LMFDB - Embedded newform 62.2.g.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(7,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("62.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, 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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			19.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	62.19
Dual form			62.2.g.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(1.47815 + 0.658114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.204489 + 0.354185i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.898504i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.255585 - 0.283856i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(1.47815 + 0.658114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.204489 + 0.354185i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.898504i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.255585 - 0.283856i) q^{9} +(0.373619 - 0.166346i) q^{10} +(-2.41355 - 0.513015i) q^{11} +(-0.169131 + 1.60917i) q^{12} +(0.199920 + 1.90211i) q^{13} +(-1.18264 + 0.251377i) q^{14} +(-0.535358 + 0.388960i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-7.88696 + 1.67642i) q^{17} +(0.0399263 + 0.379874i) q^{18} +(-0.0307895 + 0.292943i) q^{19} +(-0.400040 - 0.0850311i) q^{20} +(1.78716 - 0.795697i) q^{21} +(1.65106 + 1.83368i) q^{22} +(1.96698 - 6.05373i) q^{23} +(1.08268 - 1.20243i) q^{24} +(2.41637 + 4.18527i) q^{25} +(0.956295 - 1.65635i) q^{26} +(-1.69098 - 5.20431i) q^{27} +(1.10453 + 0.491768i) q^{28} +(7.56444 + 5.49589i) q^{29} +0.661739 q^{30} +(3.20731 - 4.55117i) q^{31} +1.00000 q^{32} +(-3.22995 - 2.34670i) q^{33} +(7.36606 + 3.27958i) q^{34} +(0.152802 + 0.470275i) q^{35} +(0.190983 - 0.330792i) q^{36} +(-2.71878 - 4.70907i) q^{37} +(0.197097 - 0.218898i) q^{38} +(-0.956295 + 2.94317i) q^{39} +(0.273659 + 0.303929i) q^{40} +(-1.97124 + 0.877654i) q^{41} +(-1.91355 - 0.406737i) q^{42} +(-0.558955 + 5.31810i) q^{43} +(-0.257920 - 2.45395i) q^{44} +(0.152802 - 0.0324790i) q^{45} +(-5.14961 + 3.74141i) q^{46} +(1.19837 - 0.870670i) q^{47} +(-1.58268 + 0.336408i) q^{48} +(0.578898 + 5.50784i) q^{49} +(0.505159 - 4.80626i) q^{50} +(-12.7614 - 2.71251i) q^{51} +(-1.74724 + 0.777921i) q^{52} +(1.93589 + 2.15002i) q^{53} +(-1.69098 + 5.20431i) q^{54} +(0.675244 - 0.749935i) q^{55} +(-0.604528 - 1.04707i) q^{56} +(-0.238301 + 0.412750i) q^{57} +(-2.88936 - 8.89253i) q^{58} +(8.67081 + 3.86049i) q^{59} +(-0.535358 - 0.388960i) q^{60} +1.44704 q^{61} +(-5.26988 + 1.79676i) q^{62} -0.461819 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.714580 - 0.318152i) q^{65} +(1.23373 + 3.79704i) q^{66} +(4.02090 - 6.96440i) q^{67} +(-4.03158 - 6.98290i) q^{68} +(6.89153 - 7.65382i) q^{69} +(0.152802 - 0.470275i) q^{70} +(5.51206 + 6.12177i) q^{71} +(-0.348943 + 0.155360i) q^{72} +(-6.70528 - 1.42525i) q^{73} +(-0.568381 + 5.40778i) q^{74} +(0.817364 + 7.77670i) q^{75} +(-0.288120 + 0.0612417i) q^{76} +(-2.41355 + 1.75354i) q^{77} +(2.50361 - 1.81898i) q^{78} +(-5.91414 + 1.25709i) q^{79} +(-0.0427497 - 0.406737i) q^{80} +(0.805727 - 7.66598i) q^{81} +(2.11064 + 0.448631i) q^{82} +(-4.61797 + 2.05605i) q^{83} +(1.30902 + 1.45381i) q^{84} +(1.01903 - 3.13625i) q^{85} +(3.57811 - 3.97389i) q^{86} +(7.56444 + 13.1020i) q^{87} +(-1.23373 + 2.13689i) q^{88} +(-0.362449 - 1.11550i) q^{89} +(-0.142710 - 0.0635385i) q^{90} +(1.87080 + 1.35921i) q^{91} +6.36527 q^{92} +(7.73607 - 4.61653i) q^{93} -1.48127 q^{94} +(-0.0974597 - 0.0708086i) q^{95} +(1.47815 + 0.658114i) q^{96} +(-3.44482 - 10.6021i) q^{97} +(2.76909 - 4.79621i) q^{98} +(0.471244 + 0.816219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	1.47815	+	0.658114i	0.853409	+	0.379962i	0.786346	−	0.617787i	$-0.211970\pi$
$3$	1.47815	+	0.658114i	0.853409	+	0.379962i	0.0670631	+	0.997749i	$0.478637\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.204489	+	0.354185i	−0.0914501	+	0.158396i	−0.908121	−	0.418707i	$-0.862484\pi$
$5$	−0.204489	+	0.354185i	−0.0914501	+	0.158396i	0.816671	+	0.577103i	$0.195817\pi$
$6$	−0.809017	−	1.40126i	−0.330280	−	0.572061i
$7$	0.809017	−	0.898504i	0.305780	−	0.339603i	−0.570596	−	0.821231i	$-0.693288\pi$
$7$	0.809017	−	0.898504i	0.305780	−	0.339603i	0.876376	+	0.481628i	$0.159954\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.255585	−	0.283856i	−0.0851950	−	0.0946187i
$10$	0.373619	−	0.166346i	0.118149	−	0.0526032i
$11$	−2.41355	−	0.513015i	−0.727711	−	0.154680i	−0.170864	−	0.985295i	$-0.554656\pi$
$11$	−2.41355	−	0.513015i	−0.727711	−	0.154680i	−0.556847	+	0.830615i	$0.687989\pi$
$12$	−0.169131	+	1.60917i	−0.0488238	+	0.464527i
$13$	0.199920	+	1.90211i	0.0554479	+	0.527551i	0.986628	+	0.162991i	$0.0521141\pi$
$13$	0.199920	+	1.90211i	0.0554479	+	0.527551i	−0.931180	+	0.364560i	$0.881219\pi$
$14$	−1.18264	+	0.251377i	−0.316073	+	0.0671833i
$15$	−0.535358	+	0.388960i	−0.138229	+	0.100429i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−7.88696	+	1.67642i	−1.91287	+	0.406593i	−0.999999	−	0.00165751i	$-0.999472\pi$
$17$	−7.88696	+	1.67642i	−1.91287	+	0.406593i	−0.912870	+	0.408250i	$0.866139\pi$
$18$	0.0399263	+	0.379874i	0.00941072	+	0.0895371i
$19$	−0.0307895	+	0.292943i	−0.00706360	+	0.0672057i	−0.997486	−	0.0708659i	$-0.977424\pi$
$19$	−0.0307895	+	0.292943i	−0.00706360	+	0.0672057i	0.990422	+	0.138072i	$0.0440904\pi$
$20$	−0.400040	−	0.0850311i	−0.0894516	−	0.0190135i
$21$	1.78716	−	0.795697i	0.389991	−	0.173635i
$22$	1.65106	+	1.83368i	0.352006	+	0.390943i
$23$	1.96698	−	6.05373i	0.410143	−	1.26229i	−0.506380	−	0.862310i	$-0.669017\pi$
$23$	1.96698	−	6.05373i	0.410143	−	1.26229i	0.916524	−	0.399981i	$-0.130983\pi$
$24$	1.08268	−	1.20243i	0.221000	−	0.245446i
$25$	2.41637	+	4.18527i	0.483274	+	0.837055i
$26$	0.956295	−	1.65635i	0.187545	−	0.324837i
$27$	−1.69098	−	5.20431i	−0.325430	−	1.00157i
$28$	1.10453	+	0.491768i	0.208736	+	0.0929354i
$29$	7.56444	+	5.49589i	1.40468	+	1.02056i	0.994069	+	0.108750i	$0.0346848\pi$
$29$	7.56444	+	5.49589i	1.40468	+	1.02056i	0.410612	+	0.911810i	$0.365315\pi$
$30$	0.661739			0.120816
$31$	3.20731	−	4.55117i	0.576050	−	0.817414i
$31$	3.20731	−	4.55117i	0.576050	−	0.817414i
$32$	1.00000			0.176777
$33$	−3.22995	−	2.34670i	−0.562263	−	0.408508i
$34$	7.36606	+	3.27958i	1.26327	+	0.562444i
$35$	0.152802	+	0.470275i	0.0258282	+	0.0794910i
$36$	0.190983	−	0.330792i	0.0318305	−	0.0551320i
$37$	−2.71878	−	4.70907i	−0.446965	−	0.774167i	0.551221	−	0.834359i	$-0.314162\pi$
$37$	−2.71878	−	4.70907i	−0.446965	−	0.774167i	−0.998187	+	0.0601923i	$0.980829\pi$
$38$	0.197097	−	0.218898i	0.0319733	−	0.0355100i
$39$	−0.956295	+	2.94317i	−0.153130	+	0.471285i
$40$	0.273659	+	0.303929i	0.0432693	+	0.0480554i
$41$	−1.97124	+	0.877654i	−0.307857	+	0.137067i	−0.554850	−	0.831951i	$-0.687224\pi$
$41$	−1.97124	+	0.877654i	−0.307857	+	0.137067i	0.246993	+	0.969017i	$0.420558\pi$
$42$	−1.91355	−	0.406737i	−0.295266	−	0.0627608i
$43$	−0.558955	+	5.31810i	−0.0852399	+	0.811003i	0.865478	+	0.500947i	$0.167015\pi$
$43$	−0.558955	+	5.31810i	−0.0852399	+	0.811003i	−0.950718	+	0.310057i	$0.899652\pi$
$44$	−0.257920	−	2.45395i	−0.0388830	−	0.369947i
$45$	0.152802	−	0.0324790i	0.0227783	−	0.00484168i
$46$	−5.14961	+	3.74141i	−0.759269	+	0.551641i
$47$	1.19837	−	0.870670i	0.174801	−	0.127000i	−0.496945	−	0.867782i	$-0.665545\pi$
$47$	1.19837	−	0.870670i	0.174801	−	0.127000i	0.671746	+	0.740782i	$0.265545\pi$
$48$	−1.58268	+	0.336408i	−0.228440	+	0.0485563i
$49$	0.578898	+	5.50784i	0.0826997	+	0.786835i
$50$	0.505159	−	4.80626i	0.0714402	−	0.679708i
$51$	−12.7614	−	2.71251i	−1.78695	−	0.379828i
$52$	−1.74724	+	0.777921i	−0.242298	+	0.107878i
$53$	1.93589	+	2.15002i	0.265914	+	0.295328i	0.861284	−	0.508124i	$-0.169661\pi$
$53$	1.93589	+	2.15002i	0.265914	+	0.295328i	−0.595369	+	0.803452i	$0.702994\pi$
$54$	−1.69098	+	5.20431i	−0.230114	+	0.708217i
$55$	0.675244	−	0.749935i	0.0910499	−	0.101121i
$56$	−0.604528	−	1.04707i	−0.0807835	−	0.139921i
$57$	−0.238301	+	0.412750i	−0.0315638	+	0.0546700i
$58$	−2.88936	−	8.89253i	−0.379391	−	1.16765i
$59$	8.67081	+	3.86049i	1.12884	+	0.502594i	0.884241	−	0.467030i	$-0.154676\pi$
$59$	8.67081	+	3.86049i	1.12884	+	0.502594i	0.244602	+	0.969624i	$0.421343\pi$
$60$	−0.535358	−	0.388960i	−0.0691144	−	0.0502146i
$61$	1.44704			0.185274			0.0926369	−	0.995700i	$-0.470470\pi$
$61$	1.44704			0.185274			0.0926369	+	0.995700i	$0.470470\pi$
$62$	−5.26988	+	1.79676i	−0.669276	+	0.228189i
$63$	−0.461819			−0.0581837
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.714580	−	0.318152i	−0.0886328	−	0.0394619i
$66$	1.23373	+	3.79704i	0.151862	+	0.467383i
$67$	4.02090	−	6.96440i	0.491231	−	0.850837i	−0.508718	−	0.860933i	$-0.669880\pi$
$67$	4.02090	−	6.96440i	0.491231	−	0.850837i	0.999949	+	0.0100964i	$0.00321383\pi$
$68$	−4.03158	−	6.98290i	−0.488901	−	0.846801i
$69$	6.89153	−	7.65382i	0.829642	−	0.921411i
$70$	0.152802	−	0.470275i	0.0182633	−	0.0562086i
$71$	5.51206	+	6.12177i	0.654161	+	0.726520i	0.975391	−	0.220481i	$-0.0707628\pi$
$71$	5.51206	+	6.12177i	0.654161	+	0.726520i	−0.321230	+	0.947001i	$0.604096\pi$
$72$	−0.348943	+	0.155360i	−0.0411234	+	0.0183093i
$73$	−6.70528	−	1.42525i	−0.784793	−	0.166813i	−0.201948	−	0.979396i	$-0.564727\pi$
$73$	−6.70528	−	1.42525i	−0.784793	−	0.166813i	−0.582845	+	0.812583i	$0.698061\pi$
$74$	−0.568381	+	5.40778i	−0.0660729	+	0.628642i
$75$	0.817364	+	7.77670i	0.0943810	+	0.897976i
$76$	−0.288120	+	0.0612417i	−0.0330496	+	0.00702491i
$77$	−2.41355	+	1.75354i	−0.275049	+	0.199835i
$78$	2.50361	−	1.81898i	0.283478	−	0.205959i
$79$	−5.91414	+	1.25709i	−0.665392	+	0.141433i	−0.528212	−	0.849113i	$-0.677137\pi$
$79$	−5.91414	+	1.25709i	−0.665392	+	0.141433i	−0.137180	+	0.990546i	$0.543804\pi$
$80$	−0.0427497	−	0.406737i	−0.00477957	−	0.0454745i
$81$	0.805727	−	7.66598i	0.0895252	−	0.851775i
$82$	2.11064	+	0.448631i	0.233081	+	0.0495430i
$83$	−4.61797	+	2.05605i	−0.506888	+	0.225681i	−0.644215	−	0.764845i	$-0.722816\pi$
$83$	−4.61797	+	2.05605i	−0.506888	+	0.225681i	0.137327	+	0.990526i	$0.456149\pi$
$84$	1.30902	+	1.45381i	0.142825	+	0.158624i
$85$	1.01903	−	3.13625i	0.110529	−	0.340174i
$86$	3.57811	−	3.97389i	0.385837	−	0.428516i
$87$	7.56444	+	13.1020i	0.810993	+	1.40468i
$88$	−1.23373	+	2.13689i	−0.131516	+	0.227793i
$89$	−0.362449	−	1.11550i	−0.0384195	−	0.118243i	0.930007	−	0.367541i	$-0.119800\pi$
$89$	−0.362449	−	1.11550i	−0.0384195	−	0.118243i	−0.968427	+	0.249298i	$0.919800\pi$
$90$	−0.142710	−	0.0635385i	−0.0150429	−	0.00669755i
$91$	1.87080	+	1.35921i	0.196113	+	0.142484i
$92$	6.36527			0.663626
$93$	7.73607	−	4.61653i	0.802193	−	0.478711i
$94$	−1.48127			−0.152782
$95$	−0.0974597	−	0.0708086i	−0.00999915	−	0.00726481i
$96$	1.47815	+	0.658114i	0.150863	+	0.0671684i
$97$	−3.44482	−	10.6021i	−0.349769	−	1.07648i	−0.958981	−	0.283470i	$-0.908514\pi$
$97$	−3.44482	−	10.6021i	−0.349769	−	1.07648i	0.609212	−	0.793007i	$-0.291486\pi$
$98$	2.76909	−	4.79621i	0.279720	−	0.484490i
$99$	0.471244	+	0.816219i	0.0473618	+	0.0820330i
$100$	−3.23373	+	3.59142i	−0.323373	+	0.359142i
$101$	−1.74064	+	5.35713i	−0.173200	+	0.533054i	−0.999547	−	0.0301073i	$-0.990415\pi$
$101$	−1.74064	+	5.35713i	−0.173200	+	0.533054i	0.826347	+	0.563161i	$0.190415\pi$
$102$	8.72979	+	9.69541i	0.864378	+	0.959989i
$103$	−14.7252	+	6.55609i	−1.45092	+	0.645991i	−0.972661	−	0.232229i	$-0.925398\pi$
$103$	−14.7252	+	6.55609i	−1.45092	+	0.645991i	−0.478258	+	0.878219i	$0.658732\pi$
$104$	1.87080	+	0.397650i	0.183447	+	0.0389928i
$105$	−0.0836311	+	0.795697i	−0.00816156	+	0.0776521i
$106$	−0.302415	−	2.87729i	−0.0293732	−	0.279467i
$107$	11.7747	−	2.50278i	1.13830	−	0.241953i	0.400059	−	0.916489i	$-0.368990\pi$
$107$	11.7747	−	2.50278i	1.13830	−	0.241953i	0.738242	+	0.674536i	$0.235656\pi$
$108$	4.42705	−	3.21644i	0.425993	−	0.309502i
$109$	15.4704	−	11.2399i	1.48180	−	1.07659i	0.504826	−	0.863221i	$-0.331557\pi$
$109$	15.4704	−	11.2399i	1.48180	−	1.07659i	0.976972	−	0.213368i	$-0.0684434\pi$
$110$	−0.987085	+	0.209811i	−0.0941148	+	0.0200047i
$111$	−0.919659	−	8.74997i	−0.0872902	−	0.830511i
$112$	−0.126381	+	1.20243i	−0.0119419	+	0.113619i
$113$	−11.1384	−	2.36755i	−1.04782	−	0.222720i	−0.348334	−	0.937370i	$-0.613253\pi$
$113$	−11.1384	−	2.36755i	−1.04782	−	0.222720i	−0.699482	+	0.714650i	$0.746586\pi$
$114$	0.435398	−	0.193852i	0.0407787	−	0.0181559i
$115$	1.74191	+	1.93459i	0.162434	+	0.180402i
$116$	−2.88936	+	8.89253i	−0.268270	+	0.825651i
$117$	0.488830	−	0.542900i	0.0451923	−	0.0501912i
$118$	−4.74569	−	8.21978i	−0.436876	−	0.756692i
$119$	−4.87441	+	8.44272i	−0.446836	+	0.773943i
$120$	0.204489	+	0.629351i	0.0186672	+	0.0574516i
$121$	−4.48698	−	1.99773i	−0.407908	−	0.181612i
$122$	−1.17068	−	0.850546i	−0.105988	−	0.0770048i
$123$	−3.49139			−0.314808
$124$	5.31953	+	1.64395i	0.477708	+	0.147631i
$125$	−4.02136			−0.359682
$126$	0.373619	+	0.271450i	0.0332846	+	0.0241827i
$127$	−15.5012	−	6.90159i	−1.37551	−	0.612417i	−0.420041	−	0.907505i	$-0.637984\pi$
$127$	−15.5012	−	6.90159i	−1.37551	−	0.612417i	−0.955470	+	0.295089i	$0.904651\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−4.32614	+	7.49309i	−0.380895	+	0.659730i
$130$	0.391103	+	0.677410i	0.0343020	+	0.0594128i
$131$	10.0287	−	11.1380i	0.876211	−	0.973131i	−0.123605	−	0.992332i	$-0.539445\pi$
$131$	10.0287	−	11.1380i	0.876211	−	0.973131i	0.999816	+	0.0192007i	$0.00611214\pi$
$132$	1.23373	−	3.79704i	0.107383	−	0.330490i
$133$	0.238301	+	0.264660i	0.0206633	+	0.0229490i
$134$	−7.34655	+	3.27089i	−0.634645	+	0.282562i
$135$	2.18907	+	0.465302i	0.188405	+	0.0400468i
$136$	−0.842830	+	8.01899i	−0.0722720	+	0.687623i
$137$	1.01982	+	9.70293i	0.0871290	+	0.828977i	0.947596	+	0.319471i	$0.103505\pi$
$137$	1.01982	+	9.70293i	0.0871290	+	0.828977i	−0.860467	+	0.509506i	$0.829828\pi$
$138$	−10.0742	+	2.14133i	−0.857570	+	0.182282i
$139$	−15.8370	+	11.5062i	−1.34327	+	0.975946i	−0.343958	+	0.938985i	$0.611768\pi$
$139$	−15.8370	+	11.5062i	−1.34327	+	0.975946i	−0.999317	+	0.0369612i	$0.988232\pi$
$140$	−0.400040	+	0.290646i	−0.0338095	+	0.0245641i
$141$	2.34437	−	0.498312i	0.197432	−	0.0419655i
$142$	−0.861069	−	8.19252i	−0.0722593	−	0.687501i
$143$	0.493296	−	4.69340i	0.0412515	−	0.392482i
$144$	0.373619	+	0.0794152i	0.0311349	+	0.00661793i
$145$	−3.49340	+	1.55536i	−0.290111	+	0.129166i
$146$	4.58694	+	5.09432i	0.379618	+	0.421609i
$147$	−2.76909	+	8.52238i	−0.228391	+	0.702914i
$148$	3.63844	−	4.04090i	0.299078	−	0.332160i
$149$	−7.92640	−	13.7289i	−0.649356	−	1.12472i	−0.983277	−	0.182116i	$-0.941705\pi$
$149$	−7.92640	−	13.7289i	−0.649356	−	1.12472i	0.333921	−	0.942601i	$-0.391628\pi$
$150$	3.90977	−	6.77192i	0.319231	−	0.552925i
$151$	2.35634	+	7.25205i	0.191756	+	0.590164i	0.999999	+	0.00131509i	$0.000418608\pi$
$151$	2.35634	+	7.25205i	0.191756	+	0.590164i	−0.808243	+	0.588849i	$0.799581\pi$
$152$	0.269091	+	0.119807i	0.0218261	+	0.00971762i
$153$	2.49165	+	1.81029i	0.201438	+	0.146353i
$154$	2.98331			0.240402
$155$	0.956096	+	2.06664i	0.0767954	+	0.165997i
$156$	−3.09464			−0.247769
$157$	5.64051	+	4.09807i	0.450162	+	0.327062i	0.789660	−	0.613545i	$-0.210257\pi$
$157$	5.64051	+	4.09807i	0.450162	+	0.327062i	−0.339498	+	0.940607i	$0.610257\pi$
$158$	5.52353	+	2.45924i	0.439429	+	0.195646i
$159$	1.44657	+	4.45208i	0.114720	+	0.353073i
$160$	−0.204489	+	0.354185i	−0.0161662	+	0.0280007i
$161$	−3.84799	−	6.66491i	−0.303264	−	0.525269i
$162$	−5.15780	+	5.72831i	−0.405235	+	0.450059i
$163$	5.93414	−	18.2634i	0.464798	−	1.43050i	−0.394439	−	0.918922i	$-0.629061\pi$
$163$	5.93414	−	18.2634i	0.464798	−	1.43050i	0.859237	−	0.511578i	$-0.170939\pi$
$164$	−1.44385	−	1.60355i	−0.112745	−	0.125217i
$165$	1.49165	−	0.664127i	0.116125	−	0.0517022i
$166$	4.94453	+	1.05099i	0.383770	+	0.0815729i
$167$	1.30810	−	12.4458i	0.101224	−	0.963083i	−0.819556	−	0.573000i	$-0.805780\pi$
$167$	1.30810	−	12.4458i	0.101224	−	0.963083i	0.920780	−	0.390083i	$-0.127554\pi$
$168$	−0.204489	−	1.94558i	−0.0157766	−	0.150105i
$169$	9.13785	−	1.94231i	0.702912	−	0.149409i
$170$	−2.66785	+	1.93831i	−0.204615	+	0.148661i
$171$	0.0910229	−	0.0661320i	0.00696070	−	0.00505724i
$172$	−5.23054	+	1.11179i	−0.398825	+	0.0847729i
$173$	2.16712	+	20.6188i	0.164763	+	1.56761i	0.694525	+	0.719469i	$0.255615\pi$
$173$	2.16712	+	20.6188i	0.164763	+	1.56761i	−0.529762	+	0.848146i	$0.677719\pi$
$174$	1.58140	−	15.0460i	0.119885	−	1.14063i
$175$	5.71537	+	1.21484i	0.432041	+	0.0918332i
$176$	2.25414	−	1.00361i	0.169912	−	0.0756498i
$177$	10.2761	+	11.4128i	0.772399	+	0.857836i
$178$	−0.362449	+	1.11550i	−0.0271667	+	0.0836105i
$179$	−1.14728	+	1.27418i	−0.0857516	+	0.0952368i	−0.784493	−	0.620137i	$-0.787077\pi$
$179$	−1.14728	+	1.27418i	−0.0857516	+	0.0952368i	0.698742	+	0.715374i	$0.253744\pi$
$180$	0.0781077	+	0.135286i	0.00582180	+	0.0100837i
$181$	−2.68487	+	4.65033i	−0.199565	+	0.345656i	−0.948387	−	0.317114i	$-0.897286\pi$
$181$	−2.68487	+	4.65033i	−0.199565	+	0.345656i	0.748823	+	0.662770i	$0.230619\pi$
$182$	−0.714580	−	2.19925i	−0.0529682	−	0.163019i
$183$	2.13893	+	0.952314i	0.158114	+	0.0703970i
$184$	−5.14961	−	3.74141i	−0.379635	−	0.275821i
$185$	2.22384			0.163500
$186$	−8.97214	−	0.812299i	−0.657869	−	0.0595607i
$187$	19.8956			1.45491
$188$	1.19837	+	0.870670i	0.0874005	+	0.0635002i
$189$	−6.04413	−	2.69102i	−0.439646	−	0.195743i
$190$	0.0372263	+	0.114571i	0.00270068	+	0.00831184i
$191$	2.33672	−	4.04731i	0.169079	−	0.292853i	−0.769017	−	0.639228i	$-0.779254\pi$
$191$	2.33672	−	4.04731i	0.169079	−	0.292853i	0.938096	+	0.346375i	$0.112587\pi$
$192$	−0.809017	−	1.40126i	−0.0583858	−	0.101127i
$193$	2.51416	−	2.79226i	0.180973	−	0.200991i	−0.645832	−	0.763480i	$-0.723489\pi$
$193$	2.51416	−	2.79226i	0.180973	−	0.200991i	0.826805	+	0.562489i	$0.190156\pi$
$194$	−3.44482	+	10.6021i	−0.247324	+	0.761185i
$195$	−0.846875	−	0.940550i	−0.0606460	−	0.0673542i
$196$	−5.05938	+	2.25258i	−0.361384	+	0.160899i
$197$	10.8239	+	2.30069i	0.771171	+	0.163917i	0.576662	−	0.816983i	$-0.304355\pi$
$197$	10.8239	+	2.30069i	0.771171	+	0.163917i	0.194510	+	0.980901i	$0.437688\pi$
$198$	0.0985168	−	0.937325i	0.00700129	−	0.0666128i
$199$	0.399942	+	3.80520i	0.0283512	+	0.269743i	0.999510	+	0.0313088i	$0.00996754\pi$
$199$	0.399942	+	3.80520i	0.0283512	+	0.269743i	−0.971159	+	0.238434i	$0.923366\pi$
$200$	4.72713	−	1.00478i	0.334259	−	0.0710489i
$201$	10.5268	−	7.64820i	0.742506	−	0.539463i
$202$	4.55705	−	3.31089i	0.320633	−	0.232953i
$203$	11.0578	−	2.35042i	0.776108	−	0.164967i
$204$	−1.36373	−	12.9750i	−0.0954800	−	0.908431i
$205$	0.0922452	−	0.877654i	0.00644268	−	0.0612980i
$206$	15.7665	+	3.35128i	1.09851	+	0.233495i
$207$	−2.22112	+	0.988906i	−0.154378	+	0.0687337i
$208$	−1.27977	−	1.42133i	−0.0887363	−	0.0985516i
$209$	0.224596	−	0.691235i	0.0155356	−	0.0478137i
$210$	0.535358	−	0.594575i	0.0369432	−	0.0410296i
$211$	−4.59773	−	7.96350i	−0.316521	−	0.548230i	0.663239	−	0.748408i	$-0.269181\pi$
$211$	−4.59773	−	7.96350i	−0.316521	−	0.548230i	−0.979760	+	0.200178i	$0.935848\pi$
$212$	−1.44657	+	2.50553i	−0.0993507	+	0.172080i
$213$	4.11882	+	12.6764i	0.282217	+	0.868575i
$214$	−10.9970	−	4.89618i	−0.751740	−	0.334696i
$215$	−1.76929	−	1.28546i	−0.120665	−	0.0876680i
$216$	−5.47214			−0.372332
$217$	−1.49448	−	6.56376i	−0.101452	−	0.445577i
$218$	−19.1225			−1.29514
$219$	−8.97341	−	6.51957i	−0.606367	−	0.440552i
$220$	0.921892	+	0.410453i	0.0621540	+	0.0276727i
$221$	−4.76551	−	14.6667i	−0.320563	−	0.986592i
$222$	−4.39908	+	7.61944i	−0.295247	+	0.511383i
$223$	9.51929	+	16.4879i	0.637459	+	1.10411i	0.985989	+	0.166813i	$0.0533477\pi$
$223$	9.51929	+	16.4879i	0.637459	+	1.10411i	−0.348530	+	0.937298i	$0.613319\pi$
$224$	0.809017	−	0.898504i	0.0540547	−	0.0600339i
$225$	0.570427	−	1.75559i	0.0380285	−	0.117040i
$226$	7.61958	+	8.46240i	0.506847	+	0.562910i
$227$	−11.5679	+	5.15034i	−0.767785	+	0.341840i	−0.752974	−	0.658050i	$-0.771381\pi$
$227$	−11.5679	+	5.15034i	−0.767785	+	0.341840i	−0.0148112	+	0.999890i	$0.504715\pi$
$228$	−0.466187	−	0.0990912i	−0.0308740	−	0.00656247i
$229$	−0.855359	+	8.13819i	−0.0565237	+	0.537787i	0.929219	+	0.369529i	$0.120481\pi$
$229$	−0.855359	+	8.13819i	−0.0565237	+	0.537787i	−0.985743	+	0.168258i	$0.946186\pi$
$230$	−0.272114	−	2.58899i	−0.0179426	−	0.170713i
$231$	−4.72161	+	1.00361i	−0.310659	+	0.0660326i
$232$	7.56444	−	5.49589i	0.496630	−	0.360823i
$233$	−16.2543	+	11.8094i	−1.06485	+	0.773662i	−0.974980	−	0.222291i	$-0.928647\pi$
$233$	−16.2543	+	11.8094i	−1.06485	+	0.773662i	−0.0898742	+	0.995953i	$0.528647\pi$
$234$	−0.714580	+	0.151889i	−0.0467136	+	0.00992928i
$235$	0.0633240	+	0.602488i	0.00413080	+	0.0393020i
$236$	−0.992120	+	9.43939i	−0.0645815	+	0.614452i
$237$	−9.56927	−	2.03401i	−0.621591	−	0.132123i
$238$	8.90599	−	3.96520i	0.577289	−	0.257026i
$239$	−15.1603	−	16.8372i	−0.980639	−	1.08911i	−0.996011	−	0.0892285i	$-0.971560\pi$
$239$	−15.1603	−	16.8372i	−0.980639	−	1.08911i	0.0153718	−	0.999882i	$-0.495107\pi$
$240$	0.204489	−	0.629351i	0.0131997	−	0.0406244i
$241$	−19.6300	+	21.8014i	−1.26448	+	1.40435i	−0.388899	+	0.921280i	$0.627145\pi$
$241$	−19.6300	+	21.8014i	−1.26448	+	1.40435i	−0.875582	+	0.483069i	$0.839522\pi$
$242$	2.45581	+	4.25358i	0.157865	+	0.273431i
$243$	−1.97214	+	3.41584i	−0.126513	+	0.219126i
$244$	0.447158	+	1.37621i	0.0286264	+	0.0881030i
$245$	−2.06917	−	0.921254i	−0.132194	−	0.0588568i
$246$	2.82459	+	2.05219i	0.180089	+	0.130843i
$247$	−0.563366			−0.0358461
$248$	−3.33731	−	4.45672i	−0.211919	−	0.283002i
$249$	−8.17916			−0.518333
$250$	3.25335	+	2.36370i	0.205760	+	0.149493i
$251$	−3.09703	−	1.37889i	−0.195483	−	0.0870347i	0.306660	−	0.951819i	$-0.400788\pi$
$251$	−3.09703	−	1.37889i	−0.195483	−	0.0870347i	−0.502143	+	0.864784i	$0.667455\pi$
$252$	−0.142710	−	0.439216i	−0.00898987	−	0.0276680i
$253$	−7.85304	+	13.6019i	−0.493717	+	0.855142i
$254$	8.48410	+	14.6949i	0.532340	+	0.922039i
$255$	3.57028	−	3.96520i	0.223580	−	0.248311i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−11.0458	−	12.2676i	−0.689018	−	0.765232i	0.292570	−	0.956244i	$-0.405490\pi$
$257$	−11.0458	−	12.2676i	−0.689018	−	0.765232i	−0.981588	+	0.191012i	$0.938823\pi$
$258$	7.90424	−	3.51920i	0.492097	−	0.219096i
$259$	−6.43066	−	1.36688i	−0.399582	−	0.0849338i
$260$	0.0817627	−	0.777921i	0.00507071	−	0.0482446i
$261$	−0.373317	−	3.55188i	−0.0231078	−	0.219856i
$262$	−14.6601	+	3.11611i	−0.905706	+	0.192514i
$263$	14.4809	−	10.5210i	0.892931	−	0.648752i	−0.0437095	−	0.999044i	$-0.513918\pi$
$263$	14.4809	−	10.5210i	0.892931	−	0.648752i	0.936641	+	0.350292i	$0.113918\pi$
$264$	−3.22995	+	2.34670i	−0.198790	+	0.144429i
$265$	−1.15737	+	0.246007i	−0.0710967	+	0.0151121i
$266$	−0.0372263	−	0.354185i	−0.00228249	−	0.0217164i
$267$	0.198375	−	1.88741i	0.0121403	−	0.115508i
$268$	7.86606	+	1.67198i	0.480496	+	0.102133i
$269$	11.4771	−	5.10995i	0.699773	−	0.311559i	−0.0258361	−	0.999666i	$-0.508225\pi$
$269$	11.4771	−	5.10995i	0.699773	−	0.311559i	0.725609	+	0.688107i	$0.241558\pi$
$270$	−1.49750	−	1.66314i	−0.0911349	−	0.101216i
$271$	3.36944	−	10.3701i	0.204679	−	0.629936i	−0.795048	−	0.606547i	$-0.792554\pi$
$271$	3.36944	−	10.3701i	0.204679	−	0.629936i	0.999726	−	0.0233894i	$-0.00744576\pi$
$272$	5.39531	−	5.99209i	0.327139	−	0.363324i
$273$	1.87080	+	3.24031i	0.113226	+	0.196113i
$274$	4.87819	−	8.44927i	0.294702	−	0.510439i
$275$	−3.68491	−	11.3410i	−0.222208	−	0.683887i
$276$	9.40881	+	4.18907i	0.566344	+	0.252153i
$277$	−10.8079	−	7.85240i	−0.649384	−	0.471805i	0.213678	−	0.976904i	$-0.431456\pi$
$277$	−10.8079	−	7.85240i	−0.649384	−	0.471805i	−0.863061	+	0.505099i	$0.831456\pi$
$278$	19.5756			1.17407
$279$	−2.11162	+	0.252797i	−0.126419	+	0.0151345i
$280$	0.494477			0.0295506
$281$	−3.47181	−	2.52242i	−0.207111	−	0.150475i	0.479395	−	0.877599i	$-0.340856\pi$
$281$	−3.47181	−	2.52242i	−0.207111	−	0.150475i	−0.686506	+	0.727125i	$0.740856\pi$
$282$	−2.18954	−	0.974846i	−0.130385	−	0.0580512i
$283$	6.79798	+	20.9220i	0.404098	+	1.24369i	0.921646	+	0.388032i	$0.126845\pi$
$283$	6.79798	+	20.9220i	0.404098	+	1.24369i	−0.517548	+	0.855654i	$0.673155\pi$
$284$	−4.11882	+	7.13401i	−0.244407	+	0.423326i
$285$	−0.0974597	−	0.168805i	−0.00577301	−	0.00999915i
$286$	−3.15780	+	3.50709i	−0.186724	+	0.207378i
$287$	−0.806194	+	2.48121i	−0.0475881	+	0.146461i
$288$	−0.255585	−	0.283856i	−0.0150605	−	0.0167264i
$289$	43.8635	−	19.5293i	2.58020	−	1.14878i
$290$	3.74044	+	0.795054i	0.219646	+	0.0466872i
$291$	1.88541	−	17.9385i	0.110525	−	1.05157i
$292$	−0.716551	−	6.81753i	−0.0419330	−	0.398966i
$293$	12.4982	−	2.65657i	0.730152	−	0.155199i	0.172189	−	0.985064i	$-0.444916\pi$
$293$	12.4982	−	2.65657i	0.730152	−	0.155199i	0.557964	+	0.829865i	$0.311583\pi$
$294$	7.24957	−	5.26712i	0.422804	−	0.307185i
$295$	−3.14041	+	2.28164i	−0.182842	+	0.132842i
$296$	−5.31874	+	1.13053i	−0.309146	+	0.0657110i
$297$	1.41138	+	13.4283i	0.0818963	+	0.779191i
$298$	−1.65707	+	15.7660i	−0.0959914	+	0.913297i
$299$	11.9081	+	2.53115i	0.688665	+	0.146380i
$300$	−7.14350	+	3.18049i	−0.412430	+	0.183626i
$301$	4.32614	+	4.80466i	0.249354	+	0.276936i
$302$	2.35634	−	7.25205i	0.135592	−	0.417309i
$303$	−6.09852	+	6.77309i	−0.350351	+	0.389104i
$304$	−0.147278	−	0.255093i	−0.00844698	−	0.0146306i
$305$	−0.295902	+	0.512517i	−0.0169433	+	0.0293467i
$306$	−0.951727	−	2.92911i	−0.0544066	−	0.167446i
$307$	8.24023	+	3.66879i	0.470295	+	0.209389i	0.628179	−	0.778069i	$-0.283801\pi$
$307$	8.24023	+	3.66879i	0.470295	+	0.209389i	−0.157884	+	0.987458i	$0.550467\pi$
$308$	−2.41355	−	1.75354i	−0.137525	−	0.0999174i
$309$	−26.0807			−1.48368
$310$	0.441244	−	2.23393i	0.0250610	−	0.126879i
$311$	8.73773			0.495471			0.247736	−	0.968828i	$-0.420314\pi$
$311$	8.73773			0.495471			0.247736	+	0.968828i	$0.420314\pi$
$312$	2.50361	+	1.81898i	0.141739	+	0.102980i
$313$	19.0583	+	8.48531i	1.07724	+	0.479618i	0.867141	−	0.498062i	$-0.165955\pi$
$313$	19.0583	+	8.48531i	1.07724	+	0.479618i	0.210099	+	0.977680i	$0.432621\pi$
$314$	−2.15448	−	6.63082i	−0.121585	−	0.374199i
$315$	0.0944366	−	0.163569i	0.00532090	−	0.00921607i
$316$	−3.02313	−	5.23622i	−0.170064	−	0.294560i
$317$	−14.1293	+	15.6922i	−0.793579	+	0.881359i	−0.995176	−	0.0981096i	$-0.968720\pi$
$317$	−14.1293	+	15.6922i	−0.793579	+	0.881359i	0.201596	+	0.979469i	$0.435387\pi$
$318$	1.44657	−	4.45208i	0.0811195	−	0.249660i
$319$	−15.4376	−	17.1452i	−0.864342	−	0.959949i
$320$	0.373619	−	0.166346i	0.0208859	−	0.00929902i
$321$	19.0518	+	4.04959i	1.06337	+	0.226026i
$322$	−0.804449	+	7.65382i	−0.0448302	+	0.426531i
$323$	−0.248261	−	2.36204i	−0.0138136	−	0.131428i
$324$	7.53976	−	1.60263i	0.418876	−	0.0890348i
$325$	−7.47778	+	5.43293i	−0.414793	+	0.301365i
$326$	−15.5358	+	11.2874i	−0.860447	+	0.625152i
$327$	30.2647	−	6.43296i	1.67364	−	0.355744i
$328$	0.225551	+	2.14597i	0.0124540	+	0.118492i
$329$	0.187205	−	1.78113i	0.0103209	−	0.0981970i
$330$	−1.59714	−	0.339482i	−0.0879195	−	0.0186879i
$331$	−25.1679	+	11.2055i	−1.38336	+	0.615910i	−0.957382	−	0.288826i	$-0.906735\pi$
$331$	−25.1679	+	11.2055i	−1.38336	+	0.615910i	−0.425974	+	0.904735i	$0.640068\pi$
$332$	−3.38245	−	3.75660i	−0.185636	−	0.206170i
$333$	−0.641818	+	1.97531i	−0.0351714	+	0.108246i
$334$	−8.37372	+	9.29996i	−0.458190	+	0.508871i
$335$	1.64445	+	2.84828i	0.0898462	+	0.155618i
$336$	−0.978148	+	1.69420i	−0.0533623	+	0.0924263i
$337$	1.20341	+	3.70372i	0.0655539	+	0.201754i	0.978468	−	0.206397i	$-0.0661737\pi$
$337$	1.20341	+	3.70372i	0.0655539	+	0.201754i	−0.912914	+	0.408151i	$0.866174\pi$
$338$	−8.53434	−	3.79973i	−0.464207	−	0.206678i
$339$	−14.9061	−	10.8299i	−0.809591	−	0.588202i
$340$	3.29765			0.178840
$341$	−10.0758	+	9.33906i	−0.545636	+	0.505738i
$342$	−0.112511			−0.00608387
$343$	12.2642	+	8.91046i	0.662204	+	0.481119i
$344$	4.88509	+	2.17498i	0.263386	+	0.117267i
$345$	1.30163	+	4.00599i	0.0700771	+	0.215675i
$346$	10.3662	−	17.9547i	0.557288	−	0.965252i
$347$	0.745960	+	1.29204i	0.0400452	+	0.0693604i	0.885353	−	0.464919i	$-0.153916\pi$
$347$	0.745960	+	1.29204i	0.0400452	+	0.0693604i	−0.845308	+	0.534279i	$0.820583\pi$
$348$	−10.1232	+	11.2429i	−0.542660	+	0.602685i
$349$	−0.238831	+	0.735046i	−0.0127843	+	0.0393461i	−0.957245	−	0.289278i	$-0.906585\pi$
$349$	−0.238831	+	0.735046i	−0.0127843	+	0.0393461i	0.944461	+	0.328624i	$0.106585\pi$
$350$	−3.90977	−	4.34224i	−0.208986	−	0.232102i
$351$	9.56113	−	4.25689i	0.510335	−	0.227216i
$352$	−2.41355	−	0.513015i	−0.128642	−	0.0273438i
$353$	2.04570	−	19.4635i	0.108881	−	1.03594i	−0.794548	−	0.607201i	$-0.792292\pi$
$353$	2.04570	−	19.4635i	0.108881	−	1.03594i	0.903430	−	0.428737i	$-0.141041\pi$
$354$	−1.60528	−	15.2733i	−0.0853199	−	0.811764i
$355$	−3.29539	+	0.700456i	−0.174901	+	0.0371764i
$356$	0.948903	−	0.689419i	0.0502918	−	0.0365391i
$357$	−12.7614	+	9.27168i	−0.675403	+	0.490709i
$358$	1.67711	−	0.356481i	0.0886382	−	0.0188406i
$359$	−0.211188	−	2.00932i	−0.0111461	−	0.106048i	0.987534	−	0.157404i	$-0.0503124\pi$
$359$	−0.211188	−	2.00932i	−0.0111461	−	0.106048i	−0.998680	+	0.0513559i	$0.983646\pi$
$360$	0.0163289	−	0.155360i	0.000860611	−	0.00818817i
$361$	18.4999	+	3.93228i	0.973681	+	0.206962i
$362$	4.90550	−	2.18407i	0.257827	−	0.114792i
$363$	−5.31769	−	5.90589i	−0.279106	−	0.309979i
$364$	−0.714580	+	2.19925i	−0.0374542	+	0.115272i
$365$	1.87595	−	2.08346i	0.0981919	−	0.109053i
$366$	−1.17068	−	2.02767i	−0.0611922	−	0.105988i
$367$	13.7881	−	23.8817i	0.719732	−	1.24661i	−0.241374	−	0.970432i	$-0.577598\pi$
$367$	13.7881	−	23.8817i	0.719732	−	1.24661i	0.961106	−	0.276180i	$-0.0890686\pi$
$368$	1.96698	+	6.05373i	0.102536	+	0.315573i
$369$	0.752948	+	0.335234i	0.0391969	+	0.0174516i
$370$	−1.79912	−	1.30714i	−0.0935320	−	0.0679550i
$371$	3.49797			0.181605
$372$	6.78115	+	5.93085i	0.351586	+	0.307500i
$373$	13.1128			0.678954			0.339477	−	0.940614i	$-0.389750\pi$
$373$	13.1128			0.678954			0.339477	+	0.940614i	$0.389750\pi$
$374$	−16.0959	−	11.6943i	−0.832297	−	0.604699i
$375$	−5.94417	−	2.64651i	−0.306956	−	0.136665i
$376$	−0.457738	−	1.40877i	−0.0236061	−	0.0726520i
$377$	−8.94151	+	15.4872i	−0.460511	+	0.797629i
$378$	3.30806	+	5.72973i	0.170148	+	0.294706i
$379$	−10.7276	+	11.9142i	−0.551039	+	0.611991i	−0.952743	−	0.303779i	$-0.901752\pi$
$379$	−10.7276	+	11.9142i	−0.551039	+	0.611991i	0.401704	+	0.915770i	$0.368418\pi$
$380$	0.0372263	−	0.114571i	0.00190967	−	0.00587736i
$381$	−18.3711	−	20.4031i	−0.941178	−	1.04528i
$382$	−4.26939	+	1.90086i	−0.218441	+	0.0972563i
$383$	−27.8637	−	5.92262i	−1.42377	−	0.302632i	−0.569299	−	0.822131i	$-0.692785\pi$
$383$	−27.8637	−	5.92262i	−1.42377	−	0.302632i	−0.854471	+	0.519499i	$0.826119\pi$
$384$	−0.169131	+	1.60917i	−0.00863091	+	0.0821176i
$385$	−0.127536	−	1.21342i	−0.00649981	−	0.0618416i
$386$	−3.67524	+	0.781197i	−0.187065	+	0.0397619i
$387$	1.65244	−	1.20057i	0.0839981	−	0.0610282i
$388$	9.01866	−	6.55244i	0.457853	−	0.332650i
$389$	−5.15720	+	1.09620i	−0.261481	+	0.0555794i	−0.336786	−	0.941581i	$-0.609340\pi$
$389$	−5.15720	+	1.09620i	−0.261481	+	0.0555794i	0.0753058	+	0.997160i	$0.476007\pi$
$390$	0.132295	+	1.25870i	0.00669901	+	0.0637369i
$391$	−5.36484	+	51.0430i	−0.271312	+	2.58136i
$392$	5.41716	+	1.15145i	0.273608	+	0.0581571i
$393$	22.1540	−	9.86358i	1.11752	−	0.497552i
$394$	−7.40441	−	8.22343i	−0.373029	−	0.414290i
$395$	0.764132	−	2.35176i	0.0384476	−	0.118330i
$396$	−0.630648	+	0.700405i	−0.0316912	+	0.0351967i
$397$	−9.40378	−	16.2878i	−0.471962	−	0.817462i	0.527523	−	0.849541i	$-0.323121\pi$
$397$	−9.40378	−	16.2878i	−0.471962	−	0.817462i	−0.999485	+	0.0320783i	$0.989787\pi$
$398$	1.91308	−	3.31355i	0.0958940	−	0.166093i
$399$	0.178068	+	0.548036i	0.00891454	+	0.0274361i
$400$	−4.41493	−	1.96565i	−0.220746	−	0.0982826i
$401$	18.8528	+	13.6974i	0.941465	+	0.684014i	0.948773	−	0.315959i	$-0.102326\pi$
$401$	18.8528	+	13.6974i	0.941465	+	0.684014i	−0.00730807	+	0.999973i	$0.502326\pi$
$402$	−13.0119			−0.648974
$403$	9.29805	+	5.19080i	0.463169	+	0.258572i
$404$	−5.63282			−0.280243
$405$	2.55041	+	1.85298i	0.126731	+	0.0920753i
$406$	−10.3275	−	4.59811i	−0.512546	−	0.228200i
$407$	4.14608	+	12.7603i	0.205514	+	0.632506i
$408$	−6.52323	+	11.2986i	−0.322948	+	0.559363i
$409$	4.26318	+	7.38405i	0.210801	+	0.365118i	0.951965	−	0.306206i	$-0.0990595\pi$
$409$	4.26318	+	7.38405i	0.210801	+	0.365118i	−0.741165	+	0.671323i	$0.765726\pi$
$410$	−0.590500	+	0.655817i	−0.0291627	+	0.0323885i
$411$	−4.87819	+	15.0135i	−0.240623	+	0.740562i
$412$	−10.7856	−	11.9786i	−0.531366	−	0.590142i
$413$	10.4835	−	4.66756i	0.515860	−	0.229675i
$414$	2.37819	+	0.505499i	0.116882	+	0.0248439i
$415$	0.216100	−	2.05605i	0.0106079	−	0.100928i
$416$	0.199920	+	1.90211i	0.00980189	+	0.0932588i
$417$	−30.9818	+	6.58538i	−1.51719	+	0.322488i
$418$	−0.588000	+	0.427207i	−0.0287600	+	0.0208954i
$419$	−9.10559	+	6.61560i	−0.444837	+	0.323193i	−0.787554	−	0.616246i	$-0.788653\pi$
$419$	−9.10559	+	6.61560i	−0.444837	+	0.323193i	0.342717	+	0.939439i	$0.388653\pi$
$420$	−0.782596	+	0.166346i	−0.0381868	+	0.00811685i
$421$	−1.65582	−	15.7541i	−0.0807000	−	0.767809i	−0.957787	−	0.287478i	$-0.907183\pi$
$421$	−1.65582	−	15.7541i	−0.0807000	−	0.767809i	0.877087	−	0.480331i	$-0.159483\pi$
$422$	−0.961187	+	9.14508i	−0.0467898	+	0.445176i
$423$	−0.553432	−	0.117636i	−0.0269088	−	0.00571964i
$424$	2.64301	−	1.17674i	0.128356	−	0.0571478i
$425$	−26.0741	−	28.9582i	−1.26478	−	1.40468i
$426$	4.11882	−	12.6764i	0.199558	−	0.614175i
$427$	1.17068	−	1.30017i	0.0566530	−	0.0629195i
$428$	6.01886	+	10.4250i	0.290933	+	0.503910i
$429$	3.81795	−	6.61289i	0.184333	−	0.319273i
$430$	0.675809	+	2.07993i	0.0325904	+	0.100303i
$431$	15.0493	+	6.70038i	0.724900	+	0.322746i	0.735804	−	0.677194i	$-0.236804\pi$
$431$	15.0493	+	6.70038i	0.724900	+	0.322746i	−0.0109044	+	0.999941i	$0.503471\pi$
$432$	4.42705	+	3.21644i	0.212997	+	0.154751i
$433$	8.28838			0.398314			0.199157	−	0.979968i	$-0.436180\pi$
$433$	8.28838			0.398314			0.199157	+	0.979968i	$0.436180\pi$
$434$	−2.64902	+	6.18862i	−0.127157	+	0.297063i
$435$	−6.18736			−0.296661
$436$	15.4704	+	11.2399i	0.740899	+	0.538295i
$437$	1.71284	+	0.762603i	0.0819360	+	0.0364803i
$438$	3.42754	+	10.5489i	0.163774	+	0.504045i
$439$	12.8822	−	22.3126i	0.614834	−	1.06492i	−0.375580	−	0.926790i	$-0.622556\pi$
$439$	12.8822	−	22.3126i	0.614834	−	1.06492i	0.990414	−	0.138134i	$-0.0441104\pi$
$440$	−0.504568	−	0.873938i	−0.0240544	−	0.0416634i
$441$	1.41548	−	1.57205i	0.0674037	−	0.0748594i
$442$	−4.76551	+	14.6667i	−0.226672	+	0.697626i
$443$	13.3119	+	14.7844i	0.632469	+	0.702429i	0.971149	−	0.238473i	$-0.0766469\pi$
$443$	13.3119	+	14.7844i	0.632469	+	0.702429i	−0.338680	+	0.940902i	$0.609980\pi$
$444$	8.03753	−	3.57854i	0.381444	−	0.169830i
$445$	0.469210	+	0.0997338i	0.0222427	+	0.00472783i
$446$	1.99007	−	18.9343i	0.0942327	−	0.896564i
$447$	−2.68119	−	25.5098i	−0.126816	−	1.20657i
$448$	−1.18264	+	0.251377i	−0.0558743	+	0.0118765i
$449$	10.1143	−	7.34844i	0.477321	−	0.346794i	−0.322966	−	0.946410i	$-0.604680\pi$
$449$	10.1143	−	7.34844i	0.477321	−	0.346794i	0.800288	+	0.599616i	$0.204680\pi$
$450$	−1.49340	+	1.08502i	−0.0703995	+	0.0511482i
$451$	5.20794	−	1.10698i	0.245232	−	0.0521257i
$452$	−1.19030	−	11.3249i	−0.0559868	−	0.532679i
$453$	−1.28966	+	12.2703i	−0.0605937	+	0.576511i
$454$	12.3859	+	2.63270i	0.581298	+	0.123559i
$455$	−0.863968	+	0.384663i	−0.0405035	+	0.0180333i
$456$	0.318909	+	0.354185i	0.0149343	+	0.0165862i
$457$	8.60327	−	26.4781i	0.402444	−	1.23860i	−0.520567	−	0.853821i	$-0.674279\pi$
$457$	8.60327	−	26.4781i	0.402444	−	1.23860i	0.923011	−	0.384774i	$-0.125721\pi$
$458$	5.47551	−	6.08117i	0.255854	−	0.284154i
$459$	22.0614	+	38.2114i	1.02974	+	1.78355i
$460$	−1.30163	+	2.25448i	−0.0606886	+	0.105116i
$461$	10.9622	+	33.7383i	0.510563	+	1.57135i	0.791213	+	0.611540i	$0.209450\pi$
$461$	10.9622	+	33.7383i	0.510563	+	1.57135i	−0.280651	+	0.959810i	$0.590550\pi$
$462$	4.40977	+	1.96335i	0.205161	+	0.0913435i
$463$	−16.4563	−	11.9562i	−0.764789	−	0.555651i	0.135587	−	0.990765i	$-0.456708\pi$
$463$	−16.4563	−	11.9562i	−0.764789	−	0.555651i	−0.900375	+	0.435114i	$0.856708\pi$
$464$	−9.35016			−0.434070
$465$	0.0531646	+	3.68402i	0.00246545	+	0.170842i
$466$	20.0914			0.930717
$467$	0.800045	+	0.581267i	0.0370217	+	0.0268978i	0.606142	−	0.795356i	$-0.292716\pi$
$467$	0.800045	+	0.581267i	0.0370217	+	0.0268978i	−0.569121	+	0.822254i	$0.692716\pi$
$468$	0.667386	+	0.297139i	0.0308499	+	0.0137353i
$469$	−3.00457	−	9.24711i	−0.138738	−	0.426992i
$470$	0.302903	−	0.524644i	0.0139719	−	0.0242000i
$471$	5.64051	+	9.76965i	0.259901	+	0.450162i
$472$	6.35098	−	7.05347i	0.292327	−	0.324662i
$473$	4.07733	−	12.5487i	0.187476	−	0.576991i
$474$	6.54614	+	7.27023i	0.300674	+	0.333933i
$475$	−1.30044	+	0.578995i	−0.0596685	+	0.0265661i
$476$	−9.53578	−	2.02689i	−0.437072	−	0.0929025i
$477$	0.115512	−	1.09903i	0.00528894	−	0.0503209i
$478$	2.36827	+	22.5326i	0.108322	+	1.03062i
$479$	2.37711	−	0.505270i	0.108613	−	0.0230864i	−0.153285	−	0.988182i	$-0.548985\pi$
$479$	2.37711	−	0.505270i	0.108613	−	0.0230864i	0.261897	+	0.965096i	$0.415652\pi$
$480$	−0.535358	+	0.388960i	−0.0244356	+	0.0177535i
$481$	8.41365	−	6.11287i	0.383629	−	0.278723i
$482$	28.6955	−	6.09943i	1.30705	−	0.277821i
$483$	−1.30163	−	12.3841i	−0.0592260	−	0.563498i
$484$	0.513403	−	4.88471i	0.0233365	−	0.222032i
$485$	4.45952	+	0.947900i	0.202496	+	0.0430419i
$486$	3.60327	−	1.60428i	0.163448	−	0.0727716i
$487$	−1.03821	−	1.15305i	−0.0470458	−	0.0522496i	0.719163	−	0.694842i	$-0.244526\pi$
$487$	−1.03821	−	1.15305i	−0.0470458	−	0.0522496i	−0.766208	+	0.642592i	$0.777859\pi$
$488$	0.447158	−	1.37621i	0.0202419	−	0.0622982i
$489$	20.7909	−	23.0907i	0.940199	−	1.04420i
$490$	1.13249	+	1.96154i	0.0511609	+	0.0886133i
$491$	−4.00828	+	6.94255i	−0.180891	+	0.313313i	−0.942184	−	0.335095i	$-0.891232\pi$
$491$	−4.00828	+	6.94255i	−0.180891	+	0.313313i	0.761293	+	0.648408i	$0.224565\pi$
$492$	−1.07890	−	3.32051i	−0.0486405	−	0.149700i
$493$	−68.8738	−	30.6646i	−3.10192	−	1.38106i
$494$	0.455772	+	0.331138i	0.0205062	+	0.0148986i
$495$	−0.385456			−0.0173250
$496$	0.0803408	+	5.56718i	0.00360741	+	0.249974i
$497$	9.95979			0.446757
$498$	6.61708	+	4.80759i	0.296518	+	0.215433i
$499$	−23.8691	−	10.6272i	−1.06853	−	0.475738i	−0.204334	−	0.978901i	$-0.565503\pi$
$499$	−23.8691	−	10.6272i	−1.06853	−	0.475738i	−0.864192	+	0.503163i	$0.832170\pi$
$500$	−1.24267	−	3.82454i	−0.0555739	−	0.171039i
$501$	10.1243	−	17.5358i	0.452321	−	0.783442i
$502$	1.69506	+	2.93594i	0.0756544	+	0.131037i
$503$	−23.0506	+	25.6002i	−1.02777	+	1.14146i	−0.0379329	+	0.999280i	$0.512077\pi$
$503$	−23.0506	+	25.6002i	−1.02777	+	1.14146i	−0.989841	+	0.142178i	$0.954589\pi$
$504$	−0.142710	+	0.439216i	−0.00635680	+	0.0195642i
$505$	−1.54147	−	1.71198i	−0.0685946	−	0.0761820i
$506$	14.3482	−	6.38824i	0.637856	−	0.283992i
$507$	14.7854	+	3.14272i	0.656641	+	0.139573i
$508$	1.77366	−	16.8752i	0.0786934	−	0.748718i
$509$	0.107145	+	1.01942i	0.00474912	+	0.0451848i	0.996640	−	0.0819091i	$-0.0261017\pi$
$509$	0.107145	+	1.01942i	0.00474912	+	0.0451848i	−0.991891	+	0.127094i	$0.959435\pi$
$510$	−5.21911	+	1.10936i	−0.231106	+	0.0491231i
$511$	−6.70528	+	4.87167i	−0.296624	+	0.215510i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.57663	−	0.335123i	0.0696099	−	0.0147960i
$514$	1.72552	+	16.4172i	0.0761095	+	0.724134i
$515$	0.689073	−	6.55609i	0.0303642	−	0.288896i
$516$	−8.46320	−	1.79891i	−0.372572	−	0.0791925i
$517$	−3.33900	+	1.48662i	−0.146849	+	0.0653814i
$518$	4.39908	+	4.88568i	0.193285	+	0.214664i
$519$	−10.3662	+	31.9038i	−0.455024	+	1.40042i
$520$	−0.523398	+	0.581292i	−0.0229525	+	0.0254913i
$521$	−6.57055	−	11.3805i	−0.287861	−	0.498590i	0.685438	−	0.728131i	$-0.259611\pi$
$521$	−6.57055	−	11.3805i	−0.287861	−	0.498590i	−0.973299	+	0.229541i	$0.926277\pi$
$522$	−1.78572	+	3.09296i	−0.0781589	+	0.135375i
$523$	−0.771812	−	2.37539i	−0.0337490	−	0.103869i	0.932763	−	0.360490i	$-0.117391\pi$
$523$	−0.771812	−	2.37539i	−0.0337490	−	0.103869i	−0.966512	+	0.256622i	$0.917391\pi$
$524$	13.6919	+	6.09602i	0.598133	+	0.266306i
$525$	7.64866	+	5.55708i	0.333815	+	0.242531i
$526$	−17.8994			−0.780450
$527$	−17.6662	+	41.2717i	−0.769554	+	1.79782i
$528$	3.99244			0.173749
$529$	−14.1713	−	10.2961i	−0.616144	−	0.447654i
$530$	1.08093	+	0.481262i	0.0469526	+	0.0209047i
$531$	−1.12031	−	3.44795i	−0.0486171	−	0.149628i
$532$	−0.178068	+	0.308422i	−0.00772022	+	0.0133718i
$533$	−2.06349	−	3.57407i	−0.0893796	−	0.154810i
$534$	−1.26988	+	1.41035i	−0.0549531	+	0.0610316i
$535$	−1.52134	+	4.68220i	−0.0657732	+	0.202429i
$536$	−5.38101	−	5.97622i	−0.232424	−	0.258133i
$537$	−2.53440	+	1.12839i	−0.109368	+	0.0486936i
$538$	−12.2887	−	2.61205i	−0.529805	−	0.112614i
$539$	1.42841	−	13.5904i	0.0615260	−	0.585380i
$540$	0.233932	+	2.22572i	0.0100668	+	0.0957797i
$541$	−11.1968	+	2.37995i	−0.481387	+	0.102322i	−0.442212	−	0.896911i	$-0.645806\pi$
$541$	−11.1968	+	2.37995i	−0.481387	+	0.102322i	−0.0391745	+	0.999232i	$0.512473\pi$
$542$	−8.82130	+	6.40905i	−0.378907	+	0.275292i
$543$	−7.02908	+	5.10692i	−0.301647	+	0.219159i
$544$	−7.88696	+	1.67642i	−0.338151	+	0.0718761i
$545$	0.817482	+	7.77782i	0.0350171	+	0.333165i
$546$	0.391103	−	3.72109i	0.0167377	−	0.159248i
$547$	−6.80182	−	1.44577i	−0.290825	−	0.0618168i	0.0601889	−	0.998187i	$-0.480830\pi$
$547$	−6.80182	−	1.44577i	−0.290825	−	0.0618168i	−0.351014	+	0.936370i	$0.614163\pi$
$548$	−8.91289	+	3.96828i	−0.380740	+	0.169516i
$549$	−0.369841	−	0.410750i	−0.0157844	−	0.0175304i
$550$	−3.68491	+	11.3410i	−0.157125	+	0.483581i
$551$	−1.84289	+	2.04673i	−0.0785096	+	0.0871937i
$552$	−5.14961	−	8.91939i	−0.219182	−	0.379635i
$553$	−3.65514	+	6.33088i	−0.155432	+	0.269217i
$554$	4.12825	+	12.7054i	0.175393	+	0.539803i
$555$	3.28716	+	1.46354i	0.139532	+	0.0621238i
$556$	−15.8370	−	11.5062i	−0.671637	−	0.487973i
$557$	−13.2546			−0.561616			−0.280808	−	0.959764i	$-0.590602\pi$
$557$	−13.2546			−0.561616			−0.280808	+	0.959764i	$0.590602\pi$
$558$	1.85693	+	1.03666i	0.0786099	+	0.0438854i
$559$	−10.2274			−0.432572
$560$	−0.400040	−	0.290646i	−0.0169048	−	0.0122820i
$561$	29.4086	+	13.0935i	1.24163	+	0.552810i
$562$	1.32611	+	4.08136i	0.0559388	+	0.172162i
$563$	9.20226	−	15.9388i	0.387829	−	0.671739i	−0.604328	−	0.796735i	$-0.706559\pi$
$563$	9.20226	−	15.9388i	0.387829	−	0.671739i	0.992157	+	0.124996i	$0.0398918\pi$
$564$	1.19837	+	2.07565i	0.0504607	+	0.0874005i
$565$	3.11623	−	3.46093i	0.131101	−	0.145602i
$566$	6.79798	−	20.9220i	0.285741	−	0.879419i
$567$	−6.23607	−	6.92586i	−0.261890	−	0.290859i
$568$	7.52547	−	3.35055i	0.315762	−	0.140586i
$569$	−2.02983	−	0.431455i	−0.0850951	−	0.0180875i	0.165167	−	0.986266i	$-0.447184\pi$
$569$	−2.02983	−	0.431455i	−0.0850951	−	0.0180875i	−0.250262	+	0.968178i	$0.580517\pi$
$570$	−0.0203746	+	0.193852i	−0.000853399	+	0.00811955i
$571$	−0.804543	−	7.65472i	−0.0336691	−	0.320340i	−0.998374	−	0.0570061i	$-0.981845\pi$
$571$	−0.804543	−	7.65472i	−0.0336691	−	0.320340i	0.964705	−	0.263334i	$-0.0848221\pi$
$572$	4.61612	−	0.981187i	0.193010	−	0.0410255i
$573$	6.11760	−	4.44470i	0.255566	−	0.185680i
$574$	2.11064	−	1.53347i	0.0880965	−	0.0640059i
$575$	30.0895	−	6.39572i	1.25482	−	0.266720i
$576$	0.0399263	+	0.379874i	0.00166360	+	0.0158281i
$577$	−2.74650	+	26.1312i	−0.114338	+	1.08786i	0.775426	+	0.631438i	$0.217535\pi$
$577$	−2.74650	+	26.1312i	−0.114338	+	1.08786i	−0.889765	+	0.456420i	$0.849132\pi$
$578$	−46.9653	−	9.98278i	−1.95350	−	0.415229i
$579$	5.55392	−	2.47276i	0.230813	−	0.102765i
$580$	−2.55876	−	2.84179i	−0.106247	−	0.117999i
$581$	−1.88864	+	5.81265i	−0.0783542	+	0.241149i
$582$	−12.0693	+	13.4043i	−0.500290	+	0.555628i
$583$	−3.56936	−	6.18231i	−0.147828	−	0.256045i
$584$	−3.42754	+	5.93667i	−0.141833	+	0.245661i
$585$	0.0923268	+	0.284153i	0.00381725	+	0.0117483i
$586$	−11.6727	−	5.19704i	−0.482197	−	0.214688i
$587$	16.7439	+	12.1652i	0.691096	+	0.502110i	0.877020	−	0.480454i	$-0.159528\pi$
$587$	16.7439	+	12.1652i	0.691096	+	0.502110i	−0.185925	+	0.982564i	$0.559528\pi$
$588$	−8.96097			−0.369544
$589$	1.23448	+	1.07969i	0.0508659	+	0.0444877i
$590$	3.88176			0.159809
$591$	14.4852	+	10.5241i	0.595842	+	0.432904i
$592$	4.96747	+	2.21166i	0.204162	+	0.0908986i
$593$	−5.13950	−	15.8177i	−0.211054	−	0.649557i	−0.999410	−	0.0343381i	$-0.989068\pi$
$593$	−5.13950	−	15.8177i	−0.211054	−	0.649557i	0.788356	−	0.615219i	$-0.210932\pi$
$594$	6.75115	−	11.6933i	0.277003	−	0.479784i
$595$	−1.99352	−	3.45288i	−0.0817264	−	0.141554i
$596$	10.6076	−	11.7809i	0.434504	−	0.482565i
$597$	−1.91308	+	5.88785i	−0.0782971	+	0.240974i
$598$	−8.14610	−	9.04716i	−0.333119	−	0.369966i
$599$	13.4037	−	5.96769i	0.547658	−	0.243833i	−0.114206	−	0.993457i	$-0.536432\pi$
$599$	13.4037	−	5.96769i	0.547658	−	0.243833i	0.661864	+	0.749624i	$0.269766\pi$
$600$	7.64866	+	1.62577i	0.312255	+	0.0663719i
$601$	−3.82985	+	36.4386i	−0.156223	+	1.48636i	0.582764	+	0.812642i	$0.301971\pi$
$601$	−3.82985	+	36.4386i	−0.156223	+	1.48636i	−0.738987	+	0.673720i	$0.764695\pi$
$602$	−0.675809	−	6.42989i	−0.0275439	−	0.262063i
$603$	−3.00457	+	0.638641i	−0.122355	+	0.0260075i
$604$	−6.16897	+	4.48202i	−0.251012	+	0.182371i
$605$	1.62510	−	1.18071i	0.0660698	−	0.0480025i
$606$	8.91493	−	1.89493i	0.362144	−	0.0769761i
$607$	−3.30626	−	31.4570i	−0.134197	−	1.27680i	−0.829673	−	0.558250i	$-0.811473\pi$
$607$	−3.30626	−	31.4570i	−0.134197	−	1.27680i	0.695476	−	0.718549i	$-0.255194\pi$
$608$	−0.0307895	+	0.292943i	−0.00124868	+	0.0118804i
$609$	17.8920	+	3.80305i	0.725019	+	0.154107i
$610$	0.540640	−	0.240708i	0.0218899	−	0.00974600i
$611$	1.89569	+	2.10538i	0.0766915	+	0.0851746i
$612$	−0.951727	+	2.92911i	−0.0384713	+	0.118402i
$613$	21.2875	−	23.6422i	0.859796	−	0.954900i	−0.139581	−	0.990211i	$-0.544575\pi$
$613$	21.2875	−	23.6422i	0.859796	−	0.954900i	0.999376	+	0.0353108i	$0.0112421\pi$
$614$	−4.51003	−	7.81160i	−0.182010	−	0.315250i
$615$	0.713948	−	1.23659i	0.0287892	−	0.0498643i
$616$	0.921892	+	2.83729i	0.0371441	+	0.114318i
$617$	19.7979	+	8.81458i	0.797033	+	0.354862i	0.764512	−	0.644609i	$-0.222980\pi$
$617$	19.7979	+	8.81458i	0.797033	+	0.354862i	0.0325205	+	0.999471i	$0.489647\pi$
$618$	21.0997	+	15.3299i	0.848756	+	0.616657i
$619$	13.0974			0.526427			0.263214	−	0.964738i	$-0.415218\pi$
$619$	13.0974			0.526427			0.263214	+	0.964738i	$0.415218\pi$
$620$	−1.67004	+	1.54793i	−0.0670706	+	0.0621663i
$621$	−34.8316			−1.39775
$622$	−7.06897	−	5.13591i	−0.283440	−	0.205931i
$623$	−1.29551	−	0.576799i	−0.0519036	−	0.0231090i
$624$	−0.956295	−	2.94317i	−0.0382824	−	0.117821i
$625$	−11.2595	+	19.5021i	−0.450381	+	0.780083i
$626$	−10.4310	−	18.0670i	−0.416905	−	0.722101i
$627$	0.786897	−	0.873938i	0.0314257	−	0.0349017i
$628$	−2.15448	+	6.63082i	−0.0859733	+	0.264598i
$629$	29.3373	+	32.5824i	1.16976	+	1.29915i
$630$	−0.172544	+	0.0768217i	−0.00687433	+	0.00306065i
$631$	2.53536	+	0.538907i	0.100931	+	0.0214535i	0.258100	−	0.966118i	$-0.416903\pi$
$631$	2.53536	+	0.538907i	0.100931	+	0.0214535i	−0.157169	+	0.987572i	$0.550237\pi$
$632$	−0.632006	+	6.01314i	−0.0251399	+	0.239190i
$633$	−1.55523	−	14.7971i	−0.0618149	−	0.588130i
$634$	20.6544	−	4.39024i	0.820293	−	0.174359i
$635$	5.61426	−	4.07900i	0.222795	−	0.161870i
$636$	−3.78716	+	2.75154i	−0.150171	+	0.109106i
$637$	−10.3608	+	2.20226i	−0.410510	+	0.0872566i
$638$	2.41160	+	22.9448i	0.0954760	+	0.908394i
$639$	0.328899	−	3.12926i	0.0130110	−	0.123792i
$640$	−0.400040	−	0.0850311i	−0.0158130	−	0.00336115i
$641$	23.3660	−	10.4032i	0.922902	−	0.410902i	0.110418	−	0.993885i	$-0.464781\pi$
$641$	23.3660	−	10.4032i	0.922902	−	0.410902i	0.812484	+	0.582983i	$0.198115\pi$
$642$	−13.0330	−	14.4746i	−0.514370	−	0.571266i
$643$	5.57977	−	17.1728i	0.220045	−	0.677228i	−0.778712	−	0.627381i	$-0.784127\pi$
$643$	5.57977	−	17.1728i	0.220045	−	0.677228i	0.998757	−	0.0498464i	$-0.0158732\pi$
$644$	5.14961	−	5.71923i	0.202923	−	0.225369i
$645$	−1.76929	−	3.06450i	−0.0696657	−	0.120665i
$646$	−1.18753	+	2.05686i	−0.0467226	+	0.0809260i
$647$	−4.54443	−	13.9863i	−0.178660	−	0.549859i	0.821122	−	0.570753i	$-0.193349\pi$
$647$	−4.54443	−	13.9863i	−0.178660	−	0.549859i	−0.999782	+	0.0208941i	$0.993349\pi$
$648$	−7.04179	−	3.13521i	−0.276628	−	0.123163i
$649$	−18.9469	−	13.7657i	−0.743731	−	0.540352i
$650$	9.24305			0.362542
$651$	2.11064	−	10.6857i	0.0827226	−	0.418807i
$652$	19.2033			0.752059
$653$	36.9617	+	26.8542i	1.44642	+	1.05089i	0.986651	+	0.162848i	$0.0520682\pi$
$653$	36.9617	+	26.8542i	1.44642	+	1.05089i	0.459770	+	0.888038i	$0.347932\pi$
$654$	−28.2659	−	12.5848i	−1.10528	−	0.492104i
$655$	1.89415	+	5.82960i	0.0740106	+	0.227781i
$656$	1.07890	−	1.86871i	0.0421239	−	0.0729607i
$657$	1.30920	+	2.26761i	0.0510769	+	0.0884678i
$658$	−1.19837	+	1.33093i	−0.0467175	+	0.0518851i
$659$	−10.5990	+	32.6205i	−0.412880	+	1.27071i	0.501253	+	0.865301i	$0.332873\pi$
$659$	−10.5990	+	32.6205i	−0.412880	+	1.27071i	−0.914133	+	0.405414i	$0.867127\pi$
$660$	1.09257	+	1.21342i	0.0425282	+	0.0472323i
$661$	−5.49575	+	2.44686i	−0.213760	+	0.0951720i	−0.510823	−	0.859686i	$-0.670659\pi$
$661$	−5.49575	+	2.44686i	−0.213760	+	0.0951720i	0.297064	+	0.954858i	$0.403993\pi$
$662$	26.9477	+	5.72791i	1.04735	+	0.222622i
$663$	2.60825	−	24.8159i	0.101296	−	0.963768i
$664$	0.528391	+	5.02731i	0.0205056	+	0.195097i
$665$	−0.142468	+	0.0302826i	−0.00552469	+	0.00117431i
$666$	1.68030	−	1.22081i	0.0651103	−	0.0473054i
$667$	48.1497	−	34.9828i	1.86436	−	1.35454i
$668$	12.2409	−	2.60188i	0.473613	−	0.100670i
$669$	3.22001	+	30.6363i	0.124493	+	1.18447i
$670$	0.343785	−	3.27089i	0.0132816	−	0.126366i
$671$	−3.49248	−	0.742351i	−0.134826	−	0.0286581i
$672$	1.78716	−	0.795697i	0.0689414	−	0.0306947i
$673$	13.7350	+	15.2542i	0.529444	+	0.588008i	0.947237	−	0.320535i	$-0.103863\pi$
$673$	13.7350	+	15.2542i	0.529444	+	0.588008i	−0.417792	+	0.908543i	$0.637196\pi$
$674$	1.20341	−	3.70372i	0.0463536	−	0.142662i
$675$	17.6954	−	19.6528i	0.681097	−	0.756435i
$676$	4.67100	+	8.09041i	0.179654	+	0.311170i
$677$	−8.02687	+	13.9029i	−0.308498	+	0.534333i	−0.978034	−	0.208446i	$-0.933160\pi$
$677$	−8.02687	+	13.9029i	−0.308498	+	0.534333i	0.669536	+	0.742779i	$0.266493\pi$
$678$	5.69364	+	17.5232i	0.218663	+	0.672975i
$679$	−12.3129	−	5.48207i	−0.472527	−	0.210383i
$680$	−2.66785	−	1.93831i	−0.102307	−	0.0743307i
$681$	−20.4885			−0.785121
$682$	13.6409	−	1.63304i	0.522336	−	0.0625324i
$683$	−42.5294			−1.62734			−0.813671	−	0.581326i	$-0.802534\pi$
$683$	−42.5294			−1.62734			−0.813671	+	0.581326i	$0.802534\pi$
$684$	0.0910229	+	0.0661320i	0.00348035	+	0.00252862i
$685$	−3.64517	−	1.62293i	−0.139275	−	0.0620091i
$686$	−4.68450	−	14.4174i	−0.178855	−	0.550460i
$687$	−6.62020	+	11.4665i	−0.252577	+	0.437475i
$688$	−2.67370	−	4.63098i	−0.101934	−	0.176555i
$689$	−3.70256	+	4.11211i	−0.141056	+	0.156659i
$690$	1.30163	−	4.00599i	0.0495520	−	0.152505i
$691$	14.7745	+	16.4087i	0.562047	+	0.624217i	0.955451	−	0.295149i	$-0.0953693\pi$
$691$	14.7745	+	16.4087i	0.562047	+	0.624217i	−0.393404	+	0.919366i	$0.628703\pi$
$692$	−18.9399	+	8.43260i	−0.719988	+	0.320559i
$693$	1.11462	+	0.236920i	0.0423409	+	0.00899984i
$694$	0.155948	−	1.48375i	0.00591971	−	0.0563223i
$695$	−0.836851	−	7.96211i	−0.0317436	−	0.302020i
$696$	14.7983	−	3.14547i	0.560927	−	0.119229i
$697$	14.0758	−	10.2267i	0.533159	−	0.387363i
$698$	0.625268	−	0.454284i	0.0236667	−	0.0171949i
$699$	−31.7982	+	6.75892i	−1.20272	+	0.255646i
$700$	0.610766	+	5.81105i	0.0230848	+	0.219637i
$701$	3.39234	−	32.2760i	0.128127	−	1.21905i	−0.721783	−	0.692120i	$-0.756677\pi$
$701$	3.39234	−	32.2760i	0.128127	−	1.21905i	0.849910	−	0.526928i	$-0.176656\pi$
$702$	−10.2372	−	2.17599i	−0.386380	−	0.0821276i
$703$	1.46320	−	0.651458i	0.0551856	−	0.0245702i
$704$	1.65106	+	1.83368i	0.0622265	+	0.0691096i
$705$	−0.302903	+	0.932240i	−0.0114080	+	0.0351102i
$706$	−13.0954	+	14.5439i	−0.492850	+	0.547366i
$707$	3.40520	+	5.89798i	0.128066	+	0.221816i
$708$	−7.67869	+	13.2999i	−0.288583	+	0.499840i
$709$	7.48960	+	23.0506i	0.281278	+	0.865684i	0.987490	+	0.157683i	$0.0504026\pi$
$709$	7.48960	+	23.0506i	0.281278	+	0.865684i	−0.706212	+	0.708000i	$0.749597\pi$
$710$	3.07774	+	1.37030i	0.115506	+	0.0514264i
$711$	1.86840	+	1.35747i	0.0700704	+	0.0509091i
$712$	−1.17291			−0.0439566
$713$	−21.2429	−	28.3683i	−0.795551	−	1.06240i
$714$	15.7739			0.590324
$715$	1.56146	+	1.13446i	0.0583951	+	0.0424265i
$716$	−1.56635	−	0.697383i	−0.0585371	−	0.0260624i
$717$	−11.3284	−	34.8651i	−0.423066	−	1.30206i
$718$	−1.01019	+	1.74971i	−0.0377001	+	0.0652985i
$719$	0.997478	+	1.72768i	0.0371997	+	0.0644317i	0.884026	−	0.467438i	$-0.154823\pi$
$719$	0.997478	+	1.72768i	0.0371997	+	0.0644317i	−0.846826	+	0.531870i	$0.821490\pi$
$720$	−0.104528	+	0.116091i	−0.00389555	+	0.00432644i
$721$	−6.02228	+	18.5347i	−0.224281	+	0.690267i
$722$	−12.6554	−	14.0553i	−0.470986	−	0.523083i
$723$	−43.3639	+	19.3068i	−1.61272	+	0.718029i
$724$	−5.25240	−	1.11643i	−0.195204	−	0.0414918i
$725$	−4.72331	+	44.9393i	−0.175419	+	1.66900i
$726$	0.830704	+	7.90362i	0.0308303	+	0.293331i
$727$	−7.87488	+	1.67386i	−0.292063	+	0.0620799i	−0.351613	−	0.936145i	$-0.614367\pi$
$727$	−7.87488	+	1.67386i	−0.292063	+	0.0620799i	0.0595501	+	0.998225i	$0.481033\pi$
$728$	1.87080	−	1.35921i	0.0693363	−	0.0503758i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	−2.74231	+	0.582895i	−0.101497	+	0.0215739i
$731$	−4.50695	−	42.8807i	−0.166695	−	1.58600i
$732$	−0.244738	+	2.32853i	−0.00904577	+	0.0860648i
$733$	14.0976	+	2.99655i	0.520708	+	0.110680i	0.460766	−	0.887522i	$-0.347575\pi$
$733$	14.0976	+	2.99655i	0.520708	+	0.110680i	0.0599426	+	0.998202i	$0.480908\pi$
$734$	−25.1921	+	11.2162i	−0.929856	+	0.413999i
$735$	−2.45225	−	2.72350i	−0.0904526	−	0.100458i
$736$	1.96698	−	6.05373i	0.0725037	−	0.223144i
$737$	−13.2775	+	14.7461i	−0.489081	+	0.543180i
$738$	−0.412102	−	0.713782i	−0.0151697	−	0.0262747i
$739$	18.1854	−	31.4981i	0.668962	−	1.15868i	−0.309233	−	0.950986i	$-0.600072\pi$
$739$	18.1854	−	31.4981i	0.668962	−	1.15868i	0.978195	−	0.207690i	$-0.0665945\pi$
$740$	0.687205	+	2.11500i	0.0252621	+	0.0777489i
$741$	−0.832738	−	0.370759i	−0.0305914	−	0.0136202i
$742$	−2.82991	−	2.05605i	−0.103889	−	0.0754801i
$743$	10.7395			0.393993			0.196997	−	0.980404i	$-0.436881\pi$
$743$	10.7395			0.393993			0.196997	+	0.980404i	$0.436881\pi$
$744$	−2.00000	−	8.78402i	−0.0733236	−	0.322038i
$745$	6.48343			0.237534
$746$	−10.6085	−	7.70750i	−0.388403	−	0.282192i
$747$	1.76391	+	0.785342i	0.0645380	+	0.0287342i
$748$	6.14807	+	18.9218i	0.224796	+	0.691850i
$749$	7.27715	−	12.6044i	0.265901	−	0.460554i
$750$	3.25335	+	5.63497i	0.118796	+	0.205760i
$751$	−7.83921	+	8.70632i	−0.286057	+	0.317698i	−0.868998	−	0.494816i	$-0.835235\pi$
$751$	−7.83921	+	8.70632i	−0.286057	+	0.317698i	0.582941	+	0.812515i	$0.301902\pi$
$752$	−0.457738	+	1.40877i	−0.0166920	+	0.0513727i
$753$	−3.67041	−	4.07640i	−0.133757	−	0.148552i
$754$	16.3370	−	7.27368i	0.594957	−	0.264892i
$755$	−3.05041	−	0.648384i	−0.111016	−	0.0235971i
$756$	0.691573	−	6.57988i	0.0251523	−	0.239308i
$757$	2.09492	+	19.9319i	0.0761413	+	0.724436i	0.964284	+	0.264869i	$0.0853288\pi$
$757$	2.09492	+	19.9319i	0.0761413	+	0.724436i	−0.888143	+	0.459567i	$0.848005\pi$
$758$	15.6818	−	3.33327i	0.569588	−	0.121070i
$759$	−20.5595	+	14.9374i	−0.746264	+	0.542193i
$760$	−0.0974597	+	0.0708086i	−0.00353523	+	0.00256850i
$761$	−41.6273	+	8.84815i	−1.50899	+	0.320745i	−0.886811	−	0.462132i	$-0.847085\pi$
$761$	−41.6273	+	8.84815i	−1.50899	+	0.320745i	−0.622176	+	0.782877i	$0.713751\pi$
$762$	2.86984	+	27.3047i	0.103963	+	0.989145i
$763$	2.41672	−	22.9935i	0.0874911	−	0.832422i
$764$	4.57131	+	0.971661i	0.165384	+	0.0351535i
$765$	−1.15069	+	0.512321i	−0.0416034	+	0.0185230i
$766$	19.0610	+	21.1694i	0.688702	+	0.764881i
$767$	−5.60963	+	17.2647i	−0.202552	+	0.623391i
$768$	1.08268	−	1.20243i	0.0390677	−	0.0433891i
$769$	−6.66562	−	11.5452i	−0.240368	−	0.416330i	0.720451	−	0.693506i	$-0.243935\pi$
$769$	−6.66562	−	11.5452i	−0.240368	−	0.416330i	−0.960819	+	0.277176i	$0.910602\pi$
$770$	−0.610052	+	1.05664i	−0.0219847	+	0.0380787i
$771$	−8.25384	−	25.4027i	−0.297255	−	0.914856i
$772$	3.43251	+	1.52825i	0.123539	+	0.0550030i
$773$	−23.0261	−	16.7294i	−0.828191	−	0.601716i	0.0908559	−	0.995864i	$-0.471040\pi$
$773$	−23.0261	−	16.7294i	−0.828191	−	0.601716i	−0.919047	+	0.394148i	$0.871040\pi$
$774$	−2.04252			−0.0734170
$775$	26.7979	+	2.42617i	0.962610	+	0.0871507i
$776$	−11.1477			−0.400178
$777$	−8.60591	−	6.25256i	−0.308735	−	0.224309i
$778$	4.81660	+	2.14449i	0.172683	+	0.0768836i
$779$	−0.196409	−	0.604484i	−0.00703708	−	0.0216579i
$780$	0.632818	−	1.09607i	0.0226585	−	0.0392457i
$781$	−10.1631	−	17.6029i	−0.363663	−	0.629882i
$782$	34.3426	−	38.1413i	1.22809	−	1.36393i
$783$	15.8110	−	48.6611i	0.565038	−	1.73901i
$784$	−3.70577	−	4.11567i	−0.132349	−	0.146988i
$785$	−2.60489	+	1.15977i	−0.0929726	+	0.0413941i
$786$	−23.7206	−	5.04197i	−0.846085	−	0.179841i
$787$	−4.41260	+	41.9831i	−0.157292	+	1.49654i	0.576463	+	0.817123i	$0.304432\pi$
$787$	−4.41260	+	41.9831i	−0.157292	+	1.49654i	−0.733756	+	0.679414i	$0.762234\pi$
$788$	1.15668	+	11.0051i	0.0412051	+	0.392040i
$789$	28.3289	−	6.02150i	1.00854	−	0.214371i
$790$	−2.00052	+	1.45346i	−0.0711754	+	0.0517120i
$791$	−11.1384	+	8.09255i	−0.396037	+	0.287738i
$792$	0.921892	−	0.195954i	0.0327580	−	0.00696293i
$793$	0.289291	+	2.75242i	0.0102730	+	0.0977414i
$794$	−1.96592	+	18.7045i	−0.0697681	+	0.663799i
$795$	−1.87266	−	0.398047i	−0.0664166	−	0.0141173i
$796$	−3.49537	+	1.55624i	−0.123890	+	0.0551594i
$797$	4.64428	+	5.15800i	0.164509	+	0.182706i	0.819763	−	0.572703i	$-0.194105\pi$
$797$	4.64428	+	5.15800i	0.164509	+	0.182706i	−0.655254	+	0.755409i	$0.727438\pi$
$798$	0.178068	−	0.548036i	0.00630353	−	0.0194003i
$799$	−7.99192	+	8.87593i	−0.282734	+	0.314008i
$800$	2.41637	+	4.18527i	0.0854315	+	0.147972i
$801$	−0.224006	+	0.387989i	−0.00791485	+	0.0137089i
$802$	−7.20114	−	22.1628i	−0.254281	−	0.782596i
$803$	15.4523	+	6.87982i	0.545301	+	0.242783i
$804$	10.5268	+	7.64820i	0.371253	+	0.269731i
$805$	3.14748			0.110934
$806$	−4.47120	−	9.66470i	−0.157491	−	0.340425i
$807$	20.3278			0.715573
$808$	4.55705	+	3.31089i	0.160316	+	0.116477i
$809$	16.1722	+	7.20033i	0.568584	+	0.253150i	0.670833	−	0.741609i	$-0.265937\pi$
$809$	16.1722	+	7.20033i	0.568584	+	0.253150i	−0.102248	+	0.994759i	$0.532604\pi$
$810$	−0.974169	−	2.99819i	−0.0342288	−	0.105345i
$811$	−10.3266	+	17.8862i	−0.362615	+	0.628068i	−0.988390	−	0.151936i	$-0.951449\pi$
$811$	−10.3266	+	17.8862i	−0.362615	+	0.628068i	0.625775	+	0.780003i	$0.284783\pi$
$812$	5.65244	+	9.79031i	0.198362	+	0.343572i
$813$	11.8052	−	13.1110i	0.414027	−	0.459823i
$814$	4.14608	−	12.7603i	0.145320	−	0.447250i
$815$	5.25515	+	5.83644i	0.184080	+	0.204442i
$816$	11.9185	−	5.30648i	0.417232	−	0.185764i
$817$	−1.54069	−	0.327484i	−0.0539019	−	0.0114572i
$818$	0.891248	−	8.47965i	0.0311617	−	0.296484i
$819$	−0.0923268	−	0.878431i	−0.00322616	−	0.0306949i
$820$	0.863204	−	0.183480i	0.0301444	−	0.00640739i
$821$	21.3750	−	15.5298i	0.745993	−	0.541995i	−0.148590	−	0.988899i	$-0.547473\pi$
$821$	21.3750	−	15.5298i	0.745993	−	0.541995i	0.894582	+	0.446904i	$0.147473\pi$
$822$	12.7713	−	9.27886i	0.445449	−	0.323638i
$823$	20.3638	−	4.32846i	0.709838	−	0.150881i	0.161177	−	0.986926i	$-0.448471\pi$
$823$	20.3638	−	4.32846i	0.709838	−	0.150881i	0.548661	+	0.836045i	$0.315138\pi$
$824$	1.68487	+	16.0305i	0.0586952	+	0.558448i
$825$	2.01682	−	19.1887i	0.0702166	−	0.668066i
$826$	−11.2249	−	2.38592i	−0.390563	−	0.0830167i
$827$	7.08457	−	3.15425i	0.246355	−	0.109684i	−0.279845	−	0.960045i	$-0.590283\pi$
$827$	7.08457	−	3.15425i	0.246355	−	0.109684i	0.526200	+	0.850361i	$0.323616\pi$
$828$	−1.62687	−	1.80682i	−0.0565376	−	0.0627914i
$829$	−5.96278	+	18.3516i	−0.207096	+	0.637376i	0.792525	+	0.609840i	$0.208766\pi$
$829$	−5.96278	+	18.3516i	−0.207096	+	0.637376i	−0.999621	+	0.0275364i	$0.991234\pi$
$830$	−1.38335	+	1.53636i	−0.0480166	+	0.0533279i
$831$	−10.8079	−	18.7198i	−0.374922	−	0.649384i
$832$	0.956295	−	1.65635i	0.0331536	−	0.0574237i
$833$	−13.7992	−	42.4697i	−0.478115	−	1.47149i
$834$	28.9356	+	12.8830i	1.00196	+	0.446100i
$835$	4.14061	+	3.00833i	0.143292	+	0.104107i
$836$	0.726808			0.0251372
$837$	−29.1092	−	8.99590i	−1.00616	−	0.310944i
$838$	11.2551			0.388802
$839$	−42.3183	−	30.7460i	−1.46099	−	1.06147i	−0.983104	−	0.183049i	$-0.941403\pi$
$839$	−42.3183	−	30.7460i	−1.46099	−	1.06147i	−0.477886	−	0.878422i	$-0.658597\pi$
$840$	0.730909	+	0.325422i	0.0252188	+	0.0112281i
$841$	18.0545	+	55.5659i	0.622568	+	1.91607i
$842$	−7.92045	+	13.7186i	−0.272957	+	0.472775i
$843$	−3.47181	−	6.01336i	−0.119576	−	0.207111i
$844$	6.15296	−	6.83355i	0.211794	−	0.235221i
$845$	−1.18065	+	3.63367i	−0.0406156	+	0.125002i
$846$	0.378591	+	0.420468i	0.0130162	+	0.0144560i
$847$	−5.42502	+	2.41537i	−0.186406	+	0.0829932i
$848$	−2.82991	−	0.601517i	−0.0971797	−	0.0206562i
$849$	−3.72066	+	35.3997i	−0.127693	+	1.21491i
$850$	4.07317	+	38.7537i	0.139709	+	1.32924i
$851$	−33.8553	+	7.19616i	−1.16054	+	0.246681i
$852$	−10.7832	+	7.83447i	−0.369427	+	0.268404i
$853$	15.1645	−	11.0177i	0.519224	−	0.377238i	−0.297088	−	0.954850i	$-0.596015\pi$
$853$	15.1645	−	11.0177i	0.519224	−	0.377238i	0.816311	+	0.577612i	$0.196015\pi$
$854$	−1.71132	+	0.363751i	−0.0585600	+	0.0124473i
$855$	0.00480980	+	0.0457622i	0.000164492	+	0.00156503i
$856$	1.25829	−	11.9718i	0.0430073	−	0.409187i
$857$	−2.20501	−	0.468690i	−0.0753217	−	0.0160101i	0.170097	−	0.985427i	$-0.445592\pi$
$857$	−2.20501	−	0.468690i	−0.0753217	−	0.0160101i	−0.245418	+	0.969417i	$0.578925\pi$
$858$	−6.97575	+	3.10580i	−0.238148	+	0.106030i
$859$	22.7792	+	25.2989i	0.777216	+	0.863186i	0.993581	−	0.113127i	$-0.0360866\pi$
$859$	22.7792	+	25.2989i	0.777216	+	0.863186i	−0.216364	+	0.976313i	$0.569420\pi$
$860$	0.675809	−	2.07993i	0.0230449	−	0.0709249i
$861$	−2.82459	+	3.13703i	−0.0962618	+	0.106910i
$862$	−8.23676	−	14.2665i	−0.280545	−	0.485918i
$863$	−11.9533	+	20.7037i	−0.406895	+	0.704764i	−0.994540	−	0.104356i	$-0.966722\pi$
$863$	−11.9533	+	20.7037i	−0.406895	+	0.704764i	0.587645	+	0.809119i	$0.300055\pi$
$864$	−1.69098	−	5.20431i	−0.0575284	−	0.177054i
$865$	−7.74599	−	3.44874i	−0.263372	−	0.117261i
$866$	−6.70544	−	4.87178i	−0.227860	−	0.165550i
$867$	77.6891			2.63846
$868$	5.78069	−	3.44964i	0.196209	−	0.117089i
$869$	14.9189			0.506090
$870$	5.00568	+	3.63684i	0.169708	+	0.123300i
$871$	14.0509	+	6.25588i	0.476098	+	0.211972i
$872$	−5.90918	−	18.1866i	−0.200110	−	0.615875i
$873$	−2.12902	+	3.68757i	−0.0720563	+	0.124805i
$874$	−0.937466	−	1.62374i	−0.0317103	−	0.0549238i
$875$	−3.25335	+	3.61321i	−0.109983	+	0.122149i
$876$	3.42754	−	10.5489i	0.115806	−	0.356414i
$877$	27.4444	+	30.4801i	0.926733	+	1.02924i	0.999491	+	0.0318914i	$0.0101531\pi$
$877$	27.4444	+	30.4801i	0.926733	+	1.02924i	−0.0727586	+	0.997350i	$0.523180\pi$
$878$	−23.5370	+	10.4793i	−0.794334	+	0.353660i
$879$	20.2225	+	4.29842i	0.682088	+	0.144982i
$880$	−0.105484	+	1.00361i	−0.00355585	+	0.0338316i
$881$	−1.29412	−	12.3128i	−0.0436001	−	0.414828i	−0.994453	−	0.105184i	$-0.966457\pi$
$881$	−1.29412	−	12.3128i	−0.0436001	−	0.414828i	0.950853	−	0.309644i	$-0.100210\pi$
$882$	−2.06917	+	0.439816i	−0.0696726	+	0.0148094i
$883$	−20.8574	+	15.1538i	−0.701908	+	0.509966i	−0.880553	−	0.473948i	$-0.842829\pi$
$883$	−20.8574	+	15.1538i	−0.701908	+	0.509966i	0.178645	+	0.983914i	$0.442829\pi$
$884$	12.4763	−	9.06454i	0.419622	−	0.304874i
$885$	−6.14357	+	1.30586i	−0.206514	+	0.0438959i
$886$	−2.07953	−	19.7854i	−0.0698632	−	0.664704i
$887$	2.14675	−	20.4249i	0.0720808	−	0.685803i	−0.897497	−	0.441020i	$-0.854617\pi$
$887$	2.14675	−	20.4249i	0.0720808	−	0.685803i	0.969578	−	0.244783i	$-0.0787166\pi$
$888$	−8.60591	−	1.82924i	−0.288795	−	0.0613854i
$889$	−18.7419	+	8.34441i	−0.628582	+	0.279863i
$890$	−0.320977	−	0.356481i	−0.0107592	−	0.0119493i
$891$	−5.87742	+	18.0888i	−0.196901	+	0.605999i
$892$	−12.7393	+	14.1484i	−0.426543	+	0.473724i
$893$	0.218159	+	0.377863i	0.00730042	+	0.0126447i
$894$	−12.8252	+	22.2139i	−0.428938	+	0.742943i
$895$	−0.216690	−	0.666904i	−0.00724315	−	0.0222921i
$896$	1.10453	+	0.491768i	0.0368997	+	0.0164288i
$897$	15.9362	+	11.5783i	0.532094	+	0.386589i
$898$	−12.5019			−0.417194
$899$	49.2742	−	16.8000i	1.64339	−	0.560312i
$900$	1.84594			0.0615314
$901$	−18.8726	−	13.7117i	−0.628737	−	0.456805i
$902$	−4.86398	−	2.16558i	−0.161953	−	0.0721060i
$903$	3.23265	+	9.94909i	0.107576	+	0.331085i
$904$	−5.69364	+	9.86168i	−0.189368	+	0.327994i
$905$	−1.09805	−	1.90188i	−0.0365004	−	0.0632206i
$906$	8.25569	−	9.16887i	0.274277	−	0.304615i
$907$	6.00339	−	18.4765i	0.199339	−	0.613503i	−0.800559	−	0.599254i	$-0.795464\pi$
$907$	6.00339	−	18.4765i	0.199339	−	0.613503i	0.999898	−	0.0142494i	$-0.00453589\pi$
$908$	−8.47293	−	9.41014i	−0.281184	−	0.312286i
$909$	1.96553	−	0.875112i	0.0651926	−	0.0290256i
$910$	0.925065	+	0.196629i	0.0306656	+	0.00651817i
$911$	6.14715	−	58.4862i	0.203664	−	1.93774i	−0.122598	−	0.992456i	$-0.539123\pi$
$911$	6.14715	−	58.4862i	0.203664	−	1.93774i	0.326262	−	0.945279i	$-0.394211\pi$
$912$	−0.0498185	−	0.473991i	−0.00164966	−	0.0156954i
$913$	12.2005	−	2.59329i	0.403777	−	0.0858254i
$914$	−22.5237	+	16.3644i	−0.745016	+	0.541286i
$915$	−0.774682	+	0.562839i	−0.0256102	+	0.0186069i
$916$	−8.00420	+	1.70135i	−0.264466	+	0.0562141i
$917$	−1.89415	−	18.0216i	−0.0625504	−	0.595127i
$918$	4.61208	−	43.8810i	0.152221	−	1.44829i
$919$	44.3455	+	9.42592i	1.46282	+	0.310932i	0.869460	−	0.494003i	$-0.164467\pi$
$919$	44.3455	+	9.42592i	1.46282	+	0.310932i	0.593362	+	0.804936i	$0.297800\pi$
$920$	2.37819	−	1.05884i	0.0784065	−	0.0349088i
$921$	9.76580	+	10.8460i	0.321794	+	0.357389i
$922$	10.9622	−	33.7383i	0.361022	−	1.11111i
$923$	−10.5423	+	11.7084i	−0.347005	+	0.385388i
$924$	−2.41355	−	4.18038i	−0.0793998	−	0.137525i
$925$	13.1392	−	22.7577i	0.432013	−	0.748269i
$926$	6.28574	+	19.3455i	0.206562	+	0.635733i
$927$	5.62453	+	2.50420i	0.184734	+	0.0822488i
$928$	7.56444	+	5.49589i	0.248315	+	0.180411i
$929$	2.82441			0.0926658			0.0463329	−	0.998926i	$-0.485246\pi$
$929$	2.82441			0.0926658			0.0463329	+	0.998926i	$0.485246\pi$
$930$	2.12240	−	3.01169i	0.0695963	−	0.0987571i
$931$	−1.63131			−0.0534639
$932$	−16.2543	−	11.8094i	−0.532427	−	0.386831i
$933$	12.9157	+	5.75042i	0.422839	+	0.188260i
$934$	−0.305590	−	0.940510i	−0.00999921	−	0.0307744i
$935$	−4.06842	+	7.04670i	−0.133051	+	0.230452i
$936$	−0.365272	−	0.632670i	−0.0119393	−	0.0206795i
$937$	18.3389	−	20.3674i	0.599105	−	0.665373i	−0.364965	−	0.931021i	$-0.618919\pi$
$937$	18.3389	−	20.3674i	0.599105	−	0.665373i	0.964070	+	0.265648i	$0.0855858\pi$
$938$	−3.00457	+	9.24711i	−0.0981026	+	0.301929i
$939$	22.5867	+	25.0851i	0.737090	+	0.818621i
$940$	−0.553432	+	0.246404i	−0.0180510	+	0.00803680i
$941$	36.9164	+	7.84682i	1.20344	+	0.255799i	0.765638	−	0.643272i	$-0.222424\pi$
$941$	36.9164	+	7.84682i	1.20344	+	0.255799i	0.437803	+	0.899071i	$0.355757\pi$
$942$	1.17919	−	11.2192i	0.0384200	−	0.365542i
$943$	1.43569	+	13.6597i	0.0467526	+	0.444821i
$944$	−9.28398	+	1.97337i	−0.302168	+	0.0642277i
$945$	2.18907	−	1.59045i	0.0712105	−	0.0517375i
$946$	−10.6746	+	7.75554i	−0.347061	+	0.252154i
$947$	−59.0298	+	12.5472i	−1.91821	+	0.407728i	−0.918279	+	0.395934i	$0.870421\pi$
$947$	−59.0298	+	12.5472i	−1.91821	+	0.407728i	−0.999930	+	0.0117942i	$0.996246\pi$
$948$	−1.02261	−	9.72946i	−0.0332128	−	0.315998i
$949$	1.37047	−	13.0391i	0.0444873	−	0.423268i
$950$	1.39241	+	0.295965i	0.0451756	+	0.00960238i
$951$	−31.2124	+	13.8966i	−1.01213	+	0.450630i
$952$	6.52323	+	7.24478i	0.211419	+	0.234805i
$953$	1.77899	−	5.47518i	0.0576272	−	0.177358i	−0.918100	−	0.396350i	$-0.870277\pi$
$953$	1.77899	−	5.47518i	0.0576272	−	0.177358i	0.975727	+	0.218992i	$0.0702767\pi$
$954$	−0.739443	+	0.821234i	−0.0239403	+	0.0265884i
$955$	0.955663	+	1.65526i	0.0309245	+	0.0535629i
$956$	11.3284	−	19.6213i	0.366386	−	0.634599i
$957$	−11.5356	−	35.5029i	−0.372893	−	1.14765i
$958$	−2.22011	−	0.988458i	−0.0717286	−	0.0319356i
$959$	9.54317	+	6.93352i	0.308165	+	0.223895i
$960$	0.661739			0.0213575
$961$	−10.4263	−	29.1940i	−0.336332	−	0.941743i
$962$	−10.3998			−0.335304
$963$	−3.71986	−	2.70264i	−0.119871	−	0.0870913i
$964$	−26.8003	−	11.9323i	−0.863181	−	0.384313i
$965$	0.474857	+	1.46146i	0.0152862	+	0.0470461i
$966$	−6.22618	+	10.7841i	−0.200324	+	0.346971i
$967$	−11.5441	−	19.9949i	−0.371233	−	0.642994i	0.618523	−	0.785767i	$-0.287732\pi$
$967$	−11.5441	−	19.9949i	−0.371233	−	0.642994i	−0.989755	+	0.142773i	$0.954398\pi$
$968$	−3.28651	+	3.65004i	−0.105632	+	0.117317i
$969$	1.18753	−	3.65483i	0.0381489	−	0.117410i
$970$	−3.05066	−	3.38811i	−0.0979509	−	0.108786i
$971$	−48.4893	+	21.5888i	−1.55610	+	0.692818i	−0.991203	−	0.132347i	$-0.957749\pi$
$971$	−48.4893	+	21.5888i	−1.55610	+	0.692818i	−0.564892	+	0.825165i	$0.691082\pi$
$972$	−3.85808	−	0.820060i	−0.123748	−	0.0263034i
$973$	−2.47398	+	23.5383i	−0.0793121	+	0.754604i
$974$	0.162184	+	1.54308i	0.00519672	+	0.0494435i
$975$	−14.6288	+	3.10944i	−0.468495	+	0.0995817i
$976$	−1.17068	+	0.850546i	−0.0374724	+	0.0272253i
$977$	−35.9665	+	26.1312i	−1.15067	+	0.836011i	−0.988570	−	0.150764i	$-0.951827\pi$
$977$	−35.9665	+	26.1312i	−1.15067	+	0.836011i	−0.162100	+	0.986774i	$0.551827\pi$
$978$	−30.3926	+	6.46014i	−0.971847	+	0.206573i
$979$	0.302517	+	2.87826i	0.00966849	+	0.0919895i
$980$	0.236756	−	2.25258i	0.00756289	−	0.0719561i
$981$	−7.14453	−	1.51862i	−0.228107	−	0.0484857i
$982$	7.32350	−	3.26063i	0.233702	−	0.104051i
$983$	24.0819	+	26.7457i	0.768094	+	0.853055i	0.992602	−	0.121417i	$-0.0387440\pi$
$983$	24.0819	+	26.7457i	0.768094	+	0.853055i	−0.224507	+	0.974472i	$0.572077\pi$
$984$	−1.07890	+	3.32051i	−0.0343940	+	0.105854i
$985$	−3.02823	+	3.36319i	−0.0964875	+	0.107160i
$986$	37.6959	+	65.2912i	1.20048	+	2.07930i
$987$	1.44890	−	2.50957i	0.0461191	−	0.0798806i
$988$	−0.174090	−	0.535793i	−0.00553853	−	0.0170458i
$989$	31.0949	+	13.8444i	0.988761	+	0.440225i
$990$	0.311840	+	0.226565i	0.00991094	+	0.00720072i
$991$	27.2175			0.864594			0.432297	−	0.901731i	$-0.357703\pi$
$991$	27.2175			0.864594			0.432297	+	0.901731i	$0.357703\pi$
$992$	3.20731	−	4.55117i	0.101832	−	0.144500i
$993$	−44.5764			−1.41459
$994$	−8.05764	−	5.85421i	−0.255573	−	0.185684i
$995$	−1.42953	−	0.636466i	−0.0453190	−	0.0201773i
$996$	−2.52750	−	7.77884i	−0.0800869	−	0.246482i
$997$	−10.5995	+	18.3589i	−0.335691	+	0.581433i	−0.983617	−	0.180270i	$-0.942303\pi$
$997$	−10.5995	+	18.3589i	−0.335691	+	0.581433i	0.647927	+	0.761703i	$0.275636\pi$
$998$	13.0640	+	22.6275i	0.413533	+	0.716260i
$999$	−19.9101	+	22.1124i	−0.629926	+	0.699604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.g.a.19.1	✓	8
3.2	odd	2		558.2.ba.f.19.1		8
4.3	odd	2		496.2.bg.a.81.1		8
31.7	even	15		1922.2.a.q.1.3		4
31.18	even	15	inner	62.2.g.a.49.1	yes	8
31.24	odd	30		1922.2.a.o.1.1		4
93.80	odd	30		558.2.ba.f.235.1		8
124.111	odd	30		496.2.bg.a.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.a.19.1	✓	8	1.1	even	1	trivial
62.2.g.a.49.1	yes	8	31.18	even	15	inner
496.2.bg.a.49.1		8	124.111	odd	30
496.2.bg.a.81.1		8	4.3	odd	2
558.2.ba.f.19.1		8	3.2	odd	2
558.2.ba.f.235.1		8	93.80	odd	30
1922.2.a.o.1.1		4	31.24	odd	30
1922.2.a.q.1.3		4	31.7	even	15

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.47815 + 0.658114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.204489 + 0.354185i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.898504i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.255585 - 0.283856i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.47815 + 0.658114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.204489 + 0.354185i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.898504i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.255585 - 0.283856i) q^{9} +(0.373619 - 0.166346i) q^{10} +(-2.41355 - 0.513015i) q^{11} +(-0.169131 + 1.60917i) q^{12} +(0.199920 + 1.90211i) q^{13} +(-1.18264 + 0.251377i) q^{14} +(-0.535358 + 0.388960i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-7.88696 + 1.67642i) q^{17} +(0.0399263 + 0.379874i) q^{18} +(-0.0307895 + 0.292943i) q^{19} +(-0.400040 - 0.0850311i) q^{20} +(1.78716 - 0.795697i) q^{21} +(1.65106 + 1.83368i) q^{22} +(1.96698 - 6.05373i) q^{23} +(1.08268 - 1.20243i) q^{24} +(2.41637 + 4.18527i) q^{25} +(0.956295 - 1.65635i) q^{26} +(-1.69098 - 5.20431i) q^{27} +(1.10453 + 0.491768i) q^{28} +(7.56444 + 5.49589i) q^{29} +0.661739 q^{30} +(3.20731 - 4.55117i) q^{31} +1.00000 q^{32} +(-3.22995 - 2.34670i) q^{33} +(7.36606 + 3.27958i) q^{34} +(0.152802 + 0.470275i) q^{35} +(0.190983 - 0.330792i) q^{36} +(-2.71878 - 4.70907i) q^{37} +(0.197097 - 0.218898i) q^{38} +(-0.956295 + 2.94317i) q^{39} +(0.273659 + 0.303929i) q^{40} +(-1.97124 + 0.877654i) q^{41} +(-1.91355 - 0.406737i) q^{42} +(-0.558955 + 5.31810i) q^{43} +(-0.257920 - 2.45395i) q^{44} +(0.152802 - 0.0324790i) q^{45} +(-5.14961 + 3.74141i) q^{46} +(1.19837 - 0.870670i) q^{47} +(-1.58268 + 0.336408i) q^{48} +(0.578898 + 5.50784i) q^{49} +(0.505159 - 4.80626i) q^{50} +(-12.7614 - 2.71251i) q^{51} +(-1.74724 + 0.777921i) q^{52} +(1.93589 + 2.15002i) q^{53} +(-1.69098 + 5.20431i) q^{54} +(0.675244 - 0.749935i) q^{55} +(-0.604528 - 1.04707i) q^{56} +(-0.238301 + 0.412750i) q^{57} +(-2.88936 - 8.89253i) q^{58} +(8.67081 + 3.86049i) q^{59} +(-0.535358 - 0.388960i) q^{60} +1.44704 q^{61} +(-5.26988 + 1.79676i) q^{62} -0.461819 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.714580 - 0.318152i) q^{65} +(1.23373 + 3.79704i) q^{66} +(4.02090 - 6.96440i) q^{67} +(-4.03158 - 6.98290i) q^{68} +(6.89153 - 7.65382i) q^{69} +(0.152802 - 0.470275i) q^{70} +(5.51206 + 6.12177i) q^{71} +(-0.348943 + 0.155360i) q^{72} +(-6.70528 - 1.42525i) q^{73} +(-0.568381 + 5.40778i) q^{74} +(0.817364 + 7.77670i) q^{75} +(-0.288120 + 0.0612417i) q^{76} +(-2.41355 + 1.75354i) q^{77} +(2.50361 - 1.81898i) q^{78} +(-5.91414 + 1.25709i) q^{79} +(-0.0427497 - 0.406737i) q^{80} +(0.805727 - 7.66598i) q^{81} +(2.11064 + 0.448631i) q^{82} +(-4.61797 + 2.05605i) q^{83} +(1.30902 + 1.45381i) q^{84} +(1.01903 - 3.13625i) q^{85} +(3.57811 - 3.97389i) q^{86} +(7.56444 + 13.1020i) q^{87} +(-1.23373 + 2.13689i) q^{88} +(-0.362449 - 1.11550i) q^{89} +(-0.142710 - 0.0635385i) q^{90} +(1.87080 + 1.35921i) q^{91} +6.36527 q^{92} +(7.73607 - 4.61653i) q^{93} -1.48127 q^{94} +(-0.0974597 - 0.0708086i) q^{95} +(1.47815 + 0.658114i) q^{96} +(-3.44482 - 10.6021i) q^{97} +(2.76909 - 4.79621i) q^{98} +(0.471244 + 0.816219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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