LMFDB - Embedded newform 531.2.m.a.4.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [531,2,Mod(4,531)] 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("531.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(174)) chi = DirichletCharacter(H, H._module([58, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.m (of order $87$, degree $56$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$3248$
Relative dimension:	$58$ over $\Q(\zeta_{87})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{87}]$

Embedding invariants

Embedding label			4.16
Character	$\chi$	$=$	531.4
Dual form			531.2.m.a.133.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.585309 - 1.32751i) q^{2} +(1.25099 - 1.19792i) q^{3} +(-0.0707233 + 0.0774144i) q^{4} +(-2.01564 + 0.845586i) q^{5} +(-2.32246 - 0.959547i) q^{6} +(3.08503 - 0.448730i) q^{7} +(-2.60557 - 0.877919i) q^{8} +(0.129969 - 2.99718i) q^{9} +(2.30229 + 2.18085i) q^{10} +(-3.31453 - 2.33575i) q^{11} +(0.00426204 + 0.181566i) q^{12} +(1.54746 + 1.26705i) q^{13} +(-2.40139 - 3.83275i) q^{14} +(-1.50861 + 3.47240i) q^{15} +(0.378527 + 4.18162i) q^{16} +(-0.848111 - 2.12860i) q^{17} +(-4.05485 + 1.58174i) q^{18} +(-4.11780 - 6.07331i) q^{19} +(0.0770923 - 0.215842i) q^{20} +(3.32181 - 4.25698i) q^{21} +(-1.16070 + 5.76719i) q^{22} +(6.84394 + 4.46210i) q^{23} +(-4.31123 + 2.02300i) q^{24} +(-0.155671 + 0.158507i) q^{25} +(0.776272 - 2.79588i) q^{26} +(-3.42780 - 3.90515i) q^{27} +(-0.183445 + 0.270562i) q^{28} +(-2.77802 - 3.79472i) q^{29} +(5.49264 - 0.0297394i) q^{30} +(-3.29449 - 6.79619i) q^{31} +(0.518432 - 0.286964i) q^{32} +(-6.94450 + 1.04853i) q^{33} +(-2.32932 + 2.37176i) q^{34} +(-5.83888 + 3.51314i) q^{35} +(0.222833 + 0.222032i) q^{36} +(0.758437 - 0.255547i) q^{37} +(-5.65216 + 9.02116i) q^{38} +(3.45369 - 0.268667i) q^{39} +(5.99426 - 0.433663i) q^{40} +(7.04752 + 3.57488i) q^{41} +(-7.59545 - 1.91807i) q^{42} +(0.549289 + 6.06804i) q^{43} +(0.415235 - 0.0914002i) q^{44} +(2.27240 + 6.15115i) q^{45} +(1.91764 - 11.6971i) q^{46} +(11.1880 + 4.69348i) q^{47} +(5.48279 + 4.77773i) q^{48} +(2.60612 - 0.774528i) q^{49} +(0.301535 + 0.113878i) q^{50} +(-3.61088 - 1.64689i) q^{51} +(-0.207529 + 0.0301860i) q^{52} +(8.34123 - 7.90123i) q^{53} +(-3.17779 + 6.83614i) q^{54} +(8.65599 + 1.90533i) q^{55} +(-8.43222 - 1.53921i) q^{56} +(-12.4267 - 2.66486i) q^{57} +(-3.41152 + 5.90892i) q^{58} +(-6.94332 + 3.28487i) q^{59} +(-0.162120 - 0.362368i) q^{60} +(2.81771 + 6.39069i) q^{61} +(-7.09368 + 8.35133i) q^{62} +(-0.943967 - 9.30473i) q^{63} +(6.00075 + 4.56165i) q^{64} +(-4.19053 - 1.24541i) q^{65} +(5.45661 + 8.60515i) q^{66} +(-1.35462 + 1.19339i) q^{67} +(0.224765 + 0.0848854i) q^{68} +(13.9070 - 2.61645i) q^{69} +(8.08126 + 5.69488i) q^{70} +(-0.165380 + 0.125719i) q^{71} +(-2.96993 + 7.69527i) q^{72} +(3.43604 - 6.48106i) q^{73} +(-0.783160 - 0.857255i) q^{74} +(-0.00486409 + 0.384773i) q^{75} +(0.761386 + 0.110747i) q^{76} +(-11.2735 - 5.71854i) q^{77} +(-2.37813 - 4.42754i) q^{78} +(-1.89323 + 5.30066i) q^{79} +(-4.29889 - 8.10858i) q^{80} +(-8.96622 - 0.779084i) q^{81} +(0.620694 - 11.4480i) q^{82} +(-9.53080 - 5.27551i) q^{83} +(0.0946226 + 0.558224i) q^{84} +(3.50940 + 3.57334i) q^{85} +(7.73385 - 4.28086i) q^{86} +(-8.02106 - 1.41933i) q^{87} +(6.58563 + 8.99586i) q^{88} +(17.5012 - 1.90337i) q^{89} +(6.83563 - 6.61695i) q^{90} +(5.34253 + 3.21449i) q^{91} +(-0.829457 + 0.214246i) q^{92} +(-12.2627 - 4.55544i) q^{93} +(-0.317790 - 17.5992i) q^{94} +(13.4355 + 8.75966i) q^{95} +(0.304795 - 0.980031i) q^{96} +(8.36647 - 13.3534i) q^{97} +(-2.55357 - 3.00630i) q^{98} +(-7.43147 + 9.63067i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) $ 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{29}\right)$

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 $

$2$	−0.585309	−	1.32751i	−0.413876	−	0.938688i	−0.992404	−	0.123025i	$-0.960740\pi$
$2$	−0.585309	−	1.32751i	−0.413876	−	0.938688i	0.578528	−	0.815663i	$-0.303627\pi$
$3$	1.25099	−	1.19792i	0.722261	−	0.691620i
$3$	1.25099	−	1.19792i	0.722261	−	0.691620i
$4$	−0.0707233	+	0.0774144i	−0.0353616	+	0.0387072i
$5$	−2.01564	+	0.845586i	−0.901423	+	0.378158i	−0.788205	−	0.615413i	$-0.788989\pi$
$5$	−2.01564	+	0.845586i	−0.901423	+	0.378158i	−0.113218	+	0.993570i	$0.536116\pi$
$6$	−2.32246	−	0.959547i	−0.948142	−	0.391733i
$7$	3.08503	−	0.448730i	1.16603	−	0.169604i	0.466710	−	0.884410i	$-0.345439\pi$
$7$	3.08503	−	0.448730i	1.16603	−	0.169604i	0.699322	+	0.714806i	$0.253485\pi$
$8$	−2.60557	−	0.877919i	−0.921208	−	0.310391i
$9$	0.129969	−	2.99718i	0.0433231	−	0.999061i
$10$	2.30229	+	2.18085i	0.728049	+	0.689645i
$11$	−3.31453	−	2.33575i	−0.999368	−	0.704256i	−0.0438039	−	0.999040i	$-0.513948\pi$
$11$	−3.31453	−	2.33575i	−0.999368	−	0.704256i	−0.955564	+	0.294784i	$0.904752\pi$
$12$	0.00426204	+	0.181566i	0.00123034	+	0.0524135i
$13$	1.54746	+	1.26705i	0.429189	+	0.351416i	0.823261	−	0.567663i	$-0.192152\pi$
$13$	1.54746	+	1.26705i	0.429189	+	0.351416i	−0.394072	+	0.919079i	$0.628934\pi$
$14$	−2.40139	−	3.83275i	−0.641798	−	1.02435i
$15$	−1.50861	+	3.47240i	−0.389522	+	0.896571i
$16$	0.378527	+	4.18162i	0.0946318	+	1.04540i
$17$	−0.848111	−	2.12860i	−0.205697	−	0.516261i	0.789545	−	0.613693i	$-0.210317\pi$
$17$	−0.848111	−	2.12860i	−0.205697	−	0.516261i	−0.995242	+	0.0974316i	$0.968937\pi$
$18$	−4.05485	+	1.58174i	−0.955737	+	0.372820i
$19$	−4.11780	−	6.07331i	−0.944689	−	1.39331i	−0.919267	−	0.393635i	$-0.871217\pi$
$19$	−4.11780	−	6.07331i	−0.944689	−	1.39331i	−0.0254222	−	0.999677i	$-0.508093\pi$
$20$	0.0770923	−	0.215842i	0.0172384	−	0.0482638i
$21$	3.32181	−	4.25698i	0.724879	−	0.928950i
$22$	−1.16070	+	5.76719i	−0.247463	+	1.22957i
$23$	6.84394	+	4.46210i	1.42706	+	0.930412i	0.999653	+	0.0263528i	$0.00838934\pi$
$23$	6.84394	+	4.46210i	1.42706	+	0.930412i	0.427408	+	0.904059i	$0.359427\pi$
$24$	−4.31123	+	2.02300i	−0.880026	+	0.412943i
$25$	−0.155671	+	0.158507i	−0.0311342	+	0.0317014i
$26$	0.776272	−	2.79588i	0.152239	−	0.548317i
$27$	−3.42780	−	3.90515i	−0.659680	−	0.751546i
$28$	−0.183445	+	0.270562i	−0.0346679	+	0.0511313i
$29$	−2.77802	−	3.79472i	−0.515865	−	0.704663i	0.467969	−	0.883745i	$-0.344986\pi$
$29$	−2.77802	−	3.79472i	−0.515865	−	0.704663i	−0.983834	+	0.179082i	$0.942687\pi$
$30$	5.49264	−	0.0297394i	1.00281	−	0.00542964i
$31$	−3.29449	−	6.79619i	−0.591709	−	1.22063i	−0.957095	−	0.289776i	$-0.906419\pi$
$31$	−3.29449	−	6.79619i	−0.591709	−	1.22063i	0.365386	−	0.930856i	$-0.380937\pi$
$32$	0.518432	−	0.286964i	0.0916467	−	0.0507285i
$33$	−6.94450	+	1.04853i	−1.20888	+	0.182526i
$34$	−2.32932	+	2.37176i	−0.399475	+	0.406753i
$35$	−5.83888	+	3.51314i	−0.986951	+	0.593829i
$36$	0.222833	+	0.222032i	0.0371389	+	0.0370053i
$37$	0.758437	−	0.255547i	0.124686	−	0.0420117i	−0.256267	−	0.966606i	$-0.582493\pi$
$37$	0.758437	−	0.255547i	0.124686	−	0.0420117i	0.380953	+	0.924594i	$0.375596\pi$
$38$	−5.65216	+	9.02116i	−0.916901	+	1.46343i
$39$	3.45369	−	0.268667i	0.553033	−	0.0430211i
$40$	5.99426	−	0.433663i	0.947775	−	0.0685681i
$41$	7.04752	+	3.57488i	1.10064	+	0.558302i	0.906301	−	0.422633i	$-0.138894\pi$
$41$	7.04752	+	3.57488i	1.10064	+	0.558302i	0.194337	+	0.980935i	$0.437745\pi$
$42$	−7.59545	−	1.91807i	−1.17200	−	0.295965i
$43$	0.549289	+	6.06804i	0.0837658	+	0.925367i	0.923811	+	0.382850i	$0.125057\pi$
$43$	0.549289	+	6.06804i	0.0837658	+	0.925367i	−0.840045	+	0.542517i	$0.817471\pi$
$44$	0.415235	−	0.0914002i	0.0625991	−	0.0137791i
$45$	2.27240	+	6.15115i	0.338750	+	0.916960i
$46$	1.91764	−	11.6971i	0.282740	−	1.72464i
$47$	11.1880	+	4.69348i	1.63193	+	0.684614i	0.996184	−	0.0872831i	$-0.0278185\pi$
$47$	11.1880	+	4.69348i	1.63193	+	0.684614i	0.635747	+	0.771897i	$0.280692\pi$
$48$	5.48279	+	4.77773i	0.791372	+	0.689606i
$49$	2.60612	−	0.774528i	0.372303	−	0.110647i
$50$	0.301535	+	0.113878i	0.0426434	+	0.0161048i
$51$	−3.61088	−	1.64689i	−0.505624	−	0.230611i
$52$	−0.207529	+	0.0301860i	−0.0287791	+	0.00418604i
$53$	8.34123	−	7.90123i	1.14576	−	1.08532i	0.150442	−	0.988619i	$-0.451930\pi$
$53$	8.34123	−	7.90123i	1.14576	−	1.08532i	0.995314	−	0.0966987i	$-0.0308283\pi$
$54$	−3.17779	+	6.83614i	−0.432442	+	0.930281i
$55$	8.65599	+	1.90533i	1.16717	+	0.256914i
$56$	−8.43222	−	1.53921i	−1.12680	−	0.205686i
$57$	−12.4267	−	2.66486i	−1.64596	−	0.352970i
$58$	−3.41152	+	5.90892i	−0.447954	+	0.775879i
$59$	−6.94332	+	3.28487i	−0.903943	+	0.427653i
$59$	−6.94332	+	3.28487i	−0.903943	+	0.427653i
$60$	−0.162120	−	0.362368i	−0.0209296	−	0.0467815i
$61$	2.81771	+	6.39069i	0.360771	+	0.818244i	0.998835	+	0.0482603i	$0.0153677\pi$
$61$	2.81771	+	6.39069i	0.360771	+	0.818244i	−0.638064	+	0.769983i	$0.720264\pi$
$62$	−7.09368	+	8.35133i	−0.900898	+	1.06062i
$63$	−0.943967	−	9.30473i	−0.118929	−	1.17229i
$64$	6.00075	+	4.56165i	0.750094	+	0.570206i
$65$	−4.19053	−	1.24541i	−0.519771	−	0.154474i
$66$	5.45661	+	8.60515i	0.671662	+	1.05922i
$67$	−1.35462	+	1.19339i	−0.165494	+	0.145796i	−0.739756	−	0.672875i	$-0.765059\pi$
$67$	−1.35462	+	1.19339i	−0.165494	+	0.145796i	0.574262	+	0.818671i	$0.305289\pi$
$68$	0.224765	+	0.0848854i	0.0272568	+	0.0102939i
$69$	13.9070	−	2.61645i	1.67420	−	0.314984i
$70$	8.08126	+	5.69488i	0.965895	+	0.680668i
$71$	−0.165380	+	0.125719i	−0.0196270	+	0.0149201i	−0.614942	−	0.788573i	$-0.710820\pi$
$71$	−0.165380	+	0.125719i	−0.0196270	+	0.0149201i	0.595315	+	0.803493i	$0.297027\pi$
$72$	−2.96993	+	7.69527i	−0.350009	+	0.906896i
$73$	3.43604	−	6.48106i	0.402158	−	0.758551i	−0.596883	−	0.802328i	$-0.703594\pi$
$73$	3.43604	−	6.48106i	0.402158	−	0.758551i	0.999041	+	0.0437775i	$0.0139393\pi$
$74$	−0.783160	−	0.857255i	−0.0910405	−	0.0996539i
$75$	−0.00486409	+	0.384773i	−0.000561656	+	0.0444297i
$76$	0.761386	+	0.110747i	0.0873370	+	0.0127035i
$77$	−11.2735	−	5.71854i	−1.28474	−	0.651689i
$78$	−2.37813	−	4.42754i	−0.269270	−	0.501320i
$79$	−1.89323	+	5.30066i	−0.213006	+	0.596371i	−0.999782	−	0.0208665i	$-0.993358\pi$
$79$	−1.89323	+	5.30066i	−0.213006	+	0.596371i	0.786777	+	0.617238i	$0.211748\pi$
$80$	−4.29889	−	8.10858i	−0.480631	−	0.906566i
$81$	−8.96622	−	0.779084i	−0.996246	−	0.0865649i
$82$	0.620694	−	11.4480i	0.0685442	−	1.26422i
$83$	−9.53080	−	5.27551i	−1.04614	−	0.579063i	−0.134867	−	0.990864i	$-0.543061\pi$
$83$	−9.53080	−	5.27551i	−1.04614	−	0.579063i	−0.911274	+	0.411801i	$0.864900\pi$
$84$	0.0946226	+	0.558224i	0.0103242	+	0.0609072i
$85$	3.50940	+	3.57334i	0.380648	+	0.387584i
$86$	7.73385	−	4.28086i	0.833962	−	0.461617i
$87$	−8.02106	−	1.41933i	−0.859948	−	0.152168i
$88$	6.58563	+	8.99586i	0.702031	+	0.958962i
$89$	17.5012	−	1.90337i	1.85512	−	0.201757i	0.888661	−	0.458564i	$-0.151636\pi$
$89$	17.5012	−	1.90337i	1.85512	−	0.201757i	0.966463	+	0.256808i	$0.0826707\pi$
$90$	6.83563	−	6.61695i	0.720539	−	0.697488i
$91$	5.34253	+	3.21449i	0.560049	+	0.336971i
$92$	−0.829457	+	0.214246i	−0.0864768	+	0.0223367i
$93$	−12.2627	−	4.55544i	−1.27158	−	0.472378i
$94$	−0.317790	−	17.5992i	−0.0327776	−	1.81522i
$95$	13.4355	+	8.75966i	1.37846	+	0.898722i
$96$	0.304795	−	0.980031i	0.0311080	−	0.100024i
$97$	8.36647	−	13.3534i	0.849486	−	1.35583i	−0.0837214	−	0.996489i	$-0.526681\pi$
$97$	8.36647	−	13.3534i	0.849486	−	1.35583i	0.933207	−	0.359338i	$-0.116998\pi$
$98$	−2.55357	−	3.00630i	−0.257950	−	0.303682i
$99$	−7.43147	+	9.63067i	−0.746891	+	0.967919i
$100$	−0.00126119	−	0.0232613i	−0.000126119	−	0.00232613i
$101$	−1.43511	+	1.81874i	−0.142799	+	0.180971i	−0.851205	−	0.524834i	$-0.824127\pi$
$101$	−1.43511	+	1.81874i	−0.142799	+	0.180971i	0.708406	+	0.705805i	$0.249415\pi$
$102$	−0.0727818	+	5.75740i	−0.00720647	+	0.570067i
$103$	−1.55367	+	4.90188i	−0.153088	+	0.482997i	−0.998710	−	0.0507856i	$-0.983827\pi$
$103$	−1.55367	+	4.90188i	−0.153088	+	0.482997i	0.845622	+	0.533782i	$0.179230\pi$
$104$	−2.91965	−	4.65993i	−0.286296	−	0.456944i
$105$	−3.09594	+	11.3894i	−0.302133	+	1.11150i
$106$	−15.3711	−	6.44836i	−1.49297	−	0.626320i
$107$	−0.813926	+	0.376562i	−0.0786852	+	0.0364036i	−0.458837	−	0.888520i	$-0.651734\pi$
$107$	−0.813926	+	0.376562i	−0.0786852	+	0.0364036i	0.380152	+	0.924924i	$0.375872\pi$
$108$	0.544740	+	0.0108239i	0.0524176	+	0.00104153i
$109$	0.572879	+	3.49440i	0.0548718	+	0.334703i	0.999969	+	0.00791299i	$0.00251881\pi$
$109$	0.572879	+	3.49440i	0.0548718	+	0.334703i	−0.945097	+	0.326790i	$0.894033\pi$
$110$	−2.53709	−	12.6061i	−0.241902	−	1.20194i
$111$	0.642674	−	1.22824i	0.0610000	−	0.116579i
$112$	3.04419	+	12.7306i	0.287649	+	1.20293i
$113$	15.2187	−	6.38443i	1.43166	−	0.600596i	0.471956	−	0.881622i	$-0.343548\pi$
$113$	15.2187	−	6.38443i	1.43166	−	0.600596i	0.959700	+	0.281026i	$0.0906746\pi$
$114$	3.73583	+	18.0563i	0.349893	+	1.69112i
$115$	−17.5680	−	3.20685i	−1.63823	−	0.299041i
$116$	0.490237	+	0.0533165i	0.0455174	+	0.00495031i
$117$	3.99870	−	4.47335i	0.369680	−	0.413561i
$118$	8.42466	+	7.29463i	0.775553	+	0.671525i
$119$	−3.57162	−	6.18622i	−0.327410	−	0.567090i
$120$	6.97928	−	7.72316i	0.637118	−	0.705025i
$121$	1.83041	+	5.12477i	0.166401	+	0.465888i
$122$	6.83444	−	7.48105i	0.618761	−	0.677302i
$123$	13.0988	−	3.97023i	1.18108	−	0.357983i
$124$	0.759120	+	0.225607i	0.0681710	+	0.0202601i
$125$	4.22503	−	10.6040i	0.377898	−	0.948454i
$126$	−11.7996	+	6.69926i	−1.05119	+	0.596817i
$127$	−1.80869	−	11.0325i	−0.160495	−	0.978979i	−0.937118	−	0.349013i	$-0.886517\pi$
$127$	−1.80869	−	11.0325i	−0.160495	−	0.978979i	0.776623	−	0.629966i	$-0.216931\pi$
$128$	2.81894	−	11.7886i	0.249162	−	1.04198i
$129$	7.95619	+	6.93307i	0.700503	+	0.610423i
$130$	0.799468	+	6.29190i	0.0701180	+	0.551836i
$131$	4.58603	+	3.75500i	0.400683	+	0.328076i	0.812256	−	0.583301i	$-0.198239\pi$
$131$	4.58603	+	3.75500i	0.400683	+	0.328076i	−0.411573	+	0.911377i	$0.635021\pi$
$132$	0.409966	−	0.611760i	0.0356830	−	0.0532469i
$133$	−15.4288	−	16.8886i	−1.33785	−	1.46442i
$134$	2.37711	+	1.09977i	0.205351	+	0.0950054i
$135$	10.2114	+	4.97289i	0.878854	+	0.427998i
$136$	0.341077	+	6.29079i	0.0292471	+	0.539431i
$137$	−2.25189	+	4.64541i	−0.192392	+	0.396884i	−0.973889	−	0.227025i	$-0.927100\pi$
$137$	−2.25189	+	4.64541i	−0.192392	+	0.396884i	0.781497	+	0.623909i	$0.214456\pi$
$138$	−11.6132	−	16.9301i	−0.988583	−	1.44119i
$139$	15.9065	+	0.574637i	1.34917	+	0.0487400i	0.701221	−	0.712944i	$-0.252639\pi$
$139$	15.9065	+	0.574637i	1.34917	+	0.0487400i	0.647949	+	0.761684i	$0.275627\pi$
$140$	0.140977	−	0.700474i	0.0119147	−	0.0592009i
$141$	19.6185	−	7.53078i	1.65217	−	0.634206i
$142$	0.263691	+	0.145959i	0.0221284	+	0.0122486i
$143$	−2.16959	−	7.81416i	−0.181430	−	0.653453i
$144$	12.5823	−	0.591033i	1.04852	−	0.0492528i
$145$	8.80826	+	5.29976i	0.731486	+	0.440121i
$146$	−10.6148	−	0.767941i	−0.878486	−	0.0635552i
$147$	2.33242	−	4.09086i	0.192374	−	0.337408i
$148$	−0.0338561	+	0.0767871i	−0.00278295	+	0.00631186i
$149$	−2.50592	−	5.16945i	−0.205293	−	0.423498i	0.771931	−	0.635706i	$-0.219291\pi$
$149$	−2.50592	−	5.16945i	−0.205293	−	0.423498i	−0.977225	+	0.212208i	$0.931935\pi$
$150$	0.513635	−	0.218754i	0.0419381	−	0.0178612i
$151$	18.5281	−	4.78573i	1.50779	−	0.389458i	0.596972	−	0.802262i	$-0.296370\pi$
$151$	18.5281	−	4.78573i	1.50779	−	0.389458i	0.910820	+	0.412804i	$0.135451\pi$
$152$	5.39736	+	19.4395i	0.437784	+	1.57675i
$153$	−6.49003	+	2.26529i	−0.524688	+	0.183138i
$154$	−0.992891	+	18.3128i	−0.0800095	+	1.47569i
$155$	12.3873	+	10.9129i	0.994971	+	0.876547i
$156$	−0.223457	+	0.286366i	−0.0178909	+	0.0229277i
$157$	−2.06282	+	0.376545i	−0.164631	+	0.0300516i	−0.261258	−	0.965269i	$-0.584137\pi$
$157$	−2.06282	+	0.376545i	−0.164631	+	0.0300516i	0.0966268	+	0.995321i	$0.469195\pi$
$158$	8.14478	−	0.589245i	0.647964	−	0.0468778i
$159$	0.969769	−	19.8765i	0.0769077	−	1.57631i
$160$	−0.802321	+	1.01680i	−0.0634291	+	0.0803847i
$161$	23.1161	+	10.6946i	1.82180	+	0.842855i
$162$	4.21377	+	12.3587i	0.331065	+	0.970991i
$163$	−5.90445	+	11.1370i	−0.462472	+	0.872315i	0.537113	+	0.843510i	$0.319515\pi$
$163$	−5.90445	+	11.1370i	−0.462472	+	0.872315i	−0.999585	+	0.0288044i	$0.990830\pi$
$164$	−0.775171	+	0.292753i	−0.0605307	+	0.0228601i
$165$	13.1110	−	7.98564i	1.02069	−	0.621681i
$166$	−1.42481	+	15.7400i	−0.110587	+	1.22166i
$167$	−8.86988	+	2.63609i	−0.686372	+	0.203987i	−0.609183	−	0.793030i	$-0.708503\pi$
$167$	−8.86988	+	2.63609i	−0.686372	+	0.203987i	−0.0771890	+	0.997016i	$0.524595\pi$
$168$	−12.3925	+	8.17559i	−0.956102	+	0.630760i
$169$	−1.77572	−	8.82303i	−0.136594	−	0.678695i
$170$	2.68955	−	6.75026i	0.206279	−	0.517721i
$171$	−18.7380	+	11.5525i	−1.43293	+	0.883439i
$172$	−0.508601	−	0.386628i	−0.0387805	−	0.0294801i
$173$	4.67816	+	14.7598i	0.355674	+	1.12216i	0.948485	+	0.316822i	$0.102616\pi$
$173$	4.67816	+	14.7598i	0.355674	+	1.12216i	−0.592811	+	0.805342i	$0.701982\pi$
$174$	2.81064	+	11.4787i	0.213074	+	0.870202i
$175$	−0.409123	+	0.558854i	−0.0309268	+	0.0422454i
$176$	8.51259	−	14.7442i	0.641661	−	1.11139i
$177$	−4.75103	+	12.4269i	−0.357109	+	0.934063i
$178$	−12.7703	−	22.1189i	−0.957177	−	1.65788i
$179$	−8.22680	−	0.894719i	−0.614900	−	0.0668744i	−0.204631	−	0.978839i	$-0.565600\pi$
$179$	−8.22680	−	0.894719i	−0.614900	−	0.0668744i	−0.410269	+	0.911965i	$0.634565\pi$
$180$	−0.636900	−	0.259113i	−0.0474717	−	0.0193131i
$181$	11.6829	+	2.57161i	0.868387	+	0.191146i	0.626750	−	0.779220i	$-0.284385\pi$
$181$	11.6829	+	2.57161i	0.868387	+	0.191146i	0.241637	+	0.970367i	$0.422316\pi$
$182$	1.14023	−	8.97371i	0.0845193	−	0.665175i
$183$	11.1805	+	4.61931i	0.826485	+	0.341469i
$184$	−13.9150	−	17.6347i	−1.02583	−	1.30005i
$185$	−1.31265	+	1.15642i	−0.0965081	+	0.0850214i
$186$	1.13008	+	18.9451i	0.0828617	+	1.38912i
$187$	−2.16079	+	9.03628i	−0.158013	+	0.660798i
$188$	−1.15459	+	0.534171i	−0.0842072	+	0.0389584i
$189$	−12.3272	−	10.5094i	−0.896674	−	0.764443i
$190$	3.76457	−	22.9628i	0.273110	−	1.66590i
$191$	−4.48400	+	0.161989i	−0.324451	+	0.0117211i	−0.197849	−	0.980233i	$-0.563396\pi$
$191$	−4.48400	+	0.161989i	−0.324451	+	0.0117211i	−0.126602	+	0.991954i	$0.540407\pi$
$192$	12.9714	−	1.48183i	0.936130	−	0.106942i
$193$	−4.04874	+	2.85315i	−0.291434	+	0.205374i	−0.712529	−	0.701642i	$-0.752451\pi$
$193$	−4.04874	+	2.85315i	−0.291434	+	0.205374i	0.421095	+	0.907017i	$0.361646\pi$
$194$	−22.6236	−	3.29069i	−1.62428	−	0.236258i
$195$	−6.73422	+	3.46193i	−0.482248	+	0.247914i
$196$	−0.124354	+	0.256528i	−0.00888241	+	0.0183235i
$197$	−8.73720	−	10.2862i	−0.622499	−	0.732863i	0.357046	−	0.934087i	$-0.383784\pi$
$197$	−8.73720	−	10.2862i	−0.622499	−	0.732863i	−0.979545	+	0.201224i	$0.935508\pi$
$198$	17.1345	+	4.22840i	1.21769	+	0.300499i
$199$	−4.21081	+	1.41879i	−0.298497	+	0.100575i	−0.464565	−	0.885539i	$-0.653789\pi$
$199$	−4.21081	+	1.41879i	−0.298497	+	0.100575i	0.166068	+	0.986114i	$0.446893\pi$
$200$	0.544768	−	0.276335i	0.0385209	−	0.0195399i
$201$	−0.265035	+	3.11566i	−0.0186942	+	0.219762i
$202$	3.25437	+	0.840593i	0.228977	+	0.0591439i
$203$	−10.2731	−	10.4603i	−0.721029	−	0.734166i
$204$	0.382866	−	0.163060i	0.0268060	−	0.0114165i
$205$	−17.2282	−	1.24639i	−1.20327	−	0.0870519i
$206$	7.41665	−	0.806609i	0.516742	−	0.0561991i
$207$	14.2632	−	19.9326i	0.991363	−	1.38541i
$208$	−4.71256	+	6.95051i	−0.326757	+	0.481931i
$209$	−0.537168	+	29.7483i	−0.0371567	+	2.05773i
$210$	16.9316	−	2.55646i	1.16839	−	0.176412i
$211$	11.2911	+	2.91646i	0.777312	+	0.200777i	0.617712	−	0.786405i	$-0.288060\pi$
$211$	11.2911	+	2.91646i	0.777312	+	0.200777i	0.159601	+	0.987182i	$0.448979\pi$
$212$	0.0217503	+	1.20453i	0.00149382	+	0.0827276i
$213$	−0.0562884	+	0.355386i	−0.00385682	+	0.0243506i
$214$	0.976286	+	0.860086i	0.0667375	+	0.0587942i
$215$	−6.23822	−	11.7665i	−0.425443	−	0.802470i
$216$	5.50297	+	13.1845i	0.374429	+	0.897090i
$217$	−13.2133	−	19.4881i	−0.896976	−	1.32294i
$218$	4.30353	−	2.80580i	0.291472	−	0.190033i
$219$	−3.46533	−	12.2239i	−0.234166	−	0.826012i
$220$	−0.759679	+	0.535347i	−0.0512176	+	0.0360931i
$221$	1.38462	−	4.36852i	0.0931396	−	0.293859i
$222$	−2.00665	−	0.134257i	−0.134678	−	0.00901071i
$223$	−17.7948	+	6.72044i	−1.19163	+	0.450034i	−0.868198	−	0.496218i	$-0.834722\pi$
$223$	−17.7948	+	6.72044i	−1.19163	+	0.450034i	−0.323432	+	0.946251i	$0.604837\pi$
$224$	1.47061	−	1.11793i	0.0982593	−	0.0746947i
$225$	0.454843	+	0.487175i	0.0303228	+	0.0324783i
$226$	−17.3830	−	16.4661i	−1.15630	−	1.09531i
$227$	10.6095	−	8.68699i	0.704178	−	0.576576i	−0.212037	−	0.977262i	$-0.568010\pi$
$227$	10.6095	−	8.68699i	0.704178	−	0.576576i	0.916215	+	0.400686i	$0.131228\pi$
$228$	1.08515	−	0.773537i	0.0718661	−	0.0512287i
$229$	4.68431	+	5.93651i	0.309548	+	0.392296i	0.914912	−	0.403653i	$-0.132260\pi$
$229$	4.68431	+	5.93651i	0.309548	+	0.392296i	−0.605364	+	0.795949i	$0.706972\pi$
$230$	6.02561	+	25.1987i	0.397317	+	1.66155i
$231$	−20.9535	+	6.35096i	−1.37864	+	0.417863i
$232$	3.90687	+	12.3263i	0.256498	+	0.809261i
$233$	−12.0667	+	14.2061i	−0.790518	+	0.930670i	−0.998877	−	0.0473827i	$-0.984912\pi$
$233$	−12.0667	+	14.2061i	−0.790518	+	0.930670i	0.208359	+	0.978052i	$0.433188\pi$
$234$	−8.27887	−	2.69001i	−0.541206	−	0.175851i
$235$	−26.5197			−1.72995
$236$	0.236758	−	0.769829i	0.0154116	−	0.0501116i
$237$	3.98135	+	8.89904i	0.258617	+	0.578055i
$238$	−6.12174	+	8.36219i	−0.396814	+	0.542040i
$239$	0.0550596	+	0.154155i	0.00356151	+	0.00997148i	0.943502	−	0.331368i	$-0.107510\pi$
$239$	0.0550596	+	0.154155i	0.00356151	+	0.00997148i	−0.939940	+	0.341340i	$0.889119\pi$
$240$	−15.0913	−	4.99404i	−0.974141	−	0.322364i
$241$	−3.33875	+	26.2763i	−0.215068	+	1.69261i	0.410041	+	0.912067i	$0.365514\pi$
$241$	−3.33875	+	26.2763i	−0.215068	+	1.69261i	−0.625109	+	0.780538i	$0.714945\pi$
$242$	5.73180	−	5.42945i	0.368454	−	0.349018i
$243$	−12.1500	+	9.76619i	−0.779420	+	0.626501i
$244$	−0.694009	−	0.233839i	−0.0444294	−	0.0149700i
$245$	−4.59808	+	3.76487i	−0.293761	+	0.240529i
$246$	−12.9374	−	15.0650i	−0.824855	−	0.960506i
$247$	1.32303	−	14.6157i	0.0841827	−	0.929973i
$248$	2.61753	+	20.6003i	0.166214	+	1.30812i
$249$	−18.2426	+	4.81751i	−1.15608	+	0.305298i
$250$	−16.5499	+	0.597879i	−1.04670	+	0.0378132i
$251$	5.37009	−	1.18205i	0.338957	−	0.0746101i	−0.0422303	−	0.999108i	$-0.513446\pi$
$251$	5.37009	−	1.18205i	0.338957	−	0.0746101i	0.381187	+	0.924498i	$0.375515\pi$
$252$	0.787080	+	0.584984i	0.0495814	+	0.0368505i
$253$	−12.2621	−	30.7755i	−0.770911	−	1.93484i
$254$	−13.5871	+	8.85848i	−0.852530	+	0.555831i
$255$	8.67083	+	0.266242i	0.542988	+	0.0166727i
$256$	−2.46895	+	0.450680i	−0.154309	+	0.0281675i
$257$	−8.96559	−	0.323891i	−0.559258	−	0.0202038i	−0.244969	−	0.969531i	$-0.578778\pi$
$257$	−8.96559	−	0.323891i	−0.559258	−	0.0202038i	−0.314290	+	0.949327i	$0.601766\pi$
$258$	4.54686	−	14.6199i	0.283075	−	0.910193i
$259$	2.22513	−	1.12870i	0.138263	−	0.0701343i
$260$	0.392780	−	0.236328i	0.0243592	−	0.0146564i
$261$	−11.7345	+	7.83304i	−0.726350	+	0.484853i
$262$	2.30054	−	8.28581i	0.142128	−	0.511899i
$263$	0.220387	−	12.2050i	0.0135896	−	0.752593i	−0.919529	−	0.393023i	$-0.871429\pi$
$263$	0.220387	−	12.2050i	0.0135896	−	0.752593i	0.933118	−	0.359570i	$-0.117076\pi$
$264$	19.0149	+	3.36469i	1.17029	+	0.207082i
$265$	−10.1318	+	22.9793i	−0.622390	+	1.41161i
$266$	−13.3890	+	30.3669i	−0.820933	+	1.86191i
$267$	19.6138	−	23.3462i	1.20035	−	1.42876i
$268$	0.00341763	−	0.189268i	0.000208765	−	0.0115614i
$269$	−4.90722	+	17.6742i	−0.299199	+	1.07762i	0.649221	+	0.760600i	$0.275095\pi$
$269$	−4.90722	+	17.6742i	−0.299199	+	1.07762i	−0.948420	+	0.317017i	$0.897319\pi$
$270$	0.624740	−	16.4663i	0.0380205	−	1.00211i
$271$	−5.56687	+	3.34948i	−0.338164	+	0.203466i	−0.674499	−	0.738276i	$-0.735640\pi$
$271$	−5.56687	+	3.34948i	−0.338164	+	0.203466i	0.336335	+	0.941742i	$0.390813\pi$
$272$	8.57996	−	4.35221i	0.520236	−	0.263892i
$273$	10.5342	−	2.37862i	0.637558	−	0.143961i
$274$	7.48486	+	0.270398i	0.452177	+	0.0163353i
$275$	0.886209	−	0.161768i	0.0534404	−	0.00975497i
$276$	−0.780995	+	1.26164i	−0.0470104	+	0.0759420i
$277$	−1.57287	+	1.02548i	−0.0945049	+	0.0616151i	−0.592535	−	0.805545i	$-0.701873\pi$
$277$	−1.57287	+	1.02548i	−0.0945049	+	0.0616151i	0.498030	+	0.867160i	$0.334057\pi$
$278$	−8.54736	−	21.4523i	−0.512637	−	1.28662i
$279$	−20.7976	+	8.99091i	−1.24512	+	0.538272i
$280$	18.2979	−	4.02767i	1.09351	−	0.240699i
$281$	−1.93430	+	0.0698786i	−0.115391	+	0.00416861i	−0.0937376	−	0.995597i	$-0.529881\pi$
$281$	−1.93430	+	0.0698786i	−0.115391	+	0.00416861i	−0.0216532	+	0.999766i	$0.506893\pi$
$282$	−21.4800	−	21.6358i	−1.27912	−	1.28839i
$283$	−0.0147207	−	0.115854i	−0.000875057	−	0.00688679i	0.991580	−	0.129492i	$-0.0413348\pi$
$283$	−0.0147207	−	0.115854i	−0.000875057	−	0.00688679i	−0.992455	+	0.122606i	$0.960875\pi$
$284$	0.00196378	−	0.0216940i	0.000116529	−	0.00128730i
$285$	27.3011	−	5.13642i	1.61718	−	0.304255i
$286$	−9.10345	+	7.45384i	−0.538299	+	0.440755i
$287$	23.3460	+	7.86618i	1.37807	+	0.464326i
$288$	−0.792703	−	1.59113i	−0.0467105	−	0.0937584i
$289$	8.53028	−	8.08031i	0.501781	−	0.475313i
$290$	1.87990	−	14.7950i	0.110392	−	0.868793i
$291$	−5.52987	−	26.7273i	−0.324167	−	1.56678i
$292$	0.258719	+	0.724361i	0.0151404	+	0.0423900i
$293$	−4.04131	+	5.52036i	−0.236096	+	0.322503i	−0.908661	−	0.417536i	$-0.862894\pi$
$293$	−4.04131	+	5.52036i	−0.236096	+	0.322503i	0.672565	+	0.740038i	$0.265193\pi$
$294$	−6.79582	−	0.701881i	−0.396340	−	0.0409345i
$295$	11.2176	−	12.4923i	0.653115	−	0.727329i
$296$	−2.20051			−0.127902
$297$	2.24007	+	20.9502i	0.129982	+	1.21566i
$298$	−5.39574	+	6.35235i	−0.312567	+	0.367982i
$299$	4.93704	+	15.5765i	0.285516	+	0.900814i
$300$	−0.0294430	−	0.0275889i	−0.00169989	−	0.00159285i
$301$	4.41749	+	18.4736i	0.254620	+	1.06480i
$302$	−17.1977	−	21.7950i	−0.989618	−	1.25416i
$303$	0.383393	+	3.99438i	0.0220254	+	0.229471i
$304$	23.8376	−	19.5180i	1.36718	−	1.11943i
$305$	−11.0834	−	10.4987i	−0.634632	−	0.601155i
$306$	6.80586	+	7.28965i	0.389065	+	0.416722i
$307$	15.9129	−	12.0967i	0.908200	−	0.690396i	−0.0429658	−	0.999077i	$-0.513681\pi$
$307$	15.9129	−	12.0967i	0.908200	−	0.690396i	0.951166	+	0.308681i	$0.0998876\pi$
$308$	1.24000	−	0.468301i	0.0706555	−	0.0266839i
$309$	3.92844	+	7.99339i	0.223481	+	0.454728i
$310$	7.23657	−	22.8316i	0.411009	−	1.29675i
$311$	−19.9112	+	14.0314i	−1.12906	+	0.795650i	−0.981130	−	0.193348i	$-0.938065\pi$
$311$	−19.9112	+	14.0314i	−1.12906	+	0.795650i	−0.147929	+	0.988998i	$0.547261\pi$
$312$	−9.23470	−	2.33203i	−0.522812	−	0.132025i
$313$	−27.9347	+	18.2128i	−1.57896	+	1.02945i	−0.606882	+	0.794792i	$0.707580\pi$
$313$	−27.9347	+	18.2128i	−1.57896	+	1.02945i	−0.972079	+	0.234655i	$0.924604\pi$
$314$	1.70725	+	2.51801i	0.0963457	+	0.142099i
$315$	9.77065	+	17.9568i	0.550514	+	1.01175i
$316$	−0.276452	−	0.521444i	−0.0155516	−	0.0293335i
$317$	14.6456	+	12.9024i	0.822578	+	0.724672i	0.964179	−	0.265251i	$-0.0854549\pi$
$317$	14.6456	+	12.9024i	0.822578	+	0.724672i	−0.141601	+	0.989924i	$0.545225\pi$
$318$	−26.9538	+	10.3465i	−1.51149	+	0.580204i
$319$	0.344285	+	19.0665i	0.0192763	+	1.06752i
$320$	−15.9526	−	4.12051i	−0.891780	−	0.230344i
$321$	−0.567124	+	1.44610i	−0.0316538	+	0.0807132i
$322$	0.667144	−	36.9463i	0.0371785	−	2.05894i
$323$	−9.43528	+	13.9160i	−0.524993	+	0.774306i
$324$	0.694432	−	0.639015i	0.0385796	−	0.0355008i
$325$	−0.441731	+	0.0480411i	−0.0245028	+	0.00266484i
$326$	18.2403	+	1.31962i	1.01024	+	0.0730870i
$327$	4.90269	+	3.68521i	0.271119	+	0.203793i
$328$	−15.2244	−	15.5018i	−0.840625	−	0.855941i
$329$	36.6213	+	9.45916i	2.01900	+	0.521500i
$330$	−18.2750	−	12.7309i	−1.00600	−	0.700812i
$331$	−11.5684	+	5.86811i	−0.635857	+	0.322541i	−0.740587	−	0.671960i	$-0.765453\pi$
$331$	−11.5684	+	5.86811i	−0.635857	+	0.322541i	0.104730	+	0.994501i	$0.466602\pi$
$332$	1.08245	−	0.364720i	0.0594071	−	0.0200166i
$333$	−0.667348	−	2.30639i	−0.0365705	−	0.126389i
$334$	8.69104	+	10.2319i	0.475553	+	0.559864i
$335$	1.72132	−	3.55091i	0.0940459	−	0.194007i
$336$	19.0585	+	12.2792i	1.03973	+	0.669883i
$337$	15.1577	+	2.20475i	0.825694	+	0.120101i	0.543662	−	0.839304i	$-0.317037\pi$
$337$	15.1577	+	2.20475i	0.825694	+	0.120101i	0.282032	+	0.959405i	$0.408991\pi$
$338$	−10.6733	+	7.52147i	−0.580550	+	0.409114i
$339$	11.3905	−	26.2177i	0.618645	−	1.42395i
$340$	−0.524825	+	0.0189598i	−0.0284626	+	0.00102824i
$341$	−4.95453	+	30.2213i	−0.268303	+	1.63657i
$342$	26.3035	+	18.1130i	1.42233	+	0.979441i
$343$	−12.1131	+	5.60413i	−0.654047	+	0.302595i
$344$	3.89603	−	16.2929i	0.210060	−	0.878456i
$345$	−25.8191	+	17.0334i	−1.39005	+	0.917046i
$346$	16.8555	−	14.8493i	0.906156	−	0.798303i
$347$	−9.86059	−	12.4965i	−0.529344	−	0.670847i	0.445099	−	0.895481i	$-0.353168\pi$
$347$	−9.86059	−	12.4965i	−0.529344	−	0.670847i	−0.974443	+	0.224635i	$0.927881\pi$
$348$	0.677152	−	0.520567i	0.0362992	−	0.0279053i
$349$	−1.45177	+	11.4256i	−0.0777113	+	0.611596i	0.904860	+	0.425710i	$0.139975\pi$
$349$	−1.45177	+	11.4256i	−0.0777113	+	0.611596i	−0.982571	+	0.185887i	$0.940484\pi$
$350$	0.981344	+	0.216010i	0.0524551	+	0.0115462i
$351$	−0.356370	−	10.3863i	−0.0190216	−	0.554377i
$352$	−2.38863	−	0.259780i	−0.127315	−	0.0138463i
$353$	11.0156	+	19.0796i	0.586302	+	1.01550i	0.994712	+	0.102706i	$0.0327501\pi$
$353$	11.0156	+	19.0796i	0.586302	+	1.01550i	−0.408410	+	0.912799i	$0.633917\pi$
$354$	19.2776	−	0.966551i	1.02459	−	0.0513716i
$355$	0.227041	−	0.393247i	0.0120501	−	0.0208714i
$356$	−1.09039	+	1.48946i	−0.0577907	+	0.0789411i
$357$	−11.8787	−	3.46041i	−0.628686	−	0.183144i
$358$	3.62748	+	11.4448i	0.191718	+	0.604877i
$359$	−14.9147	−	11.3378i	−0.787166	−	0.598388i	0.132458	−	0.991189i	$-0.457713\pi$
$359$	−14.9147	−	11.3378i	−0.787166	−	0.598388i	−0.919624	+	0.392801i	$0.871506\pi$
$360$	−0.520697	−	18.0222i	−0.0274431	−	0.949856i
$361$	−12.8961	+	32.3668i	−0.678743	+	1.70352i
$362$	−3.42430	−	17.0144i	−0.179977	−	0.894255i
$363$	8.42890	+	4.21836i	0.442402	+	0.221407i
$364$	−0.626689	+	0.186249i	−0.0328474	+	0.00976212i
$365$	−1.44554	+	15.9690i	−0.0756629	+	0.835854i
$366$	−0.411868	−	17.5459i	−0.0215287	−	0.917137i
$367$	8.92396	−	3.37024i	0.465827	−	0.175925i	−0.109267	−	0.994012i	$-0.534850\pi$
$367$	8.92396	−	3.37024i	0.465827	−	0.175925i	0.575094	+	0.818087i	$0.304965\pi$
$368$	−16.0682	+	30.3078i	−0.837612	+	1.57990i
$369$	11.6305	−	20.6581i	0.605461	−	1.07542i
$370$	2.30345	+	1.06569i	0.119751	+	0.0554027i
$371$	22.1874	−	28.1185i	1.15191	−	1.45984i
$372$	1.21991	−	0.627133i	0.0632496	−	0.0325153i
$373$	−12.3516	+	0.893596i	−0.639543	+	0.0462686i	−0.388120	−	0.921609i	$-0.626876\pi$
$373$	−12.3516	+	0.893596i	−0.639543	+	0.0462686i	−0.251423	+	0.967877i	$0.580899\pi$
$374$	13.2604	−	2.42055i	0.685681	−	0.125164i
$375$	−7.41731	−	18.3268i	−0.383028	−	0.946394i
$376$	−25.0305	−	22.0513i	−1.29085	−	1.13721i
$377$	0.509224	−	9.39208i	0.0262263	−	0.483717i
$378$	−6.73599	+	22.5157i	−0.346462	+	1.15808i
$379$	−6.14817	−	22.1437i	−0.315810	−	1.13745i	−0.935711	−	0.352766i	$-0.885241\pi$
$379$	−6.14817	−	22.1437i	−0.315810	−	1.13745i	0.619901	−	0.784680i	$-0.287173\pi$
$380$	−1.62833	+	0.420592i	−0.0835315	+	0.0215759i
$381$	−15.4788	−	11.6350i	−0.793001	−	0.596077i
$382$	2.83956	+	5.85772i	0.145285	+	0.299707i
$383$	−5.24156	+	11.8881i	−0.267831	+	0.607453i	−0.997044	−	0.0768342i	$-0.975519\pi$
$383$	−5.24156	+	11.8881i	−0.267831	+	0.607453i	0.729212	+	0.684287i	$0.239887\pi$
$384$	−10.5954	−	18.1243i	−0.540692	−	0.924904i
$385$	27.5590	+	1.99379i	1.40454	+	0.101613i
$386$	6.15733	+	3.70474i	0.313400	+	0.188567i
$387$	18.2584	−	0.857661i	0.928127	−	0.0435974i
$388$	0.442038	+	1.59208i	0.0224411	+	0.0808255i
$389$	25.8876	+	14.3294i	1.31255	+	0.726529i	0.976542	−	0.215329i	$-0.0690822\pi$
$389$	25.8876	+	14.3294i	1.31255	+	0.726529i	0.336013	+	0.941857i	$0.390921\pi$
$390$	8.53733	+	6.91342i	0.432304	+	0.350075i
$391$	3.69359	−	18.3524i	0.186793	−	0.928119i
$392$	−7.47040	−	0.269876i	−0.377312	−	0.0136308i
$393$	10.2353	−	0.796215i	0.516302	−	0.0401637i
$394$	−8.54106	+	17.6193i	−0.430292	+	0.887647i
$395$	−0.666081	−	12.2851i	−0.0335142	−	0.618132i
$396$	−0.219975	−	1.25642i	−0.0110542	−	0.0631372i
$397$	2.69795	+	1.24820i	0.135406	+	0.0626455i	0.486422	−	0.873724i	$-0.338302\pi$
$397$	2.69795	+	1.24820i	0.135406	+	0.0626455i	−0.351016	+	0.936369i	$0.614164\pi$
$398$	4.34807	+	4.75944i	0.217949	+	0.238569i
$399$	−39.5325	−	2.64495i	−1.97910	−	0.132413i
$400$	−0.721742	−	0.590957i	−0.0360871	−	0.0295479i
$401$	1.03107	+	8.11463i	0.0514892	+	0.405225i	0.996857	+	0.0792200i	$0.0252430\pi$
$401$	1.03107	+	8.11463i	0.0514892	+	0.405225i	−0.945368	+	0.326005i	$0.894297\pi$
$402$	4.29118	−	1.47179i	0.214025	−	0.0734061i
$403$	3.51300	−	14.6911i	0.174995	−	0.731817i
$404$	−0.0393010	−	0.239725i	−0.00195530	−	0.0119268i
$405$	18.7315	−	6.01135i	0.930774	−	0.298706i
$406$	−7.87313	+	19.7601i	−0.390737	+	0.980675i
$407$	−3.11076	−	0.924504i	−0.154194	−	0.0458259i
$408$	7.96255	+	7.46115i	0.394205	+	0.369382i
$409$	−1.59758	+	1.74873i	−0.0789952	+	0.0864690i	−0.776524	−	0.630088i	$-0.783019\pi$
$409$	−1.59758	+	1.74873i	−0.0789952	+	0.0864690i	0.697528	+	0.716557i	$0.254283\pi$
$410$	8.42919	+	23.6000i	0.416288	+	1.16552i
$411$	2.74774	+	8.50897i	0.135536	+	0.419716i
$412$	−0.269596	−	0.466953i	−0.0132820	−	0.0230051i
$413$	−19.9463	+	13.2496i	−0.981495	+	0.651970i
$414$	−34.8090	−	7.26777i	−1.71077	−	0.357192i
$415$	23.6716	+	2.57444i	1.16199	+	0.126374i
$416$	1.16585	+	0.212813i	0.0571605	+	0.0104340i
$417$	20.5873	−	18.3358i	1.00816	−	0.897910i
$418$	39.8055	−	16.6989i	1.94695	−	0.816768i
$419$	0.314877	+	1.31679i	0.0153827	+	0.0643295i	0.979740	−	0.200275i	$-0.0641837\pi$
$419$	0.314877	+	1.31679i	0.0153827	+	0.0643295i	−0.964357	+	0.264605i	$0.914758\pi$
$420$	−0.662752	−	1.04517i	−0.0323390	−	0.0509990i
$421$	−2.62426	−	13.0392i	−0.127898	−	0.635490i	−0.991370	−	0.131092i	$-0.958152\pi$
$421$	−2.62426	−	13.0392i	−0.127898	−	0.635490i	0.863472	−	0.504397i	$-0.168285\pi$
$422$	−2.73718	−	16.6960i	−0.133244	−	0.812751i
$423$	15.5213	−	32.9223i	0.754672	−	1.60074i
$424$	−28.6703	+	13.2643i	−1.39235	+	0.644171i
$425$	0.469424	+	0.196929i	0.0227704	+	0.00955246i
$426$	0.504722	−	0.133287i	0.0244539	−	0.00645779i
$427$	11.5604	+	18.4511i	0.559448	+	0.892910i
$428$	0.0284121	−	0.0896413i	0.00137335	−	0.00433298i
$429$	−12.0749	−	7.17646i	−0.582981	−	0.346483i
$430$	−11.9688	+	15.1683i	−0.577189	+	0.731481i
$431$	1.30159	+	24.0064i	0.0626954	+	1.15635i	0.845463	+	0.534034i	$0.179325\pi$
$431$	1.30159	+	24.0064i	0.0626954	+	1.15635i	−0.782767	+	0.622314i	$0.786193\pi$
$432$	15.0323	−	15.8120i	0.723244	−	0.760753i
$433$	22.8956	+	26.9548i	1.10029	+	1.29537i	0.951891	+	0.306438i	$0.0991373\pi$
$433$	22.8956	+	26.9548i	1.10029	+	1.29537i	0.148403	+	0.988927i	$0.452587\pi$
$434$	−18.1367	+	28.9473i	−0.870591	+	1.38951i
$435$	17.3678	−	3.92164i	0.832721	−	0.188028i
$436$	−0.311033	−	0.202787i	−0.0148958	−	0.00971172i
$437$	−1.08233	−	59.9394i	−0.0517749	−	2.86729i
$438$	−14.1990	+	11.7550i	−0.678452	+	0.561675i
$439$	23.0838	−	5.96248i	1.10173	−	0.284573i	0.345199	−	0.938530i	$-0.387811\pi$
$439$	23.0838	−	5.96248i	1.10173	−	0.284573i	0.756533	+	0.653956i	$0.226892\pi$
$440$	−20.8811	−	12.5637i	−0.995466	−	0.598952i
$441$	−1.98269	−	7.91169i	−0.0944136	−	0.376747i
$442$	−6.60967	+	0.718845i	−0.314390	+	0.0341919i
$443$	4.23374	+	5.78321i	0.201151	+	0.274769i	0.895683	−	0.444693i	$-0.146687\pi$
$443$	4.23374	+	5.78321i	0.201151	+	0.274769i	−0.694532	+	0.719462i	$0.744388\pi$
$444$	0.0496311	+	0.136617i	0.00235539	+	0.00648356i
$445$	−33.6667	+	18.6353i	−1.59596	+	0.883397i
$446$	19.3369	+	19.6892i	0.915628	+	0.932311i
$447$	−9.32749	−	3.46505i	−0.441175	−	0.163891i
$448$	20.5595	+	11.3801i	0.971343	+	0.537660i
$449$	0.796937	−	14.6986i	0.0376098	−	0.693672i	−0.917557	−	0.397604i	$-0.869842\pi$
$449$	0.796937	−	14.6986i	0.0376098	−	0.693672i	0.955167	−	0.296068i	$-0.0956754\pi$
$450$	0.380504	−	0.888954i	0.0179371	−	0.0419057i
$451$	−15.0092	−	28.3103i	−0.706754	−	1.33308i
$452$	−0.582070	+	1.62968i	−0.0273783	+	0.0766535i
$453$	17.4455	−	28.1821i	0.819663	−	1.32411i
$454$	−17.7419	−	8.99962i	−0.832667	−	0.422373i
$455$	−13.4868	−	1.96170i	−0.632269	−	0.0919661i
$456$	30.0391	+	17.8531i	1.40671	+	0.836048i
$457$	−19.7017	−	21.5657i	−0.921606	−	1.00880i	−0.999930	−	0.0118713i	$-0.996221\pi$
$457$	−19.7017	−	21.5657i	−0.921606	−	1.00880i	0.0783238	−	0.996928i	$-0.475043\pi$
$458$	5.13898	−	9.69314i	0.240129	−	0.452931i
$459$	−5.40534	+	10.6084i	−0.252300	+	0.495158i
$460$	1.49073	−	1.13322i	0.0695054	−	0.0528367i
$461$	−18.3879	−	12.9580i	−0.856409	−	0.603513i	0.0624721	−	0.998047i	$-0.480102\pi$
$461$	−18.3879	−	12.9580i	−0.856409	−	0.603513i	−0.918881	+	0.394534i	$0.870906\pi$
$462$	20.6952	+	24.0986i	0.962828	+	1.12117i
$463$	−19.6957	−	7.43833i	−0.915338	−	0.345689i	−0.149530	−	0.988757i	$-0.547776\pi$
$463$	−19.6957	−	7.43833i	−0.915338	−	0.345689i	−0.765809	+	0.643069i	$0.777661\pi$
$464$	14.8165	−	13.0530i	0.687840	−	0.605972i
$465$	28.5692	−	1.18701i	1.32487	−	0.0550462i
$466$	25.9214	+	7.70372i	1.20078	+	0.356868i
$467$	18.2783	+	13.8948i	0.845817	+	0.642974i	0.935629	−	0.352985i	$-0.114833\pi$
$467$	18.2783	+	13.8948i	0.845817	+	0.642974i	−0.0898115	+	0.995959i	$0.528626\pi$
$468$	0.0635004	+	0.625927i	0.00293531	+	0.0289335i
$469$	−3.64355	+	4.28952i	−0.168243	+	0.198071i
$470$	15.5222	+	35.2050i	0.715985	+	1.62389i
$471$	−2.12950	+	2.94215i	−0.0981222	+	0.135567i
$472$	20.9751	−	2.46329i	0.965459	−	0.113382i
$473$	12.3528	−	21.3957i	0.567982	−	0.983775i
$474$	9.48320	−	10.4940i	0.435578	−	0.482003i
$475$	1.60368	+	0.292735i	0.0735821	+	0.0134316i
$476$	0.731499	+	0.161015i	0.0335282	+	0.00738012i
$477$	−22.5973	−	26.0271i	−1.03466	−	1.19170i
$478$	0.172415	−	0.163320i	0.00788608	−	0.00747010i
$479$	1.02760	−	0.149469i	0.0469523	−	0.00682940i	−0.120423	−	0.992723i	$-0.538425\pi$
$479$	1.02760	−	0.149469i	0.0469523	−	0.00682940i	0.167375	+	0.985893i	$0.446471\pi$
$480$	0.214342	+	2.23312i	0.00978333	+	0.101928i
$481$	1.49744	+	0.565528i	0.0682775	+	0.0257858i
$482$	36.8361	−	10.9475i	1.67784	−	0.498647i
$483$	41.7294	−	14.3123i	1.89875	−	0.651233i
$484$	−0.526183	−	0.220740i	−0.0239174	−	0.0100336i
$485$	−5.57240	+	33.9902i	−0.253030	+	1.54341i
$486$	20.0761	+	10.4129i	0.910672	+	0.472339i
$487$	29.5800	−	6.51105i	1.34040	−	0.295044i	0.513836	−	0.857889i	$-0.328224\pi$
$487$	29.5800	−	6.51105i	1.34040	−	0.295044i	0.826563	+	0.562845i	$0.190293\pi$
$488$	−1.73124	−	19.1251i	−0.0783694	−	0.865753i
$489$	5.95479	+	21.0053i	0.269285	+	0.949894i
$490$	7.68918	+	3.90036i	0.347362	+	0.176200i
$491$	−9.30949	+	0.673507i	−0.420131	+	0.0303950i	−0.280605	−	0.959823i	$-0.590535\pi$
$491$	−9.30949	+	0.673507i	−0.420131	+	0.0303950i	−0.139526	+	0.990218i	$0.544558\pi$
$492$	−0.619039	+	1.29483i	−0.0279084	+	0.0583752i
$493$	−5.72137	+	9.13164i	−0.257678	+	0.411268i
$494$	−20.1768	+	6.79834i	−0.907795	+	0.305872i
$495$	6.83563	−	25.6959i	0.307239	−	1.15495i
$496$	27.1720	−	16.3489i	1.22006	−	0.734086i
$497$	−0.453789	+	0.462057i	−0.0203552	+	0.0207261i
$498$	17.0728	+	21.3974i	0.765052	+	0.958842i
$499$	12.4641	−	6.89918i	0.557972	−	0.308850i	−0.180016	−	0.983664i	$-0.557615\pi$
$499$	12.4641	−	6.89918i	0.557972	−	0.308850i	0.737988	+	0.674814i	$0.235776\pi$
$500$	0.522097	+	1.07703i	0.0233489	+	0.0481663i
$501$	−7.93834	+	13.9232i	−0.354659	+	0.622041i
$502$	−4.71233	−	6.43696i	−0.210322	−	0.287296i
$503$	−5.07242	+	7.48127i	−0.226168	+	0.333573i	−0.923794	−	0.382889i	$-0.874929\pi$
$503$	−5.07242	+	7.48127i	−0.226168	+	0.333573i	0.697626	+	0.716462i	$0.254240\pi$
$504$	−5.70922	+	25.0728i	−0.254309	+	1.11683i
$505$	1.35477	−	4.87944i	0.0602865	−	0.217132i
$506$	−33.6775	+	34.2912i	−1.49715	+	1.52443i
$507$	−12.7907	−	8.91038i	−0.568056	−	0.395724i
$508$	0.981993	+	0.640238i	0.0435689	+	0.0284060i
$509$	0.741863	−	3.68610i	0.0328825	−	0.163384i	−0.960492	−	0.278309i	$-0.910226\pi$
$509$	0.741863	−	3.68610i	0.0328825	−	0.163384i	0.993374	+	0.114925i	$0.0366629\pi$
$510$	−4.72167	−	11.6664i	−0.209079	−	0.516597i
$511$	7.69205	−	21.5361i	0.340276	−	0.952702i
$512$	−11.5609	−	17.0510i	−0.510924	−	0.753556i
$513$	−9.60217	+	36.8987i	−0.423946	+	1.62912i
$514$	4.81767	+	12.0914i	0.212498	+	0.533331i
$515$	−1.01332	−	11.1942i	−0.0446521	−	0.493275i
$516$	−1.09941	+	0.125594i	−0.0483987	+	0.00552898i
$517$	−26.1200	−	41.6890i	−1.14876	−	1.83348i
$518$	−2.80075	−	2.29323i	−0.123058	−	0.100759i
$519$	23.5334	+	12.8603i	1.03300	+	0.564504i
$520$	9.82535	+	6.92394i	0.430870	+	0.303635i
$521$	10.7187	+	10.1533i	0.469597	+	0.444826i	0.885539	−	0.464565i	$-0.153789\pi$
$521$	10.7187	+	10.1533i	0.469597	+	0.444826i	−0.415942	+	0.909391i	$0.636548\pi$
$522$	17.2667	+	10.9929i	0.755744	+	0.481147i
$523$	−29.7419	−	10.0212i	−1.30052	−	0.438198i	−0.417992	−	0.908451i	$-0.637266\pi$
$523$	−29.7419	−	10.0212i	−1.30052	−	0.438198i	−0.882532	+	0.470253i	$0.844163\pi$
$524$	−0.615030	+	0.0894585i	−0.0268677	+	0.00390801i
$525$	0.157653	+	1.18922i	0.00688056	+	0.0519018i
$526$	−16.3312	+	6.85113i	−0.712074	+	0.298723i
$527$	−11.6723	+	12.7766i	−0.508452	+	0.556557i
$528$	−7.01324	−	28.6424i	−0.305212	−	1.24650i
$529$	17.6502	+	40.0315i	0.767402	+	1.74050i
$530$	36.4353			1.58265
$531$	8.94293	+	21.2373i	0.388090	+	0.921621i
$532$	2.39859			0.103992
$533$	6.37622	+	14.4615i	0.276185	+	0.626399i
$534$	−42.4723	−	12.3727i	−1.83796	−	0.535419i
$535$	1.32217	−	1.44726i	0.0571623	−	0.0625705i
$536$	4.57727	−	1.92022i	0.197708	−	0.0829408i
$537$	−11.3635	+	8.73578i	−0.490370	+	0.376977i
$538$	26.3349	−	3.83051i	1.13538	−	0.165145i
$539$	−10.4472	−	3.52006i	−0.449991	−	0.151620i
$540$	−1.10715	+	0.438807i	−0.0476443	+	0.0188833i
$541$	−11.1055	−	10.5197i	−0.477464	−	0.452278i	0.410723	−	0.911760i	$-0.365276\pi$
$541$	−11.1055	−	10.5197i	−0.477464	−	0.452278i	−0.888187	+	0.459482i	$0.848035\pi$
$542$	7.70479	+	5.42958i	0.330949	+	0.233220i
$543$	17.6959	−	10.7782i	0.759403	−	0.462536i
$544$	−1.05052	−	0.860156i	−0.0450406	−	0.0368789i
$545$	−4.10954	−	6.55906i	−0.176033	−	0.280959i
$546$	−9.32338	−	12.5920i	−0.399004	−	0.538886i
$547$	−0.102740	−	1.13498i	−0.00439285	−	0.0485281i	0.993436	−	0.114390i	$-0.0364915\pi$
$547$	−0.102740	−	1.13498i	−0.00439285	−	0.0485281i	−0.997829	+	0.0658623i	$0.979020\pi$
$548$	−0.200361	−	0.502868i	−0.00855899	−	0.0214814i
$549$	19.5203	−	7.61460i	0.833105	−	0.324983i
$550$	−0.733453	−	1.08176i	−0.0312746	−	0.0461265i
$551$	−11.6072	+	32.4977i	−0.494483	+	1.38445i
$552$	−38.5326	−	5.39185i	−1.64006	−	0.229492i
$553$	−3.46212	+	17.2023i	−0.147224	+	0.731515i
$554$	2.28195	+	1.48778i	0.0969506	+	0.0632096i
$555$	−0.256823	+	3.01912i	−0.0109015	+	0.128155i
$556$	−1.16944	+	1.19075i	−0.0495954	+	0.0504991i
$557$	9.77902	−	35.2209i	0.414350	−	1.49236i	−0.402454	−	0.915440i	$-0.631843\pi$
$557$	9.77902	−	35.2209i	0.414350	−	1.49236i	0.816804	−	0.576915i	$-0.195744\pi$
$558$	24.1085	+	22.3465i	1.02059	+	0.946002i
$559$	−6.83850	+	10.0860i	−0.289238	+	0.426594i
$560$	−16.9008	−	23.0862i	−0.714189	−	0.975569i
$561$	8.12161	+	13.8928i	0.342895	+	0.586554i
$562$	1.22493	+	2.52690i	0.0516705	+	0.106591i
$563$	−20.7525	+	11.4870i	−0.874612	+	0.484118i	−0.856755	−	0.515723i	$-0.827523\pi$
$563$	−20.7525	+	11.4870i	−0.874612	+	0.484118i	−0.0178570	+	0.999841i	$0.505684\pi$
$564$	−0.804492	+	2.05135i	−0.0338752	+	0.0863776i
$565$	−25.2769	+	25.7375i	−1.06341	+	1.08278i
$566$	−0.145180	+	0.0873520i	−0.00610238	+	0.00367168i
$567$	−28.0107	+	1.61991i	−1.17634	+	0.0680300i
$568$	0.541281	−	0.182379i	0.0227116	−	0.00765244i
$569$	−4.55303	+	7.26690i	−0.190873	+	0.304644i	−0.929044	−	0.369970i	$-0.879368\pi$
$569$	−4.55303	+	7.26690i	−0.190873	+	0.304644i	0.738171	+	0.674614i	$0.235690\pi$
$570$	−22.7982	−	33.2360i	−0.954912	−	1.39210i
$571$	−1.98727	+	0.143772i	−0.0831648	+	0.00601667i	−0.113677	−	0.993518i	$-0.536263\pi$
$571$	−1.98727	+	0.143772i	−0.0831648	+	0.00601667i	0.0305126	+	0.999534i	$0.490286\pi$
$572$	0.758369	+	0.384685i	0.0317090	+	0.0160845i
$573$	−5.41540	+	5.57412i	−0.226232	+	0.232862i
$574$	−3.22221	−	35.5961i	−0.134493	−	1.48575i
$575$	−1.77268	+	0.390196i	−0.0739257	+	0.0162723i
$576$	14.4520	−	17.3925i	0.602168	−	0.724686i
$577$	−2.17630	+	13.2748i	−0.0906004	+	0.552638i	0.902051	+	0.431629i	$0.142061\pi$
$577$	−2.17630	+	13.2748i	−0.0906004	+	0.552638i	−0.992651	+	0.121009i	$0.961387\pi$
$578$	−15.7195	−	6.59452i	−0.653845	−	0.274296i
$579$	−1.64709	+	8.41934i	−0.0684508	+	0.349896i
$580$	−1.03323	+	0.307070i	−0.0429024	+	0.0127504i
$581$	−31.7701	−	11.9984i	−1.31805	−	0.497776i
$582$	−32.2440	+	22.9847i	−1.33656	+	0.952745i
$583$	−46.1026	+	6.70580i	−1.90937	+	0.277726i
$584$	−14.6427	+	13.8703i	−0.605919	+	0.573957i
$585$	−4.27735	+	12.3979i	−0.176847	+	0.512591i
$586$	9.69372	+	2.13375i	0.400444	+	0.0881443i
$587$	23.5484	+	4.29851i	0.971948	+	0.177419i	0.642105	−	0.766617i	$-0.278061\pi$
$587$	23.5484	+	4.29851i	0.971948	+	0.177419i	0.329844	+	0.944036i	$0.393004\pi$
$588$	0.151735	+	0.469881i	0.00625745	+	0.0193776i
$589$	−27.7093	+	47.9938i	−1.14174	+	1.97755i
$590$	−23.1493	−	7.57959i	−0.953044	−	0.312047i
$591$	−23.2523	−	2.40152i	−0.956470	−	0.0987855i
$592$	1.35569	+	3.07476i	0.0557185	+	0.126372i
$593$	8.74161	−	10.2914i	0.358975	−	0.422618i	−0.552796	−	0.833316i	$-0.686439\pi$
$593$	8.74161	−	10.2914i	0.358975	−	0.422618i	0.911771	+	0.410698i	$0.134715\pi$
$594$	26.5004	−	15.2360i	1.08732	−	0.625143i
$595$	12.4301	+	9.44911i	0.509584	+	0.387376i
$596$	0.577417	+	0.171606i	0.0236519	+	0.00702925i
$597$	−3.56810	+	6.81911i	−0.146033	+	0.279088i
$598$	17.7882	−	15.6710i	0.727415	−	0.640836i
$599$	7.98620	+	3.01609i	0.326307	+	0.123234i	0.511045	−	0.859554i	$-0.329259\pi$
$599$	7.98620	+	3.01609i	0.326307	+	0.123234i	−0.184738	+	0.982788i	$0.559144\pi$
$600$	0.350473	−	0.998283i	0.0143080	−	0.0407547i
$601$	−29.7547	−	20.9682i	−1.21372	−	0.855311i	−0.220944	−	0.975287i	$-0.570914\pi$
$601$	−29.7547	−	20.9682i	−1.21372	−	0.855311i	−0.992777	+	0.119976i	$0.961718\pi$
$602$	21.9382	−	16.6770i	0.894135	−	0.679704i
$603$	3.40076	+	4.21516i	0.138490	+	0.171655i
$604$	−0.939880	+	1.77280i	−0.0382432	+	0.0721343i
$605$	−8.02288	−	8.78193i	−0.326177	−	0.357036i
$606$	5.07816	−	2.84690i	0.206286	−	0.115648i
$607$	9.89564	+	1.43936i	0.401652	+	0.0584218i	0.341770	−	0.939784i	$-0.388974\pi$
$607$	9.89564	+	1.43936i	0.401652	+	0.0584218i	0.0598817	+	0.998205i	$0.480928\pi$
$608$	−3.87762	−	1.96694i	−0.157258	−	0.0797698i
$609$	−25.3821	−	0.779372i	−1.02854	−	0.0315818i
$610$	−7.44992	+	20.8582i	−0.301639	+	0.844525i
$611$	11.3661	+	21.4387i	0.459822	+	0.867316i
$612$	0.283630	−	0.662631i	0.0114651	−	0.0267853i
$613$	−1.12613	+	20.7702i	−0.0454839	+	0.838902i	0.883420	+	0.468582i	$0.155235\pi$
$613$	−1.12613	+	20.7702i	−0.0454839	+	0.838902i	−0.928904	+	0.370320i	$0.879248\pi$
$614$	−25.3724	−	14.0442i	−1.02395	−	0.566778i
$615$	−23.0454	+	19.0787i	−0.929280	+	0.769329i
$616$	24.3536	+	24.7973i	0.981235	+	0.999113i
$617$	−3.18955	+	1.76549i	−0.128406	+	0.0710758i	−0.547181	−	0.837015i	$-0.684299\pi$
$617$	−3.18955	+	1.76549i	−0.128406	+	0.0710758i	0.418774	+	0.908090i	$0.362460\pi$
$618$	8.31192	−	9.89362i	0.334355	−	0.397980i
$619$	−19.1348	−	26.1377i	−0.769091	−	1.05056i	−0.997039	−	0.0768913i	$-0.975501\pi$
$619$	−19.1348	−	26.1377i	−0.769091	−	1.05056i	0.227948	−	0.973673i	$-0.426798\pi$
$620$	−1.72089	+	0.187158i	−0.0691125	+	0.00751643i
$621$	−6.03450	−	42.0218i	−0.242156	−	1.68628i
$622$	30.2810	+	18.2195i	1.21416	+	0.730534i
$623$	53.1377	−	13.7253i	2.12892	−	0.549892i
$624$	2.43078	+	14.3403i	0.0973090	+	0.574072i
$625$	0.430407	+	23.8359i	0.0172163	+	0.953437i
$626$	40.5280	+	26.4233i	1.61982	+	1.05609i
$627$	34.9641	+	37.8584i	1.39633	+	1.51192i
$628$	0.116739	−	0.186322i	0.00465840	−	0.00743507i
$629$	−1.18720	−	1.39768i	−0.0473366	−	0.0557290i
$630$	18.1189	−	23.4809i	0.721874	−	0.935500i
$631$	−0.533898	−	9.84717i	−0.0212541	−	0.392009i	−0.989734	−	0.142919i	$-0.954351\pi$
$631$	−0.533898	−	9.84717i	−0.0212541	−	0.392009i	0.968480	−	0.249090i	$-0.0801316\pi$
$632$	9.58651	−	12.1491i	0.381331	−	0.483267i
$633$	17.6188	−	9.87740i	0.700284	−	0.392591i
$634$	8.55585	−	26.9940i	0.339796	−	1.07207i
$635$	12.9746	+	20.7082i	0.514882	+	0.821781i
$636$	1.47014	+	1.48081i	0.0582950	+	0.0587178i
$637$	5.01424	+	2.10353i	0.198671	+	0.0833449i
$638$	25.1093	−	11.6168i	0.994088	−	0.459914i
$639$	0.355308	+	0.512014i	0.0140558	+	0.0202550i
$640$	4.28630	+	26.1453i	0.169431	+	1.03348i
$641$	−9.00371	−	44.7368i	−0.355625	−	1.76700i	−0.602667	−	0.797993i	$-0.705895\pi$
$641$	−9.00371	−	44.7368i	−0.355625	−	1.76700i	0.247041	−	0.969005i	$-0.420542\pi$
$642$	2.25164	−	0.0935524i	0.0888652	−	0.00369222i
$643$	8.57373	+	35.8547i	0.338115	+	1.41397i	0.836952	+	0.547276i	$0.184335\pi$
$643$	8.57373	+	35.8547i	0.338115	+	1.41397i	−0.498837	+	0.866696i	$0.666240\pi$
$644$	−2.46276	+	1.03316i	−0.0970464	+	0.0407121i
$645$	−21.8993	−	7.24695i	−0.862286	−	0.285349i
$646$	23.9961	+	4.38023i	0.944114	+	0.172338i
$647$	−19.5288	−	2.12388i	−0.767755	−	0.0834983i	−0.284144	−	0.958782i	$-0.591709\pi$
$647$	−19.5288	−	2.12388i	−0.767755	−	0.0834983i	−0.483611	+	0.875283i	$0.660675\pi$
$648$	22.6781	+	9.90157i	0.890881	+	0.388970i
$649$	30.6865	+	5.33009i	1.20455	+	0.209224i
$650$	0.322324	+	0.558281i	0.0126426	+	0.0218976i
$651$	−39.8750	−	8.55105i	−1.56282	−	0.335142i
$652$	−0.444580	−	1.24473i	−0.0174111	−	0.0487475i
$653$	3.72064	−	4.07265i	0.145600	−	0.159375i	−0.661180	−	0.750227i	$-0.729944\pi$
$653$	3.72064	−	4.07265i	0.145600	−	0.159375i	0.806780	+	0.590852i	$0.201208\pi$
$654$	2.02255	−	8.66533i	0.0790881	−	0.338841i
$655$	−12.4190	−	3.69086i	−0.485249	−	0.144214i
$656$	−12.2811	+	30.8232i	−0.479496	+	1.20345i
$657$	−18.9783	−	11.1408i	−0.740416	−	0.434643i
$658$	−8.87769	−	54.1515i	−0.346088	−	2.11104i
$659$	−0.871387	+	3.64408i	−0.0339444	+	0.141953i	−0.986959	−	0.160971i	$-0.948538\pi$
$659$	−0.871387	+	3.64408i	−0.0339444	+	0.141953i	0.953015	+	0.302924i	$0.0979628\pi$
$660$	−0.309050	+	1.57975i	−0.0120298	+	0.0614918i
$661$	1.79493	+	14.1263i	0.0698146	+	0.549448i	0.988132	+	0.153604i	$0.0490881\pi$
$661$	1.79493	+	14.1263i	0.0698146	+	0.549448i	−0.918318	+	0.395844i	$0.870452\pi$
$662$	14.5610	+	11.9225i	0.565931	+	0.463380i
$663$	−3.50100	−	7.12366i	−0.135967	−	0.276660i
$664$	20.2017	+	22.1130i	0.783978	+	0.858150i
$665$	45.3797	+	20.9949i	1.75975	+	0.814148i
$666$	−2.67114	+	2.23586i	−0.103504	+	0.0866377i
$667$	−2.08018	−	38.3667i	−0.0805449	−	1.48556i
$668$	0.423236	−	0.873090i	0.0163755	−	0.0337809i
$669$	−14.2107	+	29.7240i	−0.549416	+	1.14920i
$670$	−5.72135	−	0.206689i	−0.221035	−	0.00798511i
$671$	5.58769	−	27.7636i	0.215710	−	1.07180i
$672$	0.500533	−	3.16020i	0.0193085	−	0.121907i
$673$	−15.0160	−	8.31167i	−0.578823	−	0.320391i	0.167609	−	0.985854i	$-0.446395\pi$
$673$	−15.0160	−	8.31167i	−0.578823	−	0.320391i	−0.746432	+	0.665462i	$0.768234\pi$
$674$	−5.94513	−	21.4124i	−0.228998	−	0.824776i
$675$	1.15260	+	0.0645872i	0.0443637	+	0.00248596i
$676$	0.808615	+	0.486527i	0.0311006	+	0.0187126i
$677$	6.78674	+	0.490996i	0.260836	+	0.0188705i	0.201956	−	0.979395i	$-0.435270\pi$
$677$	6.78674	+	0.490996i	0.260836	+	0.0188705i	0.0588796	+	0.998265i	$0.481247\pi$
$678$	−41.4711	+	0.224541i	−1.59269	+	0.00862346i
$679$	19.8188	−	44.9498i	0.760574	−	1.72502i
$680$	−6.00689	−	12.3916i	−0.230354	−	0.475195i
$681$	2.86611	−	23.5767i	0.109830	−	0.903462i
$682$	43.0188	−	11.1116i	1.64728	−	0.425486i
$683$	−11.8163	−	42.5586i	−0.452139	−	1.62846i	−0.741298	−	0.671176i	$-0.765789\pi$
$683$	−11.8163	−	42.5586i	−0.452139	−	1.62846i	0.289159	−	0.957281i	$-0.406625\pi$
$684$	0.430885	−	2.26762i	0.0164753	−	0.0867046i
$685$	0.610915	−	11.2677i	0.0233419	−	0.430515i
$686$	14.5294	+	12.8001i	0.554736	+	0.488710i
$687$	12.9715	+	1.81510i	0.494894	+	0.0692502i
$688$	−25.1663	+	4.59384i	−0.959456	+	0.175138i
$689$	22.9190	−	1.65810i	0.873143	−	0.0631687i
$690$	37.7240	+	24.3052i	1.43613	+	0.925281i
$691$	14.6212	−	18.5297i	0.556218	−	0.704904i	−0.423362	−	0.905961i	$-0.639150\pi$
$691$	14.6212	−	18.5297i	0.556218	−	0.704904i	0.979580	+	0.201056i	$0.0644374\pi$
$692$	−1.47347	−	0.681701i	−0.0560130	−	0.0259144i
$693$	−18.6047	+	33.0457i	−0.706736	+	1.25530i
$694$	−10.8177	+	20.4043i	−0.410633	+	0.774536i
$695$	−32.5477	+	12.2920i	−1.23460	+	0.466263i
$696$	19.6534	+	10.7400i	0.744960	+	0.407099i
$697$	1.63240	−	18.0332i	0.0618315	−	0.683058i
$698$	16.0172	−	4.76025i	0.606261	−	0.180178i
$699$	1.92233	+	32.2267i	0.0727093	+	1.21893i
$700$	−0.0143289	−	0.0711960i	−0.000541580	−	0.00269095i
$701$	−6.27402	+	15.7466i	−0.236966	+	0.594741i	−0.998579	−	0.0532918i	$-0.983029\pi$
$701$	−6.27402	+	15.7466i	−0.236966	+	0.594741i	0.761613	+	0.648033i	$0.224408\pi$
$702$	−13.5792	+	6.55225i	−0.512515	+	0.247299i
$703$	−4.67511	−	3.55393i	−0.176325	−	0.134039i
$704$	−9.23476	−	29.1360i	−0.348048	−	1.09810i
$705$	−33.1759	+	31.7685i	−1.24948	+	1.19647i
$706$	18.8807	−	25.7907i	0.710586	−	0.970647i
$707$	−3.61124	+	6.25485i	−0.135815	+	0.235238i
$708$	−0.626012	−	1.24667i	−0.0235270	−	0.0468527i
$709$	1.73275	+	3.00121i	0.0650748	+	0.112713i	0.896727	−	0.442584i	$-0.145938\pi$
$709$	1.73275	+	3.00121i	0.0650748	+	0.112713i	−0.831652	+	0.555297i	$0.812605\pi$
$710$	−0.654927	−	0.0712276i	−0.0245790	−	0.00267312i
$711$	15.6410	+	6.36330i	0.586583	+	0.238642i
$712$	−47.2716	−	10.4053i	−1.77158	−	0.389954i
$713$	7.77793	−	61.2131i	0.291286	−	2.29245i
$714$	2.35898	+	17.7944i	0.0882827	+	0.665939i
$715$	10.9807	+	13.9160i	0.410654	+	0.520428i
$716$	0.651090	−	0.573596i	0.0243324	−	0.0214363i
$717$	0.253545	+	0.126890i	0.00946881	+	0.00473880i
$718$	−6.32135	+	26.4354i	−0.235911	+	0.986562i
$719$	−12.9843	+	6.00717i	−0.484232	+	0.224030i	−0.646788	−	0.762670i	$-0.723888\pi$
$719$	−12.9843	+	6.00717i	−0.484232	+	0.224030i	0.162556	+	0.986699i	$0.448026\pi$
$720$	−24.8616	+	11.8307i	−0.926538	+	0.440905i
$721$	−2.59350	+	15.8196i	−0.0965869	+	0.589154i
$722$	50.5153	−	1.82491i	1.87999	−	0.0679163i
$723$	27.3002	+	36.8710i	1.01530	+	1.37125i
$724$	−1.02534	+	0.722556i	−0.0381063	+	0.0268536i
$725$	1.03395	+	0.150392i	0.0383999	+	0.00558541i
$726$	0.666391	−	13.6584i	0.0247321	−	0.506912i
$727$	0.576024	−	1.18828i	0.0213635	−	0.0440707i	−0.888895	−	0.458111i	$-0.848526\pi$
$727$	0.576024	−	1.18828i	0.0213635	−	0.0440707i	0.910259	+	0.414040i	$0.135883\pi$
$728$	−11.0983	−	13.0659i	−0.411329	−	0.484254i
$729$	−3.50039	+	26.7721i	−0.129644	+	0.991561i
$730$	22.0450	−	7.42782i	0.815921	−	0.274916i
$731$	12.4506	−	6.31559i	0.460500	−	0.233590i
$732$	−1.14832	+	0.538837i	−0.0424432	+	0.0199160i
$733$	8.94515	+	2.31050i	0.330397	+	0.0853404i	0.411620	−	0.911356i	$-0.364963\pi$
$733$	8.94515	+	2.31050i	0.330397	+	0.0853404i	−0.0812232	+	0.996696i	$0.525883\pi$
$734$	−9.69728	−	9.87397i	−0.357933	−	0.364455i
$735$	−1.24215	+	10.2180i	−0.0458173	+	0.376895i
$736$	4.82858	+	0.349330i	0.177984	+	0.0128765i
$737$	7.27741	−	0.791466i	0.268067	−	0.0291540i
$738$	−34.2312	−	3.34823i	−1.26007	−	0.123250i
$739$	−0.101800	+	0.150144i	−0.00374478	+	0.00552313i	−0.829557	−	0.558422i	$-0.811407\pi$
$739$	−0.101800	+	0.150144i	−0.00374478	+	0.00552313i	0.825812	+	0.563946i	$0.190717\pi$
$740$	0.00331174	−	0.183404i	0.000121742	−	0.00674205i
$741$	−15.8533	−	19.8690i	−0.582386	−	0.729906i
$742$	−50.3140	−	12.9959i	−1.84708	−	0.477095i
$743$	−0.307886	−	17.0507i	−0.0112953	−	0.625530i	−0.955307	−	0.295617i	$-0.904475\pi$
$743$	−0.307886	−	17.0507i	−0.0112953	−	0.625530i	0.944011	−	0.329913i	$-0.107019\pi$
$744$	27.9520	+	22.6352i	1.02477	+	0.829846i
$745$	9.42227	+	8.30080i	0.345205	+	0.304118i
$746$	8.41577	+	15.8738i	0.308123	+	0.581182i
$747$	−17.0504	+	27.8799i	−0.623841	+	1.02007i
$748$	−0.546720	−	0.806351i	−0.0199901	−	0.0294831i
$749$	−2.34201	+	1.52694i	−0.0855753	+	0.0557932i
$750$	−19.9875	+	20.5734i	−0.729842	+	0.751233i
$751$	−28.0365	+	19.7574i	−1.02307	+	0.720956i	−0.960839	−	0.277106i	$-0.910625\pi$
$751$	−28.0365	+	19.7574i	−1.02307	+	0.720956i	−0.0622263	+	0.998062i	$0.519820\pi$
$752$	−15.3914	+	48.5604i	−0.561266	+	1.77081i
$753$	5.30195	−	7.91168i	0.193214	−	0.288318i
$754$	−12.7661	+	4.82127i	−0.464913	+	0.175580i
$755$	−33.2992	+	25.3134i	−1.21188	+	0.921249i
$756$	1.68540	−	0.211049i	0.0612973	−	0.00767579i
$757$	22.9403	+	21.7302i	0.833778	+	0.789797i	0.979904	−	0.199469i	$-0.0639218\pi$
$757$	22.9403	+	21.7302i	0.833778	+	0.789797i	−0.146126	+	0.989266i	$0.546680\pi$
$758$	−25.7973	+	21.1226i	−0.937001	+	0.767209i
$759$	−52.2064	−	23.8110i	−1.89497	−	0.864283i
$760$	−27.3169	−	34.6192i	−0.990889	−	1.25577i
$761$	−9.47677	−	39.6312i	−0.343533	−	1.43663i	−0.827462	−	0.561521i	$-0.810216\pi$
$761$	−9.47677	−	39.6312i	−0.343533	−	1.43663i	0.483930	−	0.875107i	$-0.339209\pi$
$762$	−6.38561	+	27.3582i	−0.231326	+	0.991082i
$763$	3.33539	+	10.5233i	0.120749	+	0.380968i
$764$	0.304583	−	0.358582i	0.0110194	−	0.0129731i
$765$	11.1661	−	10.0539i	0.403711	−	0.363499i
$766$	18.8494			0.681058
$767$	−14.9066	−	3.71432i	−0.538246	−	0.134116i
$768$	−2.54876	+	3.52141i	−0.0919705	+	0.127068i
$769$	−11.4424	+	15.6301i	−0.412624	+	0.563636i	−0.962386	−	0.271684i	$-0.912419\pi$
$769$	−11.4424	+	15.6301i	−0.412624	+	0.563636i	0.549763	+	0.835321i	$0.314718\pi$
$770$	−13.4837	−	37.7517i	−0.485920	−	1.36048i
$771$	−11.6039	+	10.3349i	−0.417904	+	0.372202i
$772$	0.0654648	−	0.515215i	0.00235613	−	0.0185430i
$773$	27.7206	−	26.2583i	0.997040	−	0.944447i	−0.00141540	−	0.999999i	$-0.500451\pi$
$773$	27.7206	−	26.2583i	0.997040	−	0.944447i	0.998456	+	0.0555522i	$0.0176919\pi$
$774$	−11.8254	−	23.7361i	−0.425054	−	0.853178i
$775$	1.59010	+	0.535768i	0.0571181	+	0.0192453i
$776$	−33.5226	+	27.4480i	−1.20339	+	0.985327i
$777$	1.43152	−	4.07753i	0.0513557	−	0.146281i
$778$	3.87008	−	42.7531i	0.138749	−	1.53277i
$779$	−7.30898	−	57.5224i	−0.261871	−	2.06095i
$780$	0.208263	−	0.766165i	0.00745702	−	0.0274331i
$781$	0.841805	−	0.0304110i	0.0301222	−	0.00108819i
$782$	−26.5247	+	5.83854i	−0.948523	+	0.208786i
$783$	−5.29647	+	23.8561i	−0.189281	+	0.852549i
$784$	4.22527	+	10.6046i	0.150902	+	0.378737i
$785$	3.83950	−	2.50327i	0.137038	−	0.0893456i
$786$	−7.04778	−	13.1214i	−0.251386	−	0.468023i
$787$	41.9081	−	7.64986i	1.49386	−	0.272688i	0.630070	−	0.776538i	$-0.283026\pi$
$787$	41.9081	−	7.64986i	1.49386	−	0.272688i	0.863791	+	0.503850i	$0.168084\pi$
$788$	1.41422	+	0.0510902i	0.0503797	+	0.00182001i
$789$	−14.3449	−	15.5324i	−0.510693	−	0.552967i
$790$	−15.9187	+	8.07482i	−0.566363	+	0.287289i
$791$	44.0853	−	26.5253i	1.56749	−	0.943130i
$792$	27.8182	−	18.5692i	0.988475	−	0.659827i
$793$	−3.73702	+	13.4595i	−0.132705	+	0.477962i
$794$	0.0778644	−	4.31212i	0.00276330	−	0.153031i
$795$	14.8526	+	40.8840i	0.526767	+	1.45001i
$796$	0.187968	−	0.426319i	0.00666234	−	0.0151105i
$797$	−5.03662	+	11.4233i	−0.178406	+	0.404633i	−0.981564	−	0.191133i	$-0.938784\pi$
$797$	−5.03662	+	11.4233i	−0.178406	+	0.404633i	0.803158	+	0.595766i	$0.203152\pi$
$798$	19.6275	+	54.0277i	0.694807	+	1.91256i
$799$	0.501901	−	27.7953i	0.0177560	−	0.983325i
$800$	−0.0352189	+	0.126847i	−0.00124518	+	0.00448472i
$801$	−3.43013	−	52.7017i	−0.121198	−	1.86212i
$802$	10.1687	−	6.11832i	0.359070	−	0.216045i
$803$	−26.5270	+	13.4559i	−0.936118	+	0.474849i
$804$	−0.222453	−	0.240867i	−0.00784531	−	0.00849473i
$805$	−55.6370	−	2.00994i	−1.96095	−	0.0708410i
$806$	−21.5587	+	3.93531i	−0.759374	+	0.138616i
$807$	15.0334	+	27.9888i	0.529202	+	0.985253i
$808$	5.33599	−	3.47895i	0.187719	−	0.122389i
$809$	−6.25730	−	15.7046i	−0.219995	−	0.552145i	0.777010	−	0.629489i	$-0.216736\pi$
$809$	−6.25730	−	15.7046i	−0.219995	−	0.552145i	−0.997005	+	0.0773432i	$0.975356\pi$
$810$	−18.9438	−	21.3476i	−0.665617	−	0.750079i
$811$	−34.6492	+	7.62687i	−1.21670	+	0.267815i	−0.776519	−	0.630094i	$-0.783016\pi$
$811$	−34.6492	+	7.62687i	−1.21670	+	0.267815i	−0.440179	+	0.897910i	$0.645085\pi$
$812$	1.53632	−	0.0555011i	0.0539143	−	0.00194771i
$813$	−2.95171	+	10.8589i	−0.103521	+	0.380837i
$814$	0.593470	+	4.67066i	0.0208011	+	0.163707i
$815$	2.48399	−	27.4409i	0.0870105	−	0.961212i
$816$	5.51986	−	15.7227i	0.193234	−	0.550405i
$817$	34.5912	−	28.3230i	1.21019	−	0.990896i
$818$	3.25652	+	1.09725i	0.113862	+	0.0383644i
$819$	10.3288	−	15.5948i	0.360917	−	0.544925i
$820$	1.31492	−	1.24556i	0.0459190	−	0.0434968i
$821$	−6.98598	+	54.9804i	−0.243812	+	1.91883i	0.130356	+	0.991467i	$0.458388\pi$
$821$	−6.98598	+	54.9804i	−0.243812	+	1.91883i	−0.374168	+	0.927361i	$0.622072\pi$
$822$	9.68743	−	8.62801i	0.337888	−	0.300936i
$823$	−17.0088	−	47.6212i	−0.592891	−	1.65997i	−0.741402	−	0.671061i	$-0.765839\pi$
$823$	−17.0088	−	47.6212i	−0.592891	−	1.65997i	0.148511	−	0.988911i	$-0.452552\pi$
$824$	8.35165	−	11.4082i	0.290943	−	0.397423i
$825$	0.914857	−	1.26398i	0.0318512	−	0.0440061i
$826$	29.2637	+	18.7238i	1.01821	+	0.651483i
$827$	−32.4870			−1.12968			−0.564842	−	0.825199i	$-0.691063\pi$
$827$	−32.4870			−1.12968			−0.564842	+	0.825199i	$0.691063\pi$
$828$	0.534330	+	2.51388i	0.0185693	+	0.0873633i
$829$	20.9769	−	24.6959i	0.728559	−	0.857726i	−0.265774	−	0.964035i	$-0.585628\pi$
$829$	20.9769	−	24.6959i	0.728559	−	0.857726i	0.994333	+	0.106310i	$0.0339034\pi$
$830$	−10.4376	−	32.9310i	−0.362294	−	1.14305i
$831$	−0.739213	+	3.16705i	−0.0256430	+	0.109864i
$832$	3.50609	+	14.6622i	0.121552	+	0.508321i
$833$	−3.85894	−	4.89050i	−0.133704	−	0.169446i
$834$	−36.3908	−	16.5976i	−1.26011	−	0.574727i
$835$	15.6495	−	12.8137i	0.541573	−	0.443435i
$836$	−2.26496	−	2.14548i	−0.0783352	−	0.0742031i
$837$	−15.2473	+	36.1615i	−0.527023	+	1.24992i
$838$	1.56375	−	1.18873i	0.0540188	−	0.0410640i
$839$	25.4052	−	9.59459i	0.877085	−	0.331242i	0.126461	−	0.991972i	$-0.459638\pi$
$839$	25.4052	−	9.59459i	0.877085	−	0.331242i	0.750624	+	0.660730i	$0.229753\pi$
$840$	18.0657	−	26.9580i	0.623326	−	0.930139i
$841$	2.07954	−	6.56101i	0.0717081	−	0.226242i
$842$	−15.7735	+	11.1156i	−0.543592	+	0.383070i
$843$	−2.33609	+	2.40456i	−0.0804593	+	0.0828175i
$844$	−1.02432	+	0.667834i	−0.0352586	+	0.0229878i
$845$	11.0399	+	16.2826i	0.379782	+	0.560137i
$846$	−52.7893	−	1.33488i	−1.81493	−	0.0458941i
$847$	7.94651	+	14.9887i	0.273045	+	0.515018i
$848$	36.1973	+	31.8890i	1.24302	+	1.09507i
$849$	−0.157199	−	0.127298i	−0.00539506	−	0.00436885i
$850$	−0.0133339	−	0.738428i	−0.000457347	−	0.0253279i
$851$	6.33098	+	1.63527i	0.217023	+	0.0560563i
$852$	−0.0235311	−	0.0294916i	−0.000806162	−	0.00101036i
$853$	−0.258091	+	14.2931i	−0.00883688	+	0.489386i	0.965014	+	0.262198i	$0.0844474\pi$
$853$	−0.258091	+	14.2931i	−0.00883688	+	0.489386i	−0.973851	+	0.227188i	$0.927047\pi$
$854$	17.7275	−	26.1461i	0.606622	−	0.894701i
$855$	28.0005	−	39.1302i	0.957598	−	1.33823i
$856$	2.45133	−	0.266598i	0.0837848	−	0.00911215i
$857$	−19.3586	−	1.40053i	−0.661278	−	0.0478411i	−0.262561	−	0.964915i	$-0.584567\pi$
$857$	−19.3586	−	1.40053i	−0.661278	−	0.0478411i	−0.398717	+	0.917074i	$0.630544\pi$
$858$	−2.45925	+	20.2299i	−0.0839575	+	0.690638i
$859$	11.1098	+	11.3123i	0.379063	+	0.385970i	0.876397	−	0.481590i	$-0.159940\pi$
$859$	11.1098	+	11.3123i	0.379063	+	0.385970i	−0.497334	+	0.867559i	$0.665688\pi$
$860$	1.35209	+	0.349239i	0.0461057	+	0.0119090i
$861$	38.6287	−	18.1261i	1.31646	−	0.617736i
$862$	31.1068	−	15.7790i	1.05950	−	0.537436i
$863$	9.57309	−	3.22555i	0.325872	−	0.109799i	−0.151611	−	0.988440i	$-0.548446\pi$
$863$	9.57309	−	3.22555i	0.325872	−	0.109799i	0.477482	+	0.878641i	$0.341549\pi$
$864$	−2.89772	−	1.04090i	−0.0985823	−	0.0354122i
$865$	−21.9101	−	25.7946i	−0.744967	−	0.877043i
$866$	22.3816	−	46.1709i	0.760559	−	1.56895i
$867$	0.991750	−	20.3270i	0.0336816	−	0.690342i
$868$	2.44315	+	0.355366i	0.0829258	+	0.0120619i
$869$	18.6562	−	13.1471i	0.632869	−	0.445984i
$870$	−15.3715	−	20.7604i	−0.521143	−	0.703844i
$871$	−3.60832	+	0.130354i	−0.122263	+	0.00441687i
$872$	1.57513	−	9.60786i	0.0533406	−	0.325363i
$873$	−38.9351	−	26.8114i	−1.31775	−	0.907427i
$874$	−78.9364	+	36.5199i	−2.67006	+	1.23530i
$875$	8.27601	−	34.6097i	0.279780	−	1.17002i
$876$	1.19138	+	0.596245i	0.0402531	+	0.0201452i
$877$	16.8032	−	14.8033i	0.567405	−	0.499871i	−0.328268	−	0.944585i	$-0.606465\pi$
$877$	16.8032	−	14.8033i	0.567405	−	0.499871i	0.895673	+	0.444714i	$0.146695\pi$
$878$	−21.4264	−	27.1540i	−0.723106	−	0.916404i
$879$	1.55730	+	11.7471i	0.0525264	+	0.396220i
$880$	−4.69082	+	36.9173i	−0.158128	+	1.24448i
$881$	49.5545	+	10.9078i	1.66953	+	0.367492i	0.946345	−	0.323157i	$-0.104744\pi$
$881$	49.5545	+	10.9078i	1.66953	+	0.367492i	0.723190	+	0.690650i	$0.242675\pi$
$882$	−9.34232	+	7.26280i	−0.314572	+	0.244551i
$883$	−44.2152	−	4.80869i	−1.48796	−	0.161825i	−0.672266	−	0.740310i	$-0.734679\pi$
$883$	−44.2152	−	4.80869i	−1.48796	−	0.161825i	−0.815693	+	0.578485i	$0.803644\pi$
$884$	0.240262	+	0.416146i	0.00808088	+	0.0139965i
$885$	−0.931624	−	29.0656i	−0.0313162	−	0.977029i
$886$	5.19920	−	9.00528i	0.174670	−	0.302538i
$887$	5.40089	−	7.37751i	0.181344	−	0.247713i	−0.706655	−	0.707559i	$-0.749797\pi$
$887$	5.40089	−	7.37751i	0.181344	−	0.247713i	0.887999	+	0.459846i	$0.152095\pi$
$888$	−2.75283	+	2.63604i	−0.0923788	+	0.0884597i
$889$	−10.5305	−	33.2241i	−0.353182	−	1.11430i
$890$	44.4439	+	33.7853i	1.48976	+	1.13249i
$891$	27.8990	+	23.5252i	0.934653	+	0.788123i
$892$	0.738250	−	1.85287i	0.0247184	−	0.0620386i
$893$	−17.5649	−	87.2747i	−0.587786	−	2.92054i
$894$	0.859587	+	14.4104i	0.0287489	+	0.481957i
$895$	17.3389	−	5.15304i	0.579574	−	0.172247i
$896$	3.40662	−	37.6332i	0.113807	−	1.25724i
$897$	24.8357	+	13.5720i	0.829239	+	0.453154i
$898$	−19.9790	+	7.54530i	−0.666707	+	0.251790i
$899$	−16.6375	+	31.3816i	−0.554892	+	1.04664i
$900$	−0.0698823		0.000756765i	−0.00232941		2.52255e-5i
$901$	−23.8928	−	11.0540i	−0.795986	−	0.368262i
$902$	−28.7971	+	36.4950i	−0.958838	+	1.21515i
$903$	27.6562	+	17.8186i	0.920340	+	0.592964i
$904$	−45.2584	+	3.27428i	−1.50527	+	0.108901i
$905$	−25.7232	+	4.69549i	−0.855067	+	0.156083i
$906$	−47.6229	−	6.66384i	−1.58216	−	0.221391i
$907$	26.9052	+	23.7029i	0.893373	+	0.787041i	0.977833	−	0.209386i	$-0.0671464\pi$
$907$	26.9052	+	23.7029i	0.893373	+	0.787041i	−0.0844600	+	0.996427i	$0.526917\pi$
$908$	−0.0778415	+	1.43570i	−0.00258326	+	0.0476454i
$909$	5.26458	+	4.53767i	0.174615	+	0.150505i
$910$	5.28975	+	19.0520i	0.175353	+	0.631566i
$911$	−13.1412	+	3.39433i	−0.435387	+	0.112459i	−0.461379	−	0.887203i	$-0.652645\pi$
$911$	−13.1412	+	3.39433i	−0.435387	+	0.112459i	0.0259918	+	0.999662i	$0.491726\pi$
$912$	6.43960	−	52.9724i	0.213236	−	1.75409i
$913$	19.2678	+	39.7474i	0.637671	+	1.31545i
$914$	−17.0970	+	38.7767i	−0.565517	+	1.28262i
$915$	−26.4419	+	0.143167i	−0.874142	+	0.00473296i
$916$	−0.790861	−	0.0572159i	−0.0261308	−	0.00189047i
$917$	15.8330	+	9.52641i	0.522852	+	0.314590i
$918$	17.2465	+	0.966425i	0.569220	+	0.0318968i
$919$	9.37801	+	33.7765i	0.309352	+	1.11419i	0.940854	+	0.338811i	$0.110025\pi$
$919$	9.37801	+	33.7765i	0.309352	+	1.11419i	−0.631502	+	0.775374i	$0.717561\pi$
$920$	42.9594	+	23.7790i	1.41633	+	0.783970i
$921$	5.41609	−	34.1954i	0.178466	−	1.12678i
$922$	−6.43919	+	31.9944i	−0.212063	+	1.05368i
$923$	−0.415211	−	0.0149999i	−0.0136668	−	0.000493728i
$924$	0.990244	−	2.07126i	0.0325766	−	0.0681396i
$925$	−0.0775605	+	0.159999i	−0.00255017	+	0.00526073i
$926$	1.65366	+	30.4999i	0.0543425	+	1.00229i
$927$	14.4899	+	5.29373i	0.475911	+	0.173869i
$928$	−2.52916	−	1.17012i	−0.0830238	−	0.0384109i
$929$	21.3253	+	23.3429i	0.699661	+	0.765856i	0.981054	−	0.193736i	$-0.0620607\pi$
$929$	21.3253	+	23.3429i	0.699661	+	0.765856i	−0.281393	+	0.959593i	$0.590796\pi$
$930$	−18.2976	−	37.2310i	−0.600001	−	1.22085i
$931$	−15.4354	−	12.6384i	−0.505876	−	0.414207i
$932$	−0.246355	−	1.93884i	−0.00806962	−	0.0635087i
$933$	−8.10019	+	41.4053i	−0.265188	+	1.35555i
$934$	7.74696	−	32.3972i	0.253488	−	1.06007i
$935$	−3.28556	−	20.0410i	−0.107449	−	0.655412i
$936$	−14.3461	+	8.14509i	−0.468918	+	0.266231i
$937$	−8.88760	+	22.3062i	−0.290345	+	0.728712i	0.709370	+	0.704837i	$0.248980\pi$
$937$	−8.88760	+	22.3062i	−0.290345	+	0.728712i	−0.999715	+	0.0238750i	$0.992400\pi$
$938$	7.82695	+	2.32614i	0.255559	+	0.0759511i
$939$	−13.1286	+	56.2476i	−0.428436	+	1.83557i
$940$	1.87556	−	2.05300i	0.0611739	−	0.0669616i
$941$	1.06068	+	2.96967i	0.0345770	+	0.0968085i	0.957778	−	0.287510i	$-0.0928274\pi$
$941$	1.06068	+	2.96967i	0.0345770	+	0.0968085i	−0.923201	+	0.384318i	$0.874437\pi$
$942$	5.15213	+	1.10486i	0.167866	+	0.0359982i
$943$	32.2814	+	55.9130i	1.05123	+	1.82078i
$944$	−16.3643	−	27.7909i	−0.532613	−	0.904517i
$945$	33.7339	+	10.7594i	1.09736	+	0.350003i
$946$	−35.6331	−	3.87533i	−1.15853	−	0.125998i
$947$	−37.2794	−	6.80496i	−1.21142	−	0.221131i	−0.464213	−	0.885724i	$-0.653663\pi$
$947$	−37.2794	−	6.80496i	−1.21142	−	0.221131i	−0.747206	+	0.664592i	$0.768605\pi$
$948$	−0.970488	−	0.321155i	−0.0315200	−	0.0104306i
$949$	13.5290	−	5.67556i	0.439169	−	0.184236i
$950$	−0.550043	−	2.30024i	−0.0178458	−	0.0746296i
$951$	33.7776	−	1.40341i	1.09531	−	0.0455087i
$952$	3.87510	+	19.2542i	0.125593	+	0.624033i
$953$	2.03996	+	12.4432i	0.0660807	+	0.403074i	0.999068	+	0.0431650i	$0.0137441\pi$
$953$	2.03996	+	12.4432i	0.0660807	+	0.403074i	−0.932987	+	0.359909i	$0.882808\pi$
$954$	−21.3247	+	45.2320i	−0.690413	+	1.46444i
$955$	8.90117	−	4.11812i	0.288035	−	0.133259i
$956$	−0.0158278	−	0.00663996i	−0.000511909	−	0.000214752i
$957$	23.2708	+	23.4396i	0.752240	+	0.757695i
$958$	−0.799884	−	1.27666i	−0.0258431	−	0.0412470i
$959$	−4.86262	+	15.3417i	−0.157022	+	0.495410i
$960$	−24.8927	+	13.9553i	−0.803408	+	0.450405i
$961$	−16.1316	+	20.4439i	−0.520374	+	0.659479i
$962$	−0.125726	−	2.31887i	−0.00405355	−	0.0747634i
$963$	1.02284	+	2.48843i	0.0329606	+	0.0801884i
$964$	−1.79804	−	2.11681i	−0.0579109	−	0.0681779i
$965$	5.74822	−	9.17449i	0.185042	−	0.295337i
$966$	−43.4242	−	47.0188i	−1.39715	−	1.51281i
$967$	−25.2425	−	16.4575i	−0.811743	−	0.529238i	0.0718934	−	0.997412i	$-0.477096\pi$
$967$	−25.2425	−	16.4575i	−0.811743	−	0.529238i	−0.883636	+	0.468174i	$0.844912\pi$
$968$	−0.270132	−	14.9599i	−0.00868237	−	0.480829i
$969$	4.86679	+	28.7115i	0.156344	+	0.922347i
$970$	48.3837	−	12.4973i	1.55351	−	0.401265i
$971$	1.53879	+	0.925862i	0.0493823	+	0.0297123i	0.540031	−	0.841645i	$-0.318413\pi$
$971$	1.53879	+	0.925862i	0.0493823	+	0.0297123i	−0.490649	+	0.871358i	$0.663240\pi$
$972$	0.103241	−	1.63128i	0.00331145	−	0.0523233i
$973$	49.3298	−	5.36494i	1.58144	−	0.171992i
$974$	−25.9569	−	35.4566i	−0.831713	−	1.13610i
$975$	−0.495053	+	0.589258i	−0.0158544	+	0.0188714i
$976$	−25.6568	+	14.2016i	−0.821255	+	0.454583i
$977$	22.1328	+	22.5360i	0.708090	+	0.720992i	0.969732	−	0.244173i	$-0.0785166\pi$
$977$	22.1328	+	22.5360i	0.708090	+	0.720992i	−0.261641	+	0.965165i	$0.584264\pi$
$978$	24.3993	−	20.1996i	0.780204	−	0.645912i
$979$	−62.4540	−	34.5697i	−1.99604	−	1.10485i
$980$	0.0337359	−	0.622222i	0.00107765	−	0.0198761i
$981$	10.5478	−	1.26286i	0.336766	−	0.0403199i
$982$	6.34301	+	11.9642i	0.202414	+	0.381792i
$983$	5.53039	−	15.4840i	0.176392	−	0.493861i	−0.820588	−	0.571520i	$-0.806354\pi$
$983$	5.53039	−	15.4840i	0.176392	−	0.493861i	0.996980	+	0.0776591i	$0.0247446\pi$
$984$	−37.6155	−	1.15500i	−1.19914	−	0.0368202i
$985$	26.3090	+	13.3453i	0.838273	+	0.425217i
$986$	15.4711	+	2.25033i	0.492699	+	0.0716650i
$987$	57.1443	−	32.0361i	1.81892	−	1.01972i
$988$	1.03789	+	1.13609i	0.0330198	+	0.0361438i
$989$	−23.3169	+	43.9803i	−0.741433	+	1.39849i
$990$	−38.1124	+	5.96573i	−1.21129	+	0.189603i
$991$	44.2413	−	33.6313i	1.40537	−	1.06833i	0.418254	−	0.908330i	$-0.362642\pi$
$991$	44.2413	−	33.6313i	1.40537	−	1.06833i	0.987116	−	0.160005i	$-0.0511509\pi$
$992$	−3.65823	−	2.57796i	−0.116149	−	0.0818504i
$993$	−7.44247	+	21.1990i	−0.236180	+	0.672730i
$994$	0.878990	+	0.331961i	0.0278799	+	0.0105292i
$995$	7.28779	−	6.42037i	0.231038	−	0.203540i
$996$	0.917232	−	1.75295i	0.0290636	−	0.0555444i
$997$	36.9560	+	10.9832i	1.17041	+	0.347841i	0.810834	−	0.585276i	$-0.199014\pi$
$997$	36.9560	+	10.9832i	1.17041	+	0.347841i	0.359575	+	0.933116i	$0.382922\pi$
$998$	−16.4541	−	12.5081i	−0.520845	−	0.395936i
$999$	−3.59772	−	2.08585i	−0.113827	−	0.0659933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.m.a.4.16	✓	3248
9.7	even	3	inner	531.2.m.a.358.16	yes	3248
59.15	even	29	inner	531.2.m.a.310.16	yes	3248
531.133	even	87	inner	531.2.m.a.133.16	yes	3248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.2.m.a.4.16	✓	3248	1.1	even	1	trivial
531.2.m.a.133.16	yes	3248	531.133	even	87	inner
531.2.m.a.310.16	yes	3248	59.15	even	29	inner
531.2.m.a.358.16	yes	3248	9.7	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.m (of order \(87\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.585309 - 1.32751i) q^{2} +(1.25099 - 1.19792i) q^{3} +(-0.0707233 + 0.0774144i) q^{4} +(-2.01564 + 0.845586i) q^{5} +(-2.32246 - 0.959547i) q^{6} +(3.08503 - 0.448730i) q^{7} +(-2.60557 - 0.877919i) q^{8} +(0.129969 - 2.99718i) q^{9} +(2.30229 + 2.18085i) q^{10} +(-3.31453 - 2.33575i) q^{11} +(0.00426204 + 0.181566i) q^{12} +(1.54746 + 1.26705i) q^{13} +(-2.40139 - 3.83275i) q^{14} +(-1.50861 + 3.47240i) q^{15} +(0.378527 + 4.18162i) q^{16} +(-0.848111 - 2.12860i) q^{17} +(-4.05485 + 1.58174i) q^{18} +(-4.11780 - 6.07331i) q^{19} +(0.0770923 - 0.215842i) q^{20} +(3.32181 - 4.25698i) q^{21} +(-1.16070 + 5.76719i) q^{22} +(6.84394 + 4.46210i) q^{23} +(-4.31123 + 2.02300i) q^{24} +(-0.155671 + 0.158507i) q^{25} +(0.776272 - 2.79588i) q^{26} +(-3.42780 - 3.90515i) q^{27} +(-0.183445 + 0.270562i) q^{28} +(-2.77802 - 3.79472i) q^{29} +(5.49264 - 0.0297394i) q^{30} +(-3.29449 - 6.79619i) q^{31} +(0.518432 - 0.286964i) q^{32} +(-6.94450 + 1.04853i) q^{33} +(-2.32932 + 2.37176i) q^{34} +(-5.83888 + 3.51314i) q^{35} +(0.222833 + 0.222032i) q^{36} +(0.758437 - 0.255547i) q^{37} +(-5.65216 + 9.02116i) q^{38} +(3.45369 - 0.268667i) q^{39} +(5.99426 - 0.433663i) q^{40} +(7.04752 + 3.57488i) q^{41} +(-7.59545 - 1.91807i) q^{42} +(0.549289 + 6.06804i) q^{43} +(0.415235 - 0.0914002i) q^{44} +(2.27240 + 6.15115i) q^{45} +(1.91764 - 11.6971i) q^{46} +(11.1880 + 4.69348i) q^{47} +(5.48279 + 4.77773i) q^{48} +(2.60612 - 0.774528i) q^{49} +(0.301535 + 0.113878i) q^{50} +(-3.61088 - 1.64689i) q^{51} +(-0.207529 + 0.0301860i) q^{52} +(8.34123 - 7.90123i) q^{53} +(-3.17779 + 6.83614i) q^{54} +(8.65599 + 1.90533i) q^{55} +(-8.43222 - 1.53921i) q^{56} +(-12.4267 - 2.66486i) q^{57} +(-3.41152 + 5.90892i) q^{58} +(-6.94332 + 3.28487i) q^{59} +(-0.162120 - 0.362368i) q^{60} +(2.81771 + 6.39069i) q^{61} +(-7.09368 + 8.35133i) q^{62} +(-0.943967 - 9.30473i) q^{63} +(6.00075 + 4.56165i) q^{64} +(-4.19053 - 1.24541i) q^{65} +(5.45661 + 8.60515i) q^{66} +(-1.35462 + 1.19339i) q^{67} +(0.224765 + 0.0848854i) q^{68} +(13.9070 - 2.61645i) q^{69} +(8.08126 + 5.69488i) q^{70} +(-0.165380 + 0.125719i) q^{71} +(-2.96993 + 7.69527i) q^{72} +(3.43604 - 6.48106i) q^{73} +(-0.783160 - 0.857255i) q^{74} +(-0.00486409 + 0.384773i) q^{75} +(0.761386 + 0.110747i) q^{76} +(-11.2735 - 5.71854i) q^{77} +(-2.37813 - 4.42754i) q^{78} +(-1.89323 + 5.30066i) q^{79} +(-4.29889 - 8.10858i) q^{80} +(-8.96622 - 0.779084i) q^{81} +(0.620694 - 11.4480i) q^{82} +(-9.53080 - 5.27551i) q^{83} +(0.0946226 + 0.558224i) q^{84} +(3.50940 + 3.57334i) q^{85} +(7.73385 - 4.28086i) q^{86} +(-8.02106 - 1.41933i) q^{87} +(6.58563 + 8.99586i) q^{88} +(17.5012 - 1.90337i) q^{89} +(6.83563 - 6.61695i) q^{90} +(5.34253 + 3.21449i) q^{91} +(-0.829457 + 0.214246i) q^{92} +(-12.2627 - 4.55544i) q^{93} +(-0.317790 - 17.5992i) q^{94} +(13.4355 + 8.75966i) q^{95} +(0.304795 - 0.980031i) q^{96} +(8.36647 - 13.3534i) q^{97} +(-2.55357 - 3.00630i) q^{98} +(-7.43147 + 9.63067i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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