LMFDB - Embedded newform 494.2.h.d.315.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [494,2,Mod(315,494)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(494, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("494.315"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,22,0,22,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.4
Character	$\chi$	$=$	494.315
Dual form			494.2.h.d.425.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.38760 q^{3} +1.00000 q^{4} +(1.40461 - 2.43285i) q^{5} -1.38760 q^{6} +(1.16976 - 2.02609i) q^{7} +1.00000 q^{8} -1.07457 q^{9} +(1.40461 - 2.43285i) q^{10} +(-1.18901 - 2.05943i) q^{11} -1.38760 q^{12} +(-3.45686 + 1.02474i) q^{13} +(1.16976 - 2.02609i) q^{14} +(-1.94903 + 3.37582i) q^{15} +1.00000 q^{16} +(1.04698 + 1.81342i) q^{17} -1.07457 q^{18} +(-1.65015 - 4.03448i) q^{19} +(1.40461 - 2.43285i) q^{20} +(-1.62316 + 2.81140i) q^{21} +(-1.18901 - 2.05943i) q^{22} +(1.34826 - 2.33525i) q^{23} -1.38760 q^{24} +(-1.44584 - 2.50426i) q^{25} +(-3.45686 + 1.02474i) q^{26} +5.65387 q^{27} +(1.16976 - 2.02609i) q^{28} +(2.46442 - 4.26851i) q^{29} +(-1.94903 + 3.37582i) q^{30} +6.34084 q^{31} +1.00000 q^{32} +(1.64987 + 2.85766i) q^{33} +(1.04698 + 1.81342i) q^{34} +(-3.28612 - 5.69172i) q^{35} -1.07457 q^{36} +(1.93947 + 3.35926i) q^{37} +(-1.65015 - 4.03448i) q^{38} +(4.79673 - 1.42193i) q^{39} +(1.40461 - 2.43285i) q^{40} -1.62157 q^{41} +(-1.62316 + 2.81140i) q^{42} +(-2.58555 - 4.47831i) q^{43} +(-1.18901 - 2.05943i) q^{44} +(-1.50935 + 2.61428i) q^{45} +(1.34826 - 2.33525i) q^{46} +(0.561039 + 0.971749i) q^{47} -1.38760 q^{48} +(0.763303 + 1.32208i) q^{49} +(-1.44584 - 2.50426i) q^{50} +(-1.45278 - 2.51630i) q^{51} +(-3.45686 + 1.02474i) q^{52} +(3.96622 + 6.86969i) q^{53} +5.65387 q^{54} -6.68037 q^{55} +(1.16976 - 2.02609i) q^{56} +(2.28975 + 5.59823i) q^{57} +(2.46442 - 4.26851i) q^{58} +(6.10772 + 10.5789i) q^{59} +(-1.94903 + 3.37582i) q^{60} -10.4072 q^{61} +6.34084 q^{62} +(-1.25700 + 2.17718i) q^{63} +1.00000 q^{64} +(-2.36249 + 9.84939i) q^{65} +(1.64987 + 2.85766i) q^{66} +(6.75310 - 11.6967i) q^{67} +(1.04698 + 1.81342i) q^{68} +(-1.87084 + 3.24039i) q^{69} +(-3.28612 - 5.69172i) q^{70} +(3.76218 + 6.51629i) q^{71} -1.07457 q^{72} +(-3.56056 + 6.16707i) q^{73} +(1.93947 + 3.35926i) q^{74} +(2.00624 + 3.47491i) q^{75} +(-1.65015 - 4.03448i) q^{76} -5.56345 q^{77} +(4.79673 - 1.42193i) q^{78} +(-0.432764 + 0.749570i) q^{79} +(1.40461 - 2.43285i) q^{80} -4.62157 q^{81} -1.62157 q^{82} -1.47550 q^{83} +(-1.62316 + 2.81140i) q^{84} +5.88237 q^{85} +(-2.58555 - 4.47831i) q^{86} +(-3.41963 + 5.92297i) q^{87} +(-1.18901 - 2.05943i) q^{88} +(3.07686 - 5.32927i) q^{89} +(-1.50935 + 2.61428i) q^{90} +(-1.96750 + 8.20263i) q^{91} +(1.34826 - 2.33525i) q^{92} -8.79854 q^{93} +(0.561039 + 0.971749i) q^{94} +(-12.1331 - 1.65228i) q^{95} -1.38760 q^{96} +(6.92652 + 11.9971i) q^{97} +(0.763303 + 1.32208i) q^{98} +(1.27768 + 2.21301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 22 q^{4} - 2 q^{5} - 5 q^{7} + 22 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{13} - 5 q^{14} - 3 q^{15} + 22 q^{16} + q^{17} + 10 q^{18} + 12 q^{19} - 2 q^{20} + q^{21} - 2 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) $ 22 * q + 22 * q^2 + 22 * q^4 - 2 * q^5 - 5 * q^7 + 22 * q^8 + 10 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^13 - 5 * q^14 - 3 * q^15 + 22 * q^16 + q^17 + 10 * q^18 + 12 * q^19 - 2 * q^20 + q^21 - 2 * q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 6 * q^27 - 5 * q^28 - 7 * q^29 - 3 * q^30 + 6 * q^31 + 22 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 10 * q^36 - 9 * q^37 + 12 * q^38 + 13 * q^39 - 2 * q^40 - 24 * q^41 + q^42 - 10 * q^43 - 2 * q^44 - 15 * q^45 + 4 * q^46 + 19 * q^47 - 14 * q^49 - 9 * q^50 - 22 * q^51 + 2 * q^52 - 9 * q^53 - 6 * q^54 + 48 * q^55 - 5 * q^56 + 13 * q^57 - 7 * q^58 - 12 * q^59 - 3 * q^60 - 22 * q^61 + 6 * q^62 - 23 * q^63 + 22 * q^64 + 13 * q^65 - 4 * q^66 + 3 * q^67 + q^68 - 20 * q^69 - 3 * q^70 + 4 * q^71 + 10 * q^72 - 38 * q^73 - 9 * q^74 - 20 * q^75 + 12 * q^76 - 76 * q^77 + 13 * q^78 - 5 * q^79 - 2 * q^80 - 90 * q^81 - 24 * q^82 - 10 * q^83 + q^84 + 24 * q^85 - 10 * q^86 + 4 * q^87 - 2 * q^88 + 3 * q^89 - 15 * q^90 + 34 * q^91 + 4 * q^92 + 22 * q^93 + 19 * q^94 - 33 * q^95 - 31 * q^97 - 14 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.38760			−0.801130			−0.400565	−	0.916268i	$-0.631186\pi$
$3$	−1.38760			−0.801130			−0.400565	+	0.916268i	$0.631186\pi$
$4$	1.00000			0.500000
$5$	1.40461	−	2.43285i	0.628159	−	1.08800i	−0.359762	−	0.933044i	$-0.617142\pi$
$5$	1.40461	−	2.43285i	0.628159	−	1.08800i	0.987921	−	0.154959i	$-0.0495246\pi$
$6$	−1.38760			−0.566484
$7$	1.16976	−	2.02609i	0.442129	−	0.765791i	−0.555718	−	0.831371i	$-0.687557\pi$
$7$	1.16976	−	2.02609i	0.442129	−	0.765791i	0.997847	+	0.0655804i	$0.0208899\pi$
$8$	1.00000			0.353553
$9$	−1.07457			−0.358191
$10$	1.40461	−	2.43285i	0.444175	−	0.769334i
$11$	−1.18901	−	2.05943i	−0.358501	−	0.620941i	0.629210	−	0.777235i	$-0.283379\pi$
$11$	−1.18901	−	2.05943i	−0.358501	−	0.620941i	−0.987711	+	0.156294i	$0.950045\pi$
$12$	−1.38760			−0.400565
$13$	−3.45686	+	1.02474i	−0.958761	+	0.284212i
$13$	−3.45686	+	1.02474i	−0.958761	+	0.284212i
$14$	1.16976	−	2.02609i	0.312633	−	0.541496i
$15$	−1.94903	+	3.37582i	−0.503237	+	0.871632i
$16$	1.00000			0.250000
$17$	1.04698	+	1.81342i	0.253930	+	0.439819i	0.964604	−	0.263702i	$-0.0849435\pi$
$17$	1.04698	+	1.81342i	0.253930	+	0.439819i	−0.710675	+	0.703521i	$0.751610\pi$
$18$	−1.07457			−0.253279
$19$	−1.65015	−	4.03448i	−0.378571	−	0.925572i
$19$	−1.65015	−	4.03448i	−0.378571	−	0.925572i
$20$	1.40461	−	2.43285i	0.314079	−	0.544002i
$21$	−1.62316	+	2.81140i	−0.354203	+	0.613498i
$22$	−1.18901	−	2.05943i	−0.253498	−	0.439072i
$23$	1.34826	−	2.33525i	0.281132	−	0.486934i	−0.690532	−	0.723302i	$-0.742624\pi$
$23$	1.34826	−	2.33525i	0.281132	−	0.486934i	0.971664	+	0.236368i	$0.0759569\pi$
$24$	−1.38760			−0.283242
$25$	−1.44584	−	2.50426i	−0.289167	−	0.500853i
$26$	−3.45686	+	1.02474i	−0.677947	+	0.200968i
$27$	5.65387			1.08809
$28$	1.16976	−	2.02609i	0.221065	−	0.382895i
$29$	2.46442	−	4.26851i	0.457632	−	0.792642i	−0.541203	−	0.840892i	$-0.682031\pi$
$29$	2.46442	−	4.26851i	0.457632	−	0.792642i	0.998835	+	0.0482498i	$0.0153644\pi$
$30$	−1.94903	+	3.37582i	−0.355842	+	0.616337i
$31$	6.34084			1.13885			0.569425	−	0.822044i	$-0.307166\pi$
$31$	6.34084			1.13885			0.569425	+	0.822044i	$0.307166\pi$
$32$	1.00000			0.176777
$33$	1.64987	+	2.85766i	0.287205	+	0.497454i
$34$	1.04698	+	1.81342i	0.179555	+	0.310999i
$35$	−3.28612	−	5.69172i	−0.555455	−	0.962076i
$36$	−1.07457			−0.179096
$37$	1.93947	+	3.35926i	0.318847	+	0.552260i	0.980248	−	0.197773i	$-0.0633710\pi$
$37$	1.93947	+	3.35926i	0.318847	+	0.552260i	−0.661401	+	0.750033i	$0.730038\pi$
$38$	−1.65015	−	4.03448i	−0.267690	−	0.654479i
$39$	4.79673	−	1.42193i	0.768092	−	0.227691i
$40$	1.40461	−	2.43285i	0.222088	−	0.384667i
$41$	−1.62157			−0.253247			−0.126623	−	0.991951i	$-0.540414\pi$
$41$	−1.62157			−0.253247			−0.126623	+	0.991951i	$0.540414\pi$
$42$	−1.62316	+	2.81140i	−0.250459	+	0.433808i
$43$	−2.58555	−	4.47831i	−0.394293	−	0.682935i	0.598718	−	0.800960i	$-0.295677\pi$
$43$	−2.58555	−	4.47831i	−0.394293	−	0.682935i	−0.993011	+	0.118025i	$0.962344\pi$
$44$	−1.18901	−	2.05943i	−0.179250	−	0.310471i
$45$	−1.50935	+	2.61428i	−0.225001	+	0.389713i
$46$	1.34826	−	2.33525i	0.198790	−	0.344314i
$47$	0.561039	+	0.971749i	0.0818360	+	0.141744i	0.904039	−	0.427451i	$-0.140588\pi$
$47$	0.561039	+	0.971749i	0.0818360	+	0.141744i	−0.822203	+	0.569195i	$0.807255\pi$
$48$	−1.38760			−0.200282
$49$	0.763303	+	1.32208i	0.109043	+	0.188868i
$50$	−1.44584	−	2.50426i	−0.204472	−	0.354156i
$51$	−1.45278	−	2.51630i	−0.203430	−	0.352352i
$52$	−3.45686	+	1.02474i	−0.479381	+	0.142106i
$53$	3.96622	+	6.86969i	0.544802	+	0.943624i	0.998619	+	0.0525297i	$0.0167284\pi$
$53$	3.96622	+	6.86969i	0.544802	+	0.943624i	−0.453818	+	0.891095i	$0.649938\pi$
$54$	5.65387			0.769394
$55$	−6.68037			−0.900781
$56$	1.16976	−	2.02609i	0.156316	−	0.270748i
$57$	2.28975	+	5.59823i	0.303284	+	0.741504i
$58$	2.46442	−	4.26851i	0.323595	−	0.560483i
$59$	6.10772	+	10.5789i	0.795158	+	1.37725i	0.922739	+	0.385426i	$0.125945\pi$
$59$	6.10772	+	10.5789i	0.795158	+	1.37725i	−0.127581	+	0.991828i	$0.540721\pi$
$60$	−1.94903	+	3.37582i	−0.251618	+	0.435816i
$61$	−10.4072			−1.33250			−0.666250	−	0.745729i	$-0.732101\pi$
$61$	−10.4072			−1.33250			−0.666250	+	0.745729i	$0.732101\pi$
$62$	6.34084			0.805288
$63$	−1.25700	+	2.17718i	−0.158367	+	0.274299i
$64$	1.00000			0.125000
$65$	−2.36249	+	9.84939i	−0.293031	+	1.22167i
$66$	1.64987	+	2.85766i	0.203085	+	0.351753i
$67$	6.75310	−	11.6967i	0.825022	−	1.42898i	−0.0768802	−	0.997040i	$-0.524496\pi$
$67$	6.75310	−	11.6967i	0.825022	−	1.42898i	0.901902	−	0.431940i	$-0.142171\pi$
$68$	1.04698	+	1.81342i	0.126965	+	0.219909i
$69$	−1.87084	+	3.24039i	−0.225223	+	0.390097i
$70$	−3.28612	−	5.69172i	−0.392766	−	0.680291i
$71$	3.76218	+	6.51629i	0.446489	+	0.773342i	0.998155	−	0.0607236i	$-0.0193408\pi$
$71$	3.76218	+	6.51629i	0.446489	+	0.773342i	−0.551666	+	0.834065i	$0.686007\pi$
$72$	−1.07457			−0.126640
$73$	−3.56056	+	6.16707i	−0.416732	+	0.721801i	−0.995609	−	0.0936145i	$-0.970158\pi$
$73$	−3.56056	+	6.16707i	−0.416732	+	0.721801i	0.578877	+	0.815415i	$0.303491\pi$
$74$	1.93947	+	3.35926i	0.225459	+	0.390506i
$75$	2.00624	+	3.47491i	0.231661	+	0.401248i
$76$	−1.65015	−	4.03448i	−0.189285	−	0.462786i
$77$	−5.56345			−0.634014
$78$	4.79673	−	1.42193i	0.543123	−	0.161002i
$79$	−0.432764	+	0.749570i	−0.0486898	+	0.0843332i	−0.889343	−	0.457240i	$-0.848838\pi$
$79$	−0.432764	+	0.749570i	−0.0486898	+	0.0843332i	0.840653	+	0.541574i	$0.182171\pi$
$80$	1.40461	−	2.43285i	0.157040	−	0.272001i
$81$	−4.62157			−0.513508
$82$	−1.62157			−0.179072
$83$	−1.47550			−0.161957			−0.0809787	−	0.996716i	$-0.525805\pi$
$83$	−1.47550			−0.161957			−0.0809787	+	0.996716i	$0.525805\pi$
$84$	−1.62316	+	2.81140i	−0.177101	+	0.306749i
$85$	5.88237			0.638032
$86$	−2.58555	−	4.47831i	−0.278807	−	0.482908i
$87$	−3.41963	+	5.92297i	−0.366623	+	0.635009i
$88$	−1.18901	−	2.05943i	−0.126749	−	0.219536i
$89$	3.07686	−	5.32927i	0.326146	−	0.564902i	−0.655598	−	0.755111i	$-0.727583\pi$
$89$	3.07686	−	5.32927i	0.326146	−	0.564902i	0.981744	+	0.190209i	$0.0609165\pi$
$90$	−1.50935	+	2.61428i	−0.159100	+	0.275569i
$91$	−1.96750	+	8.20263i	−0.206250	+	0.859869i
$92$	1.34826	−	2.33525i	0.140566	−	0.243467i
$93$	−8.79854			−0.912366
$94$	0.561039	+	0.971749i	0.0578668	+	0.100228i
$95$	−12.1331	−	1.65228i	−1.24483	−	0.169520i
$96$	−1.38760			−0.141621
$97$	6.92652	+	11.9971i	0.703281	+	1.21812i	0.967308	+	0.253603i	$0.0816158\pi$
$97$	6.92652	+	11.9971i	0.703281	+	1.21812i	−0.264027	+	0.964515i	$0.585051\pi$
$98$	0.763303	+	1.32208i	0.0771052	+	0.133550i
$99$	1.27768	+	2.21301i	0.128412	+	0.222416i
$100$	−1.44584	−	2.50426i	−0.144584	−	0.250426i
$101$	−1.60274	+	2.77604i	−0.159479	+	0.276226i	−0.934681	−	0.355488i	$-0.884315\pi$
$101$	−1.60274	+	2.77604i	−0.159479	+	0.276226i	0.775202	+	0.631714i	$0.217648\pi$
$102$	−1.45278	−	2.51630i	−0.143847	−	0.249150i
$103$	2.97549			0.293184			0.146592	−	0.989197i	$-0.453170\pi$
$103$	2.97549			0.293184			0.146592	+	0.989197i	$0.453170\pi$
$104$	−3.45686	+	1.02474i	−0.338973	+	0.100484i
$105$	4.55981	+	7.89782i	0.444992	+	0.770748i
$106$	3.96622	+	6.86969i	0.385233	+	0.667243i
$107$	−4.01510	−	6.95436i	−0.388155	−	0.672304i	0.604047	−	0.796949i	$-0.293554\pi$
$107$	−4.01510	−	6.95436i	−0.388155	−	0.672304i	−0.992201	+	0.124645i	$0.960221\pi$
$108$	5.65387			0.544044
$109$	−7.39017	+	12.8001i	−0.707850	+	1.22603i	0.257803	+	0.966197i	$0.417001\pi$
$109$	−7.39017	+	12.8001i	−0.707850	+	1.22603i	−0.965653	+	0.259835i	$0.916332\pi$
$110$	−6.68037			−0.636949
$111$	−2.69121	−	4.66131i	−0.255438	−	0.442432i
$112$	1.16976	−	2.02609i	0.110532	−	0.191448i
$113$	−5.93677	+	10.2828i	−0.558484	+	0.967323i	0.439139	+	0.898419i	$0.355284\pi$
$113$	−5.93677	+	10.2828i	−0.558484	+	0.967323i	−0.997623	+	0.0689041i	$0.978050\pi$
$114$	2.28975	+	5.59823i	0.214454	+	0.524322i
$115$	−3.78755	−	6.56023i	−0.353191	−	0.611744i
$116$	2.46442	−	4.26851i	0.228816	−	0.396321i
$117$	3.71465	−	1.10116i	0.343420	−	0.101802i
$118$	6.10772	+	10.5789i	0.562262	+	0.973865i
$119$	4.89887			0.449079
$120$	−1.94903	+	3.37582i	−0.177921	+	0.308168i
$121$	2.67250	−	4.62891i	0.242955	−	0.420810i
$122$	−10.4072			−0.942219
$123$	2.25009			0.202883
$124$	6.34084			0.569425
$125$	5.92274			0.529746
$126$	−1.25700	+	2.17718i	−0.111982	+	0.193959i
$127$	9.88211	−	17.1163i	0.876896	−	1.51883i	0.0221659	−	0.999754i	$-0.492944\pi$
$127$	9.88211	−	17.1163i	0.876896	−	1.51883i	0.854730	−	0.519073i	$-0.173723\pi$
$128$	1.00000			0.0883883
$129$	3.58770	+	6.21409i	0.315880	+	0.547120i
$130$	−2.36249	+	9.84939i	−0.207204	+	0.863848i
$131$	−2.10933	+	3.65347i	−0.184293	+	0.319205i	−0.943338	−	0.331833i	$-0.892333\pi$
$131$	−2.10933	+	3.65347i	−0.184293	+	0.319205i	0.759045	+	0.651038i	$0.225666\pi$
$132$	1.64987	+	2.85766i	0.143603	+	0.248727i
$133$	−10.1045	−	1.37603i	−0.876172	−	0.119317i
$134$	6.75310	−	11.6967i	0.583379	−	1.01044i
$135$	7.94146	−	13.7550i	0.683492	−	1.18384i
$136$	1.04698	+	1.81342i	0.0897776	+	0.155499i
$137$	16.8310			1.43797			0.718986	−	0.695025i	$-0.244607\pi$
$137$	16.8310			1.43797			0.718986	+	0.695025i	$0.244607\pi$
$138$	−1.87084	+	3.24039i	−0.159257	+	0.275841i
$139$	−1.23156			−0.104460			−0.0522300	−	0.998635i	$-0.516633\pi$
$139$	−1.23156			−0.104460			−0.0522300	+	0.998635i	$0.516633\pi$
$140$	−3.28612	−	5.69172i	−0.277728	−	0.481038i
$141$	−0.778497	−	1.34840i	−0.0655612	−	0.113555i
$142$	3.76218	+	6.51629i	0.315715	+	0.546835i
$143$	6.22063	+	5.90074i	0.520195	+	0.493444i
$144$	−1.07457			−0.0895478
$145$	−6.92309	−	11.9911i	−0.574931	−	0.995810i
$146$	−3.56056	+	6.16707i	−0.294674	+	0.510390i
$147$	−1.05916	−	1.83451i	−0.0873578	−	0.151308i
$148$	1.93947	+	3.35926i	0.159424	+	0.276130i
$149$	3.21526	+	5.56899i	0.263404	+	0.456230i	0.967144	−	0.254228i	$-0.0818213\pi$
$149$	3.21526	+	5.56899i	0.263404	+	0.456230i	−0.703740	+	0.710458i	$0.748488\pi$
$150$	2.00624	+	3.47491i	0.163809	+	0.283725i
$151$	−20.8956			−1.70046			−0.850229	−	0.526413i	$-0.823536\pi$
$151$	−20.8956			−1.70046			−0.850229	+	0.526413i	$0.823536\pi$
$152$	−1.65015	−	4.03448i	−0.133845	−	0.327239i
$153$	−1.12506	−	1.94865i	−0.0909553	−	0.157539i
$154$	−5.56345			−0.448316
$155$	8.90639	−	15.4263i	0.715378	−	1.23907i
$156$	4.79673	−	1.42193i	0.384046	−	0.113845i
$157$	4.88362	−	8.45868i	0.389755	−	0.675076i	−0.602661	−	0.797997i	$-0.705893\pi$
$157$	4.88362	−	8.45868i	0.389755	−	0.675076i	0.992416	+	0.122921i	$0.0392263\pi$
$158$	−0.432764	+	0.749570i	−0.0344289	+	0.0596326i
$159$	−5.50351	−	9.53236i	−0.436457	−	0.755965i
$160$	1.40461	−	2.43285i	0.111044	−	0.192334i
$161$	−3.15429	−	5.46339i	−0.248593	−	0.430576i
$162$	−4.62157			−0.363105
$163$	8.06687	−	13.9722i	0.631846	−	1.09439i	−0.355328	−	0.934742i	$-0.615631\pi$
$163$	8.06687	−	13.9722i	0.631846	−	1.09439i	0.987174	−	0.159647i	$-0.0510357\pi$
$164$	−1.62157			−0.126623
$165$	9.26967			0.721643
$166$	−1.47550			−0.114521
$167$	−10.3864	+	17.9898i	−0.803724	+	1.39209i	0.113425	+	0.993547i	$0.463818\pi$
$167$	−10.3864	+	17.9898i	−0.803724	+	1.39209i	−0.917149	+	0.398545i	$0.869515\pi$
$168$	−1.62316	+	2.81140i	−0.125230	+	0.216904i
$169$	10.8998	−	7.08478i	0.838447	−	0.544983i
$170$	5.88237			0.451157
$171$	1.77321	+	4.33534i	0.135601	+	0.331532i
$172$	−2.58555	−	4.47831i	−0.197146	−	0.341468i
$173$	−5.01074	−	8.67886i	−0.380960	−	0.659842i	0.610240	−	0.792217i	$-0.291073\pi$
$173$	−5.01074	−	8.67886i	−0.380960	−	0.659842i	−0.991200	+	0.132375i	$0.957740\pi$
$174$	−3.41963	+	5.92297i	−0.259241	+	0.449019i
$175$	−6.76515			−0.511398
$176$	−1.18901	−	2.05943i	−0.0896251	−	0.155235i
$177$	−8.47506	−	14.6792i	−0.637025	−	1.10336i
$178$	3.07686	−	5.32927i	0.230620	−	0.399446i
$179$	−2.42396	−	4.19841i	−0.181175	−	0.313804i	0.761106	−	0.648628i	$-0.224657\pi$
$179$	−2.42396	−	4.19841i	−0.181175	−	0.313804i	−0.942281	+	0.334823i	$0.891323\pi$
$180$	−1.50935	+	2.61428i	−0.112501	+	0.194857i
$181$	1.17225	+	2.03040i	0.0871326	+	0.150918i	0.906298	−	0.422639i	$-0.138896\pi$
$181$	1.17225	+	2.03040i	0.0871326	+	0.150918i	−0.819165	+	0.573557i	$0.805563\pi$
$182$	−1.96750	+	8.20263i	−0.145841	+	0.608019i
$183$	14.4409			1.06750
$184$	1.34826	−	2.33525i	0.0993950	−	0.172157i
$185$	10.8968			0.801147
$186$	−8.79854			−0.645140
$187$	2.48974	−	4.31235i	0.182068	−	0.315351i
$188$	0.561039	+	0.971749i	0.0409180	+	0.0708720i
$189$	6.61369	−	11.4553i	0.481075	−	0.833247i
$190$	−12.1331	−	1.65228i	−0.880227	−	0.119869i
$191$	−9.09327	+	15.7500i	−0.657966	+	1.13963i	0.323175	+	0.946339i	$0.395250\pi$
$191$	−9.09327	+	15.7500i	−0.657966	+	1.13963i	−0.981141	+	0.193291i	$0.938084\pi$
$192$	−1.38760			−0.100141
$193$	7.23156			0.520539			0.260270	−	0.965536i	$-0.416189\pi$
$193$	7.23156			0.520539			0.260270	+	0.965536i	$0.416189\pi$
$194$	6.92652	+	11.9971i	0.497295	+	0.861340i
$195$	3.27819	−	13.6670i	0.234756	−	0.978713i
$196$	0.763303	+	1.32208i	0.0545216	+	0.0944342i
$197$	0.958690	+	1.66050i	0.0683038	+	0.118306i	0.898155	−	0.439679i	$-0.144908\pi$
$197$	0.958690	+	1.66050i	0.0683038	+	0.118306i	−0.829851	+	0.557985i	$0.811575\pi$
$198$	1.27768	+	2.21301i	0.0908008	+	0.157272i
$199$	−2.92434			−0.207301			−0.103651	−	0.994614i	$-0.533052\pi$
$199$	−2.92434			−0.207301			−0.103651	+	0.994614i	$0.533052\pi$
$200$	−1.44584	−	2.50426i	−0.102236	−	0.177078i
$201$	−9.37058	+	16.2303i	−0.660950	+	1.14480i
$202$	−1.60274	+	2.77604i	−0.112769	+	0.195321i
$203$	−5.76559	−	9.98630i	−0.404665	−	0.700901i
$204$	−1.45278	−	2.51630i	−0.101715	−	0.176176i
$205$	−2.27767	+	3.94504i	−0.159079	+	0.275533i
$206$	2.97549			0.207312
$207$	−1.44880	+	2.50940i	−0.100699	+	0.174416i
$208$	−3.45686	+	1.02474i	−0.239690	+	0.0710530i
$209$	−6.34667	+	8.19541i	−0.439008	+	0.566888i
$210$	4.55981	+	7.89782i	0.314657	+	0.545001i
$211$	25.8219			1.77765			0.888825	−	0.458247i	$-0.151523\pi$
$211$	25.8219			1.77765			0.888825	+	0.458247i	$0.151523\pi$
$212$	3.96622	+	6.86969i	0.272401	+	0.471812i
$213$	−5.22040	−	9.04199i	−0.357696	−	0.619547i
$214$	−4.01510	−	6.95436i	−0.274467	−	0.475390i
$215$	−14.5267			−0.990715
$216$	5.65387			0.384697
$217$	7.41729	−	12.8471i	0.503519	−	0.872120i
$218$	−7.39017	+	12.8001i	−0.500525	+	0.866936i
$219$	4.94062	−	8.55741i	0.333856	−	0.578256i
$220$	−6.68037			−0.450391
$221$	−5.47755	−	5.19586i	−0.368460	−	0.349512i
$222$	−2.69121	−	4.66131i	−0.180622	−	0.312846i
$223$	−3.20937			−0.214915			−0.107458	−	0.994210i	$-0.534271\pi$
$223$	−3.20937			−0.214915			−0.107458	+	0.994210i	$0.534271\pi$
$224$	1.16976	−	2.02609i	0.0781582	−	0.135374i
$225$	1.55366	+	2.69102i	0.103577	+	0.179401i
$226$	−5.93677	+	10.2828i	−0.394908	+	0.684001i
$227$	−4.47319	+	7.74779i	−0.296896	+	0.514239i	−0.975424	−	0.220336i	$-0.929285\pi$
$227$	−4.47319	+	7.74779i	−0.296896	+	0.514239i	0.678528	+	0.734574i	$0.262618\pi$
$228$	2.28975	+	5.59823i	0.151642	+	0.370752i
$229$	−16.6547			−1.10057			−0.550286	−	0.834976i	$-0.685481\pi$
$229$	−16.6547			−1.10057			−0.550286	+	0.834976i	$0.685481\pi$
$230$	−3.78755	−	6.56023i	−0.249744	−	0.432568i
$231$	7.71983			0.507928
$232$	2.46442	−	4.26851i	0.161797	−	0.280241i
$233$	7.58077	−	13.1303i	0.496633	−	0.860193i	−0.503360	−	0.864077i	$-0.667903\pi$
$233$	7.58077	−	13.1303i	0.496633	−	0.860193i	0.999992	+	0.00388387i	$0.00123628\pi$
$234$	3.71465	−	1.10116i	0.242835	−	0.0719850i
$235$	3.15216			0.205624
$236$	6.10772	+	10.5789i	0.397579	+	0.688627i
$237$	0.600503	−	1.04010i	0.0390068	−	0.0675618i
$238$	4.89887			0.317547
$239$	15.5321			1.00469			0.502345	−	0.864668i	$-0.332471\pi$
$239$	15.5321			1.00469			0.502345	+	0.864668i	$0.332471\pi$
$240$	−1.94903	+	3.37582i	−0.125809	+	0.217908i
$241$	−3.57219			−0.230105			−0.115053	−	0.993359i	$-0.536704\pi$
$241$	−3.57219			−0.230105			−0.115053	+	0.993359i	$0.536704\pi$
$242$	2.67250	−	4.62891i	0.171795	−	0.297558i
$243$	−10.5487			−0.676701
$244$	−10.4072			−0.666250
$245$	4.28856			0.273986
$246$	2.25009			0.143460
$247$	9.83864	+	12.2557i	0.626018	+	0.779809i
$248$	6.34084			0.402644
$249$	2.04740			0.129749
$250$	5.92274			0.374587
$251$	−18.4927			−1.16725			−0.583626	−	0.812023i	$-0.698367\pi$
$251$	−18.4927			−1.16725			−0.583626	+	0.812023i	$0.698367\pi$
$252$	−1.25700	+	2.17718i	−0.0791834	+	0.137150i
$253$	−6.41239			−0.403143
$254$	9.88211	−	17.1163i	0.620059	−	1.07397i
$255$	−8.16236			−0.511147
$256$	1.00000			0.0625000
$257$	−9.63436	+	16.6872i	−0.600975	+	1.04092i	0.391699	+	0.920093i	$0.371887\pi$
$257$	−9.63436	+	16.6872i	−0.600975	+	1.04092i	−0.992674	+	0.120825i	$0.961446\pi$
$258$	3.58770	+	6.21409i	0.223361	+	0.386872i
$259$	9.07490			0.563887
$260$	−2.36249	+	9.84939i	−0.146516	+	0.610833i
$261$	−2.64821	+	4.58683i	−0.163920	+	0.283917i
$262$	−2.10933	+	3.65347i	−0.130315	+	0.225712i
$263$	−17.4662			−1.07701			−0.538505	−	0.842622i	$-0.681011\pi$
$263$	−17.4662			−1.07701			−0.538505	+	0.842622i	$0.681011\pi$
$264$	1.64987	+	2.85766i	0.101542	+	0.175877i
$265$	22.2839			1.36889
$266$	−10.1045	−	1.37603i	−0.619547	−	0.0843698i
$267$	−4.26944	+	7.39488i	−0.261285	+	0.452559i
$268$	6.75310	−	11.6967i	0.412511	−	0.714490i
$269$	12.7277	+	22.0450i	0.776021	+	1.34411i	0.934219	+	0.356700i	$0.116098\pi$
$269$	12.7277	+	22.0450i	0.776021	+	1.34411i	−0.158198	+	0.987407i	$0.550569\pi$
$270$	7.94146	−	13.7550i	0.483302	−	0.837103i
$271$	−25.1953			−1.53051			−0.765254	−	0.643729i	$-0.777386\pi$
$271$	−25.1953			−1.53051			−0.765254	+	0.643729i	$0.777386\pi$
$272$	1.04698	+	1.81342i	0.0634824	+	0.109955i
$273$	2.73009	−	11.3819i	0.165233	−	0.688866i
$274$	16.8310			1.01680
$275$	−3.43823	+	5.95520i	−0.207333	+	0.359112i
$276$	−1.87084	+	3.24039i	−0.112611	+	0.195049i
$277$	4.90789	−	8.50071i	0.294886	−	0.510758i	−0.680072	−	0.733145i	$-0.738052\pi$
$277$	4.90789	−	8.50071i	0.294886	−	0.510758i	0.974958	+	0.222387i	$0.0713849\pi$
$278$	−1.23156			−0.0738643
$279$	−6.81370			−0.407926
$280$	−3.28612	−	5.69172i	−0.196383	−	0.340145i
$281$	−3.19421	−	5.53254i	−0.190551	−	0.330044i	0.754882	−	0.655861i	$-0.227694\pi$
$281$	−3.19421	−	5.53254i	−0.190551	−	0.330044i	−0.945433	+	0.325817i	$0.894361\pi$
$282$	−0.778497	−	1.34840i	−0.0463588	−	0.0802958i
$283$	−11.1381			−0.662092			−0.331046	−	0.943615i	$-0.607402\pi$
$283$	−11.1381			−0.662092			−0.331046	+	0.943615i	$0.607402\pi$
$284$	3.76218	+	6.51629i	0.223245	+	0.386671i
$285$	16.8358	+	2.29270i	0.997269	+	0.135808i
$286$	6.22063	+	5.90074i	0.367834	+	0.348918i
$287$	−1.89686	+	3.28545i	−0.111968	+	0.193934i
$288$	−1.07457			−0.0633199
$289$	6.30767	−	10.9252i	0.371040	−	0.642659i
$290$	−6.92309	−	11.9911i	−0.406538	−	0.704144i
$291$	−9.61121	−	16.6471i	−0.563419	−	0.975871i
$292$	−3.56056	+	6.16707i	−0.208366	+	0.360900i
$293$	12.2695	−	21.2514i	0.716793	−	1.24152i	−0.245471	−	0.969404i	$-0.578943\pi$
$293$	12.2695	−	21.2514i	0.716793	−	1.24152i	0.962264	−	0.272118i	$-0.0877242\pi$
$294$	−1.05916	−	1.83451i	−0.0617713	−	0.106991i
$295$	34.3158			1.99794
$296$	1.93947	+	3.35926i	0.112730	+	0.195253i
$297$	−6.72251	−	11.6437i	−0.390080	−	0.675638i
$298$	3.21526	+	5.56899i	0.186255	+	0.322603i
$299$	−2.26772	+	9.45427i	−0.131146	+	0.546755i
$300$	2.00624	+	3.47491i	0.115830	+	0.200624i
$301$	−12.0979			−0.697314
$302$	−20.8956			−1.20240
$303$	2.22396	−	3.85202i	0.127763	−	0.221293i
$304$	−1.65015	−	4.03448i	−0.0946427	−	0.231393i
$305$	−14.6179	+	25.3190i	−0.837021	+	1.44976i
$306$	−1.12506	−	1.94865i	−0.0643151	−	0.111397i
$307$	7.65103	−	13.2520i	0.436667	−	0.756330i	−0.560763	−	0.827977i	$-0.689492\pi$
$307$	7.65103	−	13.2520i	0.436667	−	0.756330i	0.997430	+	0.0716465i	$0.0228254\pi$
$308$	−5.56345			−0.317007
$309$	−4.12879			−0.234878
$310$	8.90639	−	15.4263i	0.505849	−	0.876156i
$311$	4.78866			0.271540			0.135770	−	0.990740i	$-0.456649\pi$
$311$	4.78866			0.271540			0.135770	+	0.990740i	$0.456649\pi$
$312$	4.79673	−	1.42193i	0.271562	−	0.0805008i
$313$	−1.25040	−	2.16575i	−0.0706767	−	0.122416i	0.828521	−	0.559957i	$-0.189183\pi$
$313$	−1.25040	−	2.16575i	−0.0706767	−	0.122416i	−0.899198	+	0.437542i	$0.855849\pi$
$314$	4.88362	−	8.45868i	0.275599	−	0.477351i
$315$	3.53117	+	6.11617i	0.198959	+	0.344607i
$316$	−0.432764	+	0.749570i	−0.0243449	+	0.0421666i
$317$	0.442735	+	0.766840i	0.0248665	+	0.0430700i	0.878191	−	0.478310i	$-0.158751\pi$
$317$	0.442735	+	0.766840i	0.0248665	+	0.0430700i	−0.853324	+	0.521380i	$0.825417\pi$
$318$	−5.50351	−	9.53236i	−0.308622	−	0.534548i
$319$	−11.7209			−0.656245
$320$	1.40461	−	2.43285i	0.0785199	−	0.136000i
$321$	5.57135	+	9.64986i	0.310962	+	0.538602i
$322$	−3.15429	−	5.46339i	−0.175782	−	0.304463i
$323$	5.58853	−	7.21643i	0.310954	−	0.401533i
$324$	−4.62157			−0.256754
$325$	7.56428	+	7.17529i	0.419591	+	0.398013i
$326$	8.06687	−	13.9722i	0.446782	−	0.773850i
$327$	10.2546	−	17.7615i	0.567080	−	0.982211i
$328$	−1.62157			−0.0895362
$329$	2.62513			0.144728
$330$	9.26967			0.510278
$331$	2.04780	−	3.54690i	0.112557	−	0.194955i	−0.804243	−	0.594300i	$-0.797429\pi$
$331$	2.04780	−	3.54690i	0.112557	−	0.194955i	0.916801	+	0.399345i	$0.130762\pi$
$332$	−1.47550			−0.0809787
$333$	−2.08411	−	3.60978i	−0.114208	−	0.197815i
$334$	−10.3864	+	17.9898i	−0.568319	+	0.984357i
$335$	−18.9709	−	32.8585i	−1.03649	−	1.79525i
$336$	−1.62316	+	2.81140i	−0.0885507	+	0.153374i
$337$	10.4281	−	18.0620i	0.568055	−	0.983901i	−0.428703	−	0.903446i	$-0.641029\pi$
$337$	10.4281	−	18.0620i	0.568055	−	0.983901i	0.996758	−	0.0804553i	$-0.0256374\pi$
$338$	10.8998	−	7.08478i	0.592872	−	0.385361i
$339$	8.23785	−	14.2684i	0.447418	−	0.774951i
$340$	5.88237			0.319016
$341$	−7.53934	−	13.0585i	−0.408278	−	0.707158i
$342$	1.77321	+	4.33534i	0.0958842	+	0.234428i
$343$	19.9482			1.07710
$344$	−2.58555	−	4.47831i	−0.139404	−	0.241454i
$345$	5.25559	+	9.10295i	0.282952	+	0.490086i
$346$	−5.01074	−	8.67886i	−0.269379	−	0.466579i
$347$	6.11829	+	10.5972i	0.328447	+	0.568887i	0.982204	−	0.187818i	$-0.0601414\pi$
$347$	6.11829	+	10.5972i	0.328447	+	0.568887i	−0.653757	+	0.756705i	$0.726808\pi$
$348$	−3.41963	+	5.92297i	−0.183311	+	0.317505i
$349$	−15.1673	−	26.2706i	−0.811889	−	1.40623i	−0.911540	−	0.411211i	$-0.865106\pi$
$349$	−15.1673	−	26.2706i	−0.811889	−	1.40623i	0.0996508	−	0.995022i	$-0.468227\pi$
$350$	−6.76515			−0.361613
$351$	−19.5446	+	5.79375i	−1.04322	+	0.309247i
$352$	−1.18901	−	2.05943i	−0.0633745	−	0.109768i
$353$	12.6305	+	21.8767i	0.672254	+	1.16438i	0.977263	+	0.212029i	$0.0680072\pi$
$353$	12.6305	+	21.8767i	0.672254	+	1.16438i	−0.305009	+	0.952349i	$0.598659\pi$
$354$	−8.47506	−	14.6792i	−0.450444	−	0.780193i
$355$	21.1375			1.12186
$356$	3.07686	−	5.32927i	0.163073	−	0.282451i
$357$	−6.79766			−0.359770
$358$	−2.42396	−	4.19841i	−0.128110	−	0.221893i
$359$	5.44751	−	9.43536i	0.287509	−	0.497979i	−0.685706	−	0.727879i	$-0.740506\pi$
$359$	5.44751	−	9.43536i	0.287509	−	0.497979i	0.973214	+	0.229899i	$0.0738397\pi$
$360$	−1.50935	+	2.61428i	−0.0795499	+	0.137784i
$361$	−13.5540	+	13.3150i	−0.713368	+	0.700789i
$362$	1.17225	+	2.03040i	0.0616121	+	0.106715i
$363$	−3.70836	+	6.42306i	−0.194638	+	0.337123i
$364$	−1.96750	+	8.20263i	−0.103125	+	0.429934i
$365$	10.0024	+	17.3246i	0.523548	+	0.906811i
$366$	14.4409			0.754840
$367$	4.68294	−	8.11108i	0.244447	−	0.423395i	−0.717529	−	0.696529i	$-0.754727\pi$
$367$	4.68294	−	8.11108i	0.244447	−	0.423395i	0.961976	+	0.273134i	$0.0880602\pi$
$368$	1.34826	−	2.33525i	0.0702829	−	0.121734i
$369$	1.74250			0.0907108
$370$	10.8968			0.566496
$371$	18.5582			0.963491
$372$	−8.79854			−0.456183
$373$	15.1058	−	26.1641i	0.782150	−	1.35472i	−0.148536	−	0.988907i	$-0.547456\pi$
$373$	15.1058	−	26.1641i	0.782150	−	1.35472i	0.930687	−	0.365817i	$-0.119211\pi$
$374$	2.48974	−	4.31235i	0.128741	−	0.222986i
$375$	−8.21837			−0.424395
$376$	0.561039	+	0.971749i	0.0289334	+	0.0501141i
$377$	−4.14506	+	17.2810i	−0.213482	+	0.890019i
$378$	6.61369	−	11.4553i	0.340172	−	0.589195i
$379$	−8.13181	−	14.0847i	−0.417703	−	0.723482i	0.578005	−	0.816033i	$-0.303831\pi$
$379$	−8.13181	−	14.0847i	−0.417703	−	0.723482i	−0.995708	+	0.0925506i	$0.970498\pi$
$380$	−12.1331	−	1.65228i	−0.622414	−	0.0847602i
$381$	−13.7124	+	23.7506i	−0.702507	+	1.21678i
$382$	−9.09327	+	15.7500i	−0.465252	+	0.805840i
$383$	15.2397	+	26.3960i	0.778715	+	1.34877i	0.932683	+	0.360697i	$0.117461\pi$
$383$	15.2397	+	26.3960i	0.778715	+	1.34877i	−0.153968	+	0.988076i	$0.549205\pi$
$384$	−1.38760			−0.0708105
$385$	−7.81446	+	13.5350i	−0.398262	+	0.689810i
$386$	7.23156			0.368077
$387$	2.77837	+	4.81227i	0.141232	+	0.244621i
$388$	6.92652	+	11.9971i	0.351641	+	0.609059i
$389$	−13.0031	−	22.5220i	−0.659282	−	1.14191i	−0.980802	−	0.195007i	$-0.937527\pi$
$389$	−13.0031	−	22.5220i	−0.659282	−	1.14191i	0.321520	−	0.946903i	$-0.395806\pi$
$390$	3.27819	−	13.6670i	0.165998	−	0.692054i
$391$	5.64639			0.285550
$392$	0.763303	+	1.32208i	0.0385526	+	0.0667751i
$393$	2.92691	−	5.06955i	0.147643	−	0.255725i
$394$	0.958690	+	1.66050i	0.0482981	+	0.0836548i
$395$	1.21573	+	2.10570i	0.0611699	+	0.105949i
$396$	1.27768	+	2.21301i	0.0642059	+	0.111208i
$397$	−9.39318	−	16.2695i	−0.471430	−	0.816541i	0.528036	−	0.849222i	$-0.322929\pi$
$397$	−9.39318	−	16.2695i	−0.471430	−	0.816541i	−0.999466	+	0.0326811i	$0.989595\pi$
$398$	−2.92434			−0.146584
$399$	14.0210	+	1.90938i	0.701927	+	0.0955883i
$400$	−1.44584	−	2.50426i	−0.0722919	−	0.125213i
$401$	−32.9758			−1.64674			−0.823368	−	0.567508i	$-0.807907\pi$
$401$	−32.9758			−1.64674			−0.823368	+	0.567508i	$0.807907\pi$
$402$	−9.37058	+	16.2303i	−0.467362	+	0.809495i
$403$	−21.9194	+	6.49772i	−1.09188	+	0.323675i
$404$	−1.60274	+	2.77604i	−0.0797395	+	0.138113i
$405$	−6.49149	+	11.2436i	−0.322565	+	0.558698i
$406$	−5.76559	−	9.98630i	−0.286141	−	0.495612i
$407$	4.61211	−	7.98841i	0.228614	−	0.395971i
$408$	−1.45278	−	2.51630i	−0.0719235	−	0.124575i
$409$	−26.2302			−1.29700			−0.648501	−	0.761214i	$-0.724604\pi$
$409$	−26.2302			−1.29700			−0.648501	+	0.761214i	$0.724604\pi$
$410$	−2.27767	+	3.94504i	−0.112486	+	0.194831i
$411$	−23.3547			−1.15200
$412$	2.97549			0.146592
$413$	28.5784			1.40625
$414$	−1.44880	+	2.50940i	−0.0712049	+	0.123330i
$415$	−2.07250	+	3.58967i	−0.101735	+	0.176210i
$416$	−3.45686	+	1.02474i	−0.169487	+	0.0502420i
$417$	1.70892			0.0836860
$418$	−6.34667	+	8.19541i	−0.310426	+	0.400851i
$419$	−2.14701	−	3.71874i	−0.104888	−	0.181672i	0.808804	−	0.588078i	$-0.200115\pi$
$419$	−2.14701	−	3.71874i	−0.104888	−	0.181672i	−0.913693	+	0.406406i	$0.866782\pi$
$420$	4.55981	+	7.89782i	0.222496	+	0.385374i
$421$	−17.3511	+	30.0529i	−0.845639	+	1.46469i	0.0394257	+	0.999223i	$0.487447\pi$
$421$	−17.3511	+	30.0529i	−0.845639	+	1.46469i	−0.885065	+	0.465468i	$0.845886\pi$
$422$	25.8219			1.25699
$423$	−0.602878	−	1.04422i	−0.0293129	−	0.0507715i
$424$	3.96622	+	6.86969i	0.192617	+	0.333622i
$425$	3.02752	−	5.24382i	0.146856	−	0.254363i
$426$	−5.22040	−	9.04199i	−0.252929	−	0.438086i
$427$	−12.1739	+	21.0858i	−0.589137	+	1.02042i
$428$	−4.01510	−	6.95436i	−0.194077	−	0.336152i
$429$	−8.63173	−	8.18784i	−0.416744	−	0.395313i
$430$	−14.5267			−0.700541
$431$	−16.5456	+	28.6578i	−0.796974	+	1.38040i	0.124605	+	0.992206i	$0.460234\pi$
$431$	−16.5456	+	28.6578i	−0.796974	+	1.38040i	−0.921578	+	0.388192i	$0.873100\pi$
$432$	5.65387			0.272022
$433$	−5.44937			−0.261880			−0.130940	−	0.991390i	$-0.541800\pi$
$433$	−5.44937			−0.261880			−0.130940	+	0.991390i	$0.541800\pi$
$434$	7.41729	−	12.8471i	0.356041	−	0.616682i
$435$	9.60646	+	16.6389i	0.460595	+	0.797773i
$436$	−7.39017	+	12.8001i	−0.353925	+	0.613016i
$437$	−11.6464	−	1.58600i	−0.557121	−	0.0758686i
$438$	4.94062	−	8.55741i	0.236072	−	0.408889i
$439$	13.4761			0.643181			0.321591	−	0.946879i	$-0.395782\pi$
$439$	13.4761			0.643181			0.321591	+	0.946879i	$0.395782\pi$
$440$	−6.68037			−0.318474
$441$	−0.820225	−	1.42067i	−0.0390583	−	0.0676510i
$442$	−5.47755	−	5.19586i	−0.260540	−	0.247142i
$443$	16.9939	+	29.4343i	0.807406	+	1.39847i	0.914655	+	0.404236i	$0.132463\pi$
$443$	16.9939	+	29.4343i	0.807406	+	1.39847i	−0.107249	+	0.994232i	$0.534204\pi$
$444$	−2.69121	−	4.66131i	−0.127719	−	0.221216i
$445$	−8.64354	−	14.9711i	−0.409743	−	0.709696i
$446$	−3.20937			−0.151968
$447$	−4.46149	−	7.72752i	−0.211021	−	0.365499i
$448$	1.16976	−	2.02609i	0.0552662	−	0.0957238i
$449$	−15.6351	+	27.0808i	−0.737865	+	1.27802i	0.215589	+	0.976484i	$0.430833\pi$
$449$	−15.6351	+	27.0808i	−0.737865	+	1.27802i	−0.953455	+	0.301536i	$0.902501\pi$
$450$	1.55366	+	2.69102i	0.0732402	+	0.126856i
$451$	1.92807	+	3.33951i	0.0907891	+	0.157251i
$452$	−5.93677	+	10.2828i	−0.279242	+	0.483662i
$453$	28.9946			1.36229
$454$	−4.47319	+	7.74779i	−0.209937	+	0.363622i
$455$	17.1922	+	16.3081i	0.805983	+	0.764535i
$456$	2.28975	+	5.59823i	0.107227	+	0.262161i
$457$	18.4366	+	31.9331i	0.862426	+	1.49377i	0.869580	+	0.493792i	$0.164390\pi$
$457$	18.4366	+	31.9331i	0.862426	+	1.49377i	−0.00715366	+	0.999974i	$0.502277\pi$
$458$	−16.6547			−0.778221
$459$	5.91948	+	10.2528i	0.276297	+	0.478561i
$460$	−3.78755	−	6.56023i	−0.176595	−	0.305872i
$461$	3.63655	+	6.29869i	0.169371	+	0.293359i	0.938199	−	0.346096i	$-0.112493\pi$
$461$	3.63655	+	6.29869i	0.169371	+	0.293359i	−0.768828	+	0.639456i	$0.779160\pi$
$462$	7.71983			0.359159
$463$	34.5778			1.60697			0.803483	−	0.595327i	$-0.202978\pi$
$463$	34.5778			1.60697			0.803483	+	0.595327i	$0.202978\pi$
$464$	2.46442	−	4.26851i	0.114408	−	0.198161i
$465$	−12.3585	+	21.4055i	−0.573111	+	0.992657i
$466$	7.58077	−	13.1303i	0.351172	−	0.608248i
$467$	15.2312			0.704818			0.352409	−	0.935846i	$-0.385363\pi$
$467$	15.2312			0.704818			0.352409	+	0.935846i	$0.385363\pi$
$468$	3.71465	−	1.10116i	0.171710	−	0.0509011i
$469$	−15.7991	−	27.3648i	−0.729533	−	1.26359i
$470$	3.15216			0.145398
$471$	−6.77650	+	11.7372i	−0.312245	+	0.540823i
$472$	6.10772	+	10.5789i	0.281131	+	0.486933i
$473$	−6.14850	+	10.6495i	−0.282708	+	0.489665i
$474$	0.600503	−	1.04010i	0.0275820	−	0.0477734i
$475$	−7.71754	+	9.96561i	−0.354105	+	0.457253i
$476$	4.89887			0.224539
$477$	−4.26199	−	7.38199i	−0.195143	−	0.337998i
$478$	15.5321			0.710423
$479$	9.68398	−	16.7731i	0.442472	−	0.766385i	−0.555400	−	0.831583i	$-0.687435\pi$
$479$	9.68398	−	16.7731i	0.442472	−	0.766385i	0.997872	+	0.0651988i	$0.0207682\pi$
$480$	−1.94903	+	3.37582i	−0.0889605	+	0.154084i
$481$	−10.1469	−	9.62506i	−0.462657	−	0.438865i
$482$	−3.57219			−0.162709
$483$	4.37689	+	7.58099i	0.199155	+	0.344947i
$484$	2.67250	−	4.62891i	0.121477	−	0.210405i
$485$	38.9161			1.76709
$486$	−10.5487			−0.478500
$487$	12.4588	−	21.5792i	0.564560	−	0.977847i	−0.432530	−	0.901620i	$-0.642379\pi$
$487$	12.4588	−	21.5792i	0.564560	−	0.977847i	0.997090	−	0.0762279i	$-0.0242876\pi$
$488$	−10.4072			−0.471110
$489$	−11.1936	+	19.3878i	−0.506190	+	0.876747i
$490$	4.28856			0.193737
$491$	1.82011			0.0821403			0.0410702	−	0.999156i	$-0.486923\pi$
$491$	1.82011			0.0821403			0.0410702	+	0.999156i	$0.486923\pi$
$492$	2.25009			0.101442
$493$	10.3208			0.464825
$494$	9.83864	+	12.2557i	0.442661	+	0.551408i
$495$	7.17855			0.322652
$496$	6.34084			0.284712
$497$	17.6035			0.789624
$498$	2.04740			0.0917463
$499$	−2.39407	+	4.14665i	−0.107173	+	0.185630i	−0.914624	−	0.404305i	$-0.867513\pi$
$499$	−2.39407	+	4.14665i	−0.107173	+	0.185630i	0.807451	+	0.589935i	$0.200847\pi$
$500$	5.92274			0.264873
$501$	14.4122	−	24.9626i	0.643887	−	1.11525i
$502$	−18.4927			−0.825372
$503$	−10.9591			−0.488641			−0.244320	−	0.969695i	$-0.578565\pi$
$503$	−10.9591			−0.488641			−0.244320	+	0.969695i	$0.578565\pi$
$504$	−1.25700	+	2.17718i	−0.0559911	+	0.0969795i
$505$	4.50245	+	7.79847i	0.200356	+	0.347027i
$506$	−6.41239			−0.285065
$507$	−15.1246	+	9.83082i	−0.671705	+	0.436602i
$508$	9.88211	−	17.1163i	0.438448	−	0.759414i
$509$	−1.94292	+	3.36523i	−0.0861183	+	0.149161i	−0.905867	−	0.423562i	$-0.860780\pi$
$509$	−1.94292	+	3.36523i	−0.0861183	+	0.149161i	0.819749	+	0.572723i	$0.194113\pi$
$510$	−8.16236			−0.361435
$511$	8.33003	+	14.4280i	0.368499	+	0.638258i
$512$	1.00000			0.0441942
$513$	−9.32974	−	22.8104i	−0.411918	−	1.00710i
$514$	−9.63436	+	16.6872i	−0.424953	+	0.736041i
$515$	4.17940	−	7.23893i	0.184166	−	0.318985i
$516$	3.58770	+	6.21409i	0.157940	+	0.273560i
$517$	1.33416	−	2.31084i	0.0586765	−	0.101631i
$518$	9.07490			0.398728
$519$	6.95289	+	12.0428i	0.305198	+	0.528619i
$520$	−2.36249	+	9.84939i	−0.103602	+	0.431924i
$521$	−38.7728			−1.69867			−0.849333	−	0.527858i	$-0.822995\pi$
$521$	−38.7728			−1.69867			−0.849333	+	0.527858i	$0.822995\pi$
$522$	−2.64821	+	4.58683i	−0.115909	+	0.200760i
$523$	−8.66955	+	15.0161i	−0.379093	+	0.656608i	−0.990931	−	0.134375i	$-0.957097\pi$
$523$	−8.66955	+	15.0161i	−0.379093	+	0.656608i	0.611838	+	0.790983i	$0.290431\pi$
$524$	−2.10933	+	3.65347i	−0.0921467	+	0.159603i
$525$	9.38731			0.409696
$526$	−17.4662			−0.761561
$527$	6.63873	+	11.4986i	0.289187	+	0.500887i
$528$	1.64987	+	2.85766i	0.0718013	+	0.124364i
$529$	7.86439	+	13.6215i	0.341930	+	0.592240i
$530$	22.2839			0.967950
$531$	−6.56320	−	11.3678i	−0.284819	−	0.493320i
$532$	−10.1045	−	1.37603i	−0.438086	−	0.0596585i
$533$	5.60555	−	1.66169i	0.242803	−	0.0719757i
$534$	−4.26944	+	7.39488i	−0.184757	+	0.320008i
$535$	−22.5586			−0.975291
$536$	6.75310	−	11.6967i	0.291689	−	0.505221i
$537$	3.36347	+	5.82571i	0.145145	+	0.251398i
$538$	12.7277	+	22.0450i	0.548729	+	0.950427i
$539$	1.81515	−	3.14394i	0.0781841	−	0.135419i
$540$	7.94146	−	13.7550i	0.341746	−	0.591921i
$541$	13.4896	+	23.3647i	0.579965	+	1.00453i	0.995483	+	0.0949434i	$0.0302670\pi$
$541$	13.4896	+	23.3647i	0.579965	+	1.00453i	−0.415518	+	0.909585i	$0.636400\pi$
$542$	−25.1953			−1.08223
$543$	−1.62661	−	2.81737i	−0.0698045	−	0.120905i
$544$	1.04698	+	1.81342i	0.0448888	+	0.0777497i
$545$	20.7606	+	35.9583i	0.889285	+	1.54029i
$546$	2.73009	−	11.3819i	0.116837	−	0.487102i
$547$	−15.0180	−	26.0119i	−0.642122	−	1.11219i	−0.984958	−	0.172793i	$-0.944721\pi$
$547$	−15.0180	−	26.0119i	−0.642122	−	1.11219i	0.342836	−	0.939395i	$-0.388613\pi$
$548$	16.8310			0.718986
$549$	11.1833			0.477290
$550$	−3.43823	+	5.95520i	−0.146607	+	0.253930i
$551$	−21.2879	−	2.89898i	−0.906894	−	0.123501i
$552$	−1.87084	+	3.24039i	−0.0796283	+	0.137920i
$553$	1.01246	+	1.75364i	0.0430544	+	0.0745724i
$554$	4.90789	−	8.50071i	0.208516	−	0.361160i
$555$	−15.1203			−0.641823
$556$	−1.23156			−0.0522300
$557$	−7.60545	+	13.1730i	−0.322253	+	0.558159i	−0.980953	−	0.194247i	$-0.937774\pi$
$557$	−7.60545	+	13.1730i	−0.322253	+	0.558159i	0.658699	+	0.752406i	$0.271107\pi$
$558$	−6.81370			−0.288447
$559$	13.5270	+	12.8314i	0.572131	+	0.542709i
$560$	−3.28612	−	5.69172i	−0.138864	−	0.240519i
$561$	−3.45475	+	5.98381i	−0.145860	+	0.252637i
$562$	−3.19421	−	5.53254i	−0.134740	−	0.233376i
$563$	3.58305	−	6.20603i	0.151008	−	0.261553i	−0.780591	−	0.625043i	$-0.785082\pi$
$563$	3.58305	−	6.20603i	0.151008	−	0.261553i	0.931598	+	0.363490i	$0.118415\pi$
$564$	−0.778497	−	1.34840i	−0.0327806	−	0.0567777i
$565$	16.6776	+	28.8865i	0.701634	+	1.21527i
$566$	−11.1381			−0.468170
$567$	−5.40615	+	9.36372i	−0.227037	+	0.393239i
$568$	3.76218	+	6.51629i	0.157858	+	0.273418i
$569$	3.46539	+	6.00222i	0.145277	+	0.251626i	0.929476	−	0.368882i	$-0.120259\pi$
$569$	3.46539	+	6.00222i	0.145277	+	0.251626i	−0.784200	+	0.620509i	$0.786926\pi$
$570$	16.8358	+	2.29270i	0.705176	+	0.0960307i
$571$	−30.3420			−1.26977			−0.634886	−	0.772606i	$-0.718953\pi$
$571$	−30.3420			−1.26977			−0.634886	+	0.772606i	$0.718953\pi$
$572$	6.22063	+	5.90074i	0.260098	+	0.246722i
$573$	12.6178	−	21.8547i	0.527116	−	0.912992i
$574$	−1.89686	+	3.28545i	−0.0791732	+	0.137132i
$575$	−7.79746			−0.325176
$576$	−1.07457			−0.0447739
$577$	−38.2171			−1.59100			−0.795499	−	0.605955i	$-0.792791\pi$
$577$	−38.2171			−1.59100			−0.795499	+	0.605955i	$0.792791\pi$
$578$	6.30767	−	10.9252i	0.262365	−	0.454429i
$579$	−10.0345			−0.417020
$580$	−6.92309	−	11.9911i	−0.287466	−	0.497905i
$581$	−1.72599	+	2.98950i	−0.0716061	+	0.124025i
$582$	−9.61121	−	16.6471i	−0.398398	−	0.690045i
$583$	9.43176	−	16.3363i	0.390623	−	0.676580i
$584$	−3.56056	+	6.16707i	−0.147337	+	0.255195i
$585$	2.53867	−	10.5839i	0.104961	−	0.437590i
$586$	12.2695	−	21.2514i	0.506849	−	0.877889i
$587$	−14.1261			−0.583049			−0.291524	−	0.956563i	$-0.594162\pi$
$587$	−14.1261			−0.583049			−0.291524	+	0.956563i	$0.594162\pi$
$588$	−1.05916	−	1.83451i	−0.0436789	−	0.0756541i
$589$	−10.4634	−	25.5820i	−0.431135	−	1.05409i
$590$	34.3158			1.41276
$591$	−1.33028	−	2.30411i	−0.0547202	−	0.0947782i
$592$	1.93947	+	3.35926i	0.0797118	+	0.138065i
$593$	12.9600	+	22.4473i	0.532202	+	0.921801i	0.999293	+	0.0375915i	$0.0119686\pi$
$593$	12.9600	+	22.4473i	0.532202	+	0.921801i	−0.467091	+	0.884209i	$0.654698\pi$
$594$	−6.72251	−	11.6437i	−0.275828	−	0.477748i
$595$	6.88098	−	11.9182i	0.282093	−	0.488599i
$596$	3.21526	+	5.56899i	0.131702	+	0.228115i
$597$	4.05781			0.166075
$598$	−2.26772	+	9.45427i	−0.0927340	+	0.386614i
$599$	16.2998	+	28.2321i	0.665993	+	1.15353i	0.979015	+	0.203787i	$0.0653251\pi$
$599$	16.2998	+	28.2321i	0.665993	+	1.15353i	−0.313022	+	0.949746i	$0.601342\pi$
$600$	2.00624	+	3.47491i	0.0819044	+	0.141863i
$601$	10.5787	+	18.3229i	0.431515	+	0.747405i	0.997004	−	0.0773503i	$-0.0246460\pi$
$601$	10.5787	+	18.3229i	0.431515	+	0.747405i	−0.565489	+	0.824756i	$0.691313\pi$
$602$	−12.0979			−0.493075
$603$	−7.25670	+	12.5690i	−0.295516	+	0.511848i
$604$	−20.8956			−0.850229
$605$	−7.50763	−	13.0036i	−0.305228	−	0.528671i
$606$	2.22396	−	3.85202i	0.0903424	−	0.156478i
$607$	−15.5855	+	26.9949i	−0.632596	+	1.09569i	0.354423	+	0.935085i	$0.384677\pi$
$607$	−15.5855	+	26.9949i	−0.632596	+	1.09569i	−0.987019	+	0.160603i	$0.948656\pi$
$608$	−1.65015	−	4.03448i	−0.0669225	−	0.163620i
$609$	8.00032	+	13.8570i	0.324189	+	0.561512i
$610$	−14.6179	+	25.3190i	−0.591863	+	1.02514i
$611$	−2.93523	−	2.78428i	−0.118747	−	0.112640i
$612$	−1.12506	−	1.94865i	−0.0454777	−	0.0787696i
$613$	−44.5630			−1.79988			−0.899941	−	0.436011i	$-0.856391\pi$
$613$	−44.5630			−1.79988			−0.899941	+	0.436011i	$0.856391\pi$
$614$	7.65103	−	13.2520i	0.308770	−	0.534806i
$615$	3.16049	−	5.47412i	0.127443	−	0.220738i
$616$	−5.56345			−0.224158
$617$	−4.74529			−0.191038			−0.0955191	−	0.995428i	$-0.530451\pi$
$617$	−4.74529			−0.191038			−0.0955191	+	0.995428i	$0.530451\pi$
$618$	−4.12879			−0.166084
$619$	−2.41354			−0.0970084			−0.0485042	−	0.998823i	$-0.515445\pi$
$619$	−2.41354			−0.0970084			−0.0485042	+	0.998823i	$0.515445\pi$
$620$	8.90639	−	15.4263i	0.357689	−	0.619536i
$621$	7.62288	−	13.2032i	0.305896	−	0.529827i
$622$	4.78866			0.192008
$623$	−7.19839	−	12.4680i	−0.288398	−	0.499519i
$624$	4.79673	−	1.42193i	0.192023	−	0.0569227i
$625$	15.5483	−	26.9304i	0.621932	−	1.07722i
$626$	−1.25040	−	2.16575i	−0.0499760	−	0.0865609i
$627$	8.80662	−	11.3719i	0.351702	−	0.454151i
$628$	4.88362	−	8.45868i	0.194878	−	0.337538i
$629$	−4.06117	+	7.03415i	−0.161929	+	0.280470i
$630$	3.53117	+	6.11617i	0.140685	+	0.243674i
$631$	−14.4928			−0.576948			−0.288474	−	0.957488i	$-0.593148\pi$
$631$	−14.4928			−0.576948			−0.288474	+	0.957488i	$0.593148\pi$
$632$	−0.432764	+	0.749570i	−0.0172144	+	0.0298163i
$633$	−35.8303			−1.42413
$634$	0.442735	+	0.766840i	0.0175833	+	0.0304551i
$635$	−27.7609	−	48.0834i	−1.10166	−	1.90813i
$636$	−5.50351	−	9.53236i	−0.218228	−	0.377983i
$637$	−3.99342	−	3.78806i	−0.158225	−	0.150088i
$638$	−11.7209			−0.464036
$639$	−4.04274	−	7.00224i	−0.159928	−	0.277004i
$640$	1.40461	−	2.43285i	0.0555219	−	0.0961668i
$641$	4.96837	+	8.60547i	0.196239	+	0.339896i	0.947306	−	0.320330i	$-0.103794\pi$
$641$	4.96837	+	8.60547i	0.196239	+	0.339896i	−0.751067	+	0.660226i	$0.770461\pi$
$642$	5.57135	+	9.64986i	0.219884	+	0.380849i
$643$	15.3159	+	26.5279i	0.604000	+	1.04616i	0.992209	+	0.124587i	$0.0397606\pi$
$643$	15.3159	+	26.5279i	0.604000	+	1.04616i	−0.388209	+	0.921571i	$0.626906\pi$
$644$	−3.15429	−	5.46339i	−0.124297	−	0.215288i
$645$	20.1572			0.793691
$646$	5.58853	−	7.21643i	0.219878	−	0.283926i
$647$	−8.79328	−	15.2304i	−0.345699	−	0.598769i	0.639781	−	0.768557i	$-0.279025\pi$
$647$	−8.79328	−	15.2304i	−0.345699	−	0.598769i	−0.985481	+	0.169788i	$0.945692\pi$
$648$	−4.62157			−0.181552
$649$	14.5243	−	25.1568i	0.570129	−	0.987492i
$650$	7.56428	+	7.17529i	0.296696	+	0.281438i
$651$	−10.2922	+	17.8266i	−0.403384	+	0.698681i
$652$	8.06687	−	13.9722i	0.315923	−	0.547194i
$653$	−2.92456	−	5.06548i	−0.114447	−	0.198227i	0.803112	−	0.595828i	$-0.203176\pi$
$653$	−2.92456	−	5.06548i	−0.114447	−	0.198227i	−0.917558	+	0.397601i	$0.869843\pi$
$654$	10.2546	−	17.7615i	0.400986	−	0.694528i
$655$	5.92557	+	10.2634i	0.231531	+	0.401024i
$656$	−1.62157			−0.0633117
$657$	3.82608	−	6.62697i	0.149270	−	0.258543i
$658$	2.62513			0.102338
$659$	1.07425			0.0418469			0.0209235	−	0.999781i	$-0.493339\pi$
$659$	1.07425			0.0418469			0.0209235	+	0.999781i	$0.493339\pi$
$660$	9.26967			0.360821
$661$	18.7884	−	32.5424i	0.730784	−	1.26575i	−0.225765	−	0.974182i	$-0.572488\pi$
$661$	18.7884	−	32.5424i	0.730784	−	1.26575i	0.956549	−	0.291573i	$-0.0941785\pi$
$662$	2.04780	−	3.54690i	0.0795900	−	0.137854i
$663$	7.60063	+	7.20976i	0.295184	+	0.280004i
$664$	−1.47550			−0.0572606
$665$	−17.5405	+	22.6500i	−0.680192	+	0.878328i
$666$	−2.08411	−	3.60978i	−0.0807574	−	0.139876i
$667$	−6.64537	−	11.5101i	−0.257310	−	0.445673i
$668$	−10.3864	+	17.9898i	−0.401862	+	0.696046i
$669$	4.45332			0.172175
$670$	−18.9709	−	32.8585i	−0.732909	−	1.26944i
$671$	12.3742	+	21.4328i	0.477702	+	0.827404i
$672$	−1.62316	+	2.81140i	−0.0626148	+	0.108452i
$673$	6.30603	+	10.9224i	0.243079	+	0.421026i	0.961590	−	0.274490i	$-0.0885091\pi$
$673$	6.30603	+	10.9224i	0.243079	+	0.421026i	−0.718510	+	0.695516i	$0.755176\pi$
$674$	10.4281	−	18.0620i	0.401676	−	0.695723i
$675$	−8.17457	−	14.1588i	−0.314639	−	0.544971i
$676$	10.8998	−	7.08478i	0.419224	−	0.272491i
$677$	11.0272			0.423810			0.211905	−	0.977290i	$-0.432033\pi$
$677$	11.0272			0.423810			0.211905	+	0.977290i	$0.432033\pi$
$678$	8.23785	−	14.2684i	0.316373	−	0.547973i
$679$	32.4096			1.24376
$680$	5.88237			0.225579
$681$	6.20698	−	10.7508i	0.237852	−	0.411972i
$682$	−7.53934	−	13.0585i	−0.288696	−	0.500036i
$683$	11.3909	−	19.7297i	0.435862	−	0.754936i	−0.561503	−	0.827475i	$-0.689777\pi$
$683$	11.3909	−	19.7297i	0.435862	−	0.754936i	0.997366	+	0.0725387i	$0.0231101\pi$
$684$	1.77321	+	4.33534i	0.0678003	+	0.165766i
$685$	23.6410	−	40.9473i	0.903275	−	1.56452i
$686$	19.9482			0.761627
$687$	23.1100			0.881700
$688$	−2.58555	−	4.47831i	−0.0985732	−	0.170734i
$689$	−20.7503	−	19.6832i	−0.790524	−	0.749871i
$690$	5.25559	+	9.10295i	0.200077	+	0.346543i
$691$	−8.21971	−	14.2370i	−0.312692	−	0.541599i	0.666252	−	0.745727i	$-0.267898\pi$
$691$	−8.21971	−	14.2370i	−0.312692	−	0.541599i	−0.978944	+	0.204128i	$0.934564\pi$
$692$	−5.01074	−	8.67886i	−0.190480	−	0.329921i
$693$	5.97834			0.227098
$694$	6.11829	+	10.5972i	0.232247	+	0.402264i
$695$	−1.72986	+	2.99621i	−0.0656175	+	0.113653i
$696$	−3.41963	+	5.92297i	−0.129621	+	0.224510i
$697$	−1.69775	−	2.94059i	−0.0643068	−	0.111383i
$698$	−15.1673	−	26.2706i	−0.574092	−	0.994357i
$699$	−10.5191	+	18.2195i	−0.397867	+	0.689126i
$700$	−6.76515			−0.255699
$701$	23.9788	−	41.5325i	0.905667	−	1.56866i	0.0856474	−	0.996326i	$-0.472704\pi$
$701$	23.9788	−	41.5325i	0.905667	−	1.56866i	0.820020	−	0.572336i	$-0.193963\pi$
$702$	−19.5446	+	5.79375i	−0.737665	+	0.218671i
$703$	10.3524	−	13.3680i	0.390450	−	0.504185i
$704$	−1.18901	−	2.05943i	−0.0448126	−	0.0776176i
$705$	−4.37392			−0.164732
$706$	12.6305	+	21.8767i	0.475356	+	0.823340i
$707$	3.74967	+	6.49461i	0.141021	+	0.244255i
$708$	−8.47506	−	14.6792i	−0.318512	−	0.551679i
$709$	−42.3999			−1.59236			−0.796182	−	0.605058i	$-0.793150\pi$
$709$	−42.3999			−1.59236			−0.796182	+	0.605058i	$0.793150\pi$
$710$	21.1375			0.793278
$711$	0.465037	−	0.805468i	0.0174403	−	0.0302074i
$712$	3.07686	−	5.32927i	0.115310	−	0.199723i
$713$	8.54910	−	14.8075i	0.320166	−	0.554545i
$714$	−6.79766			−0.254396
$715$	23.0931	−	6.84565i	0.863634	−	0.256013i
$716$	−2.42396	−	4.19841i	−0.0905875	−	0.156902i
$717$	−21.5523			−0.804886
$718$	5.44751	−	9.43536i	0.203299	−	0.352125i
$719$	−11.9700	−	20.7326i	−0.446404	−	0.773195i	0.551745	−	0.834013i	$-0.313962\pi$
$719$	−11.9700	−	20.7326i	−0.446404	−	0.773195i	−0.998149	+	0.0608183i	$0.980629\pi$
$720$	−1.50935	+	2.61428i	−0.0562503	+	0.0974283i
$721$	3.48063	−	6.02862i	0.129625	−	0.224518i
$722$	−13.5540	+	13.3150i	−0.504428	+	0.495533i
$723$	4.95677			0.184344
$724$	1.17225	+	2.03040i	0.0435663	+	0.0754591i
$725$	−14.2526			−0.529329
$726$	−3.70836	+	6.42306i	−0.137630	+	0.238382i
$727$	−4.66816	+	8.08549i	−0.173132	+	0.299874i	−0.939513	−	0.342512i	$-0.888722\pi$
$727$	−4.66816	+	8.08549i	−0.173132	+	0.299874i	0.766381	+	0.642386i	$0.222056\pi$
$728$	−1.96750	+	8.20263i	−0.0729203	+	0.304010i
$729$	28.5021			1.05563
$730$	10.0024	+	17.3246i	0.370204	+	0.641212i
$731$	5.41403	−	9.37738i	0.200245	−	0.346835i
$732$	14.4409			0.533752
$733$	21.3973			0.790328			0.395164	−	0.918611i	$-0.370688\pi$
$733$	21.3973			0.790328			0.395164	+	0.918611i	$0.370688\pi$
$734$	4.68294	−	8.11108i	0.172850	−	0.299386i
$735$	−5.95079			−0.219498
$736$	1.34826	−	2.33525i	0.0496975	−	0.0860786i
$737$	−32.1180			−1.18308
$738$	1.74250			0.0641422
$739$	3.69061			0.135761			0.0678806	−	0.997693i	$-0.478376\pi$
$739$	3.69061			0.135761			0.0678806	+	0.997693i	$0.478376\pi$
$740$	10.8968			0.400573
$741$	−13.6521	−	17.0059i	−0.501521	−	0.624728i
$742$	18.5582			0.681291
$743$	43.5167			1.59647			0.798236	−	0.602345i	$-0.205767\pi$
$743$	43.5167			1.59647			0.798236	+	0.602345i	$0.205767\pi$
$744$	−8.79854			−0.322570
$745$	18.0647			0.661839
$746$	15.1058	−	26.1641i	0.553064	−	0.957935i
$747$	1.58553			0.0580117
$748$	2.48974	−	4.31235i	0.0910339	−	0.157675i
$749$	−18.7869			−0.686458
$750$	−8.21837			−0.300092
$751$	7.21028	−	12.4886i	0.263107	−	0.455715i	−0.703959	−	0.710241i	$-0.748586\pi$
$751$	7.21028	−	12.4886i	0.263107	−	0.455715i	0.967066	+	0.254526i	$0.0819195\pi$
$752$	0.561039	+	0.971749i	0.0204590	+	0.0354360i
$753$	25.6605			0.935120
$754$	−4.14506	+	17.2810i	−0.150954	+	0.629339i
$755$	−29.3500	+	50.8358i	−1.06816	+	1.85010i
$756$	6.61369	−	11.4553i	0.240538	−	0.416623i
$757$	24.3227			0.884025			0.442012	−	0.897009i	$-0.354265\pi$
$757$	24.3227			0.884025			0.442012	+	0.897009i	$0.354265\pi$
$758$	−8.13181	−	14.0847i	−0.295360	−	0.511579i
$759$	8.89781			0.322970
$760$	−12.1331	−	1.65228i	−0.440113	−	0.0599345i
$761$	−6.73128	+	11.6589i	−0.244009	+	0.422636i	−0.961852	−	0.273569i	$-0.911796\pi$
$761$	−6.73128	+	11.6589i	−0.244009	+	0.422636i	0.717844	+	0.696204i	$0.245129\pi$
$762$	−13.7124	+	23.7506i	−0.496748	+	0.860392i
$763$	17.2895	+	29.9463i	0.625922	+	1.08413i
$764$	−9.09327	+	15.7500i	−0.328983	+	0.569815i
$765$	−6.32104			−0.228538
$766$	15.2397	+	26.3960i	0.550634	+	0.953727i
$767$	−31.9542	−	30.3109i	−1.15380	−	1.09446i
$768$	−1.38760			−0.0500706
$769$	1.29601	−	2.24475i	0.0467353	−	0.0809479i	−0.841711	−	0.539928i	$-0.818452\pi$
$769$	1.29601	−	2.24475i	0.0467353	−	0.0809479i	0.888447	+	0.458980i	$0.151785\pi$
$770$	−7.81446	+	13.5350i	−0.281614	+	0.487769i
$771$	13.3686	−	23.1551i	0.481459	−	0.833911i
$772$	7.23156			0.260270
$773$	−38.9884			−1.40232			−0.701158	−	0.713006i	$-0.747333\pi$
$773$	−38.9884			−1.40232			−0.701158	+	0.713006i	$0.747333\pi$
$774$	2.77837	+	4.81227i	0.0998663	+	0.172973i
$775$	−9.16783	−	15.8791i	−0.329318	−	0.570396i
$776$	6.92652	+	11.9971i	0.248647	+	0.430670i
$777$	−12.5923			−0.451746
$778$	−13.0031	−	22.5220i	−0.466183	−	0.807452i
$779$	2.67584	+	6.54219i	0.0958718	+	0.234398i
$780$	3.27819	−	13.6670i	0.117378	−	0.489356i
$781$	8.94656	−	15.4959i	0.320133	−	0.554487i
$782$	5.64639			0.201915
$783$	13.9335	−	24.1336i	0.497944	−	0.862464i
$784$	0.763303	+	1.32208i	0.0272608	+	0.0472171i
$785$	−13.7191	−	23.7622i	−0.489657	−	0.848110i
$786$	2.92691	−	5.06955i	0.104399	−	0.180825i
$787$	−14.7942	+	25.6243i	−0.527355	+	0.913406i	0.472137	+	0.881525i	$0.343483\pi$
$787$	−14.7942	+	25.6243i	−0.527355	+	0.913406i	−0.999492	+	0.0318805i	$0.989850\pi$
$788$	0.958690	+	1.66050i	0.0341519	+	0.0591529i
$789$	24.2360			0.862825
$790$	1.21573	+	2.10570i	0.0432536	+	0.0749175i
$791$	13.8892	+	24.0569i	0.493845	+	0.855364i
$792$	1.27768	+	2.21301i	0.0454004	+	0.0786358i
$793$	35.9761	−	10.6646i	1.27755	−	0.378712i
$794$	−9.39318	−	16.2695i	−0.333351	−	0.577382i
$795$	−30.9211			−1.09666
$796$	−2.92434			−0.103651
$797$	18.8579	−	32.6628i	0.667981	−	1.15698i	−0.310487	−	0.950578i	$-0.600492\pi$
$797$	18.8579	−	32.6628i	0.667981	−	1.15698i	0.978468	−	0.206400i	$-0.0661747\pi$
$798$	14.0210	+	1.90938i	0.496337	+	0.0675911i
$799$	−1.17479	+	2.03480i	−0.0415611	+	0.0719860i
$800$	−1.44584	−	2.50426i	−0.0511181	−	0.0885391i
$801$	−3.30631	+	5.72669i	−0.116823	+	0.202343i
$802$	−32.9758			−1.16442
$803$	16.9342			0.597594
$804$	−9.37058	+	16.2303i	−0.330475	+	0.572399i
$805$	−17.7222			−0.624624
$806$	−21.9194	+	6.49772i	−0.772079	+	0.228872i
$807$	−17.6609	−	30.5896i	−0.621693	−	1.07680i
$808$	−1.60274	+	2.77604i	−0.0563844	+	0.0976606i
$809$	23.8643	+	41.3342i	0.839025	+	1.45323i	0.890711	+	0.454570i	$0.150207\pi$
$809$	23.8643	+	41.3342i	0.839025	+	1.45323i	−0.0516860	+	0.998663i	$0.516459\pi$
$810$	−6.49149	+	11.2436i	−0.228088	+	0.395059i
$811$	−1.36064	−	2.35669i	−0.0477784	−	0.0827546i	0.841147	−	0.540806i	$-0.181881\pi$
$811$	−1.36064	−	2.35669i	−0.0477784	−	0.0827546i	−0.888926	+	0.458052i	$0.848547\pi$
$812$	−5.76559	−	9.98630i	−0.202333	−	0.350450i
$813$	34.9610			1.22613
$814$	4.61211	−	7.98841i	0.161654	−	0.279994i
$815$	−22.6615	−	39.2509i	−0.793799	−	1.37490i
$816$	−1.45278	−	2.51630i	−0.0508576	−	0.0880880i
$817$	−13.8011	+	17.8212i	−0.482838	+	0.623486i
$818$	−26.2302			−0.917118
$819$	2.11422	−	8.81433i	0.0738769	−	0.307997i
$820$	−2.27767	+	3.94504i	−0.0795396	+	0.137767i
$821$	26.9043	−	46.5996i	0.938966	−	1.62634i	0.171563	−	0.985173i	$-0.445118\pi$
$821$	26.9043	−	46.5996i	0.938966	−	1.62634i	0.767404	−	0.641164i	$-0.221548\pi$
$822$	−23.3547			−0.814588
$823$	−21.9912			−0.766566			−0.383283	−	0.923631i	$-0.625207\pi$
$823$	−21.9912			−0.766566			−0.383283	+	0.923631i	$0.625207\pi$
$824$	2.97549			0.103656
$825$	4.77088	−	8.26341i	0.166101	−	0.287695i
$826$	28.5784			0.994369
$827$	11.2891	+	19.5533i	0.392561	+	0.679936i	0.992787	−	0.119895i	$-0.0382557\pi$
$827$	11.2891	+	19.5533i	0.392561	+	0.679936i	−0.600225	+	0.799831i	$0.704922\pi$
$828$	−1.44880	+	2.50940i	−0.0503494	+	0.0872078i
$829$	13.1348	+	22.7501i	0.456190	+	0.790145i	0.998756	−	0.0498688i	$-0.0158803\pi$
$829$	13.1348	+	22.7501i	0.456190	+	0.790145i	−0.542566	+	0.840013i	$0.682547\pi$
$830$	−2.07250	+	3.58967i	−0.0719375	+	0.124599i
$831$	−6.81017	+	11.7956i	−0.236242	+	0.409183i
$832$	−3.45686	+	1.02474i	−0.119845	+	0.0355265i
$833$	−1.59832	+	2.76838i	−0.0553786	+	0.0959185i
$834$	1.70892			0.0591749
$835$	29.1776	+	50.5371i	1.00973	+	1.74891i
$836$	−6.34667	+	8.19541i	−0.219504	+	0.283444i
$837$	35.8503			1.23917
$838$	−2.14701	−	3.71874i	−0.0741673	−	0.128462i
$839$	−10.4407	−	18.0838i	−0.360452	−	0.624320i	0.627584	−	0.778549i	$-0.284044\pi$
$839$	−10.4407	−	18.0838i	−0.360452	−	0.624320i	−0.988035	+	0.154229i	$0.950711\pi$
$840$	4.55981	+	7.89782i	0.157328	+	0.272501i
$841$	2.35323	+	4.07591i	0.0811458	+	0.140549i
$842$	−17.3511	+	30.0529i	−0.597957	+	1.03569i
$843$	4.43228	+	7.67694i	0.152656	+	0.264408i
$844$	25.8219			0.888825
$845$	−1.92625	−	36.4689i	−0.0662651	−	1.25457i
$846$	−0.602878	−	1.04422i	−0.0207274	−	0.0359009i
$847$	−6.25240	−	10.8295i	−0.214835	−	0.372105i
$848$	3.96622	+	6.86969i	0.136200	+	0.235906i
$849$	15.4552			0.530421
$850$	3.02752	−	5.24382i	0.103843	−	0.179861i
$851$	10.4596			0.358552
$852$	−5.22040	−	9.04199i	−0.178848	−	0.309774i
$853$	−4.56877	+	7.91334i	−0.156432	+	0.270948i	−0.933579	−	0.358370i	$-0.883332\pi$
$853$	−4.56877	+	7.91334i	−0.156432	+	0.270948i	0.777148	+	0.629318i	$0.216666\pi$
$854$	−12.1739	+	21.0858i	−0.416583	+	0.721543i
$855$	13.0379	+	1.77550i	0.445887	+	0.0607207i
$856$	−4.01510	−	6.95436i	−0.137233	−	0.237695i
$857$	−1.33924	+	2.31963i	−0.0457475	+	0.0792370i	−0.887992	−	0.459858i	$-0.847900\pi$
$857$	−1.33924	+	2.31963i	−0.0457475	+	0.0792370i	0.842245	+	0.539095i	$0.181234\pi$
$858$	−8.63173	−	8.18784i	−0.294682	−	0.279528i
$859$	17.9583	+	31.1047i	0.612730	+	1.06128i	0.990778	+	0.135494i	$0.0432621\pi$
$859$	17.9583	+	31.1047i	0.612730	+	1.06128i	−0.378048	+	0.925786i	$0.623405\pi$
$860$	−14.5267			−0.495357
$861$	2.63207	−	4.55888i	0.0897007	−	0.155366i
$862$	−16.5456	+	28.6578i	−0.563546	+	0.976089i
$863$	−45.6414			−1.55365			−0.776825	−	0.629716i	$-0.783171\pi$
$863$	−45.6414			−1.55365			−0.776825	+	0.629716i	$0.783171\pi$
$864$	5.65387			0.192348
$865$	−28.1525			−0.957213
$866$	−5.44937			−0.185177
$867$	−8.75251	+	15.1598i	−0.297251	+	0.514854i
$868$	7.41729	−	12.8471i	0.251759	−	0.436060i
$869$	2.05825			0.0698213
$870$	9.60646	+	16.6389i	0.325690	+	0.564111i
$871$	−11.3584	+	47.3541i	−0.384866	+	1.60453i
$872$	−7.39017	+	12.8001i	−0.250263	+	0.433468i
$873$	−7.44305	−	12.8917i	−0.251909	−	0.436319i
$874$	−11.6464	−	1.58600i	−0.393944	−	0.0536472i
$875$	6.92820	−	12.0000i	0.234216	−	0.405674i
$876$	4.94062	−	8.55741i	0.166928	−	0.289128i
$877$	−5.34919	−	9.26507i	−0.180629	−	0.312859i	0.761466	−	0.648205i	$-0.224480\pi$
$877$	−5.34919	−	9.26507i	−0.180629	−	0.312859i	−0.942095	+	0.335346i	$0.891147\pi$
$878$	13.4761			0.454798
$879$	−17.0252	+	29.4884i	−0.574244	+	0.994620i
$880$	−6.68037			−0.225195
$881$	3.91733	+	6.78502i	0.131978	+	0.228593i	0.924439	−	0.381330i	$-0.124534\pi$
$881$	3.91733	+	6.78502i	0.131978	+	0.228593i	−0.792461	+	0.609923i	$0.791200\pi$
$882$	−0.820225	−	1.42067i	−0.0276184	−	0.0478365i
$883$	−18.2043	−	31.5308i	−0.612623	−	1.06109i	−0.990797	−	0.135360i	$-0.956781\pi$
$883$	−18.2043	−	31.5308i	−0.612623	−	1.06109i	0.378173	−	0.925735i	$-0.376552\pi$
$884$	−5.47755	−	5.19586i	−0.184230	−	0.174756i
$885$	−47.6165			−1.60061
$886$	16.9939	+	29.4343i	0.570922	+	0.988866i
$887$	−22.0497	+	38.1912i	−0.740356	+	1.28233i	0.211978	+	0.977275i	$0.432010\pi$
$887$	−22.0497	+	38.1912i	−0.740356	+	1.28233i	−0.952333	+	0.305059i	$0.901324\pi$
$888$	−2.69121	−	4.66131i	−0.0903110	−	0.156423i
$889$	−23.1195	−	40.0441i	−0.775403	−	1.34304i
$890$	−8.64354	−	14.9711i	−0.289732	−	0.501831i
$891$	5.49510	+	9.51779i	0.184093	+	0.318858i
$892$	−3.20937			−0.107458
$893$	2.99470	−	3.86703i	0.100214	−	0.129405i
$894$	−4.46149	−	7.72752i	−0.149214	−	0.258447i
$895$	−13.6188			−0.455227
$896$	1.16976	−	2.02609i	0.0390791	−	0.0676870i
$897$	3.14668	−	13.1187i	0.105065	−	0.438021i
$898$	−15.6351	+	27.0808i	−0.521750	+	0.903697i
$899$	15.6265	−	27.0659i	0.521174	−	0.902700i
$900$	1.55366	+	2.69102i	0.0517886	+	0.0897005i
$901$	−8.30508	+	14.3848i	−0.276682	+	0.479228i
$902$	1.92807	+	3.33951i	0.0641976	+	0.111193i
$903$	16.7871			0.558639
$904$	−5.93677	+	10.2828i	−0.197454	+	0.342000i
$905$	6.58620			0.218933
$906$	28.9946			0.963282
$907$	−21.7243			−0.721342			−0.360671	−	0.932693i	$-0.617452\pi$
$907$	−21.7243			−0.721342			−0.360671	+	0.932693i	$0.617452\pi$
$908$	−4.47319	+	7.74779i	−0.148448	+	0.257119i
$909$	1.72227	−	2.98305i	0.0571240	−	0.0989417i
$910$	17.1922	+	16.3081i	0.569916	+	0.540608i
$911$	−9.68335			−0.320824			−0.160412	−	0.987050i	$-0.551282\pi$
$911$	−9.68335			−0.320824			−0.160412	+	0.987050i	$0.551282\pi$
$912$	2.28975	+	5.59823i	0.0758211	+	0.185376i
$913$	1.75439	+	3.03869i	0.0580618	+	0.100566i
$914$	18.4366	+	31.9331i	0.609828	+	1.05625i
$915$	20.2838	−	35.1326i	0.670563	−	1.16145i
$916$	−16.6547			−0.550286
$917$	4.93485	+	8.54741i	0.162963	+	0.282260i
$918$	5.91948	+	10.2528i	0.195372	+	0.338394i
$919$	−16.2338	+	28.1178i	−0.535504	+	0.927520i	0.463635	+	0.886026i	$0.346545\pi$
$919$	−16.2338	+	28.1178i	−0.535504	+	0.927520i	−0.999139	+	0.0414937i	$0.986788\pi$
$920$	−3.78755	−	6.56023i	−0.124872	−	0.216284i
$921$	−10.6165	+	18.3884i	−0.349827	+	0.605918i
$922$	3.63655	+	6.29869i	0.119763	+	0.207436i
$923$	−19.6829	−	18.6707i	−0.647870	−	0.614553i
$924$	7.71983			0.253964
$925$	5.60832	−	9.71390i	0.184400	−	0.319391i
$926$	34.5778			1.13630
$927$	−3.19739			−0.105016
$928$	2.46442	−	4.26851i	0.0808987	−	0.140121i
$929$	2.84119	+	4.92109i	0.0932165	+	0.161456i	0.908863	−	0.417095i	$-0.136952\pi$
$929$	2.84119	+	4.92109i	0.0932165	+	0.161456i	−0.815646	+	0.578551i	$0.803618\pi$
$930$	−12.3585	+	21.4055i	−0.405251	+	0.701915i
$931$	4.07433	−	5.26116i	0.133531	−	0.172427i
$932$	7.58077	−	13.1303i	0.248316	−	0.430097i
$933$	−6.64473			−0.217539
$934$	15.2312			0.498382
$935$	−6.99420	−	12.1143i	−0.228735	−	0.396181i
$936$	3.71465	−	1.10116i	0.121417	−	0.0359925i
$937$	−15.9582	−	27.6404i	−0.521332	−	0.902973i	−0.999692	−	0.0248094i	$-0.992102\pi$
$937$	−15.9582	−	27.6404i	−0.521332	−	0.902973i	0.478360	−	0.878164i	$-0.341231\pi$
$938$	−15.7991	−	27.3648i	−0.515858	−	0.893492i
$939$	1.73505	+	3.00519i	0.0566212	+	0.0980708i
$940$	3.15216			0.102812
$941$	1.24878	+	2.16295i	0.0407091	+	0.0705102i	0.885662	−	0.464330i	$-0.153705\pi$
$941$	1.24878	+	2.16295i	0.0407091	+	0.0705102i	−0.844953	+	0.534841i	$0.820372\pi$
$942$	−6.77650	+	11.7372i	−0.220790	+	0.382420i
$943$	−2.18630	+	3.78678i	−0.0711957	+	0.123314i
$944$	6.10772	+	10.5789i	0.198789	+	0.344313i
$945$	−18.5793	−	32.1802i	−0.604384	−	1.04682i
$946$	−6.14850	+	10.6495i	−0.199905	+	0.346246i
$947$	19.7306			0.641157			0.320579	−	0.947222i	$-0.396123\pi$
$947$	19.7306			0.641157			0.320579	+	0.947222i	$0.396123\pi$
$948$	0.600503	−	1.04010i	0.0195034	−	0.0337809i
$949$	5.98872	−	24.9674i	0.194402	−	0.810475i
$950$	−7.71754	+	9.96561i	−0.250390	+	0.323327i
$951$	−0.614338	−	1.06406i	−0.0199213	−	0.0345047i
$952$	4.89887			0.158773
$953$	−27.3005	−	47.2858i	−0.884350	−	1.53174i	−0.846457	−	0.532457i	$-0.821269\pi$
$953$	−27.3005	−	47.2858i	−0.884350	−	1.53174i	−0.0378923	−	0.999282i	$-0.512064\pi$
$954$	−4.26199	−	7.38199i	−0.137987	−	0.239001i
$955$	25.5449	+	44.2451i	0.826614	+	1.43174i
$956$	15.5321			0.502345
$957$	16.2639			0.525738
$958$	9.68398	−	16.7731i	0.312875	−	0.541916i
$959$	19.6883	−	34.1012i	0.635769	−	1.10118i
$960$	−1.94903	+	3.37582i	−0.0629046	+	0.108954i
$961$	9.20630			0.296977
$962$	−10.1469	−	9.62506i	−0.327148	−	0.310324i
$963$	4.31452	+	7.47298i	0.139034	+	0.240813i
$964$	−3.57219			−0.115053
$965$	10.1575	−	17.5933i	0.326982	−	0.566349i
$966$	4.37689	+	7.58099i	0.140824	+	0.243914i
$967$	−6.70042	+	11.6055i	−0.215471	+	0.373206i	−0.953418	−	0.301652i	$-0.902462\pi$
$967$	−6.70042	+	11.6055i	−0.215471	+	0.373206i	0.737947	+	0.674858i	$0.235795\pi$
$968$	2.67250	−	4.62891i	0.0858975	−	0.148779i
$969$	−7.75462	+	10.0135i	−0.249114	+	0.321680i
$970$	38.9161			1.24952
$971$	10.5563	+	18.2841i	0.338769	+	0.586765i	0.984201	−	0.177052i	$-0.0566562\pi$
$971$	10.5563	+	18.2841i	0.338769	+	0.586765i	−0.645433	+	0.763817i	$0.723323\pi$
$972$	−10.5487			−0.338350
$973$	−1.44064	+	2.49526i	−0.0461848	+	0.0799944i
$974$	12.4588	−	21.5792i	0.399205	−	0.691443i
$975$	−10.4962	−	9.95641i	−0.336147	−	0.318860i
$976$	−10.4072			−0.333125
$977$	25.6791	+	44.4776i	0.821548	+	1.42296i	0.904529	+	0.426412i	$0.140223\pi$
$977$	25.6791	+	44.4776i	0.821548	+	1.42296i	−0.0829811	+	0.996551i	$0.526444\pi$
$978$	−11.1936	+	19.3878i	−0.357931	+	0.619954i
$979$	−14.6337			−0.467694
$980$	4.28856			0.136993
$981$	7.94128	−	13.7547i	0.253546	−	0.439154i
$982$	1.82011			0.0580820
$983$	5.19276	−	8.99412i	0.165623	−	0.286868i	−0.771253	−	0.636528i	$-0.780370\pi$
$983$	5.19276	−	8.99412i	0.165623	−	0.286868i	0.936876	+	0.349661i	$0.113703\pi$
$984$	2.25009			0.0717301
$985$	5.38633			0.171623
$986$	10.3208			0.328681
$987$	−3.64263			−0.115946
$988$	9.83864	+	12.2557i	0.313009	+	0.389904i
$989$	−13.9440			−0.443393
$990$	7.17855			0.228149
$991$	−27.4338			−0.871462			−0.435731	−	0.900077i	$-0.643510\pi$
$991$	−27.4338			−0.871462			−0.435731	+	0.900077i	$0.643510\pi$
$992$	6.34084			0.201322
$993$	−2.84152	+	4.92166i	−0.0901730	+	0.156184i
$994$	17.6035			0.558348
$995$	−4.10755	+	7.11448i	−0.130218	+	0.225544i
$996$	2.04740			0.0648744
$997$	42.8381			1.35670			0.678348	−	0.734741i	$-0.262696\pi$
$997$	42.8381			1.35670			0.678348	+	0.734741i	$0.262696\pi$
$998$	−2.39407	+	4.14665i	−0.0757830	+	0.131260i
$999$	10.9655	+	18.9928i	0.346934	+	0.600907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.h.d.315.4	yes	22
13.9	even	3		494.2.e.d.87.8	✓	22
19.7	even	3		494.2.e.d.159.8	yes	22
247.178	even	3	inner	494.2.h.d.425.4	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.e.d.87.8	✓	22	13.9	even	3
494.2.e.d.159.8	yes	22	19.7	even	3
494.2.h.d.315.4	yes	22	1.1	even	1	trivial
494.2.h.d.425.4	yes	22	247.178	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.38760 q^{3} +1.00000 q^{4} +(1.40461 - 2.43285i) q^{5} -1.38760 q^{6} +(1.16976 - 2.02609i) q^{7} +1.00000 q^{8} -1.07457 q^{9} +(1.40461 - 2.43285i) q^{10} +(-1.18901 - 2.05943i) q^{11} -1.38760 q^{12} +(-3.45686 + 1.02474i) q^{13} +(1.16976 - 2.02609i) q^{14} +(-1.94903 + 3.37582i) q^{15} +1.00000 q^{16} +(1.04698 + 1.81342i) q^{17} -1.07457 q^{18} +(-1.65015 - 4.03448i) q^{19} +(1.40461 - 2.43285i) q^{20} +(-1.62316 + 2.81140i) q^{21} +(-1.18901 - 2.05943i) q^{22} +(1.34826 - 2.33525i) q^{23} -1.38760 q^{24} +(-1.44584 - 2.50426i) q^{25} +(-3.45686 + 1.02474i) q^{26} +5.65387 q^{27} +(1.16976 - 2.02609i) q^{28} +(2.46442 - 4.26851i) q^{29} +(-1.94903 + 3.37582i) q^{30} +6.34084 q^{31} +1.00000 q^{32} +(1.64987 + 2.85766i) q^{33} +(1.04698 + 1.81342i) q^{34} +(-3.28612 - 5.69172i) q^{35} -1.07457 q^{36} +(1.93947 + 3.35926i) q^{37} +(-1.65015 - 4.03448i) q^{38} +(4.79673 - 1.42193i) q^{39} +(1.40461 - 2.43285i) q^{40} -1.62157 q^{41} +(-1.62316 + 2.81140i) q^{42} +(-2.58555 - 4.47831i) q^{43} +(-1.18901 - 2.05943i) q^{44} +(-1.50935 + 2.61428i) q^{45} +(1.34826 - 2.33525i) q^{46} +(0.561039 + 0.971749i) q^{47} -1.38760 q^{48} +(0.763303 + 1.32208i) q^{49} +(-1.44584 - 2.50426i) q^{50} +(-1.45278 - 2.51630i) q^{51} +(-3.45686 + 1.02474i) q^{52} +(3.96622 + 6.86969i) q^{53} +5.65387 q^{54} -6.68037 q^{55} +(1.16976 - 2.02609i) q^{56} +(2.28975 + 5.59823i) q^{57} +(2.46442 - 4.26851i) q^{58} +(6.10772 + 10.5789i) q^{59} +(-1.94903 + 3.37582i) q^{60} -10.4072 q^{61} +6.34084 q^{62} +(-1.25700 + 2.17718i) q^{63} +1.00000 q^{64} +(-2.36249 + 9.84939i) q^{65} +(1.64987 + 2.85766i) q^{66} +(6.75310 - 11.6967i) q^{67} +(1.04698 + 1.81342i) q^{68} +(-1.87084 + 3.24039i) q^{69} +(-3.28612 - 5.69172i) q^{70} +(3.76218 + 6.51629i) q^{71} -1.07457 q^{72} +(-3.56056 + 6.16707i) q^{73} +(1.93947 + 3.35926i) q^{74} +(2.00624 + 3.47491i) q^{75} +(-1.65015 - 4.03448i) q^{76} -5.56345 q^{77} +(4.79673 - 1.42193i) q^{78} +(-0.432764 + 0.749570i) q^{79} +(1.40461 - 2.43285i) q^{80} -4.62157 q^{81} -1.62157 q^{82} -1.47550 q^{83} +(-1.62316 + 2.81140i) q^{84} +5.88237 q^{85} +(-2.58555 - 4.47831i) q^{86} +(-3.41963 + 5.92297i) q^{87} +(-1.18901 - 2.05943i) q^{88} +(3.07686 - 5.32927i) q^{89} +(-1.50935 + 2.61428i) q^{90} +(-1.96750 + 8.20263i) q^{91} +(1.34826 - 2.33525i) q^{92} -8.79854 q^{93} +(0.561039 + 0.971749i) q^{94} +(-12.1331 - 1.65228i) q^{95} -1.38760 q^{96} +(6.92652 + 11.9971i) q^{97} +(0.763303 + 1.32208i) q^{98} +(1.27768 + 2.21301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 22 q^{4} - 2 q^{5} - 5 q^{7} + 22 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{13} - 5 q^{14} - 3 q^{15} + 22 q^{16} + q^{17} + 10 q^{18} + 12 q^{19} - 2 q^{20} + q^{21} - 2 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 22 * q^4 - 2 * q^5 - 5 * q^7 + 22 * q^8 + 10 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^13 - 5 * q^14 - 3 * q^15 + 22 * q^16 + q^17 + 10 * q^18 + 12 * q^19 - 2 * q^20 + q^21 - 2 * q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 6 * q^27 - 5 * q^28 - 7 * q^29 - 3 * q^30 + 6 * q^31 + 22 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 10 * q^36 - 9 * q^37 + 12 * q^38 + 13 * q^39 - 2 * q^40 - 24 * q^41 + q^42 - 10 * q^43 - 2 * q^44 - 15 * q^45 + 4 * q^46 + 19 * q^47 - 14 * q^49 - 9 * q^50 - 22 * q^51 + 2 * q^52 - 9 * q^53 - 6 * q^54 + 48 * q^55 - 5 * q^56 + 13 * q^57 - 7 * q^58 - 12 * q^59 - 3 * q^60 - 22 * q^61 + 6 * q^62 - 23 * q^63 + 22 * q^64 + 13 * q^65 - 4 * q^66 + 3 * q^67 + q^68 - 20 * q^69 - 3 * q^70 + 4 * q^71 + 10 * q^72 - 38 * q^73 - 9 * q^74 - 20 * q^75 + 12 * q^76 - 76 * q^77 + 13 * q^78 - 5 * q^79 - 2 * q^80 - 90 * q^81 - 24 * q^82 - 10 * q^83 + q^84 + 24 * q^85 - 10 * q^86 + 4 * q^87 - 2 * q^88 + 3 * q^89 - 15 * q^90 + 34 * q^91 + 4 * q^92 + 22 * q^93 + 19 * q^94 - 33 * q^95 - 31 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more