4736	−	21.6049i	−0.465187	−	0.805728i	−0.999210	+	0.0397421i	$0.987346\pi$
$720$	−6.64055	−	0.950343i	−0.247479	−	0.0354172i
$721$	1.43225	−	5.28521i	0.0533398	−	0.196831i
$722$	1.78551	+	3.09260i	0.0664499	+	0.115095i
$723$	−7.39463	+	13.0678i	−0.275009	+	0.485998i
$724$	−10.0159	+	5.78267i	−0.372237	+	0.214911i
$725$	17.8840	−	3.71243i	0.664194	−	0.137876i
$726$	−4.36915	+	2.57322i	−0.162154	+	0.0955011i
$727$	−0.756579	−	1.31043i	−0.0280600	−	0.0486013i	0.851654	−	0.524104i	$-0.175600\pi$
$727$	−0.756579	−	1.31043i	−0.0280600	−	0.0486013i	−0.879714	+	0.475502i	$0.842266\pi$
$728$	9.38244	+	9.43583i	0.347736	+	0.349715i
$729$	−26.9636	+	1.40179i	−0.998651	+	0.0519182i
$730$	−11.2153	−	29.4261i	−0.415096	−	1.08911i
$731$	35.3571			1.30773
$732$	8.90014	−	15.7284i	0.328959	−	0.581338i
$733$	9.92495			0.366586			0.183293	−	0.983058i	$-0.441324\pi$
$733$	9.92495			0.366586			0.183293	+	0.983058i	$0.441324\pi$
$734$	−2.63628	+	4.56616i	−0.0973067	+	0.168540i
$735$	9.73089	+	25.3043i	0.358929	+	0.933365i
$736$	−3.21075	−	5.56118i	−0.118350	−	0.204988i
$737$	8.52323	+	14.7627i	0.313957	+	0.543790i
$738$	−8.30303	+	14.9741i	−0.305639	+	0.551206i
$739$	7.69829	−	13.3338i	0.283186	−	0.490493i	−0.688981	−	0.724779i	$-0.741942\pi$
$739$	7.69829	−	13.3338i	0.283186	−	0.490493i	0.972168	+	0.234286i	$0.0752752\pi$
$740$	−1.85367	−	1.50840i	−0.0681424	−	0.0554498i
$741$	−16.8515	+	29.7801i	−0.619056	+	1.09400i
$742$	14.7398	−	3.90472i	0.541114	−	0.143347i
$743$	−22.7782	+	39.4530i	−0.835651	+	1.44739i	0.0578475	+	0.998325i	$0.481576\pi$
$743$	−22.7782	+	39.4530i	−0.835651	+	1.44739i	−0.893499	+	0.449065i	$0.851757\pi$
$744$	3.53829	−	0.0306315i	0.129720	−	0.00112301i
$745$	0.810732	−	5.04104i	0.0297029	−	0.184689i
$746$	−6.37029	−	3.67789i	−0.233233	−	0.134657i
$747$	−33.3001	−	18.4646i	−1.21839	−	0.675585i
$748$	12.8557			0.470050
$749$	−6.50660	+	1.72367i	−0.237746	+	0.0629814i
$750$	−19.3368	+	1.04275i	−0.706081	+	0.0380757i
$751$	0.980502			0.0357790			0.0178895	−	0.999840i	$-0.494305\pi$
$751$	0.980502			0.0357790			0.0178895	+	0.999840i	$0.494305\pi$
$752$	−1.93936	+	1.11969i	−0.0707210	+	0.0408308i
$753$	−23.2822	−	13.1746i	−0.848451	−	0.480109i
$754$	15.9112	+	9.18635i	0.579452	+	0.334547i
$755$	29.1207	+	4.68337i	1.05981	+	0.170445i
$756$	−3.86439	−	13.1934i	−0.140547	−	0.479840i
$757$		−	16.9068i		−	0.614489i	−0.951631	−	0.307245i	$-0.900593\pi$
$757$		−	16.9068i		−	0.614489i	0.951631	−	0.307245i	$-0.0994070\pi$
$758$	−3.24231	+	5.61584i	−0.117766	+	0.203977i
$759$	−15.5630	+	27.5030i	−0.564901	+	0.998296i
$760$	8.20731	−	3.12809i	0.297710	−	0.113468i
$761$	32.1661			1.16602			0.583010	−	0.812465i	$-0.301875\pi$
$761$	32.1661			1.16602			0.583010	+	0.812465i	$0.301875\pi$
$762$	15.9718	+	27.1190i	0.578597	+	0.982419i
$763$	22.2568	+	22.3834i	0.805750	+	0.810335i
$764$		−	9.43103i		−	0.341203i
$765$	−4.30003	+	30.0466i	−0.155468	+	1.08634i
$766$	−8.50872	−	4.91251i	−0.307432	−	0.177496i
$767$	−64.4280			−2.32636
$768$	0.0149941	+	1.73199i	0.000541051	+	0.0624977i
$769$	−44.2257	−	25.5337i	−1.59482	−	0.920770i	−0.992463	−	0.122545i	$-0.960895\pi$
$769$	−44.2257	−	25.5337i	−1.59482	−	0.920770i	−0.602358	−	0.798226i	$-0.705772\pi$
$770$	−13.6500	+	9.80889i	−0.491912	+	0.353488i
$771$	−4.96243	+	8.76963i	−0.178717	+	0.315831i
$772$	−1.28623	−	0.742606i	−0.0462925	−	0.0267270i
$773$	21.9215	+	12.6564i	0.788463	+	0.455219i	0.839421	−	0.543482i	$-0.182894\pi$
$773$	21.9215	+	12.6564i	0.788463	+	0.455219i	−0.0509584	+	0.998701i	$0.516228\pi$
$774$	20.0960	−	12.0711i	0.722335	−	0.433885i
$775$	10.0013	−	2.07612i	0.359259	−	0.0745763i
$776$	−8.91744	−	15.4455i	−0.320117	−	0.554459i
$777$	1.24007	−	4.73814i	0.0444874	−	0.169980i
$778$	−7.18549	−	4.14854i	−0.257612	−	0.148733i
$779$		−	22.4183i		−	0.803221i
$780$	−15.2145	−	12.1632i	−0.544768	−	0.435512i
$781$	22.2087			0.794691
$782$	−25.1628	+	14.5277i	−0.899819	+	0.519511i
$783$	−9.91457	−	16.1867i	−0.354318	−	0.578466i
$784$	6.08194	−	3.46554i	0.217212	−	0.123769i
$785$	14.2757	+	37.4558i	0.509521	+	1.33685i
$786$	25.5340	−	15.0383i	0.910769	−	0.536398i
$787$	12.8786	+	22.3063i	0.459071	+	0.795134i	0.998912	−	0.0466329i	$-0.0148491\pi$
$787$	12.8786	+	22.3063i	0.459071	+	0.795134i	−0.539841	+	0.841767i	$0.681516\pi$
$788$	−8.82464	−	15.2847i	−0.314365	−	0.544496i
$789$	−3.27971	−	1.85587i	−0.116761	−	0.0660707i
$790$	3.59218	+	9.42498i	0.127804	+	0.335326i
$791$	−15.2768	−	15.3637i	−0.543181	−	0.546272i
$792$	7.30680	−	4.38898i	0.259636	−	0.155956i
$793$	45.4456	−	26.2380i	1.61382	−	0.931740i
$794$	13.3007			0.472025
$795$	−20.7879	+	8.12978i	−0.737271	+	0.288334i
$796$		−	20.6620i		−	0.732344i
$797$	−42.2492	−	24.3926i	−1.49655	−	0.864031i	−0.496553	−	0.868006i	$-0.665401\pi$
$797$	−42.2492	−	24.3926i	−1.49655	−	0.864031i	−0.999992	+	0.00397561i	$0.998735\pi$
$798$	12.8019	+	12.6538i	0.453184	+	0.447940i
$799$	5.06627	+	8.77504i	0.179232	+	0.310439i
$800$	1.01626	+	4.89563i	0.0359300	+	0.173087i
$801$	−15.5232	+	27.9954i	−0.548485	+	0.989169i
$802$	18.0899	+	10.4442i	0.638777	+	0.368798i
$803$	34.6525	+	20.0066i	1.22286	+	0.706018i
$804$	5.27362	+	8.95426i	0.185986	+	0.315792i
$805$	15.6329	−	34.6246i	0.550986	−	1.22036i
$806$	8.89810	+	5.13732i	0.313422	+	0.180954i
$807$	5.24165	−	3.08708i	0.184515	−	0.108670i
$808$	10.0818			0.354677
$809$	−19.3683	−	11.1823i	−0.680953	−	0.393148i	0.119261	−	0.992863i	$-0.461947\pi$
$809$	−19.3683	−	11.1823i	−0.680953	−	0.393148i	−0.800214	+	0.599715i	$0.795281\pi$
$810$	7.81401	+	18.5457i	0.274556	+	0.651628i
$811$			0.819585i			0.0287795i	0.999896	+	0.0143898i	$0.00458056\pi$
$811$			0.819585i			0.0287795i	−0.999896	+	0.0143898i	$0.995419\pi$
$812$	6.85359	−	6.81481i	0.240514	−	0.239153i
$813$	−2.78608	+	0.0241195i	−0.0977122	+	0.000845909i
$814$	3.03661			0.106433
$815$	−7.89001	+	3.00716i	−0.276375	+	0.105336i
$816$	7.83675	−	0.0678439i	0.274341	−	0.00237501i
$817$	−15.3470	+	26.5818i	−0.536924	+	0.929980i
$818$		−	28.3129i		−	0.989938i
$819$	9.77272	−	38.7051i	0.341486	−	1.35246i
$820$	12.6001	+	2.02643i	0.440016	+	0.0707661i
$821$	46.6341	+	26.9242i	1.62754	+	0.939661i	0.984824	+	0.173556i	$0.0555259\pi$
$821$	46.6341	+	26.9242i	1.62754	+	0.939661i	0.642716	+	0.766104i	$0.277807\pi$
$822$	9.25342	−	5.44981i	0.322750	−	0.190084i
$823$	38.7643	−	22.3806i	1.35124	−	0.780138i	0.362815	−	0.931861i	$-0.381816\pi$
$823$	38.7643	−	22.3806i	1.35124	−	0.780138i	0.988423	+	0.151723i	$0.0484822\pi$
$824$	2.06967			0.0721004
$825$	18.2213	−	16.5355i	0.634384	−	0.575691i
$826$	−8.86492	+	32.7128i	−0.308450	+	1.13822i
$827$	14.5517			0.506014			0.253007	−	0.967464i	$-0.418580\pi$
$827$	14.5517			0.506014			0.253007	+	0.967464i	$0.418580\pi$
$828$	−9.34196	+	16.8478i	−0.324656	+	0.585502i
$829$	29.5474	+	17.0592i	1.02623	+	0.592491i	0.915901	−	0.401404i	$-0.131478\pi$
$829$	29.5474	+	17.0592i	1.02623	+	0.592491i	0.110324	+	0.993896i	$0.464811\pi$
$830$	−4.50646	+	28.0207i	−0.156422	+	0.972612i
$831$	−3.81985	+	6.75047i	−0.132509	+	0.234171i
$832$	−2.51471	+	4.35560i	−0.0871818	+	0.151003i
$833$	−15.6806	−	27.5191i	−0.543301	−	0.953479i
$834$	26.0252	−	0.225304i	0.901178	−	0.00780163i
$835$	41.7875	+	34.0039i	1.44611	+	1.17675i
$836$	−5.58010	+	9.66502i	−0.192992	+	0.334272i
$837$	−5.54457	−	9.05217i	−0.191648	−	0.312889i
$838$	−7.85403	−	13.6036i	−0.271313	−	0.469928i
$839$	23.2722	+	40.3087i	0.803446	+	1.39161i	0.917335	+	0.398116i	$0.130336\pi$
$839$	23.2722	+	40.3087i	0.803446	+	1.39161i	−0.113889	+	0.993493i	$0.536331\pi$
$840$	−8.26920	+	6.05148i	−0.285314	+	0.208796i
$841$	−7.82763	+	13.5578i	−0.269918	+	0.467512i
$842$	−26.5316			−0.914341
$843$	18.0860	−	0.156573i	0.622915	−	0.00539267i
$844$	−11.2791			−0.388241
$845$	−9.79129	−	25.6899i	−0.336831	−	0.883758i
$846$	5.87535	+	3.25783i	0.201999	+	0.112007i
$847$	−2.02589	+	7.47583i	−0.0696105	+	0.256872i
$848$	2.88164	+	4.99115i	0.0989559	+	0.171397i
$849$	0.277447	+	32.0484i	0.00952197	+	1.09990i
$850$	22.1514	−	4.59827i	0.759785	−	0.157719i
$851$	−5.94364	+	3.43156i	−0.203745	+	0.117632i
$852$	13.5383	−	0.117203i	0.463815	−	0.00401531i
$853$	−19.2187	−	33.2878i	−0.658037	−	1.13975i	−0.981123	−	0.193384i	$-0.938054\pi$
$853$	−19.2187	−	33.2878i	−0.658037	−	1.13975i	0.323086	−	0.946369i	$-0.395280\pi$
$854$	−7.06910	−	26.6849i	−0.241900	−	0.913137i
$855$	−20.7228	−	16.2747i	−0.708706	−	0.556585i
$856$	−1.27205	−	2.20325i	−0.0434777	−	0.0753055i
$857$			27.2178i			0.929742i	0.885378	+	0.464871i	$0.153899\pi$
$857$			27.2178i			0.929742i	−0.885378	+	0.464871i	$0.846101\pi$
$858$	24.7495	−	0.214260i	0.844933	−	0.00731471i
$859$			32.0286i			1.09280i	0.837523	+	0.546402i	$0.184003\pi$
$859$			32.0286i			1.09280i	−0.837523	+	0.546402i	$0.815997\pi$
$860$	−13.5529	−	11.0285i	−0.462152	−	0.376069i
$861$	6.91616	+	25.2234i	0.235702	+	0.859611i
$862$	14.0479	−	8.11059i	0.478475	−	0.276248i
$863$	14.0979	+	24.4183i	0.479898	+	0.831208i	0.999734	−	0.0230584i	$-0.00734037\pi$
$863$	14.0979	+	24.4183i	0.479898	+	0.831208i	−0.519836	+	0.854266i	$0.674007\pi$
$864$	4.43102	−	2.71406i	0.150746	−	0.0923340i
$865$	21.1134	+	17.1807i	0.717878	+	0.584162i
$866$	−9.86340	+	17.0839i	−0.335172	+	0.580535i
$867$	−0.0520754	−	6.01530i	−0.00176857	−	0.204290i
$868$	3.83276	−	3.81108i	0.130092	−	0.129356i
$869$	−11.0990	−	6.40799i	−0.376507	−	0.217376i
$870$	−8.83457	+	11.0509i	−0.299520	+	0.374660i
$871$			30.1751i			1.02244i
$872$	−5.96532	+	10.3322i	−0.202011	+	0.349894i
$873$	−25.9461	+	46.7926i	−0.878142	+	1.58369i
$874$		−	25.2235i		−	0.853196i
$875$	−20.0116	+	21.7839i	−0.676514	+	0.736429i
$876$	21.2295	+	12.0130i	0.717279	+	0.405883i
$877$		−	23.3387i		−	0.788092i	−0.919091	−	0.394046i	$-0.871075\pi$
$877$		−	23.3387i		−	0.788092i	0.919091	−	0.394046i	$-0.128925\pi$
$878$	−11.3678	+	6.56319i	−0.383644	+	0.221497i
$879$	−0.322129	−	0.546953i	−0.0108651	−	0.0184483i
$880$	−4.92779	−	4.00991i	−0.166116	−	0.135174i
$881$	−18.3044			−0.616690			−0.308345	−	0.951275i	$-0.599775\pi$
$881$	−18.3044			−0.616690			−0.308345	+	0.951275i	$0.599775\pi$
$882$	−18.3075	−	10.2876i	−0.616446	−	0.346402i
$883$		−	7.38295i		−	0.248456i	−0.992254	−	0.124228i	$-0.960355\pi$
$883$		−	7.38295i		−	0.248456i	0.992254	−	0.124228i	$-0.0396454\pi$
$884$	19.7079	+	11.3783i	0.662847	+	0.382695i
$885$	7.45363	−	49.0507i	0.250551	−	1.64882i
$886$	−4.31000	−	7.46514i	−0.144797	−	0.250796i
$887$			11.1403i			0.374054i	0.982355	+	0.187027i	$0.0598851\pi$
$887$			11.1403i			0.374054i	−0.982355	+	0.187027i	$0.940115\pi$
$888$	1.85110	−	0.0160252i	0.0621188	−	0.000537772i
$889$	46.4020	+	12.5746i	1.55627	+	0.421738i
$890$	23.5570	+	3.78858i	0.789632	+	0.126994i
$891$	−22.5744	−	12.0111i	−0.756272	−	0.402387i
$892$	6.07248	−	10.5178i	0.203322	−	0.352164i
$893$	−8.79621			−0.294354
$894$	2.00705	+	3.40784i	0.0671258	+	0.113975i
$895$	6.34816	+	5.16572i	0.212196	+	0.172671i
$896$	1.86551	+	1.87613i	0.0623224	+	0.0626771i
$897$	−48.2006	+	28.3878i	−1.60937	+	0.947842i
$898$	32.2354	+	18.6111i	1.07571	+	0.621061i
$899$	3.73142	−	6.46301i	0.124450	−	0.215554i
$900$	11.0203	−	10.1761i	0.367344	−	0.339203i
$901$	22.5835	−	13.0386i	0.752366	−	0.434379i
$902$	−14.0433	+	8.10791i	−0.467591	+	0.269964i
$903$	9.06666	−	34.6424i	0.301720	−	1.15283i
$904$	4.09453	−	7.09194i	0.136182	−	0.235874i
$905$	4.10634	−	25.5328i	0.136499	−	0.848738i
$906$	−19.6861	+	11.5942i	−0.654027	+	0.385190i
$907$			25.0316i			0.831160i	0.909557	+	0.415580i	$0.136421\pi$
$907$			25.0316i			0.831160i	−0.909557	+	0.415580i	$0.863579\pi$
$908$	−20.5863	+	11.8855i	−0.683180	+	0.394434i
$909$	−15.5740	−	25.9276i	−0.516556	−	0.859964i
$910$	−29.6073	+	2.95572i	−0.981471	+	0.0979813i
$911$	10.1366	−	5.85238i	0.335841	−	0.193898i	−0.322590	−	0.946539i	$-0.604554\pi$
$911$	10.1366	−	5.85238i	0.335841	−	0.193898i	0.658431	+	0.752641i	$0.271220\pi$
$912$	−3.35059	+	5.92119i	−0.110949	+	0.196070i
$913$	−18.0307	−	31.2301i	−0.596729	−	1.03356i
$914$	−35.0771	+	20.2518i	−1.16025	+	0.669868i
$915$	14.7181	+	37.6344i	0.486567	+	1.24416i
$916$	−9.88508	+	5.70716i	−0.326612	+	0.188570i
$917$	11.8396	−	43.6899i	0.390979	−	1.44277i
$918$	−12.2803	−	20.0491i	−0.405311	−	0.661719i
$919$	15.3085	+	26.5152i	0.504982	+	0.874655i	0.999983	+	0.00576276i	$0.00183435\pi$
$919$	15.3085	+	26.5152i	0.504982	+	0.874655i	−0.495001	+	0.868892i	$0.664832\pi$
$920$	14.1767	+	2.27999i	0.467393	+	0.0751691i
$921$	37.6700	+	21.3161i	1.24127	+	0.702390i
$922$	−33.7510			−1.11153
$923$	34.0462	+	19.6566i	1.12064	+	0.647004i
$924$	3.29659	−	12.5958i	0.108450	−	0.414372i
$925$	5.23232	−	1.08615i	0.172038	−	0.0357123i
$926$	23.0998	−	13.3367i	0.759108	−	0.438271i
$927$	−3.19714	−	5.32261i	−0.105008	−	0.174817i
$928$	3.16363	+	1.82652i	0.103851	+	0.0599586i
$929$	6.67642	−	11.5639i	0.219046	−	0.379399i	−0.735470	−	0.677557i	$-0.763039\pi$
$929$	6.67642	−	11.5639i	0.219046	−	0.379399i	0.954517	+	0.298157i	$0.0963721\pi$
$930$	−4.94059	+	6.18003i	−0.162008	+	0.202651i
$931$	27.4954	+	0.156022i	0.901124	+	0.00511341i
$932$	−4.16132	+	7.20762i	−0.136309	+	0.236093i
$933$	−0.360334	−	41.6227i	−0.0117968	−	1.36267i
$934$		−	5.64952i		−	0.184858i
$935$	−18.1437	+	22.2968i	−0.593363	+	0.729185i
$936$	15.0860	−	0.261223i	0.493101	−	0.00853833i
$937$	32.6519			1.06669			0.533345	−	0.845898i	$-0.320935\pi$
$937$	32.6519			1.06669			0.533345	+	0.845898i	$0.320935\pi$
$938$	15.3212	+	4.15192i	0.500253	+	0.135565i
$939$	9.70802	−	5.71755i	0.316809	−	0.186585i
$940$	0.795104	−	4.94387i	0.0259334	−	0.161251i
$941$	17.9039	+	31.0104i	0.583650	+	1.01091i	0.995042	+	0.0994526i	$0.0317092\pi$
$941$	17.9039	+	31.0104i	0.583650	+	1.01091i	−0.411393	+	0.911458i	$0.634957\pi$
$942$	−27.0226	−	15.2911i	−0.880443	−	0.498212i
$943$	18.3249	−	31.7396i	0.596740	−	1.03358i
$944$	−12.8102			−0.416937
$945$	28.3366	+	11.9180i	0.921789	+	0.387692i
$946$	22.2019			0.721845
$947$	17.1913	−	29.7762i	0.558643	−	0.967598i	−0.438967	−	0.898503i	$-0.644656\pi$
$947$	17.1913	−	29.7762i	0.558643	−	0.967598i	0.997610	−	0.0690948i	$-0.0220111\pi$
$948$	−6.79968	−	3.84770i	−0.220843	−	0.124967i
$949$	35.4150	+	61.3406i	1.14962	+	1.99120i
$950$	−6.15794	+	18.6495i	−0.199790	+	0.605070i
$951$	−11.0274	+	6.49461i	−0.357588	+	0.210602i
$952$	8.48895	−	8.44092i	0.275129	−	0.273572i
$953$	−44.0113			−1.42566			−0.712832	−	0.701334i	$-0.752588\pi$
$953$	−44.0113			−1.42566			−0.712832	+	0.701334i	$0.752588\pi$
$954$	8.38439	−	15.1209i	0.271455	−	0.489556i
$955$	16.3571	+	13.3104i	0.529305	+	0.430713i
$956$			7.40953i			0.239641i
$957$	−0.155625	−	17.9764i	−0.00503063	−	0.581095i
$958$	0.136929	−	0.237168i	0.00442397	−	0.00766254i
$959$	4.29063	−	15.8330i	0.138552	−	0.511275i
$960$	−3.02511	−	2.41841i	−0.0976350	−	0.0780539i
$961$	−13.4133	+	23.2324i	−0.432686	+	0.749434i
$962$	4.65515	+	2.68765i	0.150088	+	0.0866534i
$963$	−3.70113	+	6.67483i	−0.119267	+	0.215093i
$964$	−7.50748	+	4.33445i	−0.241800	+	0.139603i
$965$	3.10328	−	1.18277i	0.0998981	−	0.0380746i
$966$	7.78156	+	28.3795i	0.250368	+	0.913095i
$967$	−6.03415	−	3.48382i	−0.194045	−	0.112032i	0.399830	−	0.916589i	$-0.369069\pi$
$967$	−6.03415	−	3.48382i	−0.194045	−	0.112032i	−0.593875	+	0.804557i	$0.702403\pi$
$968$	−2.92751			−0.0940937
$969$	26.7917	+	15.1605i	0.860673	+	0.487025i
$970$	39.3740	+	6.33238i	1.26422	+	0.203320i
$971$	12.3672	+	21.4206i	0.396883	+	0.687421i	0.993340	−	0.115224i	$-0.0367586\pi$
$971$	12.3672	+	21.4206i	0.396883	+	0.687421i	−0.596457	+	0.802645i	$0.703425\pi$
$972$	−13.8246	−	7.20277i	−0.443425	−	0.231029i
$973$	28.1911	−	28.0316i	0.903766	−	0.898652i
$974$	12.4072	−	7.16329i	0.397552	−	0.229527i
$975$	42.5686	−	9.22166i	1.36329	−	0.295330i
$976$	9.03596	−	5.21692i	0.289234	−	0.166989i
$977$	22.5555	+	39.0672i	0.721613	+	1.24987i	0.960353	+	0.278787i	$0.0899325\pi$
$977$	22.5555	+	39.0672i	0.721613	+	1.24987i	−0.238740	+	0.971084i	$0.576734\pi$
$978$	3.22106	−	5.69227i	0.102998	−	0.182019i
$979$	−26.2551	+	15.1584i	−0.839117	+	0.484465i
$980$	−2.57304	+	15.4395i	−0.0821929	+	0.493198i
$981$	35.7866	−	0.619666i	1.14258	−	0.0197844i
$982$	31.8165	−	18.3692i	1.01530	−	0.586186i
$983$			36.7498i			1.17214i	0.810262	+	0.586068i	$0.199325\pi$
$983$			36.7498i			1.17214i	−0.810262	+	0.586068i	$0.800675\pi$
$984$	−8.51793	+	5.01664i	−0.271542	+	0.159925i
$985$	38.9643	+	6.26648i	1.24151	+	0.199667i
$986$	8.26450	−	14.3145i	0.263195	−	0.455868i
$987$	9.89681	−	2.71367i	0.315019	−	0.0863771i
$988$	−17.1087	+	9.87771i	−0.544300	+	0.314252i
$989$	−43.4563	+	25.0895i	−1.38183	+	0.797800i
$990$	−2.70013	+	18.8672i	−0.0858156	+	0.599639i
$991$	5.67076	−	9.82205i	0.180138	−	0.312008i	−0.761790	−	0.647825i	$-0.775679\pi$
$991$	5.67076	−	9.82205i	0.180138	−	0.312008i	0.941927	+	0.335817i	$0.109012\pi$
$992$	1.76921	+	1.02145i	0.0561725	+	0.0324312i
$993$	39.2721	−	23.1293i	1.24626	−	0.733987i
$994$	14.6650	−	14.5820i	0.465146	−	0.462514i
$995$	35.8360	+	29.1610i	1.13608	+	0.924466i
$996$	−11.1562	−	18.9425i	−0.353498	−	0.600216i
$997$	8.60531			0.272533			0.136266	−	0.990672i	$-0.456490\pi$
$997$	8.60531			0.272533			0.136266	+	0.990672i	$0.456490\pi$
$998$	−16.0396	+	27.7814i	−0.507725	+	0.879406i
$999$	−2.90071	−	4.73575i	−0.0917744	−	0.149832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.59.5	yes	48
3.2	odd	2		1890.2.r.a.1529.2		48
5.4	even	2		630.2.r.a.59.20	✓	48
7.5	odd	6		630.2.bi.a.509.5	yes	48
9.2	odd	6		630.2.bi.b.479.20	yes	48
9.7	even	3		1890.2.bi.a.899.6		48
15.14	odd	2		1890.2.r.b.1529.2		48
21.5	even	6		1890.2.bi.b.719.11		48
35.19	odd	6		630.2.bi.b.509.20	yes	48
45.29	odd	6		630.2.bi.a.479.5	yes	48
45.34	even	6		1890.2.bi.b.899.11		48
63.47	even	6		630.2.r.a.299.20	yes	48
63.61	odd	6		1890.2.r.b.89.2		48
105.89	even	6		1890.2.bi.a.719.6		48
315.124	odd	6		1890.2.r.a.89.2		48
315.299	even	6	inner	630.2.r.b.299.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.20	✓	48	5.4	even	2
630.2.r.a.299.20	yes	48	63.47	even	6
630.2.r.b.59.5	yes	48	1.1	even	1	trivial
630.2.r.b.299.5	yes	48	315.299	even	6	inner
630.2.bi.a.479.5	yes	48	45.29	odd	6
630.2.bi.a.509.5	yes	48	7.5	odd	6
630.2.bi.b.479.20	yes	48	9.2	odd	6
630.2.bi.b.509.20	yes	48	35.19	odd	6
1890.2.r.a.89.2		48	315.124	odd	6
1890.2.r.a.1529.2		48	3.2	odd	2
1890.2.r.b.89.2		48	63.61	odd	6
1890.2.r.b.1529.2		48	15.14	odd	2
1890.2.bi.a.719.6		48	105.89	even	6
1890.2.bi.a.899.6		48	9.7	even	3
1890.2.bi.b.719.11		48	21.5	even	6
1890.2.bi.b.899.11		48	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50744 - 0.853008i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20770 + 0.355056i) q^{5} +(-1.49245 + 0.878978i) q^{6} +(-0.692019 + 2.55365i) q^{7} -1.00000 q^{8} +(1.54476 + 2.57172i) q^{9} +(1.41134 - 1.73440i) q^{10} +2.84121i q^{11} +(0.0149941 + 1.73199i) q^{12} +(-2.51471 + 4.35560i) q^{13} +(1.86551 + 1.87613i) q^{14} +(-3.02511 - 2.41841i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.91852 + 2.26236i) q^{17} +(2.99955 - 0.0519390i) q^{18} +(-3.40172 + 1.96399i) q^{19} +(-0.796362 - 2.08945i) q^{20} +(3.22146 - 3.25917i) q^{21} +(2.46056 + 1.42061i) q^{22} -6.42150 q^{23} +(1.50744 + 0.853008i) q^{24} +(4.74787 + 1.56771i) q^{25} +(2.51471 + 4.35560i) q^{26} +(-0.134933 - 5.19440i) q^{27} +(2.55753 - 0.677517i) q^{28} +(3.16363 - 1.82652i) q^{29} +(-3.60696 + 1.41062i) q^{30} +(1.76921 - 1.02145i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.42358 - 4.28296i) q^{33} +(3.91852 - 2.26236i) q^{34} +(-2.43446 + 5.39198i) q^{35} +(1.45479 - 2.62366i) q^{36} +(0.925584 - 0.534386i) q^{37} +3.92797i q^{38} +(7.50614 - 4.42075i) q^{39} +(-2.20770 - 0.355056i) q^{40} +(-2.85368 + 4.94272i) q^{41} +(-1.21180 - 4.41945i) q^{42} +(6.76731 - 3.90711i) q^{43} +(2.46056 - 1.42061i) q^{44} +(2.49725 + 6.22605i) q^{45} +(-3.21075 + 5.56118i) q^{46} +(1.93936 + 1.11969i) q^{47} +(1.49245 - 0.878978i) q^{48} +(-6.04222 - 3.53434i) q^{49} +(3.73162 - 3.32792i) q^{50} +(-3.97713 - 6.75290i) q^{51} +5.02942 q^{52} +(2.88164 - 4.99115i) q^{53} +(-4.56595 - 2.48034i) q^{54} +(-1.00879 + 6.27254i) q^{55} +(0.692019 - 2.55365i) q^{56} +(6.80319 - 0.0588963i) q^{57} -3.65305i q^{58} +(6.40511 + 11.0940i) q^{59} +(-0.581850 + 3.82903i) q^{60} +(-9.03596 - 5.21692i) q^{61} -2.04291i q^{62} +(-7.63626 + 2.16508i) q^{63} +1.00000 q^{64} +(-7.09820 + 8.72300i) q^{65} +(-2.49736 - 4.24036i) q^{66} +(5.19591 - 2.99986i) q^{67} -4.52472i q^{68} +(9.68003 + 5.47759i) q^{69} +(3.45236 + 4.80429i) q^{70} -7.81664i q^{71} +(-1.54476 - 2.57172i) q^{72} +(7.04158 - 12.1964i) q^{73} -1.06877i q^{74} +(-5.81986 - 6.41321i) q^{75} +(3.40172 + 1.96399i) q^{76} +(-7.25545 - 1.96617i) q^{77} +(-0.0754114 - 8.71088i) q^{78} +(-2.25537 + 3.90642i) q^{79} +(-1.41134 + 1.73440i) q^{80} +(-4.22746 + 7.94535i) q^{81} +(2.85368 + 4.94272i) q^{82} +(-10.9918 + 6.34613i) q^{83} +(-4.43326 - 1.16028i) q^{84} +(7.84765 + 6.38590i) q^{85} -7.81422i q^{86} +(-6.32703 + 0.0547740i) q^{87} -2.84121i q^{88} +(5.33519 + 9.24081i) q^{89} +(6.64055 + 0.950343i) q^{90} +(-9.38244 - 9.43583i) q^{91} +(3.21075 + 5.56118i) q^{92} +(-3.53829 + 0.0306315i) q^{93} +(1.93936 - 1.11969i) q^{94} +(-8.20731 + 3.12809i) q^{95} +(-0.0149941 - 1.73199i) q^{96} +(8.91744 + 15.4455i) q^{97} +(-6.08194 + 3.46554i) q^{98} +(-7.30680 + 4.38898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

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