LMFDB - Embedded newform 637.2.bl.a.53.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.19
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01838 + 0.694320i) q^{2} +(0.670270 + 0.621920i) q^{3} +(-0.175663 - 0.447582i) q^{4} +(0.228303 - 0.0704221i) q^{5} +(0.250779 + 1.09873i) q^{6} +(2.28590 + 1.33217i) q^{7} +(0.680410 - 2.98107i) q^{8} +(-0.161712 - 2.15790i) q^{9} +O(q^{10})$	\(q+(1.01838 + 0.694320i) q^{2} +(0.670270 + 0.621920i) q^{3} +(-0.175663 - 0.447582i) q^{4} +(0.228303 - 0.0704221i) q^{5} +(0.250779 + 1.09873i) q^{6} +(2.28590 + 1.33217i) q^{7} +(0.680410 - 2.98107i) q^{8} +(-0.161712 - 2.15790i) q^{9} +(0.281395 + 0.0867987i) q^{10} +(-0.0880881 + 1.17545i) q^{11} +(0.160619 - 0.409249i) q^{12} +(0.900969 - 0.433884i) q^{13} +(1.40296 + 2.94380i) q^{14} +(0.196821 + 0.0947842i) q^{15} +(2.05780 - 1.90936i) q^{16} +(4.17595 - 0.629424i) q^{17} +(1.33359 - 2.30985i) q^{18} +(1.03747 + 1.79696i) q^{19} +(-0.0716241 - 0.0898137i) q^{20} +(0.703666 + 2.31456i) q^{21} +(-0.905849 + 1.13590i) q^{22} +(0.137468 + 0.0207200i) q^{23} +(2.31005 - 1.57496i) q^{24} +(-4.08403 + 2.78445i) q^{25} +(1.21878 + 0.183702i) q^{26} +(2.94393 - 3.69157i) q^{27} +(0.194708 - 1.25714i) q^{28} +(1.31913 + 1.65414i) q^{29} +(0.134629 + 0.233183i) q^{30} +(-0.459726 + 0.796269i) q^{31} +(-2.62583 + 0.395780i) q^{32} +(-0.790081 + 0.733088i) q^{33} +(4.68973 + 2.25846i) q^{34} +(0.615691 + 0.143160i) q^{35} +(-0.937433 + 0.451444i) q^{36} +(-1.24872 + 3.18169i) q^{37} +(-0.191120 + 2.55033i) q^{38} +(0.873733 + 0.269511i) q^{39} +(-0.0545937 - 0.728503i) q^{40} +(-1.38906 + 6.08589i) q^{41} +(-0.890444 + 2.84567i) q^{42} +(-2.52719 - 11.0723i) q^{43} +(0.541587 - 0.167057i) q^{44} +(-0.188883 - 0.481267i) q^{45} +(0.125609 + 0.116548i) q^{46} +(-5.15190 - 3.51250i) q^{47} +2.56675 q^{48} +(3.45065 + 6.09040i) q^{49} -6.09240 q^{50} +(3.19047 + 2.17522i) q^{51} +(-0.352466 - 0.327040i) q^{52} +(3.19646 + 8.14446i) q^{53} +(5.56117 - 1.71539i) q^{54} +(0.0626672 + 0.274563i) q^{55} +(5.52664 - 5.90800i) q^{56} +(-0.422176 + 1.84967i) q^{57} +(0.194876 + 2.60044i) q^{58} +(-1.16986 - 0.360854i) q^{59} +(0.00784947 - 0.104744i) q^{60} +(1.30595 - 3.32750i) q^{61} +(-1.02104 + 0.491708i) q^{62} +(2.50503 - 5.14817i) q^{63} +(-8.00724 - 3.85608i) q^{64} +(0.175139 - 0.162505i) q^{65} +(-1.31360 + 0.197994i) q^{66} +(-4.41526 + 7.64745i) q^{67} +(-1.01528 - 1.75852i) q^{68} +(0.0792546 + 0.0993821i) q^{69} +(0.527609 + 0.573278i) q^{70} +(-4.30503 + 5.39833i) q^{71} +(-6.54289 - 0.986183i) q^{72} +(10.1521 - 6.92162i) q^{73} +(-3.48079 + 2.37316i) q^{74} +(-4.46911 - 0.673609i) q^{75} +(0.622040 - 0.780014i) q^{76} +(-1.76726 + 2.56962i) q^{77} +(0.702666 + 0.881116i) q^{78} +(-6.45930 - 11.1878i) q^{79} +(0.335341 - 0.580827i) q^{80} +(-2.15027 + 0.324101i) q^{81} +(-5.64015 + 5.23329i) q^{82} +(-12.4973 - 6.01839i) q^{83} +(0.912347 - 0.721531i) q^{84} +(0.909056 - 0.437778i) q^{85} +(5.11410 - 13.0305i) q^{86} +(-0.144567 + 1.92911i) q^{87} +(3.44418 + 1.06239i) q^{88} +(0.412037 + 5.49825i) q^{89} +(0.141798 - 0.621259i) q^{90} +(2.63753 + 0.208429i) q^{91} +(-0.0148742 - 0.0651680i) q^{92} +(-0.803356 + 0.247802i) q^{93} +(-2.80779 - 7.15413i) q^{94} +(0.363403 + 0.337189i) q^{95} +(-2.00616 - 1.36778i) q^{96} -10.6154 q^{97} +(-0.714613 + 8.59821i) q^{98} +2.55076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	1.01838	+	0.694320i	0.720104	+	0.490959i	0.867072	−	0.498183i	$-0.165999\pi$
$2$	1.01838	+	0.694320i	0.720104	+	0.490959i	−0.146968	+	0.989141i	$0.546951\pi$
$3$	0.670270	+	0.621920i	0.386981	+	0.359066i	0.849541	−	0.527522i	$-0.176879\pi$
$3$	0.670270	+	0.621920i	0.386981	+	0.359066i	−0.462561	+	0.886588i	$0.653069\pi$
$4$	−0.175663	−	0.447582i	−0.0878316	−	0.223791i
$5$	0.228303	−	0.0704221i	0.102100	−	0.0314937i	−0.243284	−	0.969955i	$-0.578225\pi$
$5$	0.228303	−	0.0704221i	0.102100	−	0.0314937i	0.345384	+	0.938461i	$0.387749\pi$
$6$	0.250779	+	1.09873i	0.102380	+	0.448556i
$7$	2.28590	+	1.33217i	0.863988	+	0.503513i
$7$	2.28590	+	1.33217i	0.863988	+	0.503513i
$8$	0.680410	−	2.98107i	0.240561	−	1.05397i
$9$	−0.161712	−	2.15790i	−0.0539042	−	0.719301i
$10$	0.281395	+	0.0867987i	0.0889848	+	0.0274482i
$11$	−0.0880881	+	1.17545i	−0.0265596	+	0.354413i	0.968053	+	0.250747i	$0.0806763\pi$
$11$	−0.0880881	+	1.17545i	−0.0265596	+	0.354413i	−0.994612	+	0.103666i	$0.966943\pi$
$12$	0.160619	−	0.409249i	0.0463666	−	0.118140i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	1.40296	+	2.94380i	0.374957	+	0.786764i
$15$	0.196821	+	0.0947842i	0.0508191	+	0.0244732i
$16$	2.05780	−	1.90936i	0.514451	−	0.477341i
$17$	4.17595	−	0.629424i	1.01282	−	0.152658i	0.378395	−	0.925644i	$-0.376476\pi$
$17$	4.17595	−	0.629424i	1.01282	−	0.152658i	0.634423	+	0.772986i	$0.281238\pi$
$18$	1.33359	−	2.30985i	0.314330	−	0.544436i
$19$	1.03747	+	1.79696i	0.238013	+	0.412250i	0.960144	−	0.279506i	$-0.0901707\pi$
$19$	1.03747	+	1.79696i	0.238013	+	0.412250i	−0.722131	+	0.691756i	$0.756837\pi$
$20$	−0.0716241	−	0.0898137i	−0.0160156	−	0.0200830i
$21$	0.703666	+	2.31456i	0.153553	+	0.505078i
$22$	−0.905849	+	1.13590i	−0.193128	+	0.242175i
$23$	0.137468	+	0.0207200i	0.0286641	+	0.00432041i	0.163359	−	0.986567i	$-0.447767\pi$
$23$	0.137468	+	0.0207200i	0.0286641	+	0.00432041i	−0.134695	+	0.990887i	$0.543005\pi$
$24$	2.31005	−	1.57496i	0.471536	−	0.321488i
$25$	−4.08403	+	2.78445i	−0.816806	+	0.556889i
$26$	1.21878	+	0.183702i	0.239023	+	0.0360269i
$27$	2.94393	−	3.69157i	0.566559	−	0.710442i
$28$	0.194708	−	1.25714i	0.0367963	−	0.237577i
$29$	1.31913	+	1.65414i	0.244957	+	0.307166i	0.889076	−	0.457759i	$-0.151348\pi$
$29$	1.31913	+	1.65414i	0.244957	+	0.307166i	−0.644120	+	0.764925i	$0.722776\pi$
$30$	0.134629	+	0.233183i	0.0245797	+	0.0425733i
$31$	−0.459726	+	0.796269i	−0.0825692	+	0.143014i	−0.904353	−	0.426786i	$-0.859646\pi$
$31$	−0.459726	+	0.796269i	−0.0825692	+	0.143014i	0.821784	+	0.569800i	$0.192979\pi$
$32$	−2.62583	+	0.395780i	−0.464185	+	0.0699647i
$33$	−0.790081	+	0.733088i	−0.137535	+	0.127614i
$34$	4.68973	+	2.25846i	0.804283	+	0.387322i
$35$	0.615691	+	0.143160i	0.104071	+	0.0241985i
$36$	−0.937433	+	0.451444i	−0.156239	+	0.0752406i
$37$	−1.24872	+	3.18169i	−0.205289	+	0.523067i	−0.996023	−	0.0890920i	$-0.971603\pi$
$37$	−1.24872	+	3.18169i	−0.205289	+	0.523067i	0.790735	+	0.612159i	$0.209699\pi$
$38$	−0.191120	+	2.55033i	−0.0310038	+	0.413717i
$39$	0.873733	+	0.269511i	0.139909	+	0.0431563i
$40$	−0.0545937	−	0.728503i	−0.00863203	−	0.115186i
$41$	−1.38906	+	6.08589i	−0.216935	+	0.950456i	0.742792	+	0.669522i	$0.233501\pi$
$41$	−1.38906	+	6.08589i	−0.216935	+	0.950456i	−0.959727	+	0.280933i	$0.909356\pi$
$42$	−0.890444	+	2.84567i	−0.137399	+	0.439097i
$43$	−2.52719	−	11.0723i	−0.385392	−	1.68851i	−0.680256	−	0.732975i	$-0.738131\pi$
$43$	−2.52719	−	11.0723i	−0.385392	−	1.68851i	0.294863	−	0.955539i	$-0.404726\pi$
$44$	0.541587	−	0.167057i	0.0816473	−	0.0251848i
$45$	−0.188883	−	0.481267i	−0.0281571	−	0.0717431i
$46$	0.125609	+	0.116548i	0.0185200	+	0.0171840i
$47$	−5.15190	−	3.51250i	−0.751481	−	0.512351i	0.125960	−	0.992035i	$-0.459799\pi$
$47$	−5.15190	−	3.51250i	−0.751481	−	0.512351i	−0.877441	+	0.479684i	$0.840751\pi$
$48$	2.56675			0.370479
$49$	3.45065	+	6.09040i	0.492950	+	0.870058i
$50$	−6.09240			−0.861595
$51$	3.19047	+	2.17522i	0.446755	+	0.304592i
$52$	−0.352466	−	0.327040i	−0.0488782	−	0.0453523i
$53$	3.19646	+	8.14446i	0.439068	+	1.11873i	0.963603	+	0.267338i	$0.0861441\pi$
$53$	3.19646	+	8.14446i	0.439068	+	1.11873i	−0.524535	+	0.851389i	$0.675761\pi$
$54$	5.56117	−	1.71539i	0.756779	−	0.233435i
$55$	0.0626672	+	0.274563i	0.00845004	+	0.0370220i
$56$	5.52664	−	5.90800i	0.738528	−	0.789490i
$57$	−0.422176	+	1.84967i	−0.0559185	+	0.244995i
$58$	0.194876	+	2.60044i	0.0255885	+	0.341455i
$59$	−1.16986	−	0.360854i	−0.152303	−	0.0469792i	0.217666	−	0.976023i	$-0.430156\pi$
$59$	−1.16986	−	0.360854i	−0.152303	−	0.0469792i	−0.369969	+	0.929044i	$0.620632\pi$
$60$	0.00784947	−	0.104744i	0.00101336	−	0.0135224i
$61$	1.30595	−	3.32750i	0.167210	−	0.426043i	−0.822567	−	0.568668i	$-0.807459\pi$
$61$	1.30595	−	3.32750i	0.167210	−	0.426043i	0.989777	+	0.142625i	$0.0455542\pi$
$62$	−1.02104	+	0.491708i	−0.129672	+	0.0624469i
$63$	2.50503	−	5.14817i	0.315605	−	0.648609i
$64$	−8.00724	−	3.85608i	−1.00091	−	0.482011i
$65$	0.175139	−	0.162505i	0.0217233	−	0.0201563i
$66$	−1.31360	+	0.197994i	−0.161693	+	0.0243713i
$67$	−4.41526	+	7.64745i	−0.539409	+	0.934285i	0.459526	+	0.888164i	$0.348019\pi$
$67$	−4.41526	+	7.64745i	−0.539409	+	0.934285i	−0.998936	+	0.0461205i	$0.985314\pi$
$68$	−1.01528	−	1.75852i	−0.123121	−	0.213252i
$69$	0.0792546	+	0.0993821i	0.00954113	+	0.0119642i
$70$	0.527609	+	0.573278i	0.0630613	+	0.0685199i
$71$	−4.30503	+	5.39833i	−0.510913	+	0.640664i	−0.968652	−	0.248422i	$-0.920088\pi$
$71$	−4.30503	+	5.39833i	−0.510913	+	0.640664i	0.457739	+	0.889086i	$0.348659\pi$
$72$	−6.54289	−	0.986183i	−0.771087	−	0.116223i
$73$	10.1521	−	6.92162i	1.18822	−	0.810114i	0.202627	−	0.979256i	$-0.435052\pi$
$73$	10.1521	−	6.92162i	1.18822	−	0.810114i	0.985592	+	0.169142i	$0.0540997\pi$
$74$	−3.48079	+	2.37316i	−0.404633	+	0.275874i
$75$	−4.46911	−	0.673609i	−0.516048	−	0.0777817i
$76$	0.622040	−	0.780014i	0.0713529	−	0.0894737i
$77$	−1.76726	+	2.56962i	−0.201399	+	0.292835i
$78$	0.702666	+	0.881116i	0.0795613	+	0.0997667i
$79$	−6.45930	−	11.1878i	−0.726729	−	1.25873i	−0.958259	−	0.285903i	$-0.907706\pi$
$79$	−6.45930	−	11.1878i	−0.726729	−	1.25873i	0.231530	−	0.972828i	$-0.425627\pi$
$80$	0.335341	−	0.580827i	0.0374923	−	0.0649385i
$81$	−2.15027	+	0.324101i	−0.238919	+	0.0360112i
$82$	−5.64015	+	5.23329i	−0.622850	+	0.577921i
$83$	−12.4973	−	6.01839i	−1.37176	−	0.660604i	−0.404532	−	0.914524i	$-0.632566\pi$
$83$	−12.4973	−	6.01839i	−1.37176	−	0.660604i	−0.967225	+	0.253920i	$0.918280\pi$
$84$	0.912347	−	0.721531i	0.0995452	−	0.0787255i
$85$	0.909056	−	0.437778i	0.0986010	−	0.0474837i
$86$	5.11410	−	13.0305i	0.551468	−	1.40512i
$87$	−0.144567	+	1.92911i	−0.0154992	+	0.206823i
$88$	3.44418	+	1.06239i	0.367151	+	0.113251i
$89$	0.412037	+	5.49825i	0.0436758	+	0.582813i	0.975514	+	0.219938i	$0.0705856\pi$
$89$	0.412037	+	5.49825i	0.0436758	+	0.582813i	−0.931838	+	0.362875i	$0.881795\pi$
$90$	0.141798	−	0.621259i	0.0149468	−	0.0654864i
$91$	2.63753	+	0.208429i	0.276488	+	0.0218493i
$92$	−0.0148742	−	0.0651680i	−0.00155074	−	0.00679424i
$93$	−0.803356	+	0.247802i	−0.0833041	+	0.0256959i
$94$	−2.80779	−	7.15413i	−0.289601	−	0.737892i
$95$	0.363403	+	0.337189i	0.0372844	+	0.0345949i
$96$	−2.00616	−	1.36778i	−0.204753	−	0.139598i
$97$	−10.6154			−1.07783			−0.538914	−	0.842361i	$-0.681165\pi$
$97$	−10.6154			−1.07783			−0.538914	+	0.842361i	$0.681165\pi$
$98$	−0.714613	+	8.59821i	−0.0721869	+	0.868550i
$99$	2.55076			0.256361
$100$	1.96368	+	1.33882i	0.196368	+	0.133882i
$101$	−7.89363	−	7.32421i	−0.785445	−	0.728787i	0.181605	−	0.983372i	$-0.441871\pi$
$101$	−7.89363	−	7.32421i	−0.785445	−	0.728787i	−0.967050	+	0.254585i	$0.918061\pi$
$102$	1.73881	+	4.43041i	0.172168	+	0.438676i
$103$	−5.38702	+	1.66167i	−0.530799	+	0.163730i	−0.548558	−	0.836113i	$-0.684823\pi$
$103$	−5.38702	+	1.66167i	−0.530799	+	0.163730i	0.0177592	+	0.999842i	$0.494347\pi$
$104$	−0.680410	−	2.98107i	−0.0667197	−	0.292318i
$105$	0.323645	+	0.478866i	0.0315845	+	0.0467326i
$106$	−2.39965	+	10.5135i	−0.233074	+	1.02116i
$107$	1.01307	+	13.5185i	0.0979375	+	1.30688i	0.802247	+	0.596992i	$0.203638\pi$
$107$	1.01307	+	13.5185i	0.0979375	+	1.30688i	−0.704310	+	0.709893i	$0.748743\pi$
$108$	−2.16942	−	0.669177i	−0.208752	−	0.0643916i
$109$	−0.803961	+	10.7281i	−0.0770055	+	1.02757i	0.816156	+	0.577831i	$0.196101\pi$
$109$	−0.803961	+	10.7281i	−0.0770055	+	1.02757i	−0.893162	+	0.449736i	$0.851518\pi$
$110$	−0.126816	+	0.323121i	−0.0120914	+	0.0308083i
$111$	−2.81574	+	1.35599i	−0.267258	+	0.128705i
$112$	7.24752	−	1.62326i	0.684826	−	0.153384i
$113$	−7.06456	−	3.40211i	−0.664578	−	0.320044i	0.0710074	−	0.997476i	$-0.477379\pi$
$113$	−7.06456	−	3.40211i	−0.664578	−	0.320044i	−0.735586	+	0.677432i	$0.763093\pi$
$114$	−1.71420	+	1.59055i	−0.160550	+	0.148968i
$115$	0.0328435	−	0.00495036i	0.00306267	−	0.000461623i
$116$	0.508641	−	0.880991i	0.0472261	−	0.0817980i
$117$	−1.08198	−	1.87404i	−0.100029	−	0.173255i
$118$	−0.940814	−	1.17974i	−0.0866090	−	0.108604i
$119$	10.3843	+	4.12428i	0.951927	+	0.378072i
$120$	0.416478	−	0.522246i	0.0380190	−	0.0476744i
$121$	9.50321	+	1.43238i	0.863928	+	0.130216i
$122$	3.64031	−	2.48192i	0.329578	−	0.224702i
$123$	−4.71598	+	3.21530i	−0.425226	+	0.289914i
$124$	0.437153	+	0.0658902i	0.0392575	+	0.00591711i
$125$	−1.48112	+	1.85727i	−0.132475	+	0.166119i
$126$	6.12556	−	3.50350i	0.545708	−	0.312117i
$127$	−0.436979	−	0.547954i	−0.0387756	−	0.0486231i	0.762066	−	0.647500i	$-0.224185\pi$
$127$	−0.436979	−	0.547954i	−0.0387756	−	0.0486231i	−0.800841	+	0.598877i	$0.795614\pi$
$128$	−2.82158	−	4.88711i	−0.249395	−	0.431964i
$129$	5.19220	−	8.99316i	0.457148	−	0.791803i
$130$	0.291188	−	0.0438896i	0.0255389	−	0.00384937i
$131$	13.2019	−	12.2496i	1.15345	−	1.07025i	0.156874	−	0.987619i	$-0.449858\pi$
$131$	13.2019	−	12.2496i	1.15345	−	1.07025i	0.996580	−	0.0826309i	$-0.0263323\pi$
$132$	0.466906	+	0.224850i	0.0406389	+	0.0195707i
$133$	−0.0222927	+	5.48975i	−0.00193302	+	0.476022i
$134$	−9.80619	+	4.72241i	−0.847126	+	0.407954i
$135$	0.412139	−	1.05011i	0.0354712	−	0.0903792i
$136$	0.965004	−	12.8771i	0.0827484	−	1.10420i
$137$	−7.94398	−	2.45039i	−0.678700	−	0.209351i	−0.0638078	−	0.997962i	$-0.520324\pi$
$137$	−7.94398	−	2.45039i	−0.678700	−	0.209351i	−0.614893	+	0.788611i	$0.710801\pi$
$138$	0.0117083	+	0.156237i	0.000996680	+	0.0132998i
$139$	2.28436	−	10.0084i	0.193757	−	0.848905i	−0.780803	−	0.624777i	$-0.785190\pi$
$139$	2.28436	−	10.0084i	0.193757	−	0.848905i	0.974560	−	0.224127i	$-0.0719532\pi$
$140$	−0.0440782	−	0.300720i	−0.00372528	−	0.0254155i
$141$	−1.26867	−	5.55839i	−0.106841	−	0.468101i
$142$	−8.13233	+	2.50849i	−0.682450	+	0.210508i
$143$	0.430646	+	1.09727i	0.0360124	+	0.0917582i
$144$	−4.45299	−	4.13177i	−0.371083	−	0.344314i
$145$	0.417649	+	0.284748i	0.0346839	+	0.0236471i
$146$	15.1446			1.25337
$147$	−1.47487	+	6.22824i	−0.121646	+	0.513697i
$148$	1.64342			0.135089
$149$	−13.8292	−	9.42860i	−1.13293	−	0.772421i	−0.156380	−	0.987697i	$-0.549982\pi$
$149$	−13.8292	−	9.42860i	−1.13293	−	0.772421i	−0.976553	+	0.215276i	$0.930935\pi$
$150$	−4.08355	−	3.78898i	−0.333421	−	0.309369i
$151$	4.14440	+	10.5598i	0.337267	+	0.859341i	0.994411	+	0.105577i	$0.0336688\pi$
$151$	4.14440	+	10.5598i	0.337267	+	0.859341i	−0.657145	+	0.753765i	$0.728236\pi$
$152$	6.06276	−	1.87012i	0.491755	−	0.151686i
$153$	−2.03354	−	8.90952i	−0.164402	−	0.720292i
$154$	−3.58389	+	1.38980i	−0.288798	+	0.111994i
$155$	−0.0488818	+	0.214165i	−0.00392628	+	0.0172022i
$156$	−0.0328543	−	0.438411i	−0.00263045	−	0.0351010i
$157$	14.3218	+	4.41769i	1.14301	+	0.352570i	0.807732	−	0.589550i	$-0.200695\pi$
$157$	14.3218	+	4.41769i	1.14301	+	0.352570i	0.335274	+	0.942121i	$0.391171\pi$
$158$	1.18992	−	15.8783i	0.0946646	−	1.26321i
$159$	−2.92271	+	7.44693i	−0.231786	+	0.590580i
$160$	−0.571612	+	0.275274i	−0.0451899	+	0.0217623i
$161$	0.286635	+	0.230494i	0.0225900	+	0.0181655i
$162$	−2.41482	−	1.16292i	−0.189726	−	0.0913675i
$163$	16.2065	−	15.0375i	1.26939	−	1.17782i	0.294378	−	0.955689i	$-0.404888\pi$
$163$	16.2065	−	15.0375i	1.26939	−	1.17782i	0.975016	−	0.222136i	$-0.0713028\pi$
$164$	2.96794	−	0.447345i	0.231757	−	0.0349318i
$165$	−0.128752	+	0.223005i	−0.0100233	+	0.0173609i
$166$	−8.54833	−	14.8061i	−0.663479	−	1.14918i
$167$	2.04089	+	2.55919i	0.157929	+	0.198036i	0.854500	−	0.519451i	$-0.173864\pi$
$167$	2.04089	+	2.55919i	0.157929	+	0.198036i	−0.696572	+	0.717487i	$0.745292\pi$
$168$	7.37864	−	0.522831i	0.569275	−	0.0403373i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	1.22972	+	0.185351i	0.0943155	+	0.0142158i
$171$	3.70989	−	2.52936i	0.283702	−	0.193425i
$172$	−4.51185	+	3.07612i	−0.344025	+	0.234552i
$173$	−4.52241	−	0.681644i	−0.343833	−	0.0518244i	−0.0251438	−	0.999684i	$-0.508004\pi$
$173$	−4.52241	−	0.681644i	−0.343833	−	0.0518244i	−0.318689	+	0.947859i	$0.603242\pi$
$174$	−1.48665	+	1.86420i	−0.112702	+	0.141324i
$175$	−13.0450	+	0.924335i	−0.986111	+	0.0698732i
$176$	2.06310	+	2.58705i	0.155512	+	0.195006i
$177$	−0.559700	−	0.969428i	−0.0420696	−	0.0728667i
$178$	−3.39793	+	5.88540i	−0.254686	+	0.441129i
$179$	−13.9889	+	2.10849i	−1.04558	+	0.157596i	−0.649298	−	0.760534i	$-0.724937\pi$
$179$	−13.9889	+	2.10849i	−1.04558	+	0.157596i	−0.396280	+	0.918130i	$0.629699\pi$
$180$	−0.182227	+	0.169082i	−0.0135824	+	0.0126026i
$181$	5.74917	+	2.76865i	0.427332	+	0.205792i	0.635172	−	0.772371i	$-0.280929\pi$
$181$	5.74917	+	2.76865i	0.427332	+	0.205792i	−0.207840	+	0.978163i	$0.566643\pi$
$182$	2.54129	+	2.04355i	0.188373	+	0.151478i
$183$	2.94478	−	1.41813i	0.217684	−	0.104831i
$184$	0.155302	−	0.395704i	0.0114490	−	0.0291717i
$185$	−0.0610253	+	0.814326i	−0.00448667	+	0.0598705i
$186$	−0.990176	−	0.305429i	−0.0726033	−	0.0223951i
$187$	0.372007	+	4.96409i	0.0272039	+	0.363010i
$188$	−0.667136	+	2.92292i	−0.0486559	+	0.213175i
$189$	11.6473	−	4.51673i	0.847216	−	0.328544i
$190$	0.135966	+	0.595705i	0.00986400	+	0.0432170i
$191$	−23.9927	+	7.40076i	−1.73605	+	0.535500i	−0.991274	−	0.131817i	$-0.957919\pi$
$191$	−23.9927	+	7.40076i	−1.73605	+	0.535500i	−0.744774	+	0.667317i	$0.767443\pi$
$192$	−2.96884	−	7.56448i	−0.214258	−	0.545919i
$193$	13.6112	+	12.6294i	0.979759	+	0.909084i	0.995870	−	0.0907866i	$-0.0289381\pi$
$193$	13.6112	+	12.6294i	0.979759	+	0.909084i	−0.0161113	+	0.999870i	$0.505129\pi$
$194$	−10.8105	−	7.37047i	−0.776148	−	0.529169i
$195$	0.218455			0.0156439
$196$	2.11980	−	2.61431i	0.151415	−	0.186736i
$197$	−9.51748			−0.678092			−0.339046	−	0.940770i	$-0.610104\pi$
$197$	−9.51748			−0.678092			−0.339046	+	0.940770i	$0.610104\pi$
$198$	2.59765	+	1.77105i	0.184607	+	0.125863i
$199$	15.8048	+	14.6647i	1.12037	+	1.03955i	0.998897	+	0.0469585i	$0.0149529\pi$
$199$	15.8048	+	14.6647i	1.12037	+	1.03955i	0.121475	+	0.992595i	$0.461238\pi$
$200$	5.52181	+	14.0694i	0.390451	+	0.994853i
$201$	−7.71551	+	2.37992i	−0.544210	+	0.167867i
$202$	−2.95337	−	12.9395i	−0.207798	−	0.910423i
$203$	0.811807	+	5.53850i	0.0569777	+	0.388726i
$204$	0.413144	−	1.81010i	0.0289259	−	0.126733i
$205$	0.111454	+	1.48725i	0.00778426	+	0.103874i
$206$	−6.63977	−	2.04810i	−0.462615	−	0.142698i
$207$	0.0224814	−	0.299993i	0.00156257	−	0.0208510i
$208$	1.02558	−	2.61312i	0.0711109	−	0.181188i
$209$	−2.20363	+	1.06121i	−0.152428	+	0.0734056i
$210$	−0.00289282	+	0.712381i	−0.000199624	+	0.0491590i
$211$	−9.99720	−	4.81440i	−0.688236	−	0.331437i	0.0568716	−	0.998382i	$-0.481887\pi$
$211$	−9.99720	−	4.81440i	−0.688236	−	0.331437i	−0.745107	+	0.666945i	$0.767602\pi$
$212$	3.08382	−	2.86136i	0.211797	−	0.196519i
$213$	−6.24286	+	0.940959i	−0.427754	+	0.0644735i
$214$	−8.35449	+	14.4704i	−0.571101	+	0.989176i
$215$	−1.35670	−	2.34987i	−0.0925262	−	0.160260i
$216$	−9.00174	−	11.2878i	−0.612491	−	0.768040i
$217$	−2.11165	+	1.20776i	−0.143348	+	0.0819878i
$218$	−8.26749	+	10.3671i	−0.559945	+	0.702149i
$219$	11.1094	+	1.67447i	0.750702	+	0.113150i
$220$	0.111881	−	0.0762793i	0.00754303	−	0.00514275i
$221$	3.48931	−	2.37897i	0.234716	−	0.160027i
$222$	−3.80898	−	0.574112i	−0.255642	−	0.0385319i
$223$	8.22941	−	10.3194i	0.551082	−	0.691035i	−0.425799	−	0.904818i	$-0.640007\pi$
$223$	8.22941	−	10.3194i	0.551082	−	0.691035i	0.976881	+	0.213783i	$0.0685784\pi$
$224$	−6.52962	−	2.59334i	−0.436279	−	0.173275i
$225$	6.66900	+	8.36266i	0.444600	+	0.557511i
$226$	−4.83226	−	8.36972i	−0.321437	−	0.556745i
$227$	−9.05441	+	15.6827i	−0.600962	+	1.04090i	0.391713	+	0.920087i	$0.371883\pi$
$227$	−9.05441	+	15.6827i	−0.600962	+	1.04090i	−0.992676	+	0.120810i	$0.961451\pi$
$228$	0.902041	−	0.135961i	0.0597391	−	0.00900423i
$229$	14.5507	−	13.5010i	0.961534	−	0.892173i	−0.0326935	−	0.999465i	$-0.510409\pi$
$229$	14.5507	−	13.5010i	0.961534	−	0.892173i	0.994228	+	0.107292i	$0.0342180\pi$
$230$	0.0368843	+	0.0177625i	0.00243208	+	0.00117123i
$231$	−2.78264	+	0.623243i	−0.183084	+	0.0410063i
$232$	5.82866	−	2.80693i	0.382670	−	0.184284i
$233$	−3.11464	+	7.93597i	−0.204047	+	0.519903i	−0.995864	−	0.0908553i	$-0.971040\pi$
$233$	−3.11464	+	7.93597i	−0.204047	+	0.519903i	0.791817	+	0.610758i	$0.209135\pi$
$234$	0.199319	−	2.65972i	0.0130299	−	0.173872i
$235$	−1.42355	−	0.439107i	−0.0928621	−	0.0286442i
$236$	0.0439894	+	0.586997i	0.00286346	+	0.0382103i
$237$	2.62846	−	11.5160i	0.170737	−	0.748048i
$238$	7.71160	+	11.4101i	0.499869	+	0.739608i
$239$	2.86082	+	12.5341i	0.185051	+	0.810762i	0.979177	+	0.203009i	$0.0650719\pi$
$239$	2.86082	+	12.5341i	0.185051	+	0.810762i	−0.794126	+	0.607753i	$0.792071\pi$
$240$	0.585997	−	0.180756i	0.0378259	−	0.0116678i
$241$	9.11131	+	23.2152i	0.586911	+	1.49543i	0.847939	+	0.530094i	$0.177843\pi$
$241$	9.11131	+	23.2152i	0.586911	+	1.49543i	−0.261028	+	0.965331i	$0.584061\pi$
$242$	8.68335	+	8.05697i	0.558187	+	0.517922i
$243$	−13.3466	−	9.09953i	−0.856182	−	0.583735i
$244$	−1.71874			−0.110031
$245$	1.21669	+	1.14745i	0.0777316	+	0.0733081i
$246$	−7.03511			−0.448542
$247$	1.71440	+	1.16886i	0.109085	+	0.0743727i
$248$	2.06093	+	1.91227i	0.130869	+	0.121429i
$249$	−4.63362	−	11.8063i	−0.293644	−	0.748192i
$250$	−2.79788	+	0.863033i	−0.176954	+	0.0545830i
$251$	−0.410425	−	1.79819i	−0.0259058	−	0.113501i	0.960322	−	0.278894i	$-0.0899678\pi$
$251$	−0.410425	−	1.79819i	−0.0259058	−	0.113501i	−0.986228	+	0.165393i	$0.947111\pi$
$252$	−2.74427	−	0.216865i	−0.172873	−	0.0136612i
$253$	−0.0364647	+	0.159762i	−0.00229252	+	0.0100442i
$254$	−0.0645552	−	0.861429i	−0.00405055	−	0.0540509i
$255$	0.881576	+	0.271930i	0.0552065	+	0.0170289i
$256$	−0.808525	+	10.7890i	−0.0505328	+	0.674313i
$257$	−7.18442	+	18.3056i	−0.448152	+	1.14187i	0.511151	+	0.859491i	$0.329219\pi$
$257$	−7.18442	+	18.3056i	−0.448152	+	1.14187i	−0.959302	+	0.282381i	$0.908876\pi$
$258$	11.5318	−	5.55341i	0.717937	−	0.345740i
$259$	−7.09300	+	5.60951i	−0.440738	+	0.348558i
$260$	−0.103500	−	0.0498429i	−0.00641878	−	0.00309112i
$261$	3.35615	−	3.11405i	0.207741	−	0.192755i
$262$	21.9497	−	3.30838i	1.35606	−	0.204392i
$263$	−3.26791	+	5.66018i	−0.201508	+	0.349022i	−0.949014	−	0.315233i	$-0.897917\pi$
$263$	−3.26791	+	5.66018i	−0.201508	+	0.349022i	0.747507	+	0.664254i	$0.231251\pi$
$264$	1.64781	+	2.85409i	0.101416	+	0.175657i
$265$	1.30331	+	1.63430i	0.0800618	+	0.100394i
$266$	−3.83435	+	5.57518i	−0.235099	+	0.341836i
$267$	−3.14329	+	3.94156i	−0.192366	+	0.241220i
$268$	4.19846	+	0.632816i	0.256462	+	0.0386554i
$269$	6.08714	−	4.15014i	0.371140	−	0.253039i	−0.363359	−	0.931649i	$-0.618370\pi$
$269$	6.08714	−	4.15014i	0.371140	−	0.253039i	0.734498	+	0.678611i	$0.237418\pi$
$270$	1.14883	−	0.783258i	0.0699155	−	0.0476675i
$271$	2.19908	+	0.331458i	0.133585	+	0.0201346i	0.215494	−	0.976505i	$-0.430864\pi$
$271$	2.19908	+	0.331458i	0.133585	+	0.0201346i	−0.0819096	+	0.996640i	$0.526102\pi$
$272$	7.39149	−	9.26864i	0.448175	−	0.561994i
$273$	1.63823	+	1.78004i	0.0991502	+	0.107733i
$274$	−6.38864	−	8.01110i	−0.385952	−	0.483969i
$275$	−2.91323	−	5.04587i	−0.175675	−	0.304277i
$276$	0.0305596	−	0.0529307i	0.00183947	−	0.00318605i
$277$	−8.86683	+	1.33646i	−0.532756	+	0.0803001i	−0.409911	−	0.912126i	$-0.634440\pi$
$277$	−8.86683	+	1.33646i	−0.532756	+	0.0803001i	−0.122846	+	0.992426i	$0.539202\pi$
$278$	9.27541	−	8.60633i	0.556302	−	0.516173i
$279$	1.79261	+	0.863277i	0.107321	+	0.0516831i
$280$	0.845693	−	1.73801i	0.0505398	−	0.103866i
$281$	26.8323	−	12.9218i	1.60068	−	0.770847i	0.601083	−	0.799187i	$-0.294736\pi$
$281$	26.8323	−	12.9218i	1.60068	−	0.770847i	0.999598	+	0.0283393i	$0.00902188\pi$
$282$	2.56732	−	6.54142i	0.152882	−	0.389536i
$283$	−0.870572	+	11.6170i	−0.0517501	+	0.690558i	0.909645	+	0.415386i	$0.136354\pi$
$283$	−0.870572	+	11.6170i	−0.0517501	+	0.690558i	−0.961395	+	0.275171i	$0.911265\pi$
$284$	3.17243	+	0.978566i	0.188249	+	0.0580672i
$285$	0.0338739	+	0.452016i	0.00200652	+	0.0267751i
$286$	−0.323294	+	1.41644i	−0.0191168	+	0.0837560i
$287$	−11.2827	+	12.0612i	−0.665996	+	0.711953i
$288$	1.27868	+	5.60228i	0.0753472	+	0.330118i
$289$	0.797680	−	0.246052i	0.0469224	−	0.0144736i
$290$	0.227619	+	0.579965i	0.0133663	+	0.0340567i
$291$	−7.11517	−	6.60191i	−0.417099	−	0.387011i
$292$	−4.88135	−	3.32805i	−0.285659	−	0.194759i
$293$	11.8604			0.692891			0.346445	−	0.938070i	$-0.387389\pi$
$293$	11.8604			0.692891			0.346445	+	0.938070i	$0.387389\pi$
$294$	−5.82638	+	5.31869i	−0.339801	+	0.310192i
$295$	−0.292494			−0.0170297
$296$	8.63521	+	5.88738i	0.501911	+	0.342197i
$297$	4.07994	+	3.78563i	0.236742	+	0.219665i
$298$	−7.53694	−	19.2038i	−0.436603	−	1.11245i
$299$	0.132844	−	0.0409771i	0.00768260	−	0.00236977i
$300$	0.483561	+	2.11862i	0.0279184	+	0.122319i
$301$	8.97332	−	28.6768i	0.517214	−	1.65291i
$302$	−3.11128	+	13.6314i	−0.179034	+	0.784399i
$303$	−0.735788	−	9.81840i	−0.0422699	−	0.564053i
$304$	5.56596	+	1.71687i	0.319230	+	0.0984693i
$305$	0.0638220	−	0.851646i	0.00365444	−	0.0487651i
$306$	4.11514	−	10.4852i	0.235247	−	0.599400i
$307$	2.45831	−	1.18386i	0.140303	−	0.0675663i	−0.362415	−	0.932017i	$-0.618048\pi$
$307$	2.45831	−	1.18386i	0.140303	−	0.0675663i	0.502718	+	0.864450i	$0.332333\pi$
$308$	1.46056	+	0.339609i	0.0832231	+	0.0193510i
$309$	−4.64418	−	2.23652i	−0.264198	−	0.127231i
$310$	−0.198480	+	0.184162i	−0.0112729	+	0.0104597i
$311$	13.5538	−	2.04290i	0.768564	−	0.115842i	0.246955	−	0.969027i	$-0.420570\pi$
$311$	13.5538	−	2.04290i	0.768564	−	0.115842i	0.521609	+	0.853185i	$0.325332\pi$
$312$	1.39793	−	2.42128i	0.0791421	−	0.137078i
$313$	−10.9634	−	18.9892i	−0.619690	−	1.07333i	−0.989542	−	0.144244i	$-0.953925\pi$
$313$	−10.9634	−	18.9892i	−0.619690	−	1.07333i	0.369852	−	0.929091i	$-0.379408\pi$
$314$	11.5178	+	14.4428i	0.649985	+	0.815056i
$315$	0.209361	−	1.35175i	0.0117962	−	0.0761626i
$316$	−3.87282	+	4.85636i	−0.217863	+	0.273192i
$317$	8.41416	+	1.26823i	0.472586	+	0.0712309i	0.381017	−	0.924568i	$-0.375574\pi$
$317$	8.41416	+	1.26823i	0.472586	+	0.0712309i	0.0915688	+	0.995799i	$0.470812\pi$
$318$	−8.14698	+	5.55452i	−0.456860	+	0.311482i
$319$	−2.06057	+	1.40487i	−0.115369	+	0.0786576i
$320$	−2.09963	−	0.316468i	−0.117373	−	0.0176911i
$321$	−7.72840	+	9.69111i	−0.431357	+	0.540905i
$322$	0.131867	+	0.433748i	0.00734866	+	0.0241718i
$323$	5.46349	+	6.85100i	0.303997	+	0.381200i
$324$	0.522785	+	0.905490i	0.0290436	+	0.0503050i
$325$	−2.47146	+	4.28069i	−0.137092	+	0.237450i
$326$	26.9452	−	4.06134i	1.49236	−	0.224937i
$327$	−7.21090	+	6.69074i	−0.398764	+	0.369999i
$328$	17.1973	+	8.28180i	0.949564	+	0.457286i
$329$	−7.09746	−	14.8924i	−0.391295	−	0.821045i
$330$	−0.285956	+	0.137709i	−0.0157413	+	0.00758063i
$331$	2.87313	−	7.32061i	0.157921	−	0.402377i	−0.829912	−	0.557895i	$-0.811609\pi$
$331$	2.87313	−	7.32061i	0.157921	−	0.402377i	0.987833	+	0.155517i	$0.0497045\pi$
$332$	−0.498407	+	6.65078i	−0.0273537	+	0.365009i
$333$	7.06772	+	2.18010i	0.387308	+	0.119469i
$334$	0.301502	+	4.02326i	0.0164974	+	0.220143i
$335$	−0.469466	+	2.05687i	−0.0256497	+	0.112379i
$336$	5.86734	+	3.41935i	0.320089	+	0.186541i
$337$	−0.971168	−	4.25496i	−0.0529029	−	0.231783i	0.941564	−	0.336834i	$-0.109356\pi$
$337$	−0.971168	−	4.25496i	−0.0529029	−	0.231783i	−0.994467	+	0.105052i	$0.966499\pi$
$338$	1.17779	−	0.363301i	0.0640634	−	0.0197609i
$339$	−2.61932	−	6.67393i	−0.142262	−	0.362478i
$340$	−0.355630	−	0.329976i	−0.0192867	−	0.0178955i
$341$	−0.895481	−	0.610529i	−0.0484930	−	0.0330620i
$342$	5.53426			0.299259
$343$	−0.225613	+	18.5189i	−0.0121820	+	0.999926i
$344$	−34.7269			−1.87235
$345$	0.0250927	+	0.0171079i	0.00135095	+	0.000921060i
$346$	−4.13226	−	3.83417i	−0.222152	−	0.206127i
$347$	−3.14785	−	8.02059i	−0.168985	−	0.430568i	0.821145	−	0.570720i	$-0.193336\pi$
$347$	−3.14785	−	8.02059i	−0.168985	−	0.430568i	−0.990130	+	0.140153i	$0.955241\pi$
$348$	0.888833	−	0.274169i	0.0476464	−	0.0146970i
$349$	−4.06329	−	17.8024i	−0.217503	−	0.952943i	−0.959316	−	0.282336i	$-0.908891\pi$
$349$	−4.06329	−	17.8024i	−0.217503	−	0.952943i	0.741813	−	0.670607i	$-0.233966\pi$
$350$	−13.9266	−	8.11610i	−0.744408	−	0.433824i
$351$	1.05067	−	4.60331i	0.0560809	−	0.245706i
$352$	−0.233917	−	3.12141i	−0.0124678	−	0.166371i
$353$	29.5163	+	9.10458i	1.57099	+	0.484588i	0.953349	−	0.301869i	$-0.0976105\pi$
$353$	29.5163	+	9.10458i	1.57099	+	0.484588i	0.617645	+	0.786457i	$0.288087\pi$
$354$	0.103106	−	1.37586i	0.00548004	−	0.0731260i
$355$	−0.602687	+	1.53562i	−0.0319873	+	0.0815024i
$356$	2.38854	−	1.15026i	0.126592	−	0.0609637i
$357$	4.39532	+	9.22258i	0.232625	+	0.488111i
$358$	−15.7100	−	7.56553i	−0.830298	−	0.399850i
$359$	−10.9347	+	10.1459i	−0.577112	+	0.535481i	−0.913816	−	0.406129i	$-0.866878\pi$
$359$	−10.9347	+	10.1459i	−0.577112	+	0.535481i	0.336704	+	0.941611i	$0.390688\pi$
$360$	−1.56321	+	0.235616i	−0.0823884	+	0.0124180i
$361$	7.34730	−	12.7259i	0.386700	−	0.669784i
$362$	3.93251	+	6.81130i	0.206688	+	0.357994i
$363$	5.47889	+	6.87031i	0.287567	+	0.360598i
$364$	−0.370027	−	1.21712i	−0.0193947	−	0.0637947i
$365$	1.83033	−	2.29516i	0.0958037	−	0.120134i
$366$	3.98354	+	0.600422i	0.208223	+	0.0313846i
$367$	11.6720	−	7.95785i	0.609275	−	0.415396i	−0.218995	−	0.975726i	$-0.570278\pi$
$367$	11.6720	−	7.95785i	0.609275	−	0.415396i	0.828270	+	0.560330i	$0.189326\pi$
$368$	0.322444	−	0.219839i	0.0168086	−	0.0114599i
$369$	13.3574	+	2.01330i	0.695357	+	0.104808i
$370$	−0.627550	+	0.786923i	−0.0326248	+	0.0409102i
$371$	−3.54301	+	22.8756i	−0.183944	+	1.18764i
$372$	0.252032	+	0.316038i	0.0130673	+	0.0163858i
$373$	3.46731	+	6.00555i	0.179530	+	0.310956i	0.941720	−	0.336398i	$-0.109209\pi$
$373$	3.46731	+	6.00555i	0.179530	+	0.310956i	−0.762189	+	0.647354i	$0.775876\pi$
$374$	−3.06782	+	5.31363i	−0.158633	+	0.274761i
$375$	−2.14782	+	0.323732i	−0.110913	+	0.0167175i
$376$	−13.9764	+	12.9682i	−0.720779	+	0.668785i
$377$	1.90620	+	0.917978i	0.0981743	+	0.0472783i
$378$	14.9974	+	3.48720i	0.771385	+	0.179362i
$379$	−5.01970	+	2.41736i	−0.257844	+	0.124171i	−0.558341	−	0.829612i	$-0.688562\pi$
$379$	−5.01970	+	2.41736i	−0.257844	+	0.124171i	0.300497	+	0.953783i	$0.402848\pi$
$380$	0.0870833	−	0.221885i	0.00446728	−	0.0113824i
$381$	0.0478897	−	0.639043i	0.00245346	−	0.0327392i
$382$	−29.5722	−	9.12181i	−1.51304	−	0.466712i
$383$	1.85291	+	24.7254i	0.0946794	+	1.26341i	0.818938	+	0.573881i	$0.194563\pi$
$383$	1.85291	+	24.7254i	0.0946794	+	1.26341i	−0.724259	+	0.689528i	$0.757818\pi$
$384$	1.14817	−	5.03048i	0.0585925	−	0.256711i
$385$	−0.222513	+	0.711106i	−0.0113403	+	0.0362413i
$386$	5.09259	+	22.3121i	0.259206	+	1.13566i
$387$	−23.4843	+	7.24396i	−1.19378	+	0.368231i
$388$	1.86473	+	4.75126i	0.0946673	+	0.241208i
$389$	15.1018	+	14.0124i	0.765692	+	0.710458i	0.962887	−	0.269906i	$-0.0869927\pi$
$389$	15.1018	+	14.0124i	0.765692	+	0.710458i	−0.197195	+	0.980364i	$0.563183\pi$
$390$	0.222471	+	0.151678i	0.0112652	+	0.00768051i
$391$	0.587102			0.0296910
$392$	20.5038	−	6.14267i	1.03560	−	0.310251i
$393$	16.4671			0.830654
$394$	−9.69242	−	6.60818i	−0.488297	−	0.332915i
$395$	−2.26255	−	2.09934i	−0.113841	−	0.105629i
$396$	−0.448075	−	1.14168i	−0.0225166	−	0.0573714i
$397$	23.8475	−	7.35597i	1.19687	−	0.369185i	0.368639	−	0.929573i	$-0.379824\pi$
$397$	23.8475	−	7.35597i	1.19687	−	0.369185i	0.828231	+	0.560387i	$0.189348\pi$
$398$	5.91329	+	25.9078i	0.296407	+	1.29864i
$399$	−3.42913	+	3.66575i	−0.171671	+	0.183517i
$400$	−3.08762	+	13.5277i	−0.154381	+	0.676387i
$401$	−0.968438	−	12.9229i	−0.0483615	−	0.645339i	−0.967738	−	0.251960i	$-0.918925\pi$
$401$	−0.968438	−	12.9229i	−0.0483615	−	0.645339i	0.919376	−	0.393379i	$-0.128694\pi$
$402$	−9.50976	−	2.93337i	−0.474304	−	0.146303i
$403$	−0.0687107	+	0.916881i	−0.00342273	+	0.0456731i
$404$	−1.89157	+	4.81964i	−0.0941091	+	0.239786i
$405$	−0.468089	+	0.225420i	−0.0232595	+	0.0112012i
$406$	−3.01876	+	6.20395i	−0.149819	+	0.307897i
$407$	−3.62994	−	1.74809i	−0.179929	−	0.0866494i
$408$	8.65533	−	8.03097i	0.428502	−	0.397592i
$409$	5.81197	−	0.876013i	0.287383	−	0.0433161i	−0.00376864	−	0.999993i	$-0.501200\pi$
$409$	5.81197	−	0.876013i	0.287383	−	0.0433161i	0.291152	+	0.956677i	$0.405962\pi$
$410$	−0.919122	+	1.59197i	−0.0453922	+	0.0786216i
$411$	−3.80067	−	6.58295i	−0.187473	−	0.324713i
$412$	1.69004	+	2.11924i	0.0832621	+	0.104407i
$413$	−2.19346	−	2.38333i	−0.107933	−	0.117276i
$414$	0.231186	−	0.289898i	0.0113622	−	0.0142477i
$415$	−3.27700	−	0.493928i	−0.160861	−	0.0242460i
$416$	−2.19407	+	1.49589i	−0.107573	+	0.0733420i
$417$	7.75559	−	5.28767i	0.379793	−	0.258938i
$418$	−2.98096	−	0.449307i	−0.145803	−	0.0219763i
$419$	7.52921	−	9.44133i	0.367826	−	0.461239i	−0.563131	−	0.826367i	$-0.690403\pi$
$419$	7.52921	−	9.44133i	0.367826	−	0.461239i	0.930957	+	0.365128i	$0.118975\pi$
$420$	0.157480	−	0.228977i	0.00768422	−	0.0111729i
$421$	8.95349	+	11.2273i	0.436366	+	0.547186i	0.950581	−	0.310475i	$-0.100488\pi$
$421$	8.95349	+	11.2273i	0.436366	+	0.547186i	−0.514215	+	0.857661i	$0.671917\pi$
$422$	−6.83822	−	11.8441i	−0.332879	−	0.576564i
$423$	−6.74651	+	11.6853i	−0.328027	+	0.568159i
$424$	26.4541	−	3.98732i	1.28473	−	0.193641i
$425$	−15.3021	+	14.1983i	−0.742262	+	0.688719i
$426$	−7.01093	−	3.37629i	−0.339681	−	0.163582i
$427$	7.41806	−	5.86659i	0.358985	−	0.283904i
$428$	5.87269	−	2.82814i	0.283867	−	0.136703i
$429$	−0.393764	+	1.00329i	−0.0190111	+	0.0484394i
$430$	0.249927	−	3.33505i	0.0120526	−	0.160830i
$431$	12.5012	+	3.85612i	0.602164	+	0.185743i	0.580824	−	0.814029i	$-0.302731\pi$
$431$	12.5012	+	3.85612i	0.602164	+	0.185743i	0.0213401	+	0.999772i	$0.493207\pi$
$432$	−0.990518	−	13.2175i	−0.0476563	−	0.635929i
$433$	2.48537	−	10.8891i	0.119439	−	0.523297i	−0.879442	−	0.476006i	$-0.842084\pi$
$433$	2.48537	−	10.8891i	0.119439	−	0.523297i	0.998881	−	0.0472909i	$-0.0150588\pi$
$434$	−2.98903	−	0.236207i	−0.143478	−	0.0113383i
$435$	0.102847	+	0.450603i	0.00493114	+	0.0216047i
$436$	4.94294	−	1.52470i	0.236724	−	0.0730197i
$437$	0.105387	+	0.268521i	0.00504132	+	0.0128451i
$438$	10.1510	+	9.41871i	0.485031	+	0.450043i
$439$	−22.8505	−	15.5792i	−1.09059	−	0.743554i	−0.122081	−	0.992520i	$-0.538957\pi$
$439$	−22.8505	−	15.5792i	−1.09059	−	0.743554i	−0.968512	+	0.248966i	$0.919909\pi$
$440$	0.861131			0.0410528
$441$	12.5845	−	8.43106i	0.599261	−	0.401479i
$442$	5.20521			0.247587
$443$	−12.6756	−	8.64208i	−0.602236	−	0.410598i	0.223460	−	0.974713i	$-0.428265\pi$
$443$	−12.6756	−	8.64208i	−0.602236	−	0.410598i	−0.825696	+	0.564115i	$0.809217\pi$
$444$	1.10154	+	1.02208i	0.0522767	+	0.0485057i
$445$	0.481267	+	1.22625i	0.0228142	+	0.0581298i
$446$	15.5456	−	4.79519i	0.736106	−	0.227059i
$447$	−3.40548	−	14.9204i	−0.161073	−	0.705709i
$448$	−13.1668	−	19.4816i	−0.622072	−	0.920420i
$449$	−1.49461	+	6.54831i	−0.0705349	+	0.309034i	−0.997873	−	0.0651915i	$-0.979234\pi$
$449$	−1.49461	+	6.54831i	−0.0705349	+	0.309034i	0.927338	+	0.374225i	$0.122091\pi$
$450$	0.985216	+	13.1468i	0.0464435	+	0.619746i
$451$	−7.03132	−	2.16888i	−0.331092	−	0.102128i
$452$	−0.281743	+	3.75960i	−0.0132521	+	0.176837i
$453$	−3.78946	+	9.65538i	−0.178044	+	0.453649i
$454$	−20.1097	+	9.68430i	−0.943793	+	0.454507i
$455$	0.616833	−	0.138155i	0.0289176	−	0.00647682i
$456$	5.22675	+	2.51707i	0.244765	+	0.117873i
$457$	11.5055	−	10.6755i	0.538203	−	0.499379i	−0.363583	−	0.931562i	$-0.618447\pi$
$457$	11.5055	−	10.6755i	0.538203	−	0.499379i	0.901786	+	0.432182i	$0.142256\pi$
$458$	24.1921	−	3.64638i	1.13042	−	0.170384i
$459$	9.97014	−	17.2688i	0.465366	−	0.806038i
$460$	−0.00798508	−	0.0138306i	−0.000372306	−	0.000644854i
$461$	−14.2253	−	17.8380i	−0.662539	−	0.830798i	0.331078	−	0.943603i	$-0.392588\pi$
$461$	−14.2253	−	17.8380i	−0.662539	−	0.830798i	−0.993617	+	0.112805i	$0.964016\pi$
$462$	−3.26652	−	1.29735i	−0.151972	−	0.0603580i
$463$	10.0609	−	12.6160i	0.467570	−	0.586315i	−0.491004	−	0.871157i	$-0.663370\pi$
$463$	10.0609	−	12.6160i	0.467570	−	0.586315i	0.958574	+	0.284843i	$0.0919414\pi$
$464$	5.87286	+	0.885192i	0.272641	+	0.0410940i
$465$	−0.165958	+	0.113148i	−0.00769610	+	0.00524711i
$466$	−8.68199	+	5.91928i	−0.402186	+	0.274205i
$467$	−14.5923	−	2.19944i	−0.675253	−	0.101778i	−0.197541	−	0.980295i	$-0.563296\pi$
$467$	−14.5923	−	2.19944i	−0.675253	−	0.101778i	−0.477712	+	0.878517i	$0.658534\pi$
$468$	−0.648723	+	0.813473i	−0.0299873	+	0.0376028i
$469$	−20.2805	+	11.5994i	−0.936467	+	0.535611i
$470$	−1.14483	−	1.43558i	−0.0528073	−	0.0662182i
$471$	6.85203	+	11.8681i	0.315725	+	0.546852i
$472$	−1.87172	+	3.24191i	−0.0861527	+	0.149221i
$473$	13.2376	−	1.99525i	0.608667	−	0.0917418i
$474$	10.6726	−	9.90273i	0.490209	−	0.454847i
$475$	−9.24060	−	4.45004i	−0.423988	−	0.204182i
$476$	0.0218158	−	5.37231i	0.000999925	−	0.246240i
$477$	17.0580	−	8.21472i	0.781034	−	0.376126i
$478$	−5.78926	+	14.7508i	−0.264795	+	0.674685i
$479$	1.80796	−	24.1256i	0.0826079	−	1.10233i	−0.789741	−	0.613441i	$-0.789785\pi$
$479$	1.80796	−	24.1256i	0.0826079	−	1.10233i	0.872348	−	0.488885i	$-0.162596\pi$
$480$	−0.554333	−	0.170989i	−0.0253017	−	0.00780455i
$481$	0.255425	+	3.40841i	0.0116464	+	0.155410i
$482$	−6.84003	+	29.9681i	−0.311555	+	1.36501i
$483$	0.0487740	+	0.332758i	0.00221930	+	0.0151410i
$484$	−1.02826	−	4.50508i	−0.0467389	−	0.204777i
$485$	−2.42352	+	0.747557i	−0.110046	+	0.0339448i
$486$	−7.27389	−	18.5336i	−0.329950	−	0.840700i
$487$	−14.5409	−	13.4920i	−0.658912	−	0.611381i	0.278153	−	0.960537i	$-0.410278\pi$
$487$	−14.5409	−	13.4920i	−0.658912	−	0.611381i	−0.937065	+	0.349156i	$0.886468\pi$
$488$	−9.03094	−	6.15719i	−0.408812	−	0.278723i
$489$	20.2148			0.914147
$490$	0.442355	+	2.01332i	0.0199836	+	0.0909525i
$491$	17.0305			0.768577			0.384288	−	0.923213i	$-0.374447\pi$
$491$	17.0305			0.768577			0.384288	+	0.923213i	$0.374447\pi$
$492$	2.26754	+	1.54598i	0.102228	+	0.0696982i
$493$	6.54979	+	6.07732i	0.294988	+	0.273709i
$494$	0.934351	+	2.38069i	0.0420384	+	0.107112i
$495$	0.582346	−	0.179630i	0.0261745	−	0.00807377i
$496$	0.574340	+	2.51635i	0.0257886	+	0.112987i
$497$	−17.0323	+	6.60501i	−0.764005	+	0.296275i
$498$	3.47854	−	15.2405i	0.155877	−	0.682943i
$499$	−1.21550	−	16.2197i	−0.0544133	−	0.726096i	−0.955976	−	0.293446i	$-0.905198\pi$
$499$	−1.21550	−	16.2197i	−0.0544133	−	0.726096i	0.901562	−	0.432649i	$-0.142421\pi$
$500$	1.09146	+	0.336670i	0.0488115	+	0.0150564i
$501$	−0.223666	+	2.98462i	−0.00999267	+	0.133343i
$502$	0.830551	−	2.11621i	0.0370693	−	0.0944511i
$503$	19.8867	−	9.57692i	0.886703	−	0.427014i	0.0656347	−	0.997844i	$-0.479093\pi$
$503$	19.8867	−	9.57692i	0.886703	−	0.427014i	0.821068	+	0.570830i	$0.193378\pi$
$504$	−13.6426	−	10.9706i	−0.607691	−	0.488667i
$505$	−2.31792	−	1.11625i	−0.103146	−	0.0496726i
$506$	−0.148061	+	0.137381i	−0.00658212	+	0.00610732i
$507$	0.904143	−	0.136278i	0.0401544	−	0.00605230i
$508$	−0.168494	+	0.291839i	−0.00747569	+	0.0129483i
$509$	17.0539	+	29.5382i	0.755900	+	1.30926i	0.944926	+	0.327285i	$0.106134\pi$
$509$	17.0539	+	29.5382i	0.755900	+	1.30926i	−0.189026	+	0.981972i	$0.560533\pi$
$510$	0.708974	+	0.889025i	0.0313939	+	0.0393667i
$511$	32.4275	−	2.29773i	1.43451	−	0.101645i
$512$	−15.3513	+	19.2499i	−0.678439	+	0.850735i
$513$	9.68783	+	1.46021i	0.427728	+	0.0644696i
$514$	−20.0264	+	13.6538i	−0.883328	+	0.602243i
$515$	−1.11285	+	0.758730i	−0.0490381	+	0.0334336i
$516$	−4.93726	−	0.744172i	−0.217351	−	0.0327603i
$517$	4.58261	−	5.74641i	0.201543	−	0.252727i
$518$	−11.1182	+	0.787804i	−0.488505	+	0.0346141i
$519$	−2.60731	−	3.26946i	−0.114448	−	0.143513i
$520$	−0.365273	−	0.632671i	−0.0160183	−	0.0277445i
$521$	−18.1829	+	31.4937i	−0.796608	+	1.37976i	0.125206	+	0.992131i	$0.460041\pi$
$521$	−18.1829	+	31.4937i	−0.796608	+	1.37976i	−0.921813	+	0.387634i	$0.873292\pi$
$522$	5.57999	−	0.841048i	0.244230	−	0.0368117i
$523$	−0.431802	+	0.400653i	−0.0188814	+	0.0175193i	−0.689557	−	0.724231i	$-0.742195\pi$
$523$	−0.431802	+	0.400653i	−0.0188814	+	0.0175193i	0.670676	+	0.741751i	$0.266004\pi$
$524$	−7.80178	−	3.75714i	−0.340822	−	0.164131i
$525$	−9.31855	−	7.49341i	−0.406695	−	0.327039i
$526$	−7.25795	+	3.49525i	−0.316462	+	0.152400i
$527$	−1.41860	+	3.61454i	−0.0617954	+	0.157452i
$528$	−0.226101	+	3.01710i	−0.00983977	+	0.131303i
$529$	−21.9597	−	6.77367i	−0.954770	−	0.294507i
$530$	0.192539	+	2.56926i	0.00836337	+	0.111601i
$531$	−0.589507	+	2.58280i	−0.0255824	+	0.112084i
$532$	2.46103	−	0.954369i	0.106699	−	0.0413771i
$533$	1.38906	+	6.08589i	0.0601670	+	0.263609i
$534$	−5.93778	+	1.83156i	−0.256953	+	0.0792594i
$535$	1.18329	+	3.01497i	0.0511581	+	0.130349i
$536$	19.7934	+	18.3656i	0.854945	+	0.793273i
$537$	−10.6876	−	7.28671i	−0.461206	−	0.314445i
$538$	9.08056			0.391491
$539$	−7.46295	+	3.51959i	−0.321452	+	0.151600i
$540$	−0.542409			−0.0233416
$541$	−22.7428	−	15.5058i	−0.977789	−	0.666645i	−0.0347739	−	0.999395i	$-0.511071\pi$
$541$	−22.7428	−	15.5058i	−0.977789	−	0.666645i	−0.943015	+	0.332750i	$0.892023\pi$
$542$	2.00936	+	1.86442i	0.0863095	+	0.0800835i
$543$	2.13161	+	5.43126i	0.0914763	+	0.233078i
$544$	−10.7162	+	3.30552i	−0.459454	+	0.141723i
$545$	0.571950	+	2.50588i	0.0244996	+	0.107340i
$546$	0.432428	+	2.95021i	0.0185062	+	0.126257i
$547$	3.76752	−	16.5066i	0.161087	−	0.705770i	−0.828278	−	0.560318i	$-0.810679\pi$
$547$	3.76752	−	16.5066i	0.161087	−	0.705770i	0.989365	−	0.145453i	$-0.0464638\pi$
$548$	0.298712	+	3.98603i	0.0127603	+	0.170275i
$549$	−7.39162	−	2.28001i	−0.315467	−	0.0973085i
$550$	0.536668	−	7.16133i	0.0228836	−	0.305360i
$551$	−1.60385	+	4.08655i	−0.0683264	+	0.174093i
$552$	0.350191	−	0.168643i	0.0149051	−	0.00717792i
$553$	0.138794	−	34.1791i	0.00590212	−	1.45345i
$554$	−9.95774	−	4.79540i	−0.423064	−	0.203737i
$555$	−0.547349	+	0.507866i	−0.0232337	+	0.0215577i
$556$	−4.88088	+	0.735674i	−0.206995	+	0.0311995i
$557$	10.9018	−	18.8825i	0.461926	−	0.800079i	−0.537131	−	0.843499i	$-0.680492\pi$
$557$	10.9018	−	18.8825i	0.461926	−	0.800079i	0.999057	+	0.0434200i	$0.0138254\pi$
$558$	1.22617	+	2.12379i	0.0519080	+	0.0899074i
$559$	−7.08102	−	8.87932i	−0.299495	−	0.375555i
$560$	1.54032	−	0.880981i	0.0650902	−	0.0372282i
$561$	−2.83792	+	3.55864i	−0.119817	+	0.150246i
$562$	36.2973	+	5.47094i	1.53111	+	0.230778i
$563$	−18.7184	+	12.7620i	−0.788886	+	0.537854i	−0.889426	−	0.457079i	$-0.848896\pi$
$563$	−18.7184	+	12.7620i	−0.788886	+	0.537854i	0.100539	+	0.994933i	$0.467943\pi$
$564$	−2.26498	+	1.54424i	−0.0953729	+	0.0650241i
$565$	−1.85244	−	0.279211i	−0.0779329	−	0.0117465i
$566$	−8.95248	+	11.2261i	−0.376301	+	0.471866i
$567$	−5.34705	−	2.12366i	−0.224555	−	0.0891854i
$568$	13.1636	+	16.5067i	0.552334	+	0.692604i
$569$	−13.2657	−	22.9769i	−0.556127	−	0.963241i	−0.997815	−	0.0660719i	$-0.978953\pi$
$569$	−13.2657	−	22.9769i	−0.556127	−	0.963241i	0.441688	−	0.897169i	$-0.354380\pi$
$570$	−0.279347	+	0.483843i	−0.0117006	+	0.0202660i
$571$	−15.7172	+	2.36899i	−0.657745	+	0.0991391i	−0.469430	−	0.882970i	$-0.655541\pi$
$571$	−15.7172	+	2.36899i	−0.657745	+	0.0991391i	−0.188315	+	0.982109i	$0.560303\pi$
$572$	0.415469	−	0.385499i	0.0173716	−	0.0161185i
$573$	−20.6842	−	9.96101i	−0.864097	−	0.416127i
$574$	−19.8644	+	4.44914i	−0.829126	+	0.185703i
$575$	−0.619117	+	0.298151i	−0.0258190	+	0.0124338i
$576$	−7.02619	+	17.9024i	−0.292758	+	0.745935i
$577$	−0.191934	+	2.56118i	−0.00799032	+	0.106623i	−0.999773	−	0.0213115i	$-0.993216\pi$
$577$	−0.191934	+	2.56118i	−0.00799032	+	0.106623i	0.991783	+	0.127935i	$0.0408349\pi$
$578$	0.983181	+	0.303271i	0.0408950	+	0.0126144i
$579$	1.26874	+	16.9302i	0.0527272	+	0.703595i
$580$	0.0540828	−	0.236952i	0.00224567	−	0.00983891i
$581$	−20.5500	−	30.4059i	−0.852560	−	1.26145i
$582$	−2.66211	−	11.6635i	−0.110348	−	0.483466i
$583$	−9.85501	+	3.03987i	−0.408153	+	0.125899i
$584$	−13.7262	−	34.9738i	−0.567994	−	1.44723i
$585$	−0.378992	−	0.351653i	−0.0156694	−	0.0145391i
$586$	12.0784	+	8.23490i	0.498953	+	0.340181i
$587$	−28.3611			−1.17059			−0.585294	−	0.810821i	$-0.699021\pi$
$587$	−28.3611			−1.17059			−0.585294	+	0.810821i	$0.699021\pi$
$588$	3.04673	−	0.433945i	0.125645	−	0.0178956i
$589$	−1.90781			−0.0786101
$590$	−0.297871	−	0.203085i	−0.0122631	−	0.00836086i
$591$	−6.37928	−	5.91911i	−0.262409	−	0.243480i
$592$	3.50538	+	8.93156i	0.144070	+	0.367085i
$593$	−19.7698	+	6.09817i	−0.811848	+	0.250422i	−0.672762	−	0.739859i	$-0.734892\pi$
$593$	−19.7698	+	6.09817i	−0.811848	+	0.250422i	−0.139085	+	0.990280i	$0.544416\pi$
$594$	1.52649	+	6.68800i	0.0626328	+	0.274412i
$595$	2.66120	+	0.210300i	0.109099	+	0.00862147i
$596$	−1.79079	+	7.84597i	−0.0733537	+	0.321383i
$597$	1.47321	+	19.6586i	0.0602945	+	0.804574i
$598$	0.163738	+	0.0505063i	0.00669573	+	0.00206536i
$599$	0.146665	−	1.95710i	0.00599256	−	0.0799651i	−0.993406	−	0.114653i	$-0.963425\pi$
$599$	0.146665	−	1.95710i	0.00599256	−	0.0799651i	0.999398	+	0.0346875i	$0.0110436\pi$
$600$	−5.04890	+	12.8644i	−0.206121	+	0.525187i
$601$	30.2092	−	14.5480i	1.23226	−	0.593424i	0.299558	−	0.954078i	$-0.403161\pi$
$601$	30.2092	−	14.5480i	1.23226	−	0.593424i	0.932700	+	0.360654i	$0.117446\pi$
$602$	29.0492	−	22.9736i	1.18396	−	0.936333i
$603$	17.2165	+	8.29101i	0.701108	+	0.337636i
$604$	3.99834	−	3.70992i	0.162690	−	0.150955i
$605$	2.27048	−	0.342220i	0.0923081	−	0.0139132i
$606$	6.06781	−	10.5097i	0.246488	−	0.426929i
$607$	−12.6992	−	21.9956i	−0.515443	−	0.892774i	−0.999839	−	0.0179251i	$-0.994294\pi$
$607$	−12.6992	−	21.9956i	−0.515443	−	0.892774i	0.484396	−	0.874849i	$-0.339039\pi$
$608$	−3.43543	−	4.30789i	−0.139325	−	0.174708i
$609$	−2.90037	+	4.21717i	−0.117529	+	0.170888i
$610$	0.656310	−	0.822987i	0.0265732	−	0.0333218i
$611$	−6.16572	−	0.929332i	−0.249438	−	0.0375968i
$612$	−3.63053	+	2.47525i	−0.146755	+	0.100056i
$613$	16.2268	−	11.0633i	0.655395	−	0.446841i	−0.189422	−	0.981896i	$-0.560661\pi$
$613$	16.2268	−	11.0633i	0.655395	−	0.446841i	0.844817	+	0.535055i	$0.179709\pi$
$614$	3.32547	+	0.501234i	0.134205	+	0.0202281i
$615$	−0.850243	+	1.06617i	−0.0342851	+	0.0429922i
$616$	6.45776	+	7.01674i	0.260190	+	0.282712i
$617$	8.00173	+	10.0339i	0.322138	+	0.403948i	0.916361	−	0.400352i	$-0.131112\pi$
$617$	8.00173	+	10.0339i	0.322138	+	0.403948i	−0.594224	+	0.804300i	$0.702541\pi$
$618$	−3.17669	−	5.50218i	−0.127785	−	0.221330i
$619$	−10.3127	+	17.8621i	−0.414503	+	0.717940i	−0.995376	−	0.0960543i	$-0.969378\pi$
$619$	−10.3127	+	17.8621i	−0.414503	+	0.717940i	0.580873	+	0.813994i	$0.302711\pi$
$620$	0.104443	−	0.0157423i	0.00419454	−	0.000632226i
$621$	0.481185	−	0.446474i	0.0193093	−	0.0179164i
$622$	15.2213	+	7.33021i	0.610320	+	0.293915i
$623$	−6.38272	+	13.1173i	−0.255718	+	0.525535i
$624$	2.31257	−	1.11367i	0.0925767	−	0.0445826i
$625$	8.82190	−	22.4778i	0.352876	−	0.899114i
$626$	2.01965	−	26.9504i	0.0807216	−	1.07715i
$627$	−2.13702	−	0.659182i	−0.0853442	−	0.0263252i
$628$	−0.538533	−	7.18622i	−0.0214898	−	0.286761i
$629$	−3.21197	+	14.0726i	−0.128070	+	0.561110i
$630$	1.15176	−	1.23123i	0.0458871	−	0.0490535i
$631$	4.76601	+	20.8813i	0.189732	+	0.831270i	0.976757	+	0.214349i	$0.0687629\pi$
$631$	4.76601	+	20.8813i	0.189732	+	0.831270i	−0.787025	+	0.616921i	$0.788380\pi$
$632$	−37.7467	+	11.6433i	−1.50148	+	0.463147i
$633$	−3.70665	−	9.44440i	−0.147326	−	0.375381i
$634$	7.68826	+	7.13366i	0.305340	+	0.283314i
$635$	−0.138352	−	0.0943265i	−0.00549031	−	0.00374323i
$636$	3.84653			0.152525
$637$	5.75146	+	3.99008i	0.227881	+	0.158093i
$638$	−3.07387			−0.121696
$639$	12.3453	+	8.41685i	0.488371	+	0.332965i
$640$	−0.988334	−	0.917040i	−0.0390673	−	0.0362492i
$641$	−14.9458	−	38.0812i	−0.590323	−	1.50412i	−0.843735	−	0.536760i	$-0.819648\pi$
$641$	−14.9458	−	38.0812i	−0.590323	−	1.50412i	0.253412	−	0.967358i	$-0.418447\pi$
$642$	−14.5992	+	4.50325i	−0.576184	+	0.177729i
$643$	−0.311315	−	1.36396i	−0.0122771	−	0.0537893i	0.968418	−	0.249331i	$-0.0802107\pi$
$643$	−0.311315	−	1.36396i	−0.0122771	−	0.0537893i	−0.980695	+	0.195542i	$0.937354\pi$
$644$	0.0528140	−	0.168782i	0.00208116	−	0.00665095i
$645$	0.552077	−	2.41881i	0.0217380	−	0.0952405i
$646$	0.807125	+	10.7703i	0.0317559	+	0.423753i
$647$	−7.88940	−	2.43356i	−0.310164	−	0.0956731i	0.135765	−	0.990741i	$-0.456651\pi$
$647$	−7.88940	−	2.43356i	−0.310164	−	0.0956731i	−0.445930	+	0.895068i	$0.647127\pi$
$648$	−0.496897	+	6.63063i	−0.0195200	+	0.260476i
$649$	0.527218	−	1.34333i	0.0206951	−	0.0527303i
$650$	−5.48906	+	2.64339i	−0.215299	+	0.103682i
$651$	−2.16650	−	0.503755i	−0.0849120	−	0.0197437i
$652$	−9.57739	−	4.61223i	−0.375080	−	0.180629i
$653$	20.5545	−	19.0718i	0.804358	−	0.746335i	−0.166487	−	0.986044i	$-0.553242\pi$
$653$	20.5545	−	19.0718i	0.804358	−	0.746335i	0.970845	+	0.239708i	$0.0770518\pi$
$654$	−11.9890	+	1.80704i	−0.468805	+	0.0706610i
$655$	2.15139	−	3.72631i	0.0840617	−	0.145599i
$656$	8.76174	+	15.1758i	0.342089	+	0.592515i
$657$	−16.5779	−	20.7880i	−0.646766	−	0.811018i
$658$	3.11219	−	20.0941i	0.121326	−	0.783348i
$659$	15.3195	−	19.2100i	0.596763	−	0.748317i	−0.388107	−	0.921614i	$-0.626871\pi$
$659$	15.3195	−	19.2100i	0.596763	−	0.748317i	0.984870	+	0.173297i	$0.0554422\pi$
$660$	0.122430	+	0.0184534i	0.00476559	+	0.000718297i
$661$	−7.93579	+	5.41053i	−0.308667	+	0.210445i	−0.707739	−	0.706474i	$-0.750285\pi$
$661$	−7.93579	+	5.41053i	−0.308667	+	0.210445i	0.399072	+	0.916919i	$0.369332\pi$
$662$	8.00879	−	5.46030i	0.311271	−	0.212221i
$663$	3.81831	+	0.575517i	0.148291	+	0.0223512i
$664$	−26.4445	+	33.1604i	−1.02625	+	1.28687i
$665$	0.381510	+	1.25489i	0.0147943	+	0.0486627i
$666$	5.68394	+	7.12743i	0.220248	+	0.276182i
$667$	0.147065	+	0.254724i	0.00569437	+	0.00986294i
$668$	0.786940	−	1.36302i	0.0304476	−	0.0527369i
$669$	11.9337	−	1.79872i	0.461385	−	0.0695426i
$670$	−1.90622	+	1.76871i	−0.0736436	+	0.0683313i
$671$	3.79629	+	1.82820i	0.146554	+	0.0705768i
$672$	−2.76376	−	5.79913i	−0.106614	−	0.223706i
$673$	11.9763	−	5.76751i	0.461654	−	0.222321i	−0.188575	−	0.982059i	$-0.560387\pi$
$673$	11.9763	−	5.76751i	0.461654	−	0.222321i	0.650230	+	0.759738i	$0.274673\pi$
$674$	1.96529	−	5.00747i	0.0757001	−	0.192881i
$675$	−1.74412	+	23.2737i	−0.0671312	+	0.895804i
$676$	−0.459458	−	0.141724i	−0.0176715	−	0.00545093i
$677$	2.16912	+	28.9449i	0.0833661	+	1.11244i	0.869350	+	0.494196i	$0.164538\pi$
$677$	2.16912	+	28.9449i	0.0833661	+	1.11244i	−0.785984	+	0.618246i	$0.787843\pi$
$678$	1.96637	−	8.61525i	0.0755181	−	0.330867i
$679$	−24.2657	−	14.1415i	−0.931230	−	0.542700i
$680$	−0.686518	−	3.00783i	−0.0263268	−	0.115345i
$681$	−15.8223	+	4.88053i	−0.606311	+	0.187022i
$682$	−0.488038	−	1.24350i	−0.0186880	−	0.0476161i
$683$	−22.6279	−	20.9956i	−0.865833	−	0.803375i	0.115975	−	0.993252i	$-0.463001\pi$
$683$	−22.6279	−	20.9956i	−0.865833	−	0.803375i	−0.981808	+	0.189877i	$0.939191\pi$
$684$	−1.78379	−	1.21616i	−0.0682048	−	0.0465012i
$685$	−1.98620			−0.0758886
$686$	−13.0878	+	18.7026i	−0.499694	+	0.714070i
$687$	18.1494			0.692444
$688$	−26.3415	−	17.9594i	−1.00426	−	0.684694i
$689$	6.41366	+	5.95101i	0.244341	+	0.226715i
$690$	0.0136756	+	0.0348448i	0.000520620	+	0.00132652i
$691$	33.5351	−	10.3442i	1.27573	−	0.393512i	0.418396	−	0.908265i	$-0.362592\pi$
$691$	33.5351	−	10.3442i	1.27573	−	0.393512i	0.857339	+	0.514753i	$0.172116\pi$
$692$	0.489329	+	2.14389i	0.0186015	+	0.0814985i
$693$	5.83078	+	3.39805i	0.221493	+	0.129081i
$694$	2.36315	−	10.3536i	0.0897039	−	0.393018i
$695$	−0.183289	−	2.44582i	−0.00695255	−	0.0927754i
$696$	5.65246	+	1.74355i	0.214256	+	0.0660892i
$697$	−1.97006	+	26.2887i	−0.0746215	+	0.995755i
$698$	8.22262	−	20.9509i	0.311231	−	0.793003i
$699$	−7.02318	+	3.38219i	−0.265641	+	0.127926i
$700$	2.70525	+	5.67635i	0.102249	+	0.214546i
$701$	−23.1161	−	11.1321i	−0.873081	−	0.420454i	−0.0569887	−	0.998375i	$-0.518150\pi$
$701$	−23.1161	−	11.1321i	−0.873081	−	0.420454i	−0.816093	+	0.577921i	$0.803864\pi$
$702$	4.26616	−	3.95842i	0.161016	−	0.149401i
$703$	−7.01288	+	1.05702i	−0.264496	+	0.0398663i
$704$	5.23800	−	9.07247i	0.197414	−	0.341932i
$705$	−0.681073	−	1.17965i	−0.0256507	−	0.0444283i
$706$	23.7374	+	29.7657i	0.893367	+	1.12025i
$707$	−8.28692	−	27.2580i	−0.311662	−	1.02514i
$708$	−0.335580	+	0.420805i	−0.0126119	+	0.0158148i
$709$	6.97964	+	1.05201i	0.262126	+	0.0395091i	0.278790	−	0.960352i	$-0.410067\pi$
$709$	6.97964	+	1.05201i	0.262126	+	0.0395091i	−0.0166645	+	0.999861i	$0.505305\pi$
$710$	−1.67998	+	1.14539i	−0.0630485	+	0.0429857i
$711$	−23.0977	+	15.7478i	−0.866233	+	0.590587i
$712$	16.6710	+	2.51275i	0.624773	+	0.0941694i
$713$	−0.0796963	+	0.0999360i	−0.00298465	+	0.00374263i
$714$	−1.92732	+	12.4439i	−0.0721282	+	0.465700i
$715$	0.175590	+	0.220182i	0.00656668	+	0.00823435i
$716$	3.40105	+	5.89080i	0.127103	+	0.220149i
$717$	−5.87767	+	10.1804i	−0.219505	+	0.380195i
$718$	−18.1802	+	2.74023i	−0.678480	+	0.102264i
$719$	6.57809	−	6.10358i	0.245321	−	0.227625i	−0.547922	−	0.836529i	$-0.684581\pi$
$719$	6.57809	−	6.10358i	0.245321	−	0.227625i	0.793244	+	0.608904i	$0.208391\pi$
$720$	−1.30760	−	0.629706i	−0.0487313	−	0.0234678i
$721$	−14.5278	−	3.37800i	−0.541044	−	0.125803i
$722$	16.3182	−	7.85843i	0.607300	−	0.292460i
$723$	−8.33098	+	21.2270i	−0.309832	+	0.789440i
$724$	0.229283	−	3.05958i	0.00852125	−	0.113708i
$725$	−9.99323	−	3.08250i	−0.371139	−	0.114481i
$726$	0.809400	+	10.8007i	0.0300397	+	0.400851i
$727$	−1.70962	+	7.49033i	−0.0634062	+	0.277801i	−0.996686	−	0.0813505i	$-0.974077\pi$
$727$	−1.70962	+	7.49033i	−0.0634062	+	0.277801i	0.933279	+	0.359151i	$0.116934\pi$
$728$	2.41594	−	7.72084i	0.0895408	−	0.286153i
$729$	−1.83497	−	8.03952i	−0.0679617	−	0.297760i
$730$	3.45755	−	1.06651i	0.127970	−	0.0394734i
$731$	−17.5226	−	44.6469i	−0.648097	−	1.65132i
$732$	−1.15202	−	1.06892i	−0.0425799	−	0.0395083i
$733$	16.5409	+	11.2774i	0.610950	+	0.416539i	0.828881	−	0.559425i	$-0.188978\pi$
$733$	16.5409	+	11.2774i	0.610950	+	0.416539i	−0.217930	+	0.975964i	$0.569931\pi$
$734$	17.4119			0.642684
$735$	0.101888	+	1.52579i	0.00375820	+	0.0562796i
$736$	−0.369168			−0.0136077
$737$	−8.60030	−	5.86358i	−0.316796	−	0.215988i
$738$	12.2050	+	11.3246i	0.449273	+	0.416865i
$739$	−16.1536	−	41.1586i	−0.594218	−	1.51404i	−0.838814	−	0.544419i	$-0.816750\pi$
$739$	−16.1536	−	41.1586i	−0.594218	−	1.51404i	0.244595	−	0.969625i	$-0.421345\pi$
$740$	0.375198	−	0.115733i	0.0137926	−	0.00425444i
$741$	0.422176	+	1.84967i	0.0155090	+	0.0679494i
$742$	−19.4911	+	20.8361i	−0.715542	+	0.764918i
$743$	3.73508	−	16.3645i	0.137027	−	0.600354i	−0.859052	−	0.511888i	$-0.828946\pi$
$743$	3.73508	−	16.3645i	0.137027	−	0.600354i	0.996079	−	0.0884660i	$-0.0281965\pi$
$744$	0.192105	+	2.56347i	0.00704292	+	0.0939813i
$745$	−3.82123	−	1.17869i	−0.139999	−	0.0431840i
$746$	−0.638737	+	8.52336i	−0.0233858	+	0.312062i
$747$	−10.9661	+	27.9412i	−0.401229	+	1.02232i
$748$	2.15649	−	1.03851i	0.0788491	−	0.0379717i
$749$	−15.6932	+	32.2515i	−0.573416	+	1.17845i
$750$	−2.41207	−	1.16159i	−0.0880765	−	0.0424154i
$751$	11.4693	−	10.6419i	0.418519	−	0.388329i	−0.442611	−	0.896714i	$-0.645948\pi$
$751$	11.4693	−	10.6419i	0.418519	−	0.388329i	0.861130	+	0.508385i	$0.169757\pi$
$752$	−17.3082	+	2.60880i	−0.631166	+	0.0951330i
$753$	0.843235	−	1.46053i	0.0307292	−	0.0532245i
$754$	1.30387	+	2.25836i	0.0474841	+	0.0822448i
$755$	1.68982	+	2.11897i	0.0614988	+	0.0771170i
$756$	−4.06761	−	4.41970i	−0.147938	−	0.160743i
$757$	4.20248	−	5.26975i	0.152742	−	0.191532i	−0.699573	−	0.714561i	$-0.746627\pi$
$757$	4.20248	−	5.26975i	0.152742	−	0.191532i	0.852315	+	0.523029i	$0.175198\pi$
$758$	−6.79038	−	1.02349i	−0.246638	−	0.0371747i
$759$	−0.123801	+	0.0844058i	−0.00449367	+	0.00306373i
$760$	1.25245	−	0.853905i	0.0454311	−	0.0309744i
$761$	15.3077	+	2.30726i	0.554903	+	0.0836382i	0.420507	−	0.907289i	$-0.361852\pi$
$761$	15.3077	+	2.30726i	0.554903	+	0.0836382i	0.134396	+	0.990928i	$0.457090\pi$
$762$	0.492471	−	0.617539i	0.0178403	−	0.0223711i
$763$	−16.1294	+	23.4524i	−0.583925	+	0.849032i
$764$	7.52708	+	9.43865i	0.272320	+	0.341479i
$765$	−1.09169	−	1.89086i	−0.0394701	−	0.0683642i
$766$	−15.2804	+	26.4664i	−0.552103	+	0.956270i
$767$	−1.21058	+	0.182465i	−0.0437114	+	0.00658843i
$768$	−7.25183	+	6.72872i	−0.261678	+	0.242802i
$769$	−10.6284	−	5.11835i	−0.383269	−	0.184573i	0.232321	−	0.972639i	$-0.425368\pi$
$769$	−10.6284	−	5.11835i	−0.383269	−	0.184573i	−0.615590	+	0.788067i	$0.711082\pi$
$770$	−0.720339	+	0.569681i	−0.0259592	+	0.0205299i
$771$	−16.2001	+	7.80156i	−0.583433	+	0.280966i
$772$	3.26170	−	8.31067i	0.117391	−	0.299108i
$773$	3.03140	−	40.4513i	0.109032	−	1.45493i	−0.627546	−	0.778579i	$-0.715941\pi$
$773$	3.03140	−	40.4513i	0.109032	−	1.45493i	0.736578	−	0.676352i	$-0.236440\pi$
$774$	−28.9456	−	8.92854i	−1.04043	−	0.320930i
$775$	−0.339632	−	4.53207i	−0.0121999	−	0.162797i
$776$	−7.22281	+	31.6452i	−0.259284	+	1.13600i
$777$	−8.24289	−	0.651390i	−0.295712	−	0.0233685i
$778$	5.65028	+	24.7555i	0.202572	+	0.887527i
$779$	−12.3772	+	3.81786i	−0.443459	+	0.136789i
$780$	−0.0383745	−	0.0977767i	−0.00137403	−	0.00350097i
$781$	−5.96627	−	5.53589i	−0.213490	−	0.198090i
$782$	0.597893	+	0.407637i	0.0213806	+	0.0145771i
$783$	9.98979			0.357006
$784$	18.7295	+	5.94431i	0.668912	+	0.212297i
$785$	3.58081			0.127805
$786$	16.7698	+	11.4334i	0.598157	+	0.407817i
$787$	10.7998	+	10.0207i	0.384971	+	0.357201i	0.848791	−	0.528729i	$-0.177331\pi$
$787$	10.7998	+	10.0207i	0.384971	+	0.357201i	−0.463820	+	0.885929i	$0.653522\pi$
$788$	1.67187	+	4.25986i	0.0595579	+	0.151751i
$789$	−5.71056	+	1.76147i	−0.203301	+	0.0627101i
$790$	−0.846523	−	3.70886i	−0.0301179	−	0.131955i
$791$	−11.6167	−	17.1881i	−0.413041	−	0.611138i
$792$	1.73556	−	7.60400i	0.0616706	−	0.270196i
$793$	−0.267130	−	3.56461i	−0.00948608	−	0.126583i
$794$	29.3932	+	9.06660i	1.04313	+	0.321762i
$795$	−0.142833	+	1.90598i	−0.00506578	+	0.0675981i
$796$	3.78734	−	9.64999i	0.134239	−	0.342035i
$797$	−24.2056	+	11.6568i	−0.857408	+	0.412906i	−0.810322	−	0.585985i	$-0.800708\pi$
$797$	−24.2056	+	11.6568i	−0.857408	+	0.412906i	−0.0470860	+	0.998891i	$0.514993\pi$
$798$	−6.03736	+	1.35222i	−0.213720	+	0.0478680i
$799$	−23.7249	−	11.4253i	−0.839328	−	0.404199i
$800$	9.62194	−	8.92785i	0.340187	−	0.315647i
$801$	11.7981	−	1.77827i	0.416864	−	0.0628321i
$802$	7.98640	−	13.8328i	0.282010	−	0.488455i
$803$	7.24176	+	12.5431i	0.255556	+	0.442636i
$804$	2.42054	+	3.03526i	0.0853659	+	0.107046i
$805$	0.0816715	+	0.0324371i	0.00287854	+	0.00114326i
$806$	−0.706583	+	0.886027i	−0.0248883	+	0.0312090i
$807$	6.66108	+	1.00400i	0.234481	+	0.0353424i
$808$	−27.2049	+	18.5480i	−0.957065	+	0.652516i
$809$	−10.1175	+	6.89800i	−0.355713	+	0.242521i	−0.727970	−	0.685609i	$-0.759536\pi$
$809$	−10.1175	+	6.89800i	−0.355713	+	0.242521i	0.372258	+	0.928129i	$0.378584\pi$
$810$	−0.633206	−	0.0954404i	−0.0222486	−	0.00335344i
$811$	32.4079	−	40.6382i	1.13799	−	1.42700i	0.249343	−	0.968415i	$-0.419785\pi$
$811$	32.4079	−	40.6382i	1.13799	−	1.42700i	0.888651	−	0.458584i	$-0.151643\pi$
$812$	2.33633	−	1.33626i	0.0819891	−	0.0468935i
$813$	1.26784	+	1.58982i	0.0444650	+	0.0557573i
$814$	−2.48293	−	4.30056i	−0.0870265	−	0.150734i
$815$	2.64103	−	4.57439i	0.0925111	−	0.160234i
$816$	10.7186	−	1.61558i	0.375228	−	0.0565565i
$817$	17.2746	−	16.0285i	0.604362	−	0.560766i
$818$	6.52703	+	3.14325i	0.228212	+	0.109901i
$819$	0.0232489	−	5.72524i	0.000812383	−	0.200056i
$820$	0.646086	−	0.311139i	0.0225623	−	0.0108654i
$821$	10.8434	−	27.6284i	0.378436	−	0.964238i	−0.607078	−	0.794642i	$-0.707658\pi$
$821$	10.8434	−	27.6284i	0.378436	−	0.964238i	0.985514	−	0.169596i	$-0.0542463\pi$
$822$	0.700148	−	9.34283i	0.0244205	−	0.325869i
$823$	−22.0863	−	6.81271i	−0.769879	−	0.237476i	−0.115158	−	0.993347i	$-0.536738\pi$
$823$	−22.0863	−	6.81271i	−0.769879	−	0.237476i	−0.654721	+	0.755871i	$0.727214\pi$
$824$	1.28819	+	17.1897i	0.0448762	+	0.598832i
$825$	1.18547	−	5.19389i	0.0412728	−	0.180828i
$826$	−0.578986	−	3.95010i	−0.0201455	−	0.137441i
$827$	−7.07415	−	30.9939i	−0.245992	−	1.07776i	−0.935456	−	0.353443i	$-0.885011\pi$
$827$	−7.07415	−	30.9939i	−0.245992	−	1.07776i	0.689464	−	0.724320i	$-0.257846\pi$
$828$	−0.138221	+	0.0426355i	−0.00480351	+	0.00148169i
$829$	−6.61310	−	16.8499i	−0.229683	−	0.585222i	0.768847	−	0.639433i	$-0.220831\pi$
$829$	−6.61310	−	16.8499i	−0.229683	−	0.585222i	−0.998529	+	0.0542113i	$0.982736\pi$
$830$	−2.99429	−	2.77829i	−0.103933	−	0.0964359i
$831$	−6.77434	−	4.61867i	−0.234999	−	0.160220i
$832$	−8.88737			−0.308114
$833$	18.2432	+	23.2613i	0.632090	+	0.805957i
$834$	11.5695			0.400618
$835$	0.646164	+	0.440547i	0.0223614	+	0.0152458i
$836$	0.862077	+	0.799890i	0.0298155	+	0.0276648i
$837$	1.58608	+	4.04126i	0.0548229	+	0.139687i
$838$	14.2229	−	4.38719i	0.491322	−	0.151553i
$839$	5.36521	+	23.5065i	0.185228	+	0.811535i	0.979088	+	0.203436i	$0.0652107\pi$
$839$	5.36521	+	23.5065i	0.185228	+	0.811535i	−0.793861	+	0.608100i	$0.791932\pi$
$840$	1.64775	−	0.638983i	0.0568526	−	0.0220470i
$841$	5.45704	−	23.9089i	0.188174	−	0.824443i
$842$	1.32271	+	17.6503i	0.0455834	+	0.608269i
$843$	26.0212	+	8.02647i	0.896217	+	0.276446i
$844$	−0.398700	+	5.32028i	−0.0137238	+	0.183132i
$845$	0.0872862	−	0.222402i	0.00300274	−	0.00765085i
$846$	−14.9839	+	7.21585i	−0.515156	+	0.248086i
$847$	19.8152	+	15.9341i	0.680858	+	0.547504i
$848$	22.1284	+	10.6565i	0.759893	+	0.365945i
$849$	−7.80835	+	7.24509i	−0.267982	+	0.248651i
$850$	−25.4416	+	3.83470i	−0.872639	+	0.131529i
$851$	−0.237584	+	0.411507i	−0.00814427	+	0.0141063i
$852$	1.51780	+	2.62890i	0.0519989	+	0.0900647i
$853$	21.4693	+	26.9216i	0.735094	+	0.921778i	0.999086	−	0.0427466i	$-0.0136108\pi$
$853$	21.4693	+	26.9216i	0.735094	+	0.921778i	−0.263992	+	0.964525i	$0.585039\pi$
$854$	11.6277	−	0.823908i	0.397892	−	0.0281935i
$855$	0.668855	−	0.838717i	0.0228743	−	0.0286835i
$856$	40.9890	+	6.17809i	1.40097	+	0.211163i
$857$	−13.3907	+	9.12965i	−0.457419	+	0.311863i	−0.770018	−	0.638022i	$-0.779753\pi$
$857$	−13.3907	+	9.12965i	−0.457419	+	0.311863i	0.312599	+	0.949885i	$0.398800\pi$
$858$	−1.09761	+	0.748337i	−0.0374717	+	0.0255478i
$859$	−55.0548	−	8.29818i	−1.87845	−	0.283130i	−0.892609	−	0.450831i	$-0.851128\pi$
$859$	−55.0548	−	8.29818i	−1.87845	−	0.283130i	−0.985838	+	0.167701i	$0.946366\pi$
$860$	−0.813440	+	1.02002i	−0.0277381	+	0.0347824i
$861$	−15.0636	+	1.06736i	−0.513365	+	0.0363757i
$862$	10.0536	+	12.6069i	0.342429	+	0.429392i
$863$	26.6300	+	46.1244i	0.906494	+	1.57009i	0.818899	+	0.573938i	$0.194585\pi$
$863$	26.6300	+	46.1244i	0.906494	+	1.57009i	0.0875950	+	0.996156i	$0.472082\pi$
$864$	−6.26920	+	10.8586i	−0.213282	+	0.369416i
$865$	−1.08048	+	0.162856i	−0.0367375	+	0.00553728i
$866$	10.0916	−	9.36361i	0.342926	−	0.318189i
$867$	0.687686	+	0.331172i	0.0233550	+	0.0112472i
$868$	0.911509	+	0.732980i	0.0309386	+	0.0248789i
$869$	13.7198	−	6.60710i	0.465412	−	0.224131i
$870$	−0.208125	+	0.530294i	−0.00705610	+	0.0179787i
$871$	−0.659905	+	8.80582i	−0.0223600	+	0.298374i
$872$	31.4343	+	9.69619i	1.06450	+	0.328354i
$873$	1.71664	+	22.9070i	0.0580994	+	0.775283i
$874$	−0.0791156	+	0.346628i	−0.00267613	+	0.0117249i
$875$	−5.85988	+	2.27242i	−0.198100	+	0.0768217i
$876$	−1.20204	−	5.26650i	−0.0406133	−	0.177939i
$877$	4.95126	−	1.52726i	0.167192	−	0.0515719i	−0.210029	−	0.977695i	$-0.567356\pi$
$877$	4.95126	−	1.52726i	0.167192	−	0.0515719i	0.377221	+	0.926123i	$0.376880\pi$
$878$	−12.4535	−	31.7311i	−0.420286	−	1.07087i
$879$	7.94966	+	7.37620i	0.268135	+	0.248793i
$880$	0.653197	+	0.445342i	0.0220193	+	0.0150125i
$881$	−38.1182			−1.28424			−0.642118	−	0.766606i	$-0.721944\pi$
$881$	−38.1182			−1.28424			−0.642118	+	0.766606i	$0.721944\pi$
$882$	18.6697	+	0.151629i	0.628640	+	0.00510562i
$883$	55.3124			1.86141			0.930705	−	0.365771i	$-0.119195\pi$
$883$	55.3124			1.86141			0.930705	+	0.365771i	$0.119195\pi$
$884$	−1.67773	−	1.14386i	−0.0564281	−	0.0384720i
$885$	−0.196050	−	0.181908i	−0.00659015	−	0.00611477i
$886$	−6.90822	−	17.6019i	−0.232086	−	0.591346i
$887$	40.3748	−	12.4540i	1.35565	−	0.418164i	0.470064	−	0.882632i	$-0.344231\pi$
$887$	40.3748	−	12.4540i	1.35565	−	0.418164i	0.885590	+	0.464469i	$0.153755\pi$
$888$	2.12644	+	9.31654i	0.0713587	+	0.312643i
$889$	−0.268921	−	1.83470i	−0.00901933	−	0.0615338i
$890$	−0.361296	+	1.58294i	−0.0121107	+	0.0530603i
$891$	−0.191553	−	2.55609i	−0.00641726	−	0.0856324i
$892$	−6.06437	−	1.87061i	−0.203050	−	0.0626326i
$893$	0.966861	−	12.9019i	0.0323548	−	0.431744i
$894$	6.89144	−	17.5591i	0.230484	−	0.587264i
$895$	−3.04522	+	1.46650i	−0.101790	+	0.0490197i
$896$	0.0606285	−	14.9303i	0.00202546	−	0.498785i
$897$	0.114526	+	0.0551529i	0.00382392	+	0.00184150i
$898$	−6.06870	+	5.63093i	−0.202515	+	0.187907i
$899$	−1.92358	+	0.289933i	−0.0641549	+	0.00966980i
$900$	2.57148	−	4.45394i	0.0857161	−	0.148465i
$901$	18.4746	+	31.9990i	0.615478	+	1.06604i
$902$	−5.65467	−	7.09073i	−0.188280	−	0.236096i
$903$	23.8492	−	13.6405i	0.793653	−	0.453929i
$904$	−14.9487	+	18.7451i	−0.497188	+	0.623454i
$905$	1.50752	+	0.227223i	0.0501118	+	0.00755314i
$906$	−10.5630	+	7.20175i	−0.350933	+	0.239262i
$907$	−28.9114	+	19.7114i	−0.959986	+	0.654508i	−0.938506	−	0.345262i	$-0.887790\pi$
$907$	−28.9114	+	19.7114i	−0.959986	+	0.654508i	−0.0214799	+	0.999769i	$0.506838\pi$
$908$	8.60983	+	1.29772i	0.285727	+	0.0430664i
$909$	−14.5284	+	18.2181i	−0.481878	+	0.604256i
$910$	0.724095	+	0.287585i	0.0240035	+	0.00953335i
$911$	−8.37586	−	10.5030i	−0.277504	−	0.347980i	0.623473	−	0.781845i	$-0.285721\pi$
$911$	−8.37586	−	10.5030i	−0.277504	−	0.347980i	−0.900978	+	0.433865i	$0.857150\pi$
$912$	2.66294	+	4.61235i	0.0881787	+	0.152730i
$913$	8.17520	−	14.1599i	0.270560	−	0.468623i
$914$	19.1292	−	2.88326i	0.632737	−	0.0953697i
$915$	0.572433	−	0.531140i	0.0189241	−	0.0175590i
$916$	−8.59884	−	4.14098i	−0.284114	−	0.136822i
$917$	46.4967	−	10.4141i	1.53545	−	0.343904i
$918$	22.1435	−	10.6637i	0.730843	−	0.351956i
$919$	−19.4784	+	49.6300i	−0.642532	+	1.63714i	0.121979	+	0.992533i	$0.461076\pi$
$919$	−19.4784	+	49.6300i	−0.642532	+	1.63714i	−0.764511	+	0.644611i	$0.777019\pi$
$920$	0.00758966	−	0.101277i	0.000250224	−	0.00333900i
$921$	2.38399	+	0.735365i	0.0785552	+	0.0242311i
$922$	−2.10152	−	28.0428i	−0.0692098	−	0.923540i
$923$	−1.53645	+	6.73161i	−0.0505727	+	0.221574i
$924$	0.767760	+	1.13598i	0.0252575	+	0.0373710i
$925$	−3.75943	−	16.4711i	−0.123609	−	0.541567i
$926$	19.0054	−	5.86238i	0.624556	−	0.192650i
$927$	4.45688	+	11.3559i	0.146383	+	0.372978i
$928$	−4.11849	−	3.82140i	−0.135196	−	0.125444i
$929$	47.6968	+	32.5191i	1.56488	+	1.06692i	0.963413	+	0.268021i	$0.0863697\pi$
$929$	47.6968	+	32.5191i	1.56488	+	1.06692i	0.601468	+	0.798897i	$0.294583\pi$
$930$	−0.247569			−0.00811811
$931$	−7.36423	+	12.5193i	−0.241353	+	0.410304i
$932$	4.09913			0.134271
$933$	10.3552	+	7.06006i	0.339014	+	0.231136i
$934$	−13.3334	−	12.3716i	−0.436284	−	0.404812i
$935$	0.434512	+	1.10712i	0.0142101	+	0.0362066i
$936$	−6.32283	+	1.95034i	−0.206668	+	0.0637487i
$937$	−1.52652	−	6.68813i	−0.0498693	−	0.218492i	0.943853	−	0.330365i	$-0.107172\pi$
$937$	−1.52652	−	6.68813i	−0.0498693	−	0.218492i	−0.993722	+	0.111874i	$0.964315\pi$
$938$	−28.7070	−	2.26856i	−0.937317	−	0.0740710i
$939$	4.46131	−	19.5463i	0.145589	−	0.637869i
$940$	0.0535287	+	0.714291i	0.00174591	+	0.0232976i
$941$	32.9682	+	10.1693i	1.07473	+	0.331511i	0.781099	−	0.624407i	$-0.214659\pi$
$941$	32.9682	+	10.1693i	1.07473	+	0.331511i	0.293633	+	0.955918i	$0.405136\pi$
$942$	−1.26226	+	16.8437i	−0.0411267	+	0.548798i
$943$	−0.317051	+	0.807834i	−0.0103246	+	0.0263067i
$944$	−3.09634	+	1.49112i	−0.100777	+	0.0485318i
$945$	2.34103	−	1.85141i	0.0761538	−	0.0602264i
$946$	14.8663	+	7.15923i	0.483345	+	0.232767i
$947$	−23.6466	+	21.9409i	−0.768412	+	0.712982i	−0.963472	−	0.267809i	$-0.913700\pi$
$947$	−23.6466	+	21.9409i	−0.768412	+	0.712982i	0.195060	+	0.980791i	$0.437510\pi$
$948$	−5.61610	+	0.846491i	−0.182403	+	0.0274928i
$949$	6.14359	−	10.6410i	0.199429	−	0.345422i
$950$	−6.32070	−	10.9478i	−0.205071	−	0.355193i
$951$	4.85102	+	6.08299i	0.157305	+	0.197254i
$952$	19.3604	−	28.1501i	0.627473	−	0.912351i
$953$	0.0108868	−	0.0136516i	0.000352657	−	0.000442218i	−0.781655	−	0.623711i	$-0.785624\pi$
$953$	0.0108868	−	0.0136516i	0.000352657	−	0.000442218i	0.782008	+	0.623269i	$0.214196\pi$
$954$	23.0752	+	3.47803i	0.747088	+	0.112605i
$955$	−4.95641	+	3.37923i	−0.160386	+	0.109349i
$956$	5.10749	−	3.48223i	0.165188	−	0.112623i
$957$	−2.25485	−	0.339864i	−0.0728890	−	0.0109862i
$958$	18.5921	−	23.3137i	0.600682	−	0.753232i
$959$	−14.8948	−	16.1841i	−0.480978	−	0.522611i
$960$	−1.21050	−	1.51792i	−0.0390687	−	0.0489906i
$961$	15.0773	+	26.1147i	0.486365	+	0.842408i
$962$	−2.10641	+	3.64840i	−0.0679132	+	0.117629i
$963$	29.0078	−	4.37223i	0.934764	−	0.140893i
$964$	8.79021	−	8.15613i	0.283114	−	0.262691i
$965$	3.99687	+	1.92479i	0.128664	+	0.0619613i
$966$	−0.181370	+	0.372739i	−0.00583548	+	0.0119927i
$967$	11.0374	−	5.31532i	0.354938	−	0.170929i	−0.247914	−	0.968782i	$-0.579745\pi$
$967$	11.0374	−	5.31532i	0.354938	−	0.170929i	0.602852	+	0.797853i	$0.294031\pi$
$968$	10.7361	−	27.3551i	0.345071	−	0.879227i
$969$	−0.598758	+	7.98987i	−0.0192349	+	0.256672i
$970$	−2.98711	−	0.921401i	−0.0959103	−	0.0295844i
$971$	−2.64796	−	35.3346i	−0.0849770	−	1.13394i	−0.862830	−	0.505494i	$-0.831310\pi$
$971$	−2.64796	−	35.3346i	−0.0849770	−	1.13394i	0.777853	−	0.628446i	$-0.216309\pi$
$972$	−1.72829	+	7.57214i	−0.0554349	+	0.242876i
$973$	18.5547	−	19.8351i	0.594838	−	0.635884i
$974$	−5.44042	−	23.8361i	−0.174322	−	0.763756i
$975$	−4.31879	+	1.33217i	−0.138312	+	0.0426636i
$976$	−3.66602	−	9.34088i	−0.117347	−	0.298994i
$977$	−0.174478	−	0.161892i	−0.00558206	−	0.00517939i	0.677377	−	0.735636i	$-0.263117\pi$
$977$	−0.174478	−	0.161892i	−0.00558206	−	0.00517939i	−0.682959	+	0.730457i	$0.739307\pi$
$978$	20.5864	+	14.0356i	0.658281	+	0.448808i
$979$	−6.49924			−0.207716
$980$	0.299852	−	0.746135i	0.00957843	−	0.0238344i
$981$	23.2802			0.743281
$982$	17.3436	+	11.8246i	0.553455	+	0.377339i
$983$	−10.0560	−	9.33064i	−0.320738	−	0.297601i	0.503328	−	0.864095i	$-0.332109\pi$
$983$	−10.0560	−	9.33064i	−0.320738	−	0.297601i	−0.824066	+	0.566494i	$0.808299\pi$
$984$	6.37624	+	16.2464i	0.203267	+	0.517916i
$985$	−2.17287	+	0.670241i	−0.0692333	+	0.0213556i
$986$	2.45058	+	10.7367i	0.0780422	+	0.341925i
$987$	4.50468	−	14.3960i	0.143385	−	0.458229i
$988$	0.222004	−	0.972662i	0.00706288	−	0.0309445i
$989$	−0.117989	−	1.57445i	−0.00375183	−	0.0500647i
$990$	0.717771	+	0.221403i	0.0228122	+	0.00703665i
$991$	−3.10463	+	41.4284i	−0.0986218	+	1.31602i	0.699982	+	0.714160i	$0.253191\pi$
$991$	−3.10463	+	41.4284i	−0.0986218	+	1.31602i	−0.798604	+	0.601857i	$0.794428\pi$
$992$	0.892014	−	2.27282i	0.0283215	−	0.0721620i
$993$	6.47861	−	3.11993i	0.205592	−	0.0990081i
$994$	−21.9314	−	5.09948i	−0.695622	−	0.161746i
$995$	4.64099	+	2.23499i	0.147129	+	0.0708538i
$996$	−4.47032	+	4.14785i	−0.141648	+	0.131430i
$997$	51.7316	−	7.79728i	1.63836	−	0.246942i	0.735701	−	0.677307i	$-0.236853\pi$
$997$	51.7316	−	7.79728i	1.63836	−	0.246942i	0.902655	+	0.430364i	$0.141615\pi$
$998$	10.0239	−	17.3618i	0.317300	−	0.549579i
$999$	8.06928	+	13.9764i	0.255301	+	0.442194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.19	✓	324
49.37	even	21	inner	637.2.bl.a.625.19	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.19	✓	324	1.1	even	1	trivial
637.2.bl.a.625.19	yes	324	49.37	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01838 + 0.694320i) q^{2} +(0.670270 + 0.621920i) q^{3} +(-0.175663 - 0.447582i) q^{4} +(0.228303 - 0.0704221i) q^{5} +(0.250779 + 1.09873i) q^{6} +(2.28590 + 1.33217i) q^{7} +(0.680410 - 2.98107i) q^{8} +(-0.161712 - 2.15790i) q^{9} +O(q^{10})\)	\(q+(1.01838 + 0.694320i) q^{2} +(0.670270 + 0.621920i) q^{3} +(-0.175663 - 0.447582i) q^{4} +(0.228303 - 0.0704221i) q^{5} +(0.250779 + 1.09873i) q^{6} +(2.28590 + 1.33217i) q^{7} +(0.680410 - 2.98107i) q^{8} +(-0.161712 - 2.15790i) q^{9} +(0.281395 + 0.0867987i) q^{10} +(-0.0880881 + 1.17545i) q^{11} +(0.160619 - 0.409249i) q^{12} +(0.900969 - 0.433884i) q^{13} +(1.40296 + 2.94380i) q^{14} +(0.196821 + 0.0947842i) q^{15} +(2.05780 - 1.90936i) q^{16} +(4.17595 - 0.629424i) q^{17} +(1.33359 - 2.30985i) q^{18} +(1.03747 + 1.79696i) q^{19} +(-0.0716241 - 0.0898137i) q^{20} +(0.703666 + 2.31456i) q^{21} +(-0.905849 + 1.13590i) q^{22} +(0.137468 + 0.0207200i) q^{23} +(2.31005 - 1.57496i) q^{24} +(-4.08403 + 2.78445i) q^{25} +(1.21878 + 0.183702i) q^{26} +(2.94393 - 3.69157i) q^{27} +(0.194708 - 1.25714i) q^{28} +(1.31913 + 1.65414i) q^{29} +(0.134629 + 0.233183i) q^{30} +(-0.459726 + 0.796269i) q^{31} +(-2.62583 + 0.395780i) q^{32} +(-0.790081 + 0.733088i) q^{33} +(4.68973 + 2.25846i) q^{34} +(0.615691 + 0.143160i) q^{35} +(-0.937433 + 0.451444i) q^{36} +(-1.24872 + 3.18169i) q^{37} +(-0.191120 + 2.55033i) q^{38} +(0.873733 + 0.269511i) q^{39} +(-0.0545937 - 0.728503i) q^{40} +(-1.38906 + 6.08589i) q^{41} +(-0.890444 + 2.84567i) q^{42} +(-2.52719 - 11.0723i) q^{43} +(0.541587 - 0.167057i) q^{44} +(-0.188883 - 0.481267i) q^{45} +(0.125609 + 0.116548i) q^{46} +(-5.15190 - 3.51250i) q^{47} +2.56675 q^{48} +(3.45065 + 6.09040i) q^{49} -6.09240 q^{50} +(3.19047 + 2.17522i) q^{51} +(-0.352466 - 0.327040i) q^{52} +(3.19646 + 8.14446i) q^{53} +(5.56117 - 1.71539i) q^{54} +(0.0626672 + 0.274563i) q^{55} +(5.52664 - 5.90800i) q^{56} +(-0.422176 + 1.84967i) q^{57} +(0.194876 + 2.60044i) q^{58} +(-1.16986 - 0.360854i) q^{59} +(0.00784947 - 0.104744i) q^{60} +(1.30595 - 3.32750i) q^{61} +(-1.02104 + 0.491708i) q^{62} +(2.50503 - 5.14817i) q^{63} +(-8.00724 - 3.85608i) q^{64} +(0.175139 - 0.162505i) q^{65} +(-1.31360 + 0.197994i) q^{66} +(-4.41526 + 7.64745i) q^{67} +(-1.01528 - 1.75852i) q^{68} +(0.0792546 + 0.0993821i) q^{69} +(0.527609 + 0.573278i) q^{70} +(-4.30503 + 5.39833i) q^{71} +(-6.54289 - 0.986183i) q^{72} +(10.1521 - 6.92162i) q^{73} +(-3.48079 + 2.37316i) q^{74} +(-4.46911 - 0.673609i) q^{75} +(0.622040 - 0.780014i) q^{76} +(-1.76726 + 2.56962i) q^{77} +(0.702666 + 0.881116i) q^{78} +(-6.45930 - 11.1878i) q^{79} +(0.335341 - 0.580827i) q^{80} +(-2.15027 + 0.324101i) q^{81} +(-5.64015 + 5.23329i) q^{82} +(-12.4973 - 6.01839i) q^{83} +(0.912347 - 0.721531i) q^{84} +(0.909056 - 0.437778i) q^{85} +(5.11410 - 13.0305i) q^{86} +(-0.144567 + 1.92911i) q^{87} +(3.44418 + 1.06239i) q^{88} +(0.412037 + 5.49825i) q^{89} +(0.141798 - 0.621259i) q^{90} +(2.63753 + 0.208429i) q^{91} +(-0.0148742 - 0.0651680i) q^{92} +(-0.803356 + 0.247802i) q^{93} +(-2.80779 - 7.15413i) q^{94} +(0.363403 + 0.337189i) q^{95} +(-2.00616 - 1.36778i) q^{96} -10.6154 q^{97} +(-0.714613 + 8.59821i) q^{98} +2.55076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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Database

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