LMFDB - Embedded newform 153.2.s.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03701 - 1.35146i) q^{2} +(-0.776090 + 1.54845i) q^{3} +(-0.233410 + 0.871097i) q^{4} +(-0.974191 - 0.0638519i) q^{5} +(2.89747 - 0.556901i) q^{6} +(-0.213223 - 3.25316i) q^{7} +(-1.72831 + 0.715890i) q^{8} +(-1.79537 - 2.40347i) q^{9} +O(q^{10})$	\(q+(-1.03701 - 1.35146i) q^{2} +(-0.776090 + 1.54845i) q^{3} +(-0.233410 + 0.871097i) q^{4} +(-0.974191 - 0.0638519i) q^{5} +(2.89747 - 0.556901i) q^{6} +(-0.213223 - 3.25316i) q^{7} +(-1.72831 + 0.715890i) q^{8} +(-1.79537 - 2.40347i) q^{9} +(0.923953 + 1.38279i) q^{10} +(-2.56215 - 2.24695i) q^{11} +(-1.16770 - 1.03747i) q^{12} +(-1.81264 - 0.485696i) q^{13} +(-4.17539 + 3.66172i) q^{14} +(0.854931 - 1.45893i) q^{15} +(4.32178 + 2.49518i) q^{16} +(-3.35545 - 2.39603i) q^{17} +(-1.38637 + 4.91878i) q^{18} +(1.65080 + 0.683785i) q^{19} +(0.283007 - 0.833711i) q^{20} +(5.20282 + 2.19458i) q^{21} +(-0.379677 + 5.79275i) q^{22} +(1.00404 + 2.95780i) q^{23} +(0.232808 - 3.23179i) q^{24} +(-4.01225 - 0.528223i) q^{25} +(1.22333 + 2.95338i) q^{26} +(5.11500 - 0.914729i) q^{27} +(2.88358 + 0.573580i) q^{28} +(5.86551 - 2.89255i) q^{29} +(-2.85825 + 0.357520i) q^{30} +(0.750196 + 0.855435i) q^{31} +(-0.621243 - 4.71881i) q^{32} +(5.46774 - 2.22352i) q^{33} +(0.241494 + 7.01945i) q^{34} +3.18281i q^{35} +(2.51271 - 1.00295i) q^{36} +(-1.75772 - 8.83664i) q^{37} +(-0.787793 - 2.94008i) q^{38} +(2.15885 - 2.42984i) q^{39} +(1.72942 - 0.587058i) q^{40} +(2.13108 - 4.32140i) q^{41} +(-2.42950 - 9.30718i) q^{42} +(-1.45892 + 11.0816i) q^{43} +(2.55534 - 1.70742i) q^{44} +(1.59557 + 2.45607i) q^{45} +(2.95614 - 4.42418i) q^{46} +(3.51719 - 0.942428i) q^{47} +(-7.21774 + 4.75556i) q^{48} +(-3.59745 + 0.473613i) q^{49} +(3.44687 + 5.97016i) q^{50} +(6.31426 - 3.33619i) q^{51} +(0.846177 - 1.46562i) q^{52} +(-0.730606 + 1.76384i) q^{53} +(-6.54053 - 5.96413i) q^{54} +(2.35256 + 2.35256i) q^{55} +(2.69742 + 5.46983i) q^{56} +(-2.33998 + 2.02550i) q^{57} +(-9.99174 - 4.92738i) q^{58} +(5.03398 + 3.86271i) q^{59} +(1.07132 + 1.08526i) q^{60} +(6.66557 - 0.436884i) q^{61} +(0.378123 - 1.90095i) q^{62} +(-7.43604 + 6.35309i) q^{63} +(1.32440 - 1.32440i) q^{64} +(1.73485 + 0.588902i) q^{65} +(-8.67509 - 5.08360i) q^{66} +(-4.41090 + 2.54663i) q^{67} +(2.87037 - 2.36366i) q^{68} +(-5.35922 - 0.740820i) q^{69} +(4.30143 - 3.30061i) q^{70} +(-16.3403 + 3.25028i) q^{71} +(4.82358 + 2.86865i) q^{72} +(-13.5589 - 9.05977i) q^{73} +(-10.1196 + 11.5392i) q^{74} +(3.93179 - 5.80281i) q^{75} +(-0.980957 + 1.27841i) q^{76} +(-6.76336 + 8.81419i) q^{77} +(-5.52257 - 0.397827i) q^{78} +(-0.733584 + 0.836492i) q^{79} +(-4.05092 - 2.70674i) q^{80} +(-2.55329 + 8.63022i) q^{81} +(-8.05013 + 1.60127i) q^{82} +(6.72737 - 5.16209i) q^{83} +(-3.12608 + 4.01992i) q^{84} +(3.11586 + 2.54845i) q^{85} +(16.4893 - 9.52008i) q^{86} +(-0.0732047 + 11.3273i) q^{87} +(6.03677 + 2.04921i) q^{88} +(9.18621 - 9.18621i) q^{89} +(1.66466 - 4.70331i) q^{90} +(-1.19355 + 6.00038i) q^{91} +(-2.81088 + 0.184235i) q^{92} +(-1.90681 + 0.497744i) q^{93} +(-4.92101 - 3.77602i) q^{94} +(-1.56454 - 0.771545i) q^{95} +(7.78897 + 2.70026i) q^{96} +(-5.86063 - 11.8842i) q^{97} +(4.37066 + 4.37066i) q^{98} +(-0.800450 + 10.1921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.03701	−	1.35146i	−0.733277	−	0.955625i	0.266690	−	0.963782i	$-0.414070\pi$
$2$	−1.03701	−	1.35146i	−0.733277	−	0.955625i	−0.999967	+	0.00815771i	$0.997403\pi$
$3$	−0.776090	+	1.54845i	−0.448076	+	0.893996i
$3$	−0.776090	+	1.54845i	−0.448076	+	0.893996i
$4$	−0.233410	+	0.871097i	−0.116705	+	0.435548i
$5$	−0.974191	−	0.0638519i	−0.435672	−	0.0285554i	−0.154010	−	0.988069i	$-0.549219\pi$
$5$	−0.974191	−	0.0638519i	−0.435672	−	0.0285554i	−0.281661	+	0.959514i	$0.590886\pi$
$6$	2.89747	−	0.556901i	1.18289	−	0.227354i
$7$	−0.213223	−	3.25316i	−0.0805908	−	1.22958i	−0.826271	−	0.563273i	$-0.809542\pi$
$7$	−0.213223	−	3.25316i	−0.0805908	−	1.22958i	0.745680	−	0.666304i	$-0.232125\pi$
$8$	−1.72831	+	0.715890i	−0.611051	+	0.253105i
$9$	−1.79537	−	2.40347i	−0.598457	−	0.801155i
$10$	0.923953	+	1.38279i	0.292180	+	0.437278i
$11$	−2.56215	−	2.24695i	−0.772518	−	0.677480i	0.179419	−	0.983773i	$-0.442578\pi$
$11$	−2.56215	−	2.24695i	−0.772518	−	0.677480i	−0.951937	+	0.306292i	$0.900911\pi$
$12$	−1.16770	−	1.03747i	−0.337086	−	0.299492i
$13$	−1.81264	−	0.485696i	−0.502737	−	0.134708i	−0.00146700	−	0.999999i	$-0.500467\pi$
$13$	−1.81264	−	0.485696i	−0.502737	−	0.134708i	−0.501270	+	0.865291i	$0.667134\pi$
$14$	−4.17539	+	3.66172i	−1.11592	+	0.978635i
$15$	0.854931	−	1.45893i	0.220742	−	0.376694i
$16$	4.32178	+	2.49518i	1.08045	+	0.623795i
$17$	−3.35545	−	2.39603i	−0.813815	−	0.581123i
$17$	−3.35545	−	2.39603i	−0.813815	−	0.581123i
$18$	−1.38637	+	4.91878i	−0.326769	+	1.15937i
$19$	1.65080	+	0.683785i	0.378720	+	0.156871i	0.563919	−	0.825830i	$-0.309293\pi$
$19$	1.65080	+	0.683785i	0.378720	+	0.156871i	−0.185199	+	0.982701i	$0.559293\pi$
$20$	0.283007	−	0.833711i	0.0632823	−	0.186424i
$21$	5.20282	+	2.19458i	1.13535	+	0.478896i
$22$	−0.379677	+	5.79275i	−0.0809473	+	1.23502i
$23$	1.00404	+	2.95780i	0.209356	+	0.616744i	0.999990	+	0.00445471i	$0.00141798\pi$
$23$	1.00404	+	2.95780i	0.209356	+	0.616744i	−0.790634	+	0.612290i	$0.790249\pi$
$24$	0.232808	−	3.23179i	0.0475217	−	0.659687i
$25$	−4.01225	−	0.528223i	−0.802451	−	0.105645i
$26$	1.22333	+	2.95338i	0.239915	+	0.579206i
$27$	5.11500	−	0.914729i	0.984383	−	0.176040i
$28$	2.88358	+	0.573580i	0.544946	+	0.108396i
$29$	5.86551	−	2.89255i	1.08920	−	0.537133i	0.193185	−	0.981162i	$-0.438118\pi$
$29$	5.86551	−	2.89255i	1.08920	−	0.537133i	0.896012	+	0.444030i	$0.146451\pi$
$30$	−2.85825	+	0.357520i	−0.521843	+	0.0652739i
$31$	0.750196	+	0.855435i	0.134739	+	0.153641i	0.815274	−	0.579075i	$-0.196586\pi$
$31$	0.750196	+	0.855435i	0.134739	+	0.153641i	−0.680535	+	0.732715i	$0.738253\pi$
$32$	−0.621243	−	4.71881i	−0.109821	−	0.834176i
$33$	5.46774	−	2.22352i	0.951811	−	0.387066i
$34$	0.241494	+	7.01945i	0.0414159	+	1.20383i
$35$			3.18281i			0.537993i
$36$	2.51271	−	1.00295i	0.418785	−	0.167158i
$37$	−1.75772	−	8.83664i	−0.288967	−	1.45273i	−0.803521	−	0.595277i	$-0.797042\pi$
$37$	−1.75772	−	8.83664i	−0.288967	−	1.45273i	0.514554	−	0.857458i	$-0.327958\pi$
$38$	−0.787793	−	2.94008i	−0.127797	−	0.476944i
$39$	2.15885	−	2.42984i	0.345692	−	0.389085i
$40$	1.72942	−	0.587058i	0.273445	−	0.0928221i
$41$	2.13108	−	4.32140i	0.332818	−	0.674889i	−0.664561	−	0.747234i	$-0.731382\pi$
$41$	2.13108	−	4.32140i	0.332818	−	0.674889i	0.997380	+	0.0723450i	$0.0230483\pi$
$42$	−2.42950	−	9.30718i	−0.374879	−	1.43613i
$43$	−1.45892	+	11.0816i	−0.222484	+	1.68993i	0.407406	+	0.913247i	$0.366433\pi$
$43$	−1.45892	+	11.0816i	−0.222484	+	1.68993i	−0.629890	+	0.776685i	$0.716900\pi$
$44$	2.55534	−	1.70742i	0.385232	−	0.257404i
$45$	1.59557	+	2.45607i	0.237853	+	0.366130i
$46$	2.95614	−	4.42418i	0.435860	−	0.652310i
$47$	3.51719	−	0.942428i	0.513035	−	0.137467i	0.00699191	−	0.999976i	$-0.497774\pi$
$47$	3.51719	−	0.942428i	0.513035	−	0.137467i	0.506043	+	0.862508i	$0.331108\pi$
$48$	−7.21774	+	4.75556i	−1.04179	+	0.686406i
$49$	−3.59745	+	0.473613i	−0.513922	+	0.0676591i
$50$	3.44687	+	5.97016i	0.487462	+	0.844308i
$51$	6.31426	−	3.33619i	0.884173	−	0.467160i
$52$	0.846177	−	1.46562i	0.117344	−	0.203245i
$53$	−0.730606	+	1.76384i	−0.100356	+	0.242282i	−0.966081	−	0.258238i	$-0.916858\pi$
$53$	−0.730606	+	1.76384i	−0.100356	+	0.242282i	0.865725	+	0.500520i	$0.166858\pi$
$54$	−6.54053	−	5.96413i	−0.890053	−	0.811615i
$55$	2.35256	+	2.35256i	0.317218	+	0.317218i
$56$	2.69742	+	5.46983i	0.360458	+	0.730936i
$57$	−2.33998	+	2.02550i	−0.309937	+	0.268284i
$58$	−9.99174	−	4.92738i	−1.31198	−	0.646997i
$59$	5.03398	+	3.86271i	0.655368	+	0.502881i	0.882092	−	0.471078i	$-0.156135\pi$
$59$	5.03398	+	3.86271i	0.655368	+	0.502881i	−0.226724	+	0.973959i	$0.572801\pi$
$60$	1.07132	+	1.08526i	0.138307	+	0.140106i
$61$	6.66557	−	0.436884i	0.853438	−	0.0559373i	0.367598	−	0.929985i	$-0.380180\pi$
$61$	6.66557	−	0.436884i	0.853438	−	0.0559373i	0.485840	+	0.874048i	$0.338514\pi$
$62$	0.378123	−	1.90095i	0.0480217	−	0.241421i
$63$	−7.43604	+	6.35309i	−0.936852	+	0.800415i
$64$	1.32440	−	1.32440i	0.165550	−	0.165550i
$65$	1.73485	+	0.588902i	0.215182	+	0.0730443i
$66$	−8.67509	−	5.08360i	−1.06783	−	0.625748i
$67$	−4.41090	+	2.54663i	−0.538877	+	0.311121i	−0.744624	−	0.667485i	$-0.767371\pi$
$67$	−4.41090	+	2.54663i	−0.538877	+	0.311121i	0.205747	+	0.978605i	$0.434038\pi$
$68$	2.87037	−	2.36366i	0.348084	−	0.286636i
$69$	−5.35922	−	0.740820i	−0.645174	−	0.0891842i
$70$	4.30143	−	3.30061i	0.514120	−	0.394498i
$71$	−16.3403	+	3.25028i	−1.93923	+	0.385737i	−0.940257	+	0.340465i	$0.889415\pi$
$71$	−16.3403	+	3.25028i	−1.93923	+	0.385737i	−0.998975	+	0.0452718i	$0.985585\pi$
$72$	4.82358	+	2.86865i	0.568464	+	0.338074i
$73$	−13.5589	−	9.05977i	−1.58695	−	1.06037i	−0.959500	−	0.281709i	$-0.909099\pi$
$73$	−13.5589	−	9.05977i	−1.58695	−	1.06037i	−0.627450	−	0.778657i	$-0.715901\pi$
$74$	−10.1196	+	11.5392i	−1.17638	+	1.34140i
$75$	3.93179	−	5.80281i	0.454004	−	0.670051i
$76$	−0.980957	+	1.27841i	−0.112523	+	0.146643i
$77$	−6.76336	+	8.81419i	−0.770757	+	1.00447i
$78$	−5.52257	−	0.397827i	−0.625308	−	0.0450451i
$79$	−0.733584	+	0.836492i	−0.0825347	+	0.0941127i	−0.791633	−	0.610997i	$-0.790769\pi$
$79$	−0.733584	+	0.836492i	−0.0825347	+	0.0941127i	0.709098	+	0.705109i	$0.249102\pi$
$80$	−4.05092	−	2.70674i	−0.452906	−	0.302622i
$81$	−2.55329	+	8.63022i	−0.283699	+	0.958913i
$82$	−8.05013	+	1.60127i	−0.888988	+	0.176831i
$83$	6.72737	−	5.16209i	0.738425	−	0.566613i	−0.169608	−	0.985512i	$-0.554250\pi$
$83$	6.72737	−	5.16209i	0.738425	−	0.566613i	0.908033	+	0.418898i	$0.137584\pi$
$84$	−3.12608	+	4.01992i	−0.341083	+	0.438610i
$85$	3.11586	+	2.54845i	0.337962	+	0.276418i
$86$	16.4893	−	9.52008i	1.77808	−	1.02658i
$87$	−0.0732047	+	11.3273i	−0.00784836	+	1.21441i
$88$	6.03677	+	2.04921i	0.643522	+	0.218446i
$89$	9.18621	−	9.18621i	0.973736	−	0.973736i	−0.0259279	−	0.999664i	$-0.508254\pi$
$89$	9.18621	−	9.18621i	0.973736	−	0.973736i	0.999664	+	0.0259279i	$0.00825403\pi$
$90$	1.66466	−	4.70331i	0.175470	−	0.495773i
$91$	−1.19355	+	6.00038i	−0.125118	+	0.629010i
$92$	−2.81088	+	0.184235i	−0.293055	+	0.0192078i
$93$	−1.90681	+	0.497744i	−0.197727	+	0.0516137i
$94$	−4.92101	−	3.77602i	−0.507564	−	0.389467i
$95$	−1.56454	−	0.771545i	−0.160518	−	0.0791588i
$96$	7.78897	+	2.70026i	0.794958	+	0.275594i
$97$	−5.86063	−	11.8842i	−0.595057	−	1.20666i	−0.961137	−	0.276073i	$-0.910967\pi$
$97$	−5.86063	−	11.8842i	−0.595057	−	1.20666i	0.366079	−	0.930584i	$-0.380700\pi$
$98$	4.37066	+	4.37066i	0.441503	+	0.441503i
$99$	−0.800450	+	10.1921i	−0.0804482	+	1.02435i
$100$	1.39663	−	3.37177i	0.139663	−	0.337177i
$101$	2.84476	−	4.92726i	0.283064	−	0.490281i	−0.689074	−	0.724691i	$-0.741983\pi$
$101$	2.84476	−	4.92726i	0.283064	−	0.490281i	0.972138	+	0.234410i	$0.0753159\pi$
$102$	−11.0567	−	5.07378i	−1.09477	−	0.502379i
$103$	−1.85005	−	3.20438i	−0.182291	−	0.315737i	0.760369	−	0.649491i	$-0.225018\pi$
$103$	−1.85005	−	3.20438i	−0.182291	−	0.315737i	−0.942660	+	0.333754i	$0.891685\pi$
$104$	3.48052	−	0.458219i	0.341293	−	0.0449321i
$105$	−4.92841	−	2.47015i	−0.480964	−	0.241062i
$106$	3.14140	−	0.841735i	0.305120	−	0.0817565i
$107$	8.47713	−	12.6869i	0.819516	−	1.22649i	−0.151732	−	0.988422i	$-0.548485\pi$
$107$	8.47713	−	12.6869i	0.819516	−	1.22649i	0.971248	−	0.238070i	$-0.0765148\pi$
$108$	−0.397074	+	4.66917i	−0.0382085	+	0.449291i
$109$	3.45215	−	2.30665i	0.330656	−	0.220937i	−0.379149	−	0.925336i	$-0.623783\pi$
$109$	3.45215	−	2.30665i	0.330656	−	0.220937i	0.709805	+	0.704398i	$0.248783\pi$
$110$	0.739755	−	5.61900i	0.0705329	−	0.535751i
$111$	15.0472	+	4.13629i	1.42822	+	0.392600i
$112$	7.19571	−	14.5915i	0.679931	−	1.37876i
$113$	−10.9711	+	3.72418i	−1.03207	+	0.350341i	−0.785552	−	0.618796i	$-0.787621\pi$
$113$	−10.9711	+	3.72418i	−1.03207	+	0.350341i	−0.246521	+	0.969137i	$0.579287\pi$
$114$	5.16396	+	1.06191i	0.483649	+	0.0994573i
$115$	−0.789264	−	2.94557i	−0.0735993	−	0.274676i
$116$	1.15062	+	5.78457i	0.106833	+	0.537084i
$117$	2.08701	+	5.22863i	0.192944	+	0.483387i
$118$		−	10.8089i		−	0.995037i
$119$	−7.07921	+	11.4267i	−0.648950	+	1.04748i
$120$	−0.433155	+	3.13352i	−0.0395415	+	0.286050i
$121$	0.0800650	+	0.608154i	0.00727864	+	0.0552867i
$122$	−7.50269	−	8.55517i	−0.679261	−	0.774549i
$123$	5.03754	+	6.65365i	0.454220	+	0.599939i
$124$	−0.920270	+	0.453827i	−0.0826426	+	0.0407548i
$125$	8.66259	+	1.72310i	0.774805	+	0.154118i
$126$	16.2972	+	3.46126i	1.45187	+	0.308354i
$127$	1.80127	+	4.34866i	0.159837	+	0.385881i	0.983427	−	0.181305i	$-0.0580321\pi$
$127$	1.80127	+	4.34866i	0.159837	+	0.385881i	−0.823590	+	0.567186i	$0.808032\pi$
$128$	−12.6009	−	1.65894i	−1.11377	−	0.146631i
$129$	−16.0270	−	10.8594i	−1.41110	−	0.956117i
$130$	−1.00318	−	2.95527i	−0.0879847	−	0.259194i
$131$	0.839565	−	12.8093i	0.0733532	−	1.11915i	−0.789517	−	0.613728i	$-0.789669\pi$
$131$	0.839565	−	12.8093i	0.0733532	−	1.11915i	0.862871	−	0.505425i	$-0.168664\pi$
$132$	0.660681	+	5.28192i	0.0575049	+	0.459732i
$133$	1.87247	−	5.51612i	0.162364	−	0.478308i
$134$	8.01581	+	3.32026i	0.692460	+	0.286826i
$135$	−5.04140	+	0.564518i	−0.433895	+	0.0485860i
$136$	7.51456	+	1.73896i	0.644368	+	0.149115i
$137$	0.453041	+	0.261563i	0.0387059	+	0.0223469i	0.519228	−	0.854636i	$-0.326220\pi$
$137$	0.453041	+	0.261563i	0.0387059	+	0.0223469i	−0.480522	+	0.876983i	$0.659553\pi$
$138$	4.55638	+	8.01099i	0.387864	+	0.681941i
$139$	10.7202	−	9.40135i	0.909275	−	0.797412i	−0.0705010	−	0.997512i	$-0.522460\pi$
$139$	10.7202	−	9.40135i	0.909275	−	0.797412i	0.979776	+	0.200099i	$0.0641265\pi$
$140$	−2.77254	−	0.742899i	−0.234322	−	0.0627864i
$141$	−1.27036	+	6.17759i	−0.106983	+	0.520247i
$142$	21.3376	+	18.7126i	1.79061	+	1.57033i
$143$	3.55294	+	5.31734i	0.297111	+	0.444659i
$144$	−1.76211	−	14.8670i	−0.146843	−	1.23892i
$145$	−5.89882	+	2.44337i	−0.489870	+	0.202911i
$146$	1.81682	+	27.7194i	0.150361	+	2.29407i
$147$	2.05858	−	5.93802i	0.169789	−	0.489760i
$148$	8.10784	+	0.531416i	0.666460	+	0.0436821i
$149$	−2.25266	+	8.40704i	−0.184545	+	0.688731i	0.810183	+	0.586178i	$0.199368\pi$
$149$	−2.25266	+	8.40704i	−0.184545	+	0.688731i	−0.994727	+	0.102553i	$0.967299\pi$
$150$	−11.9196	+	0.703918i	−0.973227	+	0.0574747i
$151$	−6.37371	−	8.30638i	−0.518685	−	0.675964i	0.458416	−	0.888738i	$-0.348417\pi$
$151$	−6.37371	−	8.30638i	−0.518685	−	0.675964i	−0.977101	+	0.212774i	$0.931750\pi$
$152$	−3.34262			−0.271122
$153$	0.265485	+	12.3665i	0.0214632	+	0.999770i
$154$	18.9257			1.52507
$155$	−0.676213	−	0.881259i	−0.0543148	−	0.0707844i
$156$	1.61273	+	2.44771i	0.129122	+	0.195974i
$157$	−5.02535	+	18.7548i	−0.401066	+	1.49680i	0.410131	+	0.912027i	$0.365483\pi$
$157$	−5.02535	+	18.7548i	−0.401066	+	1.49680i	−0.811197	+	0.584773i	$0.801184\pi$
$158$	1.89122	+	0.123957i	0.150457	+	0.00986148i
$159$	−2.16419	−	2.50020i	−0.171632	−	0.198279i
$160$	0.303905	+	4.63669i	0.0240258	+	0.366563i
$161$	9.40811	−	3.89697i	0.741463	−	0.307124i
$162$	14.3112	−	5.49895i	1.12439	−	0.432039i
$163$	5.74447	+	8.59721i	0.449942	+	0.673385i	0.985221	−	0.171290i	$-0.0547936\pi$
$163$	5.74447	+	8.59721i	0.449942	+	0.673385i	−0.535279	+	0.844675i	$0.679794\pi$
$164$	3.26694	+	2.86503i	0.255105	+	0.223721i
$165$	−5.46860	+	1.81701i	−0.425730	+	0.141454i
$166$	−13.9527	−	3.73861i	−1.08294	−	0.290173i
$167$	1.99632	−	1.75073i	0.154480	−	0.135475i	−0.578617	−	0.815599i	$-0.696407\pi$
$167$	1.99632	−	1.75073i	0.154480	−	0.135475i	0.733097	+	0.680124i	$0.238074\pi$
$168$	−10.5632	−	0.0682664i	−0.814966	−	0.00526686i
$169$	−8.20855	−	4.73921i	−0.631427	−	0.364555i
$170$	0.212944	−	6.85371i	0.0163320	−	0.525656i
$171$	−1.32035	−	5.19530i	−0.100970	−	0.397294i
$172$	−9.31264	−	3.85742i	−0.710082	−	0.294126i
$173$	1.01426	−	2.98790i	0.0771125	−	0.227166i	−0.901537	−	0.432702i	$-0.857560\pi$
$173$	1.01426	−	2.98790i	0.0771125	−	0.227166i	0.978650	+	0.205536i	$0.0658937\pi$
$174$	15.3843	−	11.6476i	1.16628	−	0.883001i
$175$	−0.862887	+	13.1651i	−0.0652281	+	0.995189i
$176$	−5.46652	−	16.1038i	−0.412054	−	1.21387i
$177$	−9.88801	+	4.79703i	−0.743228	+	0.360567i
$178$	−21.9409	−	2.88858i	−1.64454	−	0.216508i
$179$	−0.762947	−	1.84192i	−0.0570253	−	0.137671i	0.892799	−	0.450455i	$-0.148738\pi$
$179$	−0.762947	−	1.84192i	−0.0570253	−	0.137671i	−0.949824	+	0.312784i	$0.898738\pi$
$180$	−2.51190	+	0.816623i	−0.187226	+	0.0608675i
$181$	−6.98647	−	1.38970i	−0.519300	−	0.103295i	−0.0715206	−	0.997439i	$-0.522785\pi$
$181$	−6.98647	−	1.38970i	−0.519300	−	0.103295i	−0.447780	+	0.894144i	$0.647785\pi$
$182$	9.34697	−	4.60942i	0.692844	−	0.341673i
$183$	−4.49658	+	10.6603i	−0.332397	+	0.788034i
$184$	−3.85275	−	4.39322i	−0.284029	−	0.323873i
$185$	1.14812	+	8.72081i	0.0844112	+	0.641167i
$186$	2.65006	+	2.06081i	0.194312	+	0.151106i
$187$	3.21341	+	13.6785i	0.234988	+	1.00027i
$188$			3.28378i			0.239495i
$189$	−4.06639	−	16.4449i	−0.295787	−	1.19619i
$190$	0.579731	+	2.91451i	0.0420581	+	0.211440i
$191$	−1.54148	−	5.75287i	−0.111537	−	0.416263i	0.887467	−	0.460871i	$-0.152463\pi$
$191$	−1.54148	−	5.75287i	−0.111537	−	0.416263i	−0.999005	+	0.0446078i	$0.985796\pi$
$192$	1.02291	+	3.07861i	0.0738221	+	0.222180i
$193$	23.4007	−	7.94348i	1.68442	−	0.571784i	0.695279	−	0.718740i	$-0.255281\pi$
$193$	23.4007	−	7.94348i	1.68442	−	0.571784i	0.989143	+	0.146955i	$0.0469473\pi$
$194$	−9.98344	+	20.2444i	−0.716769	+	1.45346i
$195$	−2.25828	+	2.22928i	−0.161719	+	0.159642i
$196$	0.427117	−	3.24427i	0.0305083	−	0.231734i
$197$	−11.5848	+	7.74071i	−0.825383	+	0.551503i	−0.894998	−	0.446071i	$-0.852823\pi$
$197$	−11.5848	+	7.74071i	−0.825383	+	0.551503i	0.0696150	+	0.997574i	$0.477823\pi$
$198$	14.6043	−	9.48758i	1.03788	−	0.674253i
$199$	−8.45329	+	12.6512i	−0.599237	+	0.896822i	−0.999811	−	0.0194424i	$-0.993811\pi$
$199$	−8.45329	+	12.6512i	−0.599237	+	0.896822i	0.400573	+	0.916265i	$0.368811\pi$
$200$	7.31258	−	1.95940i	0.517077	−	0.138550i
$201$	−0.520072	−	8.80645i	−0.0366830	−	0.621159i
$202$	−9.60902	+	1.26505i	−0.676088	+	0.0890087i
$203$	−10.6606	−	18.4647i	−0.748226	−	1.29596i
$204$	1.43234	+	6.27903i	0.100284	+	0.439620i
$205$	−2.35201	+	4.07379i	−0.164271	+	0.284526i
$206$	−2.41206	+	5.82324i	−0.168056	+	0.405724i
$207$	5.30635	−	7.72352i	0.368817	−	0.536822i
$208$	−6.62195	−	6.62195i	−0.459149	−	0.459149i
$209$	−2.69318	−	5.46123i	−0.186291	−	0.377761i
$210$	1.77251	+	9.22210i	0.122315	+	0.636386i
$211$	5.00328	+	2.46735i	0.344440	+	0.169859i	0.606278	−	0.795253i	$-0.292662\pi$
$211$	5.00328	+	2.46735i	0.344440	+	0.169859i	−0.261838	+	0.965112i	$0.584329\pi$
$212$	−1.36594	−	1.04813i	−0.0938134	−	0.0719856i
$213$	7.64862	−	27.8245i	0.524075	−	1.90650i
$214$	−25.9367	+	1.69998i	−1.77300	+	0.116208i
$215$	2.12885	−	10.7025i	0.145187	−	0.729902i
$216$	−8.18548	+	5.24272i	−0.556951	+	0.356722i
$217$	2.62290	−	2.62290i	0.178054	−	0.178054i
$218$	−6.69726	−	2.27341i	−0.453596	−	0.153975i
$219$	24.5515	−	13.9640i	1.65904	−	0.943602i
$220$	−2.59841	+	1.50019i	−0.175185	+	0.101143i
$221$	4.91849	+	5.97288i	0.330853	+	0.401780i
$222$	−10.0141	−	24.6250i	−0.672101	−	1.65272i
$223$	18.8667	−	14.4770i	1.26341	−	0.969449i	0.263422	−	0.964681i	$-0.415149\pi$
$223$	18.8667	−	14.4770i	1.26341	−	0.969449i	0.999989	−	0.00476845i	$-0.00151785\pi$
$224$	−15.2186	+	3.02716i	−1.01683	+	0.202261i
$225$	5.93391	+	10.5917i	0.395594	+	0.706111i
$226$	16.4102	+	10.9649i	1.09159	+	0.729377i
$227$	0.614467	−	0.700665i	0.0407836	−	0.0465048i	−0.731088	−	0.682283i	$-0.760987\pi$
$227$	0.614467	−	0.700665i	0.0407836	−	0.0465048i	0.771872	+	0.635778i	$0.219321\pi$
$228$	−1.21824	−	2.51112i	−0.0806796	−	0.166303i
$229$	−17.4453	+	22.7351i	−1.15282	+	1.50238i	−0.321216	+	0.947006i	$0.604091\pi$
$229$	−17.4453	+	22.7351i	−1.15282	+	1.50238i	−0.831601	+	0.555374i	$0.812575\pi$
$230$	−3.16234	+	4.12125i	−0.208519	+	0.271747i
$231$	−8.39932	−	17.3133i	−0.552634	−	1.13913i
$232$	−8.06668	+	9.19829i	−0.529604	+	0.603897i
$233$	12.9650	+	8.66292i	0.849364	+	0.567527i	0.902318	−	0.431070i	$-0.141864\pi$
$233$	12.9650	+	8.66292i	0.849364	+	0.567527i	−0.0529546	+	0.998597i	$0.516864\pi$
$234$	4.90202	−	8.24265i	0.320455	−	0.538839i
$235$	−3.48659	+	0.693526i	−0.227440	+	0.0452407i
$236$	−4.53977	+	3.48349i	−0.295514	+	0.226756i
$237$	−0.725936	−	1.78511i	−0.0471546	−	0.115955i
$238$	22.7839	−	2.28233i	1.47686	−	0.147941i
$239$	23.4527	−	13.5404i	1.51703	−	0.875856i	0.517227	−	0.855848i	$-0.326964\pi$
$239$	23.4527	−	13.5404i	1.51703	−	0.875856i	0.999800	−	0.0200072i	$-0.00636890\pi$
$240$	7.33511	−	4.17196i	0.473479	−	0.269299i
$241$	16.0987	+	5.46477i	1.03701	+	0.352017i	0.787473	−	0.616349i	$-0.211389\pi$
$241$	16.0987	+	5.46477i	1.03701	+	0.352017i	0.249534	+	0.968366i	$0.419722\pi$
$242$	0.738866	−	0.738866i	0.0474961	−	0.0474961i
$243$	−11.3818	−	10.6515i	−0.730146	−	0.683292i
$244$	−1.17524	+	5.90833i	−0.0752370	+	0.378242i
$245$	3.53485	−	0.231686i	0.225833	−	0.0148019i
$246$	3.76814	−	13.7079i	0.240248	−	0.873985i
$247$	−2.66021	−	2.04125i	−0.169265	−	0.129882i
$248$	−1.90897	−	0.941400i	−0.121220	−	0.0597790i
$249$	2.77218	+	14.4232i	0.175680	+	0.914034i
$250$	−6.65450	−	13.4940i	−0.420867	−	0.853434i
$251$	−8.24414	−	8.24414i	−0.520366	−	0.520366i	0.397316	−	0.917682i	$-0.369942\pi$
$251$	−8.24414	−	8.24414i	−0.520366	−	0.520366i	−0.917682	+	0.397316i	$0.869942\pi$
$252$	−3.79852	−	7.96038i	−0.239284	−	0.501457i
$253$	4.07353	−	9.83436i	0.256100	−	0.618281i
$254$	4.00909	−	6.94394i	0.251553	−	0.435702i
$255$	−6.36432	+	2.84691i	−0.398549	+	0.178281i
$256$	8.95229	+	15.5058i	0.559518	+	0.969114i
$257$	−6.56799	+	0.864692i	−0.409700	+	0.0539380i	−0.332560	−	0.943082i	$-0.607912\pi$
$257$	−6.56799	+	0.864692i	−0.409700	+	0.0539380i	−0.0771402	+	0.997020i	$0.524579\pi$
$258$	1.94418	+	32.9212i	0.121040	+	2.04958i
$259$	−28.3722	+	7.60231i	−1.76296	+	0.472384i
$260$	−0.917921	+	1.37377i	−0.0569271	+	0.0851974i
$261$	−17.4829	−	8.90435i	−1.08216	−	0.551166i
$262$	−18.1818	+	12.1487i	−1.12328	+	0.750551i
$263$	−2.19570	+	16.6780i	−0.135392	+	1.02841i	0.779982	+	0.625802i	$0.215228\pi$
$263$	−2.19570	+	16.6780i	−0.135392	+	1.02841i	−0.915374	+	0.402605i	$0.868105\pi$
$264$	−7.85816	+	7.75724i	−0.483636	+	0.477425i
$265$	0.824374	−	1.67167i	0.0506409	−	0.102690i
$266$	−9.39657	+	3.18971i	−0.576141	+	0.195573i
$267$	7.09503	+	21.3537i	0.434208	+	1.30682i
$268$	−1.18882	−	4.43673i	−0.0726186	−	0.271016i
$269$	2.87257	+	14.4414i	0.175144	+	0.880506i	0.963995	+	0.265922i	$0.0856763\pi$
$269$	2.87257	+	14.4414i	0.175144	+	0.880506i	−0.788851	+	0.614584i	$0.789324\pi$
$270$	5.99090	+	6.22783i	0.364595	+	0.379013i
$271$			29.5435i			1.79464i	0.441381	+	0.897320i	$0.354489\pi$
$271$			29.5435i			1.79464i	−0.441381	+	0.897320i	$0.645511\pi$
$272$	−8.52297	−	18.7276i	−0.516781	−	1.13553i
$273$	−8.36496	−	6.50498i	−0.506270	−	0.393699i
$274$	−0.116316	−	0.883509i	−0.00702692	−	0.0533747i
$275$	9.09311	+	10.3687i	0.548335	+	0.625257i
$276$	1.89622	−	4.49548i	0.114139	−	0.270596i
$277$	9.04225	−	4.45914i	0.543296	−	0.267924i	−0.149865	−	0.988706i	$-0.547884\pi$
$277$	9.04225	−	4.45914i	0.543296	−	0.267924i	0.693161	+	0.720782i	$0.256217\pi$
$278$	−23.8225	−	4.73858i	−1.42878	−	0.284201i
$279$	0.709128	−	3.33889i	0.0424544	−	0.199894i
$280$	−2.27854	−	5.50089i	−0.136169	−	0.328741i
$281$	−17.6648	−	2.32561i	−1.05379	−	0.138734i	−0.416328	−	0.909215i	$-0.636683\pi$
$281$	−17.6648	−	2.32561i	−1.05379	−	0.138734i	−0.637464	+	0.770480i	$0.720017\pi$
$282$	9.66612	−	4.68939i	0.575609	−	0.279249i
$283$	−1.95912	−	5.77138i	−0.116458	−	0.343073i	0.873035	−	0.487658i	$-0.162149\pi$
$283$	−1.95912	−	5.77138i	−0.116458	−	0.343073i	−0.989492	+	0.144585i	$0.953815\pi$
$284$	0.982666	−	14.9926i	0.0583105	−	0.889647i
$285$	2.40892	−	1.82381i	0.142692	−	0.108033i
$286$	3.50173	−	10.3158i	0.207062	−	0.609985i
$287$	−14.5126	−	6.01130i	−0.856650	−	0.354836i
$288$	−10.2261	+	9.96515i	−0.602581	+	0.587202i
$289$	5.51805	+	16.0795i	0.324591	+	0.945854i
$290$	9.41925	+	5.43820i	0.553117	+	0.319342i
$291$	22.9504	+	0.148321i	1.34538	+	0.00869473i
$292$	11.0567	−	9.69648i	0.647045	−	0.567444i
$293$	5.43750	+	1.45697i	0.317662	+	0.0851173i	0.414127	−	0.910219i	$-0.364087\pi$
$293$	5.43750	+	1.45697i	0.317662	+	0.0851173i	−0.0964649	+	0.995336i	$0.530754\pi$
$294$	−10.1598	+	3.37571i	−0.592529	+	0.196875i
$295$	−4.65741	−	4.08444i	−0.271165	−	0.237805i
$296$	9.36395	+	14.0141i	0.544269	+	0.814556i
$297$	−15.1608	−	9.14947i	−0.879717	−	0.530906i
$298$	13.6978	−	5.67381i	0.793491	−	0.328675i
$299$	−0.383370	−	5.84910i	−0.0221709	−	0.338262i
$300$	4.13709	+	4.77940i	0.238855	+	0.275939i
$301$	36.3613	+	2.38325i	2.09583	+	0.137368i
$302$	−4.61612	+	17.2276i	−0.265628	+	0.991337i
$303$	5.42181	+	8.22895i	0.311475	+	0.472741i
$304$	5.42824	+	7.07422i	0.311331	+	0.405735i
$305$	−6.52143			−0.373416
$306$	16.4374	−	13.1829i	0.939666	−	0.753618i
$307$	4.09589			0.233765			0.116882	−	0.993146i	$-0.462710\pi$
$307$	4.09589			0.233765			0.116882	+	0.993146i	$0.462710\pi$
$308$	−6.09938	−	7.94886i	−0.347544	−	0.452928i
$309$	6.39762	−	0.377816i	0.363948	−	0.0214932i
$310$	−0.489743	+	1.82775i	−0.0278156	+	0.103809i
$311$	−18.8207	−	1.23357i	−1.06722	−	0.0699496i	−0.478346	−	0.878171i	$-0.658764\pi$
$311$	−18.8207	−	1.23357i	−1.06722	−	0.0699496i	−0.588878	+	0.808222i	$0.700430\pi$
$312$	−1.99167	+	5.74502i	−0.112756	+	0.325248i
$313$	−1.35419	−	20.6610i	−0.0765434	−	1.16783i	−0.847449	−	0.530877i	$-0.821863\pi$
$313$	−1.35419	−	20.6610i	−0.0765434	−	1.16783i	0.770905	−	0.636950i	$-0.219804\pi$
$314$	30.5577	−	12.6574i	1.72447	−	0.714299i
$315$	7.64978	−	5.71432i	0.431016	−	0.321966i
$316$	−0.557440	−	0.834268i	−0.0313585	−	0.0469312i
$317$	−4.71291	−	4.13311i	−0.264704	−	0.232139i	0.516697	−	0.856168i	$-0.327161\pi$
$317$	−4.71291	−	4.13311i	−0.264704	−	0.232139i	−0.781401	+	0.624029i	$0.785495\pi$
$318$	−1.13463	+	5.51755i	−0.0636266	+	0.309409i
$319$	−21.5277	−	5.76834i	−1.20532	−	0.322965i
$320$	−1.37478	+	1.20565i	−0.0768528	+	0.0673981i
$321$	13.0660	+	22.9726i	0.729273	+	1.28220i
$322$	−15.0229	−	8.67346i	−0.837192	−	0.483353i
$323$	−3.90081	−	6.24979i	−0.217047	−	0.347747i
$324$	−6.92179	−	4.23854i	−0.384544	−	0.235475i
$325$	7.01623	+	2.90622i	0.389190	+	0.161208i
$326$	5.66169	−	16.6788i	0.313572	−	0.923753i
$327$	0.892550	+	7.13564i	0.0493581	+	0.394602i
$328$	−0.589520	+	8.99434i	−0.0325508	+	0.496629i
$329$	−3.81581	−	11.2410i	−0.210373	−	0.619738i
$330$	8.12660	+	5.50632i	0.447355	+	0.303113i
$331$	20.0193	+	2.63559i	1.10036	+	0.144865i	0.658765	−	0.752349i	$-0.271079\pi$
$331$	20.0193	+	2.63559i	1.10036	+	0.144865i	0.441596	+	0.897214i	$0.354413\pi$
$332$	2.92645	+	7.06507i	0.160610	+	0.387746i
$333$	−18.0828	+	20.0897i	−0.990932	+	1.10091i
$334$	−4.43624	−	0.882423i	−0.242740	−	0.0482840i
$335$	4.45966	−	2.19926i	0.243657	−	0.120159i
$336$	17.0096	+	22.4664i	0.927948	+	1.22565i
$337$	2.98961	+	3.40900i	0.162855	+	0.185700i	0.827512	−	0.561448i	$-0.189756\pi$
$337$	2.98961	+	3.40900i	0.162855	+	0.185700i	−0.664657	+	0.747149i	$0.731422\pi$
$338$	2.10751	+	16.0081i	0.114633	+	0.870727i
$339$	2.74785	−	19.8784i	0.149243	−	1.07965i
$340$	−2.94721	+	2.11938i	−0.159835	+	0.114940i
$341$		−	3.87741i		−	0.209973i
$342$	−5.65201	+	7.17197i	−0.305626	+	0.387816i
$343$	−2.14435	−	10.7804i	−0.115784	−	0.582086i
$344$	−5.41175	−	20.1969i	−0.291782	−	1.08895i
$345$	5.17360	+	1.06390i	0.278537	+	0.0572783i
$346$	−5.08982	+	1.72776i	−0.273630	+	0.0928849i
$347$	−14.9939	+	30.4046i	−0.804915	+	1.63221i	−0.0304952	+	0.999535i	$0.509708\pi$
$347$	−14.9939	+	30.4046i	−0.804915	+	1.63221i	−0.774420	+	0.632672i	$0.781958\pi$
$348$	−9.85009	−	2.70767i	−0.528020	−	0.145146i
$349$	3.26595	−	24.8074i	0.174822	−	1.32791i	−0.648882	−	0.760889i	$-0.724763\pi$
$349$	3.26595	−	24.8074i	0.174822	−	1.32791i	0.823705	−	0.567019i	$-0.191903\pi$
$350$	18.6869	−	12.4862i	0.998858	−	0.667415i
$351$	−9.71596	−	0.826262i	−0.518600	−	0.0441026i
$352$	−9.01120	+	13.4862i	−0.480299	+	0.718818i
$353$	29.9926	−	8.03648i	1.59634	−	0.427739i	0.652407	−	0.757869i	$-0.273759\pi$
$353$	29.9926	−	8.03648i	1.59634	−	0.427739i	0.943935	+	0.330130i	$0.107093\pi$
$354$	16.7369	+	8.38865i	0.889559	+	0.445852i
$355$	16.1261	−	2.12304i	0.855883	−	0.112679i
$356$	5.85793	+	10.1462i	0.310469	+	0.537749i
$357$	−12.1995	−	19.8299i	−0.645666	−	1.04951i
$358$	−1.69809	+	2.94118i	−0.0897468	+	0.155446i
$359$	−11.5446	+	27.8711i	−0.609301	+	1.47098i	0.254461	+	0.967083i	$0.418102\pi$
$359$	−11.5446	+	27.8711i	−0.609301	+	1.47098i	−0.863762	+	0.503900i	$0.831898\pi$
$360$	−4.51592	−	3.10261i	−0.238010	−	0.163522i
$361$	−11.1774	−	11.1774i	−0.588286	−	0.588286i
$362$	5.36693	+	10.8830i	0.282079	+	0.572000i
$363$	−1.00383	−	0.348006i	−0.0526875	−	0.0182656i
$364$	−4.94832	−	2.44024i	−0.259363	−	0.127903i
$365$	12.6305	+	9.69171i	0.661110	+	0.507287i
$366$	19.0700	−	4.97792i	0.996804	−	0.260200i
$367$	8.33450	−	0.546272i	0.435057	−	0.0285152i	0.153698	−	0.988118i	$-0.450882\pi$
$367$	8.33450	−	0.546272i	0.435057	−	0.0285152i	0.281359	+	0.959603i	$0.409215\pi$
$368$	−3.04102	+	15.2882i	−0.158524	+	0.796954i
$369$	−14.2124	+	2.63653i	−0.739868	+	0.137253i
$370$	10.5952	−	10.5952i	0.550818	−	0.550818i
$371$	5.89383	+	2.00068i	0.305992	+	0.103870i
$372$	0.0114855	−	1.77720i	0.000595493	−	0.0921434i
$373$	30.1560	−	17.4105i	1.56142	−	0.901484i	0.564302	−	0.825569i	$-0.309145\pi$
$373$	30.1560	−	17.4105i	1.56142	−	0.901484i	0.997114	−	0.0759155i	$-0.0241879\pi$
$374$	15.1536	−	18.5275i	0.783574	−	0.958036i
$375$	−9.39106	+	12.0763i	−0.484952	+	0.623616i
$376$	−5.40413	+	4.14673i	−0.278697	+	0.213851i
$377$	−12.0370	+	2.39430i	−0.619936	+	0.123313i
$378$	−18.0077	+	22.5490i	−0.926214	+	1.15980i
$379$	−9.53627	−	6.37193i	−0.489845	−	0.327304i	0.285998	−	0.958230i	$-0.407675\pi$
$379$	−9.53627	−	6.37193i	−0.489845	−	0.327304i	−0.775843	+	0.630926i	$0.782675\pi$
$380$	1.03727	−	1.18278i	0.0532107	−	0.0606752i
$381$	−8.13161	−	0.585774i	−0.416595	−	0.0300101i
$382$	−6.17623	+	8.04902i	−0.316003	+	0.411824i
$383$	3.17577	−	4.13874i	0.162274	−	0.211480i	−0.705138	−	0.709070i	$-0.749115\pi$
$383$	3.17577	−	4.13874i	0.162274	−	0.211480i	0.867412	+	0.497590i	$0.165782\pi$
$384$	12.3482	−	18.2243i	0.630142	−	0.930007i
$385$	7.15161	−	8.15485i	0.364480	−	0.415610i
$386$	−35.0021	−	23.3876i	−1.78156	−	1.19040i
$387$	29.2536	−	16.3891i	1.48704	−	0.833107i
$388$	11.7202	−	2.33129i	0.595003	−	0.118354i
$389$	−8.79206	+	6.74639i	−0.445775	+	0.342055i	−0.807131	−	0.590373i	$-0.798981\pi$
$389$	−8.79206	+	6.74639i	−0.445775	+	0.342055i	0.361355	+	0.932428i	$0.382314\pi$
$390$	5.35464	+	0.740186i	0.271143	+	0.0374808i
$391$	3.71799	−	12.3305i	0.188027	−	0.623578i
$392$	5.87846	−	3.39393i	0.296907	−	0.171419i
$393$	19.1829	+	11.2412i	0.967650	+	0.567043i
$394$	22.4748	+	7.62916i	1.13226	+	0.384352i
$395$	0.768063	−	0.768063i	0.0386454	−	0.0386454i
$396$	−8.69152	−	3.07622i	−0.436765	−	0.154586i
$397$	5.03515	−	25.3134i	0.252707	−	1.27044i	−0.620930	−	0.783866i	$-0.713245\pi$
$397$	5.03515	−	25.3134i	0.252707	−	1.27044i	0.873637	−	0.486578i	$-0.161755\pi$
$398$	25.8637	−	1.69520i	1.29643	−	0.0849727i
$399$	7.08821	+	7.18043i	0.354854	+	0.359471i
$400$	−16.0221	−	12.2942i	−0.801103	−	0.614708i
$401$	14.1713	+	6.98852i	0.707682	+	0.348990i	0.760253	−	0.649627i	$-0.225075\pi$
$401$	14.1713	+	6.98852i	0.707682	+	0.348990i	−0.0525710	+	0.998617i	$0.516742\pi$
$402$	−11.3622	+	9.83523i	−0.566696	+	0.490537i
$403$	−0.944357	−	1.91497i	−0.0470418	−	0.0953912i
$404$	3.62813	+	3.62813i	0.180506	+	0.180506i
$405$	3.03845	−	8.24445i	0.150982	−	0.409670i
$406$	−13.8991	+	33.5553i	−0.689800	+	1.66532i
$407$	−15.3519	+	26.5903i	−0.760967	+	1.31803i
$408$	−8.52466	+	10.2863i	−0.422033	+	0.509248i
$409$	−14.5112	−	25.1342i	−0.717533	−	1.24280i	−0.961974	−	0.273140i	$-0.911938\pi$
$409$	−14.5112	−	25.1342i	−0.717533	−	1.24280i	0.244441	−	0.969664i	$-0.421396\pi$
$410$	7.94461	−	1.04593i	0.392356	−	0.0516547i
$411$	−0.756617	+	0.498513i	−0.0373212	+	0.0245898i
$412$	3.22315	−	0.863639i	0.158793	−	0.0425485i
$413$	11.4926	−	17.1999i	0.565515	−	0.846353i
$414$	−15.9407	+	0.838053i	−0.783445	+	0.0411881i
$415$	−6.88336	+	4.59931i	−0.337891	+	0.225771i
$416$	−1.16582	+	8.85526i	−0.0571589	+	0.434165i
$417$	6.23766	+	23.8959i	0.305460	+	1.17019i
$418$	−4.58777	+	9.30307i	−0.224395	+	0.455028i
$419$	12.9326	−	4.39003i	0.631799	−	0.214467i	0.0128745	−	0.999917i	$-0.495902\pi$
$419$	12.9326	−	4.39003i	0.631799	−	0.214467i	0.618925	+	0.785450i	$0.287568\pi$
$420$	3.30208	−	3.71657i	0.161125	−	0.181350i
$421$	3.55418	+	13.2644i	0.173220	+	0.646467i	0.996848	+	0.0793358i	$0.0252799\pi$
$421$	3.55418	+	13.2644i	0.173220	+	0.646467i	−0.823628	+	0.567131i	$0.808053\pi$
$422$	−1.85394	−	9.32038i	−0.0902483	−	0.453709i
$423$	−8.57975	−	6.76144i	−0.417162	−	0.328752i
$424$		−	3.57150i		−	0.173447i
$425$	12.1973	+	11.3859i	0.591654	+	0.552298i
$426$	−45.5353	+	18.5175i	−2.20619	+	0.897176i
$427$	−2.84251	−	21.5910i	−0.137558	−	1.04486i
$428$	9.07290	+	10.3457i	0.438555	+	0.500076i
$429$	−10.9910	+	1.37479i	−0.530651	+	0.0663757i
$430$	−16.6716	+	8.22151i	−0.803974	+	0.396476i
$431$	−11.4427	−	2.27609i	−0.551173	−	0.109635i	−0.0883562	−	0.996089i	$-0.528161\pi$
$431$	−11.4427	−	2.27609i	−0.551173	−	0.109635i	−0.462817	+	0.886454i	$0.653161\pi$
$432$	24.3883	+	8.80961i	1.17338	+	0.423852i
$433$	1.20512	+	2.90941i	0.0579142	+	0.139817i	0.950188	−	0.311678i	$-0.100891\pi$
$433$	1.20512	+	2.90941i	0.0579142	+	0.139817i	−0.892274	+	0.451495i	$0.850891\pi$
$434$	−6.26472	−	0.824766i	−0.300716	−	0.0395900i
$435$	0.794585	−	11.0303i	0.0380974	−	0.528862i
$436$	1.20355	+	3.54555i	0.0576398	+	0.169801i
$437$	−0.365031	+	5.56930i	−0.0174618	+	0.266416i
$438$	−44.3319	−	18.6994i	−2.11826	−	0.893494i
$439$	−8.05468	+	23.7283i	−0.384429	+	1.13249i	0.566760	+	0.823883i	$0.308197\pi$
$439$	−8.05468	+	23.7283i	−0.384429	+	1.13249i	−0.951189	+	0.308608i	$0.900137\pi$
$440$	−5.75012	−	2.38178i	−0.274126	−	0.113547i
$441$	7.59707	+	7.79604i	0.361765	+	0.371240i
$442$	2.97158	−	12.8411i	0.141344	−	0.610787i
$443$	−19.8871	−	11.4818i	−0.944863	−	0.545517i	−0.0533814	−	0.998574i	$-0.517000\pi$
$443$	−19.8871	−	11.4818i	−0.944863	−	0.545517i	−0.891481	+	0.453057i	$0.850333\pi$
$444$	−7.11528	+	12.1421i	−0.337676	+	0.576240i
$445$	−9.53568	+	8.36257i	−0.452035	+	0.396424i
$446$	−39.1300	−	10.4849i	−1.85286	−	0.496472i
$447$	−11.2696	−	10.0127i	−0.533033	−	0.473586i
$448$	−4.59087	−	4.02609i	−0.216898	−	0.190215i
$449$	−12.2538	−	18.3391i	−0.578292	−	0.865476i	0.420840	−	0.907135i	$-0.361736\pi$
$449$	−12.2538	−	18.3391i	−0.578292	−	0.865476i	−0.999132	+	0.0416595i	$0.986736\pi$
$450$	8.16066	−	19.0031i	0.384697	−	0.895814i
$451$	−15.1701	+	6.28366i	−0.714332	+	0.295886i
$452$	−0.683365	−	10.4261i	−0.0321428	−	0.490404i
$453$	17.8086	−	3.42285i	0.836719	−	0.160820i
$454$	−1.58413	−	0.103829i	−0.0743468	−	0.00487295i
$455$	1.54588	−	5.76930i	0.0724720	−	0.270469i
$456$	2.59417	−	5.17587i	0.121483	−	0.242382i
$457$	−3.58241	−	4.66868i	−0.167578	−	0.218392i	0.702014	−	0.712163i	$-0.252285\pi$
$457$	−3.58241	−	4.66868i	−0.167578	−	0.218392i	−0.869592	+	0.493772i	$0.835618\pi$
$458$	48.8165			2.28104
$459$	−19.3548	−	9.18640i	−0.903407	−	0.428784i
$460$	2.75010			0.128224
$461$	−3.44403	−	4.48835i	−0.160405	−	0.209043i	0.706236	−	0.707977i	$-0.250392\pi$
$461$	−3.44403	−	4.48835i	−0.160405	−	0.209043i	−0.866640	+	0.498933i	$0.833725\pi$
$462$	−14.6880	+	29.3054i	−0.683348	+	1.36341i
$463$	4.01856	−	14.9975i	0.186758	−	0.696991i	−0.807489	−	0.589882i	$-0.799174\pi$
$463$	4.01856	−	14.9975i	0.186758	−	0.696991i	0.994247	−	0.107108i	$-0.0341592\pi$
$464$	32.5669	+	2.13455i	1.51188	+	0.0990938i
$465$	1.88938	−	0.363144i	0.0876181	−	0.0168404i
$466$	−1.73724	−	26.5051i	−0.0804760	−	1.22783i
$467$	−6.42801	+	2.66257i	−0.297453	+	0.123209i	−0.526419	−	0.850225i	$-0.676466\pi$
$467$	−6.42801	+	2.66257i	−0.297453	+	0.123209i	0.228966	+	0.973434i	$0.426466\pi$
$468$	−5.04177	+	0.597576i	−0.233056	+	0.0276229i
$469$	9.22510	+	13.8063i	0.425975	+	0.637517i
$470$	4.55290	+	3.99279i	0.210010	+	0.184173i
$471$	−25.1407	−	22.3369i	−1.15842	−	1.02923i
$472$	−11.4656	−	3.07219i	−0.527745	−	0.141409i
$473$	28.6378	−	25.1147i	1.31677	−	1.15477i
$474$	−1.65969	+	2.83225i	−0.0762323	+	0.130089i
$475$	−6.26225	−	3.61551i	−0.287332	−	0.165891i
$476$	−8.30139	−	8.83378i	−0.380494	−	0.404896i
$477$	5.55103	−	1.41076i	0.254164	−	0.0645941i
$478$	−42.6199	−	17.6537i	−1.94939	−	0.807463i
$479$	−1.44512	+	4.25719i	−0.0660292	+	0.194516i	−0.974937	−	0.222482i	$-0.928584\pi$
$479$	−1.44512	+	4.25719i	−0.0660292	+	0.194516i	0.908908	+	0.416997i	$0.136918\pi$
$480$	−7.41553	−	3.12791i	−0.338471	−	0.142769i
$481$	−1.10581	+	16.8714i	−0.0504206	+	0.769270i
$482$	−9.30909	−	27.4237i	−0.424017	−	1.24912i
$483$	−1.26729	+	17.5923i	−0.0576638	+	0.800479i
$484$	−0.548449	−	0.0722047i	−0.0249295	−	0.00328203i
$485$	4.95055	+	11.9517i	0.224793	+	0.542698i
$486$	−2.59191	+	26.4277i	−0.117572	+	1.19879i
$487$	−5.53777	−	1.10153i	−0.250941	−	0.0499152i	0.0680171	−	0.997684i	$-0.478333\pi$
$487$	−5.53777	−	1.10153i	−0.250941	−	0.0499152i	−0.318958	+	0.947769i	$0.603333\pi$
$488$	−11.2074	+	5.52689i	−0.507336	+	0.250190i
$489$	−17.7705	+	2.22280i	−0.803611	+	0.100518i
$490$	−3.97878	−	4.53693i	−0.179743	−	0.204958i
$491$	−0.544492	−	4.13583i	−0.0245726	−	0.186647i	0.974757	−	0.223270i	$-0.0716732\pi$
$491$	−0.544492	−	4.13583i	−0.0245726	−	0.186647i	−0.999329	+	0.0366231i	$0.988340\pi$
$492$	−6.97178	+	2.83516i	−0.314312	+	0.127819i
$493$	−26.6120	−	4.34816i	−1.19855	−	0.195831i
$494$			5.71195i			0.256993i
$495$	1.43058	−	9.87799i	0.0642997	−	0.443983i
$496$	1.10772	+	5.56888i	0.0497380	+	0.250050i
$497$	14.0578	+	52.4644i	0.630578	+	2.35335i
$498$	16.6176	−	18.7035i	0.744652	−	0.838124i
$499$	2.71484	−	0.921563i	0.121533	−	0.0412548i	−0.260011	−	0.965606i	$-0.583726\pi$
$499$	2.71484	−	0.921563i	0.121533	−	0.0412548i	0.381543	+	0.924351i	$0.375393\pi$
$500$	−3.52291	+	7.14376i	−0.157550	+	0.319479i
$501$	1.16158	+	4.44992i	0.0518957	+	0.198808i
$502$	−2.59235	+	19.6909i	−0.115702	+	0.878846i
$503$	4.49269	−	3.00192i	0.200319	−	0.133849i	−0.451365	−	0.892339i	$-0.649063\pi$
$503$	4.49269	−	3.00192i	0.200319	−	0.133849i	0.651684	+	0.758490i	$0.274063\pi$
$504$	8.30367	−	16.3035i	0.369875	−	0.726216i
$505$	−3.08595	+	4.61845i	−0.137323	+	0.205518i
$506$	−17.5150	+	4.69313i	−0.778637	+	0.208635i
$507$	13.7090	−	9.03245i	0.608837	−	0.401145i
$508$	−4.20854	+	0.554064i	−0.186724	+	0.0245826i
$509$	1.74709	+	3.02606i	0.0774386	+	0.134128i	0.902144	−	0.431435i	$-0.141992\pi$
$509$	1.74709	+	3.02606i	0.0774386	+	0.134128i	−0.824706	+	0.565562i	$0.808659\pi$
$510$	10.4473	+	5.64882i	0.462616	+	0.250134i
$511$	−26.5818	+	46.0410i	−1.17591	+	2.03673i
$512$	1.94431	−	4.69398i	0.0859271	−	0.207446i
$513$	9.06935	+	1.98753i	0.400421	+	0.0877515i
$514$	7.97966	+	7.97966i	0.351968	+	0.351968i
$515$	1.59770	+	3.23981i	0.0704030	+	0.142763i
$516$	13.2005	−	11.4264i	0.581117	−	0.503020i
$517$	−11.1292	−	5.48830i	−0.489460	−	0.241375i
$518$	39.6964	+	30.4601i	1.74416	+	1.33834i
$519$	3.83945	+	3.88940i	0.168533	+	0.170726i
$520$	−3.41995	+	0.224155i	−0.149975	+	0.00982987i
$521$	−6.43957	+	32.3739i	−0.282123	+	1.41833i	0.536454	+	0.843930i	$0.319764\pi$
$521$	−6.43957	+	32.3739i	−0.282123	+	1.41833i	−0.818577	+	0.574397i	$0.805236\pi$
$522$	6.09608	+	32.8613i	0.266818	+	1.43830i
$523$	5.80763	−	5.80763i	0.253950	−	0.253950i	−0.568638	−	0.822588i	$-0.692529\pi$
$523$	5.80763	−	5.80763i	0.253950	−	0.253950i	0.822588	+	0.568638i	$0.192529\pi$
$524$	10.9622	+	3.72116i	0.478885	+	0.162559i
$525$	−19.7158	−	11.5534i	−0.860468	−	0.504234i
$526$	24.8165	−	14.3278i	1.08205	−	0.624722i
$527$	−0.467593	−	4.66786i	−0.0203687	−	0.203335i
$528$	29.1785	+	4.03342i	1.26983	+	0.175532i
$529$	10.5066	−	8.06202i	0.456810	−	0.350523i
$530$	−3.11407	+	0.619427i	−0.135267	+	0.0269062i
$531$	0.246031	−	19.0340i	0.0106768	−	0.826004i
$532$	4.36802	+	2.91862i	0.189378	+	0.126538i
$533$	−5.96177	+	6.79809i	−0.258233	+	0.294458i
$534$	21.5010	−	31.7326i	0.930437	−	1.37320i
$535$	−9.06843	+	11.8182i	−0.392063	+	0.510946i
$536$	5.80030	−	7.55909i	0.250535	−	0.326503i
$537$	3.44423	+	0.248110i	0.148629	+	0.0107068i
$538$	16.5380	−	18.8580i	0.713005	−	0.813026i
$539$	10.2814	+	6.86981i	0.442851	+	0.295904i
$540$	0.684962	−	4.52331i	0.0294761	−	0.194652i
$541$	−25.8949	+	5.15082i	−1.11331	+	0.221451i	−0.717279	−	0.696786i	$-0.754613\pi$
$541$	−25.8949	+	5.15082i	−1.11331	+	0.221451i	−0.396031	+	0.918237i	$0.629613\pi$
$542$	39.9268	−	30.6369i	1.71500	−	1.31597i
$543$	7.57400	−	9.73965i	0.325031	−	0.417968i
$544$	−9.22188	+	17.3222i	−0.395385	+	0.742685i
$545$	−3.51034	+	2.02670i	−0.150366	+	0.0868141i
$546$	−0.116655	+	18.0506i	−0.00499238	+	0.772495i
$547$	28.3221	+	9.61404i	1.21096	+	0.411067i	0.852624	−	0.522525i	$-0.175010\pi$
$547$	28.3221	+	9.61404i	1.21096	+	0.411067i	0.358339	+	0.933591i	$0.383343\pi$
$548$	−0.333591	+	0.333591i	−0.0142503	+	0.0142503i
$549$	−13.0172	−	15.2361i	−0.555560	−	0.650260i
$550$	4.58322	−	23.0414i	0.195429	−	0.982489i
$551$	11.6607	−	0.764282i	0.496762	−	0.0325595i
$552$	9.79275	−	2.55625i	0.416807	−	0.108801i
$553$	2.87766	+	2.20810i	0.122370	+	0.0938982i
$554$	−15.4032	−	7.59604i	−0.654421	−	0.322725i
$555$	−14.3947	−	4.99034i	−0.611023	−	0.211828i
$556$	5.68729	+	11.5327i	0.241195	+	0.489095i
$557$	14.2778	+	14.2778i	0.604969	+	0.604969i	0.941627	−	0.336658i	$-0.109297\pi$
$557$	14.2778	+	14.2778i	0.604969	+	0.604969i	−0.336658	+	0.941627i	$0.609297\pi$
$558$	−5.24774	+	2.50411i	−0.222155	+	0.106007i
$559$	8.02681	−	19.3784i	0.339498	−	0.819621i
$560$	−7.94169	+	13.7554i	−0.335598	+	0.581272i
$561$	−23.6743	−	5.63997i	−0.999531	−	0.238120i
$562$	15.1756	+	26.2849i	0.640143	+	1.10876i
$563$	−35.1939	+	4.63336i	−1.48325	+	0.195273i	−0.828249	−	0.560360i	$-0.810663\pi$
$563$	−35.1939	+	4.63336i	−1.48325	+	0.195273i	−0.654996	+	0.755633i	$0.727330\pi$
$564$	−5.08476	−	2.54851i	−0.214107	−	0.107312i
$565$	10.9257	−	2.92754i	0.459649	−	0.123163i
$566$	−5.76814	+	8.63264i	−0.242453	+	0.362857i
$567$	28.6199	+	6.46610i	1.20192	+	0.271551i
$568$	25.9142	−	17.3153i	1.08734	−	0.726535i
$569$	0.398073	−	3.02367i	0.0166881	−	0.126759i	−0.981073	−	0.193639i	$-0.937971\pi$
$569$	0.398073	−	3.02367i	0.0166881	−	0.126759i	0.997761	+	0.0668798i	$0.0213044\pi$
$570$	−4.96288	−	1.36423i	−0.207872	−	0.0571415i
$571$	3.07762	−	6.24080i	0.128794	−	0.261169i	−0.822918	−	0.568160i	$-0.807655\pi$
$571$	3.07762	−	6.24080i	0.128794	−	0.261169i	0.951712	+	0.306991i	$0.0993221\pi$
$572$	−5.46121	+	1.85383i	−0.228345	+	0.0775126i
$573$	10.1043	+	2.07785i	0.422114	+	0.0868034i
$574$	6.92566	+	25.8469i	0.289071	+	1.07883i
$575$	−2.46608	−	12.3978i	−0.102842	−	0.517024i
$576$	−5.56094	−	0.805362i	−0.231706	−	0.0335567i
$577$			21.0815i			0.877634i	0.898576	+	0.438817i	$0.144602\pi$
$577$			21.0815i			0.877634i	−0.898576	+	0.438817i	$0.855398\pi$
$578$	16.0085	−	24.1320i	0.665867	−	1.00376i
$579$	−5.86102	+	42.3996i	−0.243576	+	1.76207i
$580$	−0.751571	−	5.70875i	−0.0312073	−	0.237043i
$581$	−18.2275	−	20.7845i	−0.756205	−	0.862287i
$582$	−23.5993	−	31.1703i	−0.978224	−	1.29205i
$583$	5.83518	−	2.87759i	0.241668	−	0.119178i
$584$	29.9198	+	5.95142i	1.23809	+	0.246272i
$585$	−1.69929	−	5.22695i	−0.0702570	−	0.216108i
$586$	−3.66970	−	8.85945i	−0.151594	−	0.365980i
$587$	17.8947	+	2.35588i	0.738591	+	0.0972374i	0.490429	−	0.871481i	$-0.336840\pi$
$587$	17.8947	+	2.35588i	0.738591	+	0.0972374i	0.248162	+	0.968718i	$0.420173\pi$
$588$	4.69210	+	3.17921i	0.193499	+	0.131109i
$589$	0.653493	+	1.92513i	0.0269267	+	0.0793235i
$590$	−0.690166	+	10.5299i	−0.0284137	+	0.433509i
$591$	−2.99524	−	23.9459i	−0.123208	−	0.985004i
$592$	14.4526	−	42.5758i	0.593996	−	1.74986i
$593$	17.5477	+	7.26851i	0.720599	+	0.298482i	0.712683	−	0.701487i	$-0.247480\pi$
$593$	17.5477	+	7.26851i	0.720599	+	0.298482i	0.00791660	+	0.999969i	$0.497480\pi$
$594$	3.35674	+	29.9772i	0.137729	+	1.22998i
$595$	7.62612	−	10.6798i	0.312641	−	0.437827i
$596$	−6.79755	−	3.92457i	−0.278438	−	0.160757i
$597$	−13.0292	−	22.9079i	−0.533252	−	0.937560i
$598$	−7.50725	+	6.58368i	−0.306994	+	0.269227i
$599$	−8.42126	−	2.25647i	−0.344083	−	0.0921968i	0.0826390	−	0.996580i	$-0.473665\pi$
$599$	−8.42126	−	2.25647i	−0.344083	−	0.0921968i	−0.426722	+	0.904383i	$0.640332\pi$
$600$	−2.64119	+	12.8438i	−0.107826	+	0.524346i
$601$	−13.8853	−	12.1770i	−0.566392	−	0.496712i	0.327587	−	0.944821i	$-0.393764\pi$
$601$	−13.8853	−	12.1770i	−0.566392	−	0.496712i	−0.893979	+	0.448109i	$0.852098\pi$
$602$	−34.4862	−	51.6122i	−1.40555	−	2.10356i
$603$	14.0399	+	6.02929i	0.571750	+	0.245532i
$604$	8.72335	−	3.61333i	0.354948	−	0.147024i
$605$	−0.0391669	−	0.597571i	−0.00159236	−	0.0242947i
$606$	5.49860	−	15.8608i	0.223365	−	0.644303i
$607$	41.2375	+	2.70285i	1.67378	+	0.109705i	0.872510	−	0.488597i	$-0.162491\pi$
$607$	41.2375	+	2.70285i	1.67378	+	0.109705i	0.801270	+	0.598302i	$0.204158\pi$
$608$	2.20110	−	8.21463i	0.0892665	−	0.333147i
$609$	36.8651	−	2.17710i	1.49385	−	0.0882204i
$610$	6.76279	+	8.81344i	0.273817	+	0.356846i
$611$	−6.83315			−0.276439
$612$	−10.8344	−	2.65519i	−0.437953	−	0.107330i
$613$	−1.39251			−0.0562429			−0.0281214	−	0.999605i	$-0.508953\pi$
$613$	−1.39251			−0.0562429			−0.0281214	+	0.999605i	$0.508953\pi$
$614$	−4.24748	−	5.53542i	−0.171414	−	0.223392i
$615$	−4.48268	−	6.80358i	−0.180759	−	0.274347i
$616$	5.37921	−	20.0755i	0.216735	−	0.808865i
$617$	16.0298	+	1.05065i	0.645334	+	0.0422974i	0.384556	−	0.923102i	$-0.374354\pi$
$617$	16.0298	+	1.05065i	0.645334	+	0.0422974i	0.260777	+	0.965399i	$0.416021\pi$
$618$	−7.14499	−	8.25431i	−0.287414	−	0.332037i
$619$	0.629295	+	9.60119i	0.0252935	+	0.385904i	0.991673	+	0.128783i	$0.0411072\pi$
$619$	0.629295	+	9.60119i	0.0252935	+	0.385904i	−0.966379	+	0.257121i	$0.917226\pi$
$620$	0.925496	−	0.383353i	0.0371688	−	0.0153958i
$621$	7.84125	+	14.2107i	0.314658	+	0.570258i
$622$	17.8501	+	26.7146i	0.715725	+	1.07116i
$623$	−31.8429	−	27.9255i	−1.27576	−	1.11881i
$624$	15.3930	−	5.11450i	0.616211	−	0.204744i
$625$	11.2159	+	3.00529i	0.448636	+	0.120212i
$626$	−26.5181	+	23.2558i	−1.05988	+	0.929487i
$627$	10.5466	+	0.0681591i	0.421190	+	0.00272201i
$628$	−15.1643	−	8.75513i	−0.605122	−	0.349368i
$629$	−15.2750	+	33.8624i	−0.609053	+	1.35018i
$630$	−15.6556	−	4.41254i	−0.623732	−	0.175800i
$631$	3.54388	+	1.46792i	0.141079	+	0.0584370i	0.452106	−	0.891964i	$-0.350673\pi$
$631$	3.54388	+	1.46792i	0.141079	+	0.0584370i	−0.311027	+	0.950401i	$0.600673\pi$
$632$	0.669026	−	1.97089i	0.0266124	−	0.0783976i
$633$	−7.70354	+	5.83243i	−0.306188	+	0.231818i
$634$	−0.698391	+	10.6554i	−0.0277366	+	0.423179i
$635$	−1.47711	−	4.35144i	−0.0586175	−	0.172682i
$636$	2.68306	−	1.30165i	0.106390	−	0.0516138i
$637$	6.75093	+	0.888777i	0.267482	+	0.0352146i
$638$	14.5288	+	35.0756i	0.575201	+	1.38866i
$639$	37.1487	+	33.4378i	1.46958	+	1.32278i
$640$	12.1698	+	2.42072i	0.481052	+	0.0956873i
$641$	−13.0883	+	6.45441i	−0.516955	+	0.254934i	−0.682000	−	0.731352i	$-0.738890\pi$
$641$	−13.0883	+	6.45441i	−0.516955	+	0.254934i	0.165045	+	0.986286i	$0.447223\pi$
$642$	17.4969	−	41.4809i	0.690547	−	1.63712i
$643$	11.4136	+	13.0147i	0.450107	+	0.513249i	0.931741	−	0.363124i	$-0.118290\pi$
$643$	11.4136	+	13.0147i	0.450107	+	0.513249i	−0.481634	+	0.876373i	$0.659956\pi$
$644$	1.19869	+	9.10496i	0.0472350	+	0.358786i
$645$	14.9200	+	11.6025i	0.587475	+	0.456847i
$646$	−4.40114	+	11.7529i	−0.173161	+	0.462410i
$647$		−	8.67540i		−	0.341065i	−0.985352	−	0.170533i	$-0.945451\pi$
$647$		−	8.67540i		−	0.341065i	0.985352	−	0.170533i	$-0.0545488\pi$
$648$	−1.76540	−	16.7436i	−0.0693516	−	0.657751i
$649$	−4.21852	−	21.2079i	−0.165591	−	0.832484i
$650$	−3.34827	−	12.4959i	−0.131330	−	0.490130i
$651$	2.02582	+	6.09703i	0.0793980	+	0.238962i
$652$	−8.82981	+	2.99732i	−0.345802	+	0.117384i
$653$	−7.57723	+	15.3651i	−0.296520	+	0.601283i	−0.993242	−	0.116058i	$-0.962974\pi$
$653$	−7.57723	+	15.3651i	−0.296520	+	0.601283i	0.696723	+	0.717341i	$0.254641\pi$
$654$	8.71793	−	8.60597i	0.340898	−	0.336520i
$655$	−1.63579	+	12.4251i	−0.0639158	+	0.485489i
$656$	19.9927	−	13.3587i	0.780584	−	0.521570i
$657$	2.56840	+	48.8540i	0.100203	+	1.90598i
$658$	−11.2347	+	16.8140i	−0.437975	+	0.655476i
$659$	−42.0808	+	11.2755i	−1.63924	+	0.439232i	−0.956571	−	0.291499i	$-0.905846\pi$
$659$	−42.0808	+	11.2755i	−1.63924	+	0.439232i	−0.682666	+	0.730731i	$0.739179\pi$
$660$	−0.306369	−	5.18779i	−0.0119254	−	0.201934i
$661$	−21.5906	+	2.84246i	−0.839778	+	0.110559i	−0.538132	−	0.842861i	$-0.680870\pi$
$661$	−21.5906	+	2.84246i	−0.839778	+	0.110559i	−0.301647	+	0.953420i	$0.597536\pi$
$662$	−17.1983	−	29.7884i	−0.668432	−	1.15776i
$663$	−13.0659	+	2.98052i	−0.507436	+	0.115754i
$664$	−7.93151	+	13.7378i	−0.307802	+	0.533129i
$665$	−2.17636	+	5.25420i	−0.0843956	+	0.203749i
$666$	45.9024	+	3.60498i	1.77868	+	0.139690i
$667$	14.4448	+	14.4448i	0.559304	+	0.559304i
$668$	1.05909	+	2.14763i	0.0409775	+	0.0830942i
$669$	7.77451	+	40.4496i	0.300580	+	1.56387i
$670$	−7.59692	−	3.74639i	−0.293495	−	0.144736i
$671$	−18.0599	−	13.8578i	−0.697193	−	0.534975i
$672$	7.12358	−	25.9145i	0.274798	−	0.999673i
$673$	−6.91104	+	0.452973i	−0.266401	+	0.0174608i	−0.198018	−	0.980198i	$-0.563451\pi$
$673$	−6.91104	+	0.452973i	−0.266401	+	0.0174608i	−0.0683826	+	0.997659i	$0.521784\pi$
$674$	1.50686	−	7.57550i	0.0580421	−	0.291798i
$675$	−21.0059	+	0.968259i	−0.808516	+	0.0372683i
$676$	6.04427	−	6.04427i	0.232472	−	0.232472i
$677$	−12.9973	−	4.41198i	−0.499525	−	0.169566i	0.0602941	−	0.998181i	$-0.480796\pi$
$677$	−12.9973	−	4.41198i	−0.499525	−	0.169566i	−0.559819	+	0.828615i	$0.689129\pi$
$678$	−29.7144	+	16.9005i	−1.14117	+	0.649061i
$679$	−37.4115	+	21.5995i	−1.43572	+	0.828914i
$680$	−7.20958	−	2.17390i	−0.276475	−	0.0833653i
$681$	0.608061	+	1.49525i	0.0233010	+	0.0572980i
$682$	−5.24015	+	4.02091i	−0.200656	+	0.153969i
$683$	16.4867	−	3.27942i	0.630848	−	0.125483i	0.130698	−	0.991422i	$-0.458278\pi$
$683$	16.4867	−	3.27942i	0.630848	−	0.125483i	0.500150	+	0.865939i	$0.333278\pi$
$684$	4.83379	+	0.0624811i	0.184825	+	0.00238902i
$685$	−0.424647	−	0.283740i	−0.0162249	−	0.0108412i
$686$	−12.3455	+	14.0773i	−0.471354	+	0.537476i
$687$	−21.6650	−	44.6576i	−0.826572	−	1.70379i
$688$	−33.9558	+	44.2521i	−1.29455	+	1.68709i
$689$	2.18102	−	2.84236i	0.0830902	−	0.108285i
$690$	−3.92727	−	8.09517i	−0.149508	−	0.308178i
$691$	23.5766	−	26.8839i	0.896894	−	1.02271i	−0.102714	−	0.994711i	$-0.532753\pi$
$691$	23.5766	−	26.8839i	0.896894	−	1.02271i	0.999608	−	0.0280010i	$-0.00891415\pi$
$692$	2.36602	+	1.58092i	0.0899424	+	0.0600976i
$693$	33.3273	+	0.430786i	1.26600	+	0.0163642i
$694$	56.6394	−	11.2663i	2.15000	−	0.427662i
$695$	−11.0438	+	8.47421i	−0.418916	+	0.321445i
$696$	−7.98258	−	19.6295i	−0.302579	−	0.744055i
$697$	−17.5049	+	9.39408i	−0.663046	+	0.355826i
$698$	−36.9129	+	21.3117i	−1.39717	+	0.806659i
$699$	−23.4760	+	13.3524i	−0.887946	+	0.505033i
$700$	−11.2667	−	3.82452i	−0.425841	−	0.144553i
$701$	21.6865	−	21.6865i	0.819088	−	0.819088i	−0.166888	−	0.985976i	$-0.553372\pi$
$701$	21.6865	−	21.6865i	0.819088	−	0.819088i	0.985976	+	0.166888i	$0.0533719\pi$
$702$	8.95889	+	13.9875i	0.338131	+	0.527926i
$703$	3.14072	−	15.7895i	0.118454	−	0.595511i
$704$	−6.36917	+	0.417457i	−0.240047	+	0.0157335i
$705$	1.63202	−	5.93704i	0.0614654	−	0.223602i
$706$	−41.9635	−	32.1997i	−1.57932	−	1.21185i
$707$	−16.6357	−	8.20383i	−0.625651	−	0.308537i
$708$	−1.87072	−	9.73309i	−0.0703061	−	0.365792i
$709$	5.85835	+	11.8796i	0.220015	+	0.446146i	0.978696	−	0.205316i	$-0.0658224\pi$
$709$	5.85835	+	11.8796i	0.220015	+	0.446146i	−0.758681	+	0.651463i	$0.774156\pi$
$710$	−19.5921	−	19.5921i	−0.735278	−	0.735278i
$711$	3.32754	+	0.261331i	0.124792	+	0.00980068i
$712$	−9.30032	+	22.4530i	−0.348544	+	0.841460i
$713$	−1.77698	+	3.07782i	−0.0665484	+	0.115265i
$714$	−14.1483	+	37.0509i	−0.529486	+	1.38660i
$715$	−3.12172	−	5.40697i	−0.116746	−	0.202209i
$716$	1.78257	−	0.234679i	0.0666177	−	0.00877038i
$717$	2.76521	+	46.8237i	0.103269	+	1.74866i
$718$	49.6385	−	13.3006i	1.85249	−	0.496374i
$719$	3.43802	−	5.14536i	0.128217	−	0.191890i	−0.761807	−	0.647804i	$-0.775688\pi$
$719$	3.43802	−	5.14536i	0.128217	−	0.191890i	0.890024	+	0.455914i	$0.150688\pi$
$720$	0.767347	+	14.5958i	0.0285974	+	0.543955i
$721$	−10.0299	+	6.70175i	−0.373532	+	0.249586i
$722$	−3.51472	+	26.6969i	−0.130804	+	0.993557i
$723$	−20.9559	+	20.6868i	−0.779359	+	0.769350i
$724$	2.84127	−	5.76153i	0.105595	−	0.214125i
$725$	−25.0618	+	8.50734i	−0.930772	+	0.315955i
$726$	0.570668	+	1.71752i	0.0211795	+	0.0637432i
$727$	1.19605	+	4.46370i	0.0443589	+	0.165550i	0.984552	−	0.175092i	$-0.0560223\pi$
$727$	1.19605	+	4.46370i	0.0443589	+	0.165550i	−0.940193	+	0.340642i	$0.889356\pi$
$728$	−2.23279	−	11.2250i	−0.0827526	−	0.416025i
$729$	25.3265	−	9.35768i	0.938020	−	0.346581i
$730$		−	27.1200i		−	1.00375i
$731$	31.4473	−	33.6882i	1.16312	−	1.24600i
$732$	−8.23663	−	6.40518i	−0.304435	−	0.236742i
$733$	5.43726	+	41.3001i	0.200830	+	1.52545i	0.733827	+	0.679336i	$0.237732\pi$
$733$	5.43726	+	41.3001i	0.200830	+	1.52545i	−0.532998	+	0.846117i	$0.678935\pi$
$734$	−9.38122	−	10.6972i	−0.346267	−	0.394842i
$735$	−2.38460	+	5.65333i	−0.0879574	+	0.208526i
$736$	13.3336	−	6.57538i	0.491481	−	0.242372i
$737$	17.0235	+	3.38619i	0.627070	+	0.124732i
$738$	18.3016	+	16.4733i	0.673690	+	0.606392i
$739$	−2.24893	−	5.42939i	−0.0827282	−	0.199723i	0.877103	−	0.480303i	$-0.159473\pi$
$739$	−2.24893	−	5.42939i	−0.0827282	−	0.199723i	−0.959831	+	0.280580i	$0.909473\pi$
$740$	−7.86465	−	1.03540i	−0.289110	−	0.0380621i
$741$	5.22532	−	2.53500i	0.191957	−	0.0931254i
$742$	−3.40812	−	10.0400i	−0.125116	−	0.368579i
$743$	0.875058	−	13.3508i	0.0321027	−	0.489793i	−0.951289	−	0.308299i	$-0.900240\pi$
$743$	0.875058	−	13.3508i	0.0321027	−	0.489793i	0.983392	−	0.181494i	$-0.0580932\pi$
$744$	2.93924	−	2.22533i	0.107758	−	0.0815845i
$745$	2.73133	−	8.04622i	0.100068	−	0.294791i
$746$	−54.8016	−	22.6996i	−2.00643	−	0.831091i
$747$	−24.4850	−	6.90114i	−0.895861	−	0.252499i
$748$	−12.6654	−	0.393511i	−0.463091	−	0.0143882i
$749$	−43.0801	−	24.8723i	−1.57411	−	0.908814i
$750$	26.0592	+	0.168412i	0.951547	+	0.00614954i
$751$	−30.9065	+	27.1043i	−1.12780	+	0.989050i	−0.999996	−	0.00275033i	$-0.999125\pi$
$751$	−30.9065	+	27.1043i	−1.12780	+	0.989050i	−0.127799	+	0.991800i	$0.540791\pi$
$752$	17.5520	+	4.70306i	0.640057	+	0.171503i
$753$	19.1638	−	6.36741i	0.698368	−	0.232041i
$754$	15.7183	+	13.7845i	0.572425	+	0.502003i
$755$	5.67884	+	8.49898i	0.206674	+	0.309310i
$756$	15.2742	+	0.296170i	0.555518	+	0.0107716i
$757$	50.5570	−	20.9414i	1.83752	−	0.761128i	0.878540	−	0.477669i	$-0.158518\pi$
$757$	50.5570	−	20.9414i	1.83752	−	0.761128i	0.958985	−	0.283458i	$-0.0914818\pi$
$758$	1.27781	+	19.4956i	0.0464122	+	0.708113i
$759$	12.0666	+	13.9400i	0.437988	+	0.505989i
$760$	3.25635	+	0.213433i	0.118120	+	0.00774201i
$761$	8.71551	−	32.5267i	0.315937	−	1.17909i	−0.607177	−	0.794567i	$-0.707698\pi$
$761$	8.71551	−	32.5267i	0.315937	−	1.17909i	0.923114	−	0.384527i	$-0.125635\pi$
$762$	7.64091	+	11.5970i	0.276801	+	0.420114i
$763$	−8.23999	−	10.7386i	−0.298308	−	0.388762i
$764$	5.37110			0.194320
$765$	0.530989	−	12.0643i	0.0191980	−	0.436184i
$766$	−8.88664			−0.321087
$767$	−7.24870	−	9.44669i	−0.261735	−	0.341100i
$768$	−30.9577	+	1.82823i	−1.11709	+	0.0659706i
$769$	0.317848	−	1.18623i	0.0114619	−	0.0427764i	−0.959958	−	0.280144i	$-0.909618\pi$
$769$	0.317848	−	1.18623i	0.0114619	−	0.0427764i	0.971420	+	0.237367i	$0.0762845\pi$
$770$	−18.4372	−	1.20844i	−0.664431	−	0.0435491i
$771$	3.75842	−	10.8413i	0.135356	−	0.390438i
$772$	1.45758	+	22.2384i	0.0524595	+	0.800378i
$773$	30.7766	−	12.7481i	1.10696	−	0.458517i	0.247068	−	0.968998i	$-0.420533\pi$
$773$	30.7766	−	12.7481i	1.10696	−	0.458517i	0.859889	+	0.510481i	$0.170533\pi$
$774$	−52.4855	−	22.5393i	−1.88655	−	0.810159i
$775$	−2.55812	−	3.82849i	−0.0918902	−	0.137523i
$776$	18.6368	+	16.3440i	0.669022	+	0.586716i
$777$	10.2476	−	49.8329i	0.367631	−	1.78774i
$778$	18.2349	+	4.88603i	0.653753	+	0.175173i
$779$	6.47290	−	5.67658i	0.231916	−	0.203385i
$780$	−1.41481	−	2.48752i	−0.0506585	−	0.0890674i
$781$	49.1694	+	28.3880i	1.75942	+	1.01580i
$782$	−20.5197	+	7.76209i	−0.733782	+	0.277572i
$783$	27.3562	−	20.1607i	0.977631	−	0.720486i
$784$	−16.7291	−	6.92944i	−0.597469	−	0.247480i
$785$	6.09318	−	17.9499i	0.217475	−	0.640661i
$786$	−4.70090	−	37.5821i	−0.167675	−	1.34051i
$787$	1.26424	−	19.2886i	0.0450653	−	0.687564i	−0.914237	−	0.405181i	$-0.867209\pi$
$787$	1.26424	−	19.2886i	0.0450653	−	0.687564i	0.959302	−	0.282383i	$-0.0911248\pi$
$788$	−4.03891	−	11.8982i	−0.143880	−	0.423857i
$789$	−24.1209	−	16.3435i	−0.858725	−	0.581844i
$790$	−1.83449	−	0.241516i	−0.0652683	−	0.00859274i
$791$	14.4546	+	34.8966i	0.513948	+	1.24078i
$792$	−5.91304	−	18.1883i	−0.210111	−	0.646291i
$793$	−12.2945	−	2.44553i	−0.436590	−	0.0868432i
$794$	−39.4315	+	19.4455i	−1.39937	+	0.690094i
$795$	1.94870	+	2.57386i	0.0691131	+	0.0912855i
$796$	−9.04737	−	10.3166i	−0.320676	−	0.365660i
$797$	3.66729	+	27.8558i	0.129902	+	0.986703i	0.924932	+	0.380133i	$0.124122\pi$
$797$	3.66729	+	27.8558i	0.129902	+	0.986703i	−0.795030	+	0.606570i	$0.792545\pi$
$798$	2.35349	−	17.0256i	0.0833128	−	0.602699i
$799$	−14.0598	−	5.26504i	−0.497401	−	0.186264i
$800$			19.2612i			0.680987i
$801$	−38.5714	−	5.58609i	−1.36285	−	0.197375i
$802$	−5.25111	−	26.3991i	−0.185423	−	0.932185i
$803$	14.3832	+	53.6787i	0.507571	+	1.89428i
$804$	7.79266	+	1.60248i	0.274826	+	0.0565150i
$805$	−9.41413	+	3.19567i	−0.331804	+	0.112632i
$806$	−1.60869	+	3.26210i	−0.0566636	+	0.114902i
$807$	−24.5911	−	6.75978i	−0.865646	−	0.237956i
$808$	−1.38925	+	10.5524i	−0.0488735	+	0.371231i
$809$	20.2201	−	13.5107i	0.710903	−	0.475010i	−0.146793	−	0.989167i	$-0.546895\pi$
$809$	20.2201	−	13.5107i	0.710903	−	0.475010i	0.857696	+	0.514157i	$0.171895\pi$
$810$	−14.2929	+	4.44324i	−0.502202	+	0.156119i
$811$	8.90598	−	13.3287i	0.312731	−	0.468035i	−0.641492	−	0.767129i	$-0.721684\pi$
$811$	8.90598	−	13.3287i	0.312731	−	0.468035i	0.954224	+	0.299094i	$0.0966844\pi$
$812$	18.5728	−	4.97656i	0.651777	−	0.174643i
$813$	−45.7465	−	22.9284i	−1.60440	−	0.804134i
$814$	51.8558	−	6.82694i	1.81754	−	0.239284i
$815$	−5.04726	−	8.74212i	−0.176798	−	0.306223i
$816$	35.6132	+	1.33692i	1.24671	+	0.0468017i
$817$	−9.98585	+	17.2960i	−0.349361	+	0.605110i
$818$	−18.9195	+	45.6757i	−0.661504	+	1.59701i
$819$	16.5646	−	7.90424i	0.578813	−	0.276197i
$820$	−2.99969	−	2.99969i	−0.104754	−	0.104754i
$821$	−1.71117	−	3.46991i	−0.0597203	−	0.121101i	0.864966	−	0.501830i	$-0.167340\pi$
$821$	−1.71117	−	3.46991i	−0.0597203	−	0.121101i	−0.924687	+	0.380729i	$0.875673\pi$
$822$	1.45834	+	0.505573i	0.0508654	+	0.0176339i
$823$	−20.0671	−	9.89598i	−0.699494	−	0.344952i	0.0575262	−	0.998344i	$-0.481679\pi$
$823$	−20.0671	−	9.89598i	−0.699494	−	0.344952i	−0.757020	+	0.653392i	$0.773345\pi$
$824$	5.49145	+	4.21374i	0.191304	+	0.146793i
$825$	−23.1125	+	6.03315i	−0.804673	+	0.210047i
$826$	−35.1629	+	2.30470i	−1.22348	+	0.0801908i
$827$	3.13912	−	15.7814i	0.109158	−	0.548774i	−0.887043	−	0.461687i	$-0.847244\pi$
$827$	3.13912	−	15.7814i	0.109158	−	0.548774i	0.996201	−	0.0870870i	$-0.0277558\pi$
$828$	5.48938	+	6.42509i	0.190769	+	0.223287i
$829$	5.87342	−	5.87342i	0.203992	−	0.203992i	−0.597716	−	0.801708i	$-0.703925\pi$
$829$	5.87342	−	5.87342i	0.203992	−	0.203992i	0.801708	+	0.597716i	$0.203925\pi$
$830$	13.3539	+	4.53303i	0.463520	+	0.157344i
$831$	−0.112852	+	17.4621i	−0.00391480	+	0.605755i
$832$	−3.04392	+	1.75741i	−0.105529	+	0.0609272i
$833$	13.2058	+	7.03043i	0.457556	+	0.243590i
$834$	25.8258	−	33.2102i	0.894275	−	1.14998i
$835$	−2.05659	+	1.57808i	−0.0711712	+	0.0546115i
$836$	5.38588	−	1.07132i	0.186274	−	0.0370523i
$837$	4.61975	+	3.68933i	0.159682	+	0.127522i
$838$	−19.3442	−	12.9254i	−0.668234	−	0.446499i
$839$	26.6777	−	30.4201i	0.921017	−	1.05022i	−0.0775653	−	0.996987i	$-0.524715\pi$
$839$	26.6777	−	30.4201i	0.921017	−	1.05022i	0.998582	−	0.0532312i	$-0.0169520\pi$
$840$	10.2862	+	0.740983i	0.354907	+	0.0255663i
$841$	8.38326	−	10.9253i	0.289078	−	0.376734i
$842$	14.2405	−	18.5586i	0.490761	−	0.639572i
$843$	17.3105	−	25.5481i	0.596206	−	0.879922i
$844$	−3.31711	+	3.78244i	−0.114180	+	0.130197i
$845$	7.69409	+	5.14103i	0.264685	+	0.176857i
$846$	−0.240510	+	18.6068i	−0.00826891	+	0.639716i
$847$	1.96135	−	0.390137i	0.0673927	−	0.0134052i
$848$	−7.55862	+	5.79993i	−0.259564	+	0.199170i
$849$	10.4571	+	1.44552i	0.358887	+	0.0496100i
$850$	2.73890	−	28.2914i	0.0939435	−	0.970386i
$851$	24.3722	−	14.0713i	0.835469	−	0.482358i
$852$	22.4526	+	13.1572i	0.769213	+	0.450758i
$853$	−44.8436	−	15.2224i	−1.53542	−	0.521204i	−0.579533	−	0.814949i	$-0.696765\pi$
$853$	−44.8436	−	15.2224i	−1.53542	−	0.521204i	−0.955884	+	0.293746i	$0.905098\pi$
$854$	−26.2316	+	26.2316i	−0.897626	+	0.897626i
$855$	0.954543	+	5.14552i	0.0326447	+	0.175973i
$856$	−5.56869	+	27.9957i	−0.190334	+	0.956872i
$857$	24.6573	−	1.61612i	0.842276	−	0.0552057i	0.361845	−	0.932238i	$-0.382147\pi$
$857$	24.6573	−	1.61612i	0.842276	−	0.0552057i	0.480431	+	0.877033i	$0.340480\pi$
$858$	13.2558	+	13.4282i	0.452544	+	0.458432i
$859$	−19.4023	−	14.8879i	−0.661998	−	0.507969i	0.222248	−	0.974990i	$-0.428661\pi$
$859$	−19.4023	−	14.8879i	−0.661998	−	0.507969i	−0.884246	+	0.467021i	$0.845327\pi$
$860$	8.82599	+	4.35250i	0.300964	+	0.148419i
$861$	20.5712	−	17.8066i	0.701066	−	0.606848i
$862$	8.79011	+	17.8246i	0.299392	+	0.607108i
$863$	−11.5923	−	11.5923i	−0.394607	−	0.394607i	0.481719	−	0.876326i	$-0.340013\pi$
$863$	−11.5923	−	11.5923i	−0.394607	−	0.394607i	−0.876326	+	0.481719i	$0.840013\pi$
$864$	−7.49410	−	23.5685i	−0.254954	−	0.801816i
$865$	−1.17886	+	2.84603i	−0.0400825	+	0.0967678i
$866$	2.68223	−	4.64575i	0.0911458	−	0.157869i
$867$	−29.1808	−	3.93475i	−0.991031	−	0.133631i
$868$	1.67259	+	2.89701i	0.0567715	+	0.0983311i
$869$	3.75911	−	0.494896i	0.127519	−	0.0167882i
$870$	−15.7309	+	10.3647i	−0.533329	+	0.351395i
$871$	9.23227	−	2.47378i	0.312824	−	0.0838208i
$872$	−4.31509	+	6.45798i	−0.146127	+	0.218695i
$873$	−18.0412	+	35.4224i	−0.610603	+	1.19886i
$874$	7.90521	−	5.28209i	0.267398	−	0.178669i
$875$	3.75844	−	28.5482i	0.127058	−	0.965104i
$876$	6.43347	+	24.6461i	0.217367	+	0.832713i
$877$	−0.126362	+	0.256237i	−0.00426694	+	0.00865250i	−0.898996	−	0.437957i	$-0.855702\pi$
$877$	−0.126362	+	0.256237i	−0.00426694	+	0.00865250i	0.894729	+	0.446610i	$0.147369\pi$
$878$	40.4206	−	13.7209i	1.36413	−	0.463060i
$879$	−6.47603	+	7.28893i	−0.218431	+	0.245850i
$880$	4.29718	+	16.0373i	0.144858	+	0.540617i
$881$	−4.52996	−	22.7737i	−0.152618	−	0.767264i	−0.978953	−	0.204085i	$-0.934578\pi$
$881$	−4.52996	−	22.7737i	−0.152618	−	0.767264i	0.826335	−	0.563179i	$-0.190422\pi$
$882$	2.65778	−	18.3517i	0.0894921	−	0.617933i
$883$			39.9852i			1.34561i	0.739821	+	0.672804i	$0.234910\pi$
$883$			39.9852i			1.34561i	−0.739821	+	0.672804i	$0.765090\pi$
$884$	−6.35098	+	2.89035i	−0.213607	+	0.0972129i
$885$	9.93911	−	4.04186i	0.334100	−	0.135866i
$886$	5.10591	+	38.7832i	0.171536	+	1.30295i
$887$	23.5617	+	26.8669i	0.791123	+	0.902103i	0.997073	−	0.0764596i	$-0.0243616\pi$
$887$	23.5617	+	26.8669i	0.791123	+	0.902103i	−0.205950	+	0.978563i	$0.566028\pi$
$888$	−28.9674	+	3.62334i	−0.972083	+	0.121591i
$889$	13.7628	−	6.78706i	0.461589	−	0.227631i
$890$	21.1902	+	4.21500i	0.710299	+	0.141287i
$891$	25.9336	−	16.3748i	0.868808	−	0.548577i
$892$	8.20715	+	19.8138i	0.274796	+	0.663416i
$893$	6.45061	+	0.849239i	0.215861	+	0.0284187i
$894$	−1.84512	+	25.6136i	−0.0617101	+	0.856649i
$895$	0.625647	+	1.84310i	0.0209131	+	0.0616079i
$896$	−2.70999	+	41.3465i	−0.0905344	+	1.38129i
$897$	9.35454	+	3.94580i	0.312339	+	0.131746i
$898$	−12.0772	+	35.5783i	−0.403022	+	1.18726i
$899$	6.87467	+	2.84758i	0.229283	+	0.0949721i
$900$	−10.6114	+	2.69681i	−0.353713	+	0.0898938i
$901$	6.67773	−	4.16791i	0.222467	−	0.138853i
$902$	24.2236	+	13.9855i	0.806559	+	0.465667i
$903$	−31.9100	+	54.4539i	−1.06190	+	1.81211i
$904$	16.2954	−	14.2906i	0.541975	−	0.475300i
$905$	6.71743	+	1.79993i	0.223295	+	0.0598317i
$906$	−23.0935	−	20.5180i	−0.767230	−	0.681664i
$907$	−21.8940	−	19.2005i	−0.726978	−	0.637543i	0.213678	−	0.976904i	$-0.431456\pi$
$907$	−21.8940	−	19.2005i	−0.726978	−	0.637543i	−0.940656	+	0.339361i	$0.889789\pi$
$908$	0.466925	+	0.698802i	0.0154954	+	0.0231906i
$909$	−16.9499	+	2.00898i	−0.562192	+	0.0666338i
$910$	−9.40006	+	3.89363i	−0.311609	+	0.129073i
$911$	−0.570435	−	8.70315i	−0.0188994	−	0.288348i	−0.996838	−	0.0794573i	$-0.974681\pi$
$911$	−0.570435	−	8.70315i	−0.0188994	−	0.288348i	0.977939	−	0.208891i	$-0.0669854\pi$
$912$	−15.1669	+	2.91511i	−0.502225	+	0.0965289i
$913$	−28.8355	−	1.88998i	−0.954316	−	0.0625492i
$914$	−2.59454	+	9.68294i	−0.0858196	+	0.320283i
$915$	5.06122	−	10.0981i	0.167319	−	0.333832i
$916$	−15.7326	−	20.5031i	−0.519820	−	0.677442i
$917$	−41.8497			−1.38200
$918$	7.65614	+	35.6836i	0.252690	+	1.17774i
$919$	20.8860			0.688965			0.344483	−	0.938793i	$-0.388054\pi$
$919$	20.8860			0.688965			0.344483	+	0.938793i	$0.388054\pi$
$920$	3.47280	+	4.52585i	0.114495	+	0.149213i
$921$	−3.17878	+	6.34227i	−0.104744	+	0.208985i
$922$	−2.49432	+	9.30893i	−0.0821460	+	0.306573i
$923$	31.1977	+	2.04481i	1.02689	+	0.0673056i
$924$	17.0420	−	3.27553i	0.560642	−	0.107757i
$925$	2.38469	+	36.3833i	0.0784080	+	1.19628i
$926$	−24.4357	+	10.1216i	−0.803007	+	0.332616i
$927$	−4.38010	+	10.1996i	−0.143861	+	0.334998i
$928$	−17.2933	−	25.8813i	−0.567680	−	0.849594i
$929$	30.2506	+	26.5291i	0.992491	+	0.870391i	0.991565	−	0.129609i	$-0.0413721\pi$
$929$	30.2506	+	26.5291i	0.992491	+	0.870391i	0.000925422		1.00000i	$0.499705\pi$
$930$	−2.45008	−	2.17684i	−0.0803414	−	0.0713813i
$931$	−6.26254	−	1.67804i	−0.205246	−	0.0549956i
$932$	−10.5724	+	9.27174i	−0.346310	+	0.303706i
$933$	16.5167	−	28.1855i	0.540732	−	0.922752i
$934$	10.2643	+	5.92607i	0.335857	+	0.193907i
$935$	−2.25707	−	13.5307i	−0.0738142	−	0.442500i
$936$	−7.35014	−	7.54264i	−0.240247	−	0.246539i
$937$	5.85654	+	2.42586i	0.191325	+	0.0792493i	0.476289	−	0.879289i	$-0.341982\pi$
$937$	5.85654	+	2.42586i	0.191325	+	0.0792493i	−0.284964	+	0.958538i	$0.591982\pi$
$938$	9.09216	−	26.7846i	0.296869	−	0.874549i
$939$	33.0434	+	13.9379i	1.07833	+	0.454845i
$940$	0.209676	−	3.19903i	0.00683887	−	0.104341i
$941$	5.82901	+	17.1717i	0.190020	+	0.559782i	0.999630	−	0.0271862i	$-0.00865472\pi$
$941$	5.82901	+	17.1717i	0.190020	+	0.559782i	−0.809610	+	0.586968i	$0.800321\pi$
$942$	−4.11619	+	57.1403i	−0.134113	+	1.86173i
$943$	14.9215	+	1.96445i	0.485911	+	0.0639714i
$944$	12.1176	+	29.2544i	0.394394	+	0.952151i
$945$	2.91141	+	16.2801i	0.0947081	+	0.529592i
$946$	−63.6391	−	12.6586i	−2.06909	−	0.411567i
$947$	29.9569	−	14.7731i	0.973469	−	0.480062i	0.115245	−	0.993337i	$-0.463235\pi$
$947$	29.9569	−	14.7731i	0.973469	−	0.480062i	0.858224	+	0.513276i	$0.171568\pi$
$948$	1.72444	−	0.215699i	0.0560073	−	0.00700558i
$949$	20.1772	+	23.0076i	0.654979	+	0.746860i
$950$	1.60780	+	12.2125i	0.0521641	+	0.396225i
$951$	10.0575	−	4.09003i	0.326138	−	0.132628i
$952$	4.05484	−	24.8168i	0.131418	−	0.804318i
$953$		−	50.5808i		−	1.63847i	−0.573455	−	0.819237i	$-0.694397\pi$
$953$		−	50.5808i		−	1.63847i	0.573455	−	0.819237i	$-0.305603\pi$
$954$	−7.66305	−	6.03902i	−0.248101	−	0.195520i
$955$	1.13436	+	5.70282i	0.0367071	+	0.184539i
$956$	6.32092	+	23.5900i	0.204433	+	0.762955i
$957$	25.6394	−	28.8578i	0.828804	−	0.932840i
$958$	7.25201	−	2.46173i	0.234302	−	0.0795348i
$959$	0.754308	−	1.52958i	0.0243579	−	0.0493929i
$960$	−0.799933	−	3.06447i	−0.0258177	−	0.0989054i
$961$	3.87734	−	29.4513i	0.125075	−	0.950042i
$962$	23.9477	−	16.0013i	0.772105	−	0.515904i
$963$	−45.7122	+	2.40323i	−1.47305	+	0.0774429i
$964$	−8.51793	+	12.7480i	−0.274344	+	0.410585i
$965$	−23.3040	+	6.24429i	−0.750183	+	0.201011i
$966$	25.0895	−	16.5307i	0.807241	−	0.531868i
$967$	0.134436	−	0.0176988i	0.00432316	−	0.000569154i	−0.128364	−	0.991727i	$-0.540973\pi$
$967$	0.134436	−	0.0176988i	0.00432316	−	0.000569154i	0.132687	+	0.991158i	$0.457639\pi$
$968$	−0.573749	−	0.993762i	−0.0184410	−	0.0319407i
$969$	12.7048	−	1.18980i	0.408138	−	0.0382220i
$970$	11.0184	−	19.0845i	0.353780	−	0.612766i
$971$	10.9066	−	26.3310i	0.350011	−	0.845001i	−0.646607	−	0.762824i	$-0.723812\pi$
$971$	10.9066	−	26.3310i	0.350011	−	0.845001i	0.996618	−	0.0821778i	$-0.0261875\pi$
$972$	11.9351	−	7.42853i	0.382818	−	0.238270i
$973$	−32.8699	−	32.8699i	−1.05376	−	1.05376i
$974$	4.25405	+	8.62636i	0.136309	+	0.276407i
$975$	−9.94534	+	8.60877i	−0.318506	+	0.275701i
$976$	29.8972	+	14.7437i	0.956986	+	0.471933i
$977$	−22.9950	−	17.6447i	−0.735676	−	0.564504i	0.171536	−	0.985178i	$-0.445127\pi$
$977$	−22.9950	−	17.6447i	−0.735676	−	0.564504i	−0.907212	+	0.420674i	$0.861794\pi$
$978$	21.4322	+	21.7110i	0.685327	+	0.694243i
$979$	−44.1774	+	2.89554i	−1.41192	+	0.0925418i
$980$	−0.623246	+	3.13327i	−0.0199089	+	0.100089i
$981$	−11.7419	−	4.15583i	−0.374889	−	0.132685i
$982$	−5.02475	+	5.02475i	−0.160346	+	0.160346i
$983$	13.2002	+	4.48085i	0.421020	+	0.142917i	0.523906	−	0.851776i	$-0.324474\pi$
$983$	13.2002	+	4.48085i	0.421020	+	0.142917i	−0.102886	+	0.994693i	$0.532808\pi$
$984$	−13.4697	−	7.89325i	−0.429399	−	0.251628i
$985$	11.7801	−	6.80123i	0.375344	−	0.216705i
$986$	21.7206	+	40.4741i	0.691725	+	1.28896i
$987$	20.3675	+	2.81546i	0.648306	+	0.0896171i
$988$	2.39904	−	1.84085i	0.0763237	−	0.0585653i
$989$	−34.2421	+	6.81117i	−1.08883	+	0.216583i
$990$	−14.8332	+	8.31021i	−0.471430	+	0.264116i
$991$	−13.4573	−	8.99189i	−0.427485	−	0.285637i	0.323157	−	0.946345i	$-0.395256\pi$
$991$	−13.4573	−	8.99189i	−0.427485	−	0.285637i	−0.750642	+	0.660709i	$0.770256\pi$
$992$	3.57058	−	4.07147i	0.113366	−	0.129269i
$993$	−19.6178	+	28.9534i	−0.622554	+	0.918807i
$994$	56.3253	−	73.4046i	1.78653	−	2.32825i
$995$	9.04292	−	11.7850i	0.286680	−	0.373609i
$996$	−13.2111	−	0.951682i	−0.418609	−	0.0301552i
$997$	4.18853	−	4.77610i	0.132652	−	0.151261i	−0.681700	−	0.731632i	$-0.738759\pi$
$997$	4.18853	−	4.77610i	0.132652	−	0.151261i	0.814352	+	0.580371i	$0.197092\pi$
$998$	−4.06076	−	2.71332i	−0.128541	−	0.0858885i
$999$	−17.0739	−	43.5916i	−0.540193	−	1.37918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.4	✓	256
3.2	odd	2		459.2.y.a.62.13		256
9.4	even	3		459.2.y.a.368.13		256
9.5	odd	6	inner	153.2.s.a.113.4	yes	256
17.14	odd	16	inner	153.2.s.a.65.4	yes	256
51.14	even	16		459.2.y.a.116.13		256
153.14	even	48	inner	153.2.s.a.14.4	yes	256
153.31	odd	48		459.2.y.a.422.13		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.4	✓	256	1.1	even	1	trivial
153.2.s.a.14.4	yes	256	153.14	even	48	inner
153.2.s.a.65.4	yes	256	17.14	odd	16	inner
153.2.s.a.113.4	yes	256	9.5	odd	6	inner
459.2.y.a.62.13		256	3.2	odd	2
459.2.y.a.116.13		256	51.14	even	16
459.2.y.a.368.13		256	9.4	even	3
459.2.y.a.422.13		256	153.31	odd	48

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03701 - 1.35146i) q^{2} +(-0.776090 + 1.54845i) q^{3} +(-0.233410 + 0.871097i) q^{4} +(-0.974191 - 0.0638519i) q^{5} +(2.89747 - 0.556901i) q^{6} +(-0.213223 - 3.25316i) q^{7} +(-1.72831 + 0.715890i) q^{8} +(-1.79537 - 2.40347i) q^{9} +O(q^{10})\)	\(q+(-1.03701 - 1.35146i) q^{2} +(-0.776090 + 1.54845i) q^{3} +(-0.233410 + 0.871097i) q^{4} +(-0.974191 - 0.0638519i) q^{5} +(2.89747 - 0.556901i) q^{6} +(-0.213223 - 3.25316i) q^{7} +(-1.72831 + 0.715890i) q^{8} +(-1.79537 - 2.40347i) q^{9} +(0.923953 + 1.38279i) q^{10} +(-2.56215 - 2.24695i) q^{11} +(-1.16770 - 1.03747i) q^{12} +(-1.81264 - 0.485696i) q^{13} +(-4.17539 + 3.66172i) q^{14} +(0.854931 - 1.45893i) q^{15} +(4.32178 + 2.49518i) q^{16} +(-3.35545 - 2.39603i) q^{17} +(-1.38637 + 4.91878i) q^{18} +(1.65080 + 0.683785i) q^{19} +(0.283007 - 0.833711i) q^{20} +(5.20282 + 2.19458i) q^{21} +(-0.379677 + 5.79275i) q^{22} +(1.00404 + 2.95780i) q^{23} +(0.232808 - 3.23179i) q^{24} +(-4.01225 - 0.528223i) q^{25} +(1.22333 + 2.95338i) q^{26} +(5.11500 - 0.914729i) q^{27} +(2.88358 + 0.573580i) q^{28} +(5.86551 - 2.89255i) q^{29} +(-2.85825 + 0.357520i) q^{30} +(0.750196 + 0.855435i) q^{31} +(-0.621243 - 4.71881i) q^{32} +(5.46774 - 2.22352i) q^{33} +(0.241494 + 7.01945i) q^{34} +3.18281i q^{35} +(2.51271 - 1.00295i) q^{36} +(-1.75772 - 8.83664i) q^{37} +(-0.787793 - 2.94008i) q^{38} +(2.15885 - 2.42984i) q^{39} +(1.72942 - 0.587058i) q^{40} +(2.13108 - 4.32140i) q^{41} +(-2.42950 - 9.30718i) q^{42} +(-1.45892 + 11.0816i) q^{43} +(2.55534 - 1.70742i) q^{44} +(1.59557 + 2.45607i) q^{45} +(2.95614 - 4.42418i) q^{46} +(3.51719 - 0.942428i) q^{47} +(-7.21774 + 4.75556i) q^{48} +(-3.59745 + 0.473613i) q^{49} +(3.44687 + 5.97016i) q^{50} +(6.31426 - 3.33619i) q^{51} +(0.846177 - 1.46562i) q^{52} +(-0.730606 + 1.76384i) q^{53} +(-6.54053 - 5.96413i) q^{54} +(2.35256 + 2.35256i) q^{55} +(2.69742 + 5.46983i) q^{56} +(-2.33998 + 2.02550i) q^{57} +(-9.99174 - 4.92738i) q^{58} +(5.03398 + 3.86271i) q^{59} +(1.07132 + 1.08526i) q^{60} +(6.66557 - 0.436884i) q^{61} +(0.378123 - 1.90095i) q^{62} +(-7.43604 + 6.35309i) q^{63} +(1.32440 - 1.32440i) q^{64} +(1.73485 + 0.588902i) q^{65} +(-8.67509 - 5.08360i) q^{66} +(-4.41090 + 2.54663i) q^{67} +(2.87037 - 2.36366i) q^{68} +(-5.35922 - 0.740820i) q^{69} +(4.30143 - 3.30061i) q^{70} +(-16.3403 + 3.25028i) q^{71} +(4.82358 + 2.86865i) q^{72} +(-13.5589 - 9.05977i) q^{73} +(-10.1196 + 11.5392i) q^{74} +(3.93179 - 5.80281i) q^{75} +(-0.980957 + 1.27841i) q^{76} +(-6.76336 + 8.81419i) q^{77} +(-5.52257 - 0.397827i) q^{78} +(-0.733584 + 0.836492i) q^{79} +(-4.05092 - 2.70674i) q^{80} +(-2.55329 + 8.63022i) q^{81} +(-8.05013 + 1.60127i) q^{82} +(6.72737 - 5.16209i) q^{83} +(-3.12608 + 4.01992i) q^{84} +(3.11586 + 2.54845i) q^{85} +(16.4893 - 9.52008i) q^{86} +(-0.0732047 + 11.3273i) q^{87} +(6.03677 + 2.04921i) q^{88} +(9.18621 - 9.18621i) q^{89} +(1.66466 - 4.70331i) q^{90} +(-1.19355 + 6.00038i) q^{91} +(-2.81088 + 0.184235i) q^{92} +(-1.90681 + 0.497744i) q^{93} +(-4.92101 - 3.77602i) q^{94} +(-1.56454 - 0.771545i) q^{95} +(7.78897 + 2.70026i) q^{96} +(-5.86063 - 11.8842i) q^{97} +(4.37066 + 4.37066i) q^{98} +(-0.800450 + 10.1921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more