LMFDB - Embedded newform 46.2.c.a.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [46,2,Mod(3,46)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("46.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(46, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.367311849298$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	46.9
Dual form			46.2.c.a.41.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.712591 + 0.822373i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.174863 + 1.21620i) q^{5} +(-0.915415 - 0.588302i) q^{6} +(0.260554 - 0.570534i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.258432 - 1.79743i) q^{9} +(-0.510424 - 1.11767i) q^{10} +(-5.65177 - 1.65951i) q^{11} +(1.04408 + 0.306569i) q^{12} +(-0.977031 - 2.13940i) q^{13} +(-0.0892619 + 0.620830i) q^{14} +(-0.875565 + 1.01046i) q^{15} +(0.415415 - 0.909632i) q^{16} +(4.49223 + 2.88698i) q^{17} +(0.258432 + 1.79743i) q^{18} +(-0.227916 + 0.146473i) q^{19} +(0.804632 + 0.928595i) q^{20} +(0.654861 - 0.192284i) q^{21} +5.89037 q^{22} +(-2.50079 + 4.09219i) q^{23} -1.08816 q^{24} +(3.34890 - 0.983325i) q^{25} +(1.54019 + 1.77748i) q^{26} +(4.40856 - 2.83321i) q^{27} +(-0.0892619 - 0.620830i) q^{28} +(-1.66810 - 1.07202i) q^{29} +(0.555420 - 1.21620i) q^{30} +(-4.32439 + 4.99061i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-2.66266 - 5.83041i) q^{33} +(-5.12362 - 1.50443i) q^{34} +(0.739446 + 0.217121i) q^{35} +(-0.754359 - 1.65182i) q^{36} +(-1.43317 + 9.96790i) q^{37} +(0.177418 - 0.204751i) q^{38} +(1.06316 - 2.32800i) q^{39} +(-1.03365 - 0.664289i) q^{40} +(-1.53880 - 10.7026i) q^{41} +(-0.574161 + 0.368991i) q^{42} +(-3.01056 - 3.47437i) q^{43} +(-5.65177 + 1.65951i) q^{44} +2.23123 q^{45} +(1.24659 - 4.63098i) q^{46} +6.97259 q^{47} +(1.04408 - 0.306569i) q^{48} +(4.32640 + 4.99294i) q^{49} +(-2.93621 + 1.88699i) q^{50} +(0.826944 + 5.75152i) q^{51} +(-1.97858 - 1.27155i) q^{52} +(-1.09543 + 2.39865i) q^{53} +(-3.43178 + 3.96048i) q^{54} +(1.03001 - 7.16387i) q^{55} +(0.260554 + 0.570534i) q^{56} +(-0.282866 - 0.0830570i) q^{57} +(1.90255 + 0.558640i) q^{58} +(0.685131 + 1.50023i) q^{59} +(-0.190279 + 1.32342i) q^{60} +(-5.98206 + 6.90366i) q^{61} +(2.74320 - 6.00678i) q^{62} +(-0.958162 - 0.615773i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(2.43109 - 1.56237i) q^{65} +(4.19742 + 4.84408i) q^{66} +(5.94311 - 1.74505i) q^{67} +5.33992 q^{68} +(-5.14735 + 0.859474i) q^{69} -0.770663 q^{70} +(8.69524 - 2.55315i) q^{71} +(1.18917 + 1.37238i) q^{72} +(-4.99580 + 3.21061i) q^{73} +(-1.43317 - 9.96790i) q^{74} +(3.19505 + 2.05334i) q^{75} +(-0.112546 + 0.246442i) q^{76} +(-2.41940 + 2.79213i) q^{77} +(-0.364223 + 2.53323i) q^{78} +(-2.49546 - 5.46429i) q^{79} +(1.17894 + 0.346167i) q^{80} +(0.244379 + 0.0717563i) q^{81} +(4.49173 + 9.83551i) q^{82} +(0.277948 - 1.93317i) q^{83} +(0.446947 - 0.515804i) q^{84} +(-2.72562 + 5.96828i) q^{85} +(3.86745 + 2.48546i) q^{86} +(-0.307069 - 2.13571i) q^{87} +(4.95529 - 3.18457i) q^{88} +(-3.00611 - 3.46923i) q^{89} +(-2.14085 + 0.628610i) q^{90} -1.47517 q^{91} +(0.108607 + 4.79460i) q^{92} -7.18567 q^{93} +(-6.69015 + 1.96441i) q^{94} +(-0.217995 - 0.251579i) q^{95} +(-0.915415 + 0.588302i) q^{96} +(-1.44938 - 10.0807i) q^{97} +(-5.55783 - 3.57180i) q^{98} +(-4.44345 + 9.72980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20}+ \cdots + 20 q^{99}+O(q^{100}) $ 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	0.712591	+	0.822373i	0.411414	+	0.474797i	0.923202	−	0.384314i	$-0.125562\pi$
$3$	0.712591	+	0.822373i	0.411414	+	0.474797i	−0.511788	+	0.859112i	$0.671017\pi$
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	0.174863	+	1.21620i	0.0782012	+	0.543902i	0.990830	+	0.135113i	$0.0431397\pi$
$5$	0.174863	+	1.21620i	0.0782012	+	0.543902i	−0.912629	+	0.408789i	$0.865951\pi$
$6$	−0.915415	−	0.588302i	−0.373717	−	0.240173i
$7$	0.260554	−	0.570534i	0.0984803	−	0.215642i	−0.853979	−	0.520307i	$-0.825817\pi$
$7$	0.260554	−	0.570534i	0.0984803	−	0.215642i	0.952459	+	0.304666i	$0.0985447\pi$
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.258432	−	1.79743i	0.0861440	−	0.599144i
$10$	−0.510424	−	1.11767i	−0.161410	−	0.353439i
$11$	−5.65177	−	1.65951i	−1.70407	−	0.500361i	−0.722486	−	0.691385i	$-0.757001\pi$
$11$	−5.65177	−	1.65951i	−1.70407	−	0.500361i	−0.981585	+	0.191025i	$0.938819\pi$
$12$	1.04408	+	0.306569i	0.301399	+	0.0884988i
$13$	−0.977031	−	2.13940i	−0.270980	−	0.593362i	0.724400	−	0.689380i	$-0.242117\pi$
$13$	−0.977031	−	2.13940i	−0.270980	−	0.593362i	−0.995380	+	0.0960174i	$0.969390\pi$
$14$	−0.0892619	+	0.620830i	−0.0238563	+	0.165924i
$15$	−0.875565	+	1.01046i	−0.226070	+	0.260899i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	4.49223	+	2.88698i	1.08953	+	0.700195i	0.956739	−	0.290949i	$-0.0939710\pi$
$17$	4.49223	+	2.88698i	1.08953	+	0.700195i	0.132787	+	0.991145i	$0.457607\pi$
$18$	0.258432	+	1.79743i	0.0609130	+	0.423659i
$19$	−0.227916	+	0.146473i	−0.0522876	+	0.0336032i	−0.566523	−	0.824046i	$-0.691712\pi$
$19$	−0.227916	+	0.146473i	−0.0522876	+	0.0336032i	0.514236	+	0.857649i	$0.328076\pi$
$20$	0.804632	+	0.928595i	0.179921	+	0.207640i
$21$	0.654861	−	0.192284i	0.142902	−	0.0419599i
$22$	5.89037			1.25583
$23$	−2.50079	+	4.09219i	−0.521451	+	0.853281i
$23$	−2.50079	+	4.09219i	−0.521451	+	0.853281i
$24$	−1.08816			−0.222119
$25$	3.34890	−	0.983325i	0.669779	−	0.196665i
$26$	1.54019	+	1.77748i	0.302057	+	0.348592i
$27$	4.40856	−	2.83321i	0.848428	−	0.545252i
$28$	−0.0892619	−	0.620830i	−0.0168689	−	0.117326i
$29$	−1.66810	−	1.07202i	−0.309758	−	0.199070i	0.376520	−	0.926408i	$-0.377121\pi$
$29$	−1.66810	−	1.07202i	−0.309758	−	0.199070i	−0.686279	+	0.727339i	$0.740757\pi$
$30$	0.555420	−	1.21620i	0.101405	−	0.222047i
$31$	−4.32439	+	4.99061i	−0.776683	+	0.896340i	−0.996865	−	0.0791185i	$-0.974789\pi$
$31$	−4.32439	+	4.99061i	−0.776683	+	0.896340i	0.220182	+	0.975459i	$0.429335\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	−2.66266	−	5.83041i	−0.463510	−	1.01494i
$34$	−5.12362	−	1.50443i	−0.878693	−	0.258008i
$35$	0.739446	+	0.217121i	0.124989	+	0.0367001i
$36$	−0.754359	−	1.65182i	−0.125727	−	0.275303i
$37$	−1.43317	+	9.96790i	−0.235611	+	1.63871i	0.437534	+	0.899202i	$0.355852\pi$
$37$	−1.43317	+	9.96790i	−0.235611	+	1.63871i	−0.673145	+	0.739510i	$0.735057\pi$
$38$	0.177418	−	0.204751i	0.0287810	−	0.0332150i
$39$	1.06316	−	2.32800i	0.170242	−	0.372778i
$40$	−1.03365	−	0.664289i	−0.163435	−	0.105033i
$41$	−1.53880	−	10.7026i	−0.240320	−	1.67146i	−0.650539	−	0.759473i	$-0.725457\pi$
$41$	−1.53880	−	10.7026i	−0.240320	−	1.67146i	0.410219	−	0.911987i	$-0.365452\pi$
$42$	−0.574161	+	0.368991i	−0.0885950	+	0.0569366i
$43$	−3.01056	−	3.47437i	−0.459106	−	0.529836i	0.478244	−	0.878227i	$-0.341274\pi$
$43$	−3.01056	−	3.47437i	−0.459106	−	0.529836i	−0.937349	+	0.348391i	$0.886728\pi$
$44$	−5.65177	+	1.65951i	−0.852036	+	0.250180i
$45$	2.23123			0.332612
$46$	1.24659	−	4.63098i	0.183799	−	0.682801i
$47$	6.97259			1.01706			0.508528	−	0.861045i	$-0.330190\pi$
$47$	6.97259			1.01706			0.508528	+	0.861045i	$0.330190\pi$
$48$	1.04408	−	0.306569i	0.150700	−	0.0442494i
$49$	4.32640	+	4.99294i	0.618058	+	0.713277i
$50$	−2.93621	+	1.88699i	−0.415243	+	0.266860i
$51$	0.826944	+	5.75152i	0.115795	+	0.805374i
$52$	−1.97858	−	1.27155i	−0.274379	−	0.176333i
$53$	−1.09543	+	2.39865i	−0.150468	+	0.329480i	−0.969824	−	0.243806i	$-0.921604\pi$
$53$	−1.09543	+	2.39865i	−0.150468	+	0.329480i	0.819356	+	0.573285i	$0.194331\pi$
$54$	−3.43178	+	3.96048i	−0.467006	+	0.538953i
$55$	1.03001	−	7.16387i	0.138886	−	0.965976i
$56$	0.260554	+	0.570534i	0.0348180	+	0.0762409i
$57$	−0.282866	−	0.0830570i	−0.0374666	−	0.0110012i
$58$	1.90255	+	0.558640i	0.249818	+	0.0733531i
$59$	0.685131	+	1.50023i	0.0891965	+	0.195313i	0.948973	−	0.315358i	$-0.102124\pi$
$59$	0.685131	+	1.50023i	0.0891965	+	0.195313i	−0.859776	+	0.510671i	$0.829397\pi$
$60$	−0.190279	+	1.32342i	−0.0245649	+	0.170852i
$61$	−5.98206	+	6.90366i	−0.765924	+	0.883923i	−0.996010	−	0.0892472i	$-0.971554\pi$
$61$	−5.98206	+	6.90366i	−0.765924	+	0.883923i	0.230086	+	0.973170i	$0.426099\pi$
$62$	2.74320	−	6.00678i	0.348387	−	0.762862i
$63$	−0.958162	−	0.615773i	−0.120717	−	0.0775801i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	2.43109	−	1.56237i	0.301540	−	0.193788i
$66$	4.19742	+	4.84408i	0.516667	+	0.596265i
$67$	5.94311	−	1.74505i	0.726066	−	0.213192i	0.102245	−	0.994759i	$-0.467398\pi$
$67$	5.94311	−	1.74505i	0.726066	−	0.213192i	0.623821	+	0.781567i	$0.285579\pi$
$68$	5.33992			0.647561
$69$	−5.14735	+	0.859474i	−0.619668	+	0.103469i
$70$	−0.770663			−0.0921118
$71$	8.69524	−	2.55315i	1.03194	−	0.303003i	0.278438	−	0.960454i	$-0.410183\pi$
$71$	8.69524	−	2.55315i	1.03194	−	0.303003i	0.753497	+	0.657451i	$0.228365\pi$
$72$	1.18917	+	1.37238i	0.140145	+	0.161736i
$73$	−4.99580	+	3.21061i	−0.584714	+	0.375773i	−0.799300	−	0.600932i	$-0.794796\pi$
$73$	−4.99580	+	3.21061i	−0.584714	+	0.375773i	0.214586	+	0.976705i	$0.431160\pi$
$74$	−1.43317	−	9.96790i	−0.166602	−	1.15874i
$75$	3.19505	+	2.05334i	0.368933	+	0.237099i
$76$	−0.112546	+	0.246442i	−0.0129099	+	0.0282688i
$77$	−2.41940	+	2.79213i	−0.275716	+	0.318193i
$78$	−0.364223	+	2.53323i	−0.0412401	+	0.286831i
$79$	−2.49546	−	5.46429i	−0.280761	−	0.614780i	0.715740	−	0.698367i	$-0.246090\pi$
$79$	−2.49546	−	5.46429i	−0.280761	−	0.614780i	−0.996501	+	0.0835867i	$0.973362\pi$
$80$	1.17894	+	0.346167i	0.131809	+	0.0387026i
$81$	0.244379	+	0.0717563i	0.0271533	+	0.00797292i
$82$	4.49173	+	9.83551i	0.496028	+	1.08615i
$83$	0.277948	−	1.93317i	0.0305087	−	0.212193i	−0.968865	−	0.247591i	$-0.920361\pi$
$83$	0.277948	−	1.93317i	0.0305087	−	0.212193i	0.999373	+	0.0353985i	$0.0112701\pi$
$84$	0.446947	−	0.515804i	0.0487659	−	0.0562789i
$85$	−2.72562	+	5.96828i	−0.295635	+	0.647351i
$86$	3.86745	+	2.48546i	0.417038	+	0.268014i
$87$	−0.307069	−	2.13571i	−0.0329213	−	0.228973i
$88$	4.95529	−	3.18457i	0.528236	−	0.339477i
$89$	−3.00611	−	3.46923i	−0.318647	−	0.367738i	0.573718	−	0.819053i	$-0.305501\pi$
$89$	−3.00611	−	3.46923i	−0.318647	−	0.367738i	−0.892365	+	0.451315i	$0.850955\pi$
$90$	−2.14085	+	0.628610i	−0.225665	+	0.0662613i
$91$	−1.47517			−0.154640
$92$	0.108607	+	4.79460i	0.0113231	+	0.499872i
$93$	−7.18567			−0.745119
$94$	−6.69015	+	1.96441i	−0.690036	+	0.202613i
$95$	−0.217995	−	0.251579i	−0.0223658	−	0.0258115i
$96$	−0.915415	+	0.588302i	−0.0934292	+	0.0600433i
$97$	−1.44938	−	10.0807i	−0.147163	−	1.02354i	−0.920835	−	0.389953i	$-0.872491\pi$
$97$	−1.44938	−	10.0807i	−0.147163	−	1.02354i	0.773672	−	0.633586i	$-0.218418\pi$
$98$	−5.55783	−	3.57180i	−0.561425	−	0.360806i
$99$	−4.44345	+	9.72980i	−0.446584	+	0.977882i
$100$	2.28565	−	2.63778i	0.228565	−	0.263778i
$101$	2.02588	−	14.0903i	0.201583	−	1.40204i	−0.598006	−	0.801492i	$-0.704040\pi$
$101$	2.02588	−	14.0903i	0.201583	−	1.40204i	0.799589	−	0.600548i	$-0.205051\pi$
$102$	−2.41384	−	5.28557i	−0.239006	−	0.523349i
$103$	0.723186	+	0.212347i	0.0712576	+	0.0209231i	0.317167	−	0.948370i	$-0.397268\pi$
$103$	0.723186	+	0.212347i	0.0712576	+	0.0209231i	−0.245909	+	0.969293i	$0.579087\pi$
$104$	2.25667	+	0.662618i	0.221285	+	0.0649750i
$105$	0.348368	+	0.762819i	0.0339972	+	0.0744435i
$106$	0.375276	−	2.61010i	0.0364500	−	0.253516i
$107$	−0.388356	+	0.448187i	−0.0375438	+	0.0433279i	−0.774211	−	0.632928i	$-0.781853\pi$
$107$	−0.388356	+	0.448187i	−0.0375438	+	0.0433279i	0.736667	+	0.676256i	$0.236398\pi$
$108$	2.17697	−	4.76690i	0.209479	−	0.458695i
$109$	−5.77288	−	3.71001i	−0.552942	−	0.355354i	0.234140	−	0.972203i	$-0.424773\pi$
$109$	−5.77288	−	3.71001i	−0.552942	−	0.355354i	−0.787082	+	0.616849i	$0.788409\pi$
$110$	1.03001	+	7.16387i	0.0982075	+	0.683048i
$111$	−9.21860	+	5.92443i	−0.874990	+	0.562322i
$112$	−0.410738	−	0.474017i	−0.0388111	−	0.0447904i
$113$	1.19580	−	0.351119i	0.112491	−	0.0330305i	−0.225002	−	0.974358i	$-0.572239\pi$
$113$	1.19580	−	0.351119i	0.112491	−	0.0330305i	0.337494	+	0.941328i	$0.390421\pi$
$114$	0.294808			0.0276113
$115$	−5.41423	−	2.32589i	−0.504879	−	0.216890i
$116$	−1.98287			−0.184105
$117$	−4.09792	+	1.20326i	−0.378853	+	0.111241i
$118$	−1.08004	−	1.24643i	−0.0994259	−	0.114744i
$119$	2.81759	−	1.81076i	0.258288	−	0.165992i
$120$	−0.190279	−	1.32342i	−0.0173700	−	0.120811i
$121$	19.9347	+	12.8113i	1.81225	+	1.16466i
$122$	3.79475	−	8.30935i	0.343561	−	0.752294i
$123$	7.70497	−	8.89201i	0.694734	−	0.801766i
$124$	−0.939780	+	6.53631i	−0.0843947	+	0.586978i
$125$	4.33364	+	9.48934i	0.387612	+	0.848753i
$126$	1.09283	+	0.320885i	0.0973573	+	0.0285867i
$127$	6.89460	+	2.02444i	0.611796	+	0.179640i	0.572929	−	0.819605i	$-0.305807\pi$
$127$	6.89460	+	2.02444i	0.611796	+	0.179640i	0.0388671	+	0.999244i	$0.487625\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	0.711933	−	4.95160i	0.0626822	−	0.435964i
$130$	−1.89245	+	2.18400i	−0.165978	+	0.191549i
$131$	−0.273443	+	0.598756i	−0.0238908	+	0.0523136i	−0.921201	−	0.389086i	$-0.872791\pi$
$131$	−0.273443	+	0.598756i	−0.0238908	+	0.0523136i	0.897310	+	0.441400i	$0.145518\pi$
$132$	−5.39213	−	3.46531i	−0.469325	−	0.301617i
$133$	0.0241832	+	0.168198i	0.00209695	+	0.0145846i
$134$	−5.21073	+	3.34873i	−0.450138	+	0.289286i
$135$	4.21665	+	4.86627i	0.362911	+	0.418822i
$136$	−5.12362	+	1.50443i	−0.439347	+	0.129004i
$137$	−12.5241			−1.07001			−0.535003	−	0.844850i	$-0.679689\pi$
$137$	−12.5241			−1.07001			−0.535003	+	0.844850i	$0.679689\pi$
$138$	4.69671	−	2.27484i	0.399810	−	0.193647i
$139$	17.0602			1.44703			0.723515	−	0.690309i	$-0.242525\pi$
$139$	17.0602			1.44703			0.723515	+	0.690309i	$0.242525\pi$
$140$	0.739446	−	0.217121i	0.0624946	−	0.0183501i
$141$	4.96860	+	5.73407i	0.418432	+	0.482896i
$142$	−7.62372	+	4.89946i	−0.639768	+	0.411154i
$143$	1.97160	+	13.7128i	0.164873	+	1.14672i
$144$	−1.52765	−	0.981759i	−0.127304	−	0.0818132i
$145$	1.01211	−	2.21620i	0.0840508	−	0.184046i
$146$	3.88890	−	4.48803i	0.321848	−	0.371432i
$147$	−1.02310	+	7.11584i	−0.0843841	+	0.586905i
$148$	4.18340	+	9.16036i	0.343873	+	0.752977i
$149$	17.6680	+	5.18781i	1.44742	+	0.425002i	0.908689	−	0.417474i	$-0.137085\pi$
$149$	17.6680	+	5.18781i	1.44742	+	0.425002i	0.538734	+	0.842476i	$0.318903\pi$
$150$	−3.64412	−	1.07001i	−0.297541	−	0.0873660i
$151$	−4.77740	−	10.4611i	−0.388780	−	0.851309i	−0.998286	−	0.0585274i	$-0.981360\pi$
$151$	−4.77740	−	10.4611i	−0.388780	−	0.851309i	0.609506	−	0.792781i	$-0.291368\pi$
$152$	0.0385566	−	0.268167i	0.00312735	−	0.0217512i
$153$	6.35009	−	7.32839i	0.513374	−	0.592465i
$154$	1.53476	−	3.36066i	0.123675	−	0.270809i
$155$	−6.82576	−	4.38665i	−0.548259	−	0.352344i
$156$	−0.364223	−	2.53323i	−0.0291612	−	0.202820i
$157$	2.71568	−	1.74526i	0.216735	−	0.139287i	−0.427769	−	0.903888i	$-0.640700\pi$
$157$	2.71568	−	1.74526i	0.216735	−	0.139287i	0.644504	+	0.764601i	$0.277064\pi$
$158$	3.93384	+	4.53989i	0.312960	+	0.361175i
$159$	−2.75317	+	0.808405i	−0.218341	+	0.0641107i
$160$	−1.22871			−0.0971379
$161$	1.68314	+	2.49303i	0.132650	+	0.196478i
$162$	−0.254696			−0.0200108
$163$	−10.6155	+	3.11700i	−0.831473	+	0.244143i	−0.669650	−	0.742677i	$-0.733556\pi$
$163$	−10.6155	+	3.11700i	−0.831473	+	0.244143i	−0.161824	+	0.986820i	$0.551738\pi$
$164$	−7.08076	−	8.17164i	−0.552915	−	0.638098i
$165$	6.62535	−	4.25785i	0.515783	−	0.331474i
$166$	0.277948	+	1.93317i	0.0215729	+	0.150043i
$167$	−18.4501	−	11.8572i	−1.42771	−	0.917536i	−0.999907	−	0.0136652i	$-0.995650\pi$
$167$	−18.4501	−	11.8572i	−1.42771	−	0.917536i	−0.427807	−	0.903870i	$-0.640714\pi$
$168$	−0.283524	+	0.620830i	−0.0218743	+	0.0478981i
$169$	4.89075	−	5.64423i	0.376212	−	0.434171i
$170$	0.933756	−	6.49442i	0.0716158	−	0.498099i
$171$	0.204374	+	0.447517i	0.0156289	+	0.0342225i
$172$	−4.41103	−	1.29519i	−0.336338	−	0.0987577i
$173$	−10.6459	−	3.12591i	−0.809391	−	0.237659i	−0.149249	−	0.988800i	$-0.547686\pi$
$173$	−10.6459	−	3.12591i	−0.809391	−	0.237659i	−0.660142	+	0.751141i	$0.729504\pi$
$174$	0.896331	+	1.96269i	0.0679507	+	0.148791i
$175$	0.311549	−	2.16687i	0.0235509	−	0.163800i
$176$	−3.85737	+	4.45164i	−0.290760	+	0.335555i
$177$	−0.745530	+	1.63248i	−0.0560374	+	0.122705i
$178$	3.86173	+	2.48178i	0.289449	+	0.186018i
$179$	2.49587	+	17.3592i	0.186550	+	1.29749i	0.840857	+	0.541257i	$0.182051\pi$
$179$	2.49587	+	17.3592i	0.186550	+	1.29749i	−0.654307	+	0.756229i	$0.727039\pi$
$180$	1.87703	−	1.20629i	0.139906	−	0.0899119i
$181$	−13.3631	−	15.4218i	−0.993269	−	1.14629i	−0.989240	−	0.146302i	$-0.953263\pi$
$181$	−13.3631	−	15.4218i	−0.993269	−	1.14629i	−0.00402916	−	0.999992i	$-0.501283\pi$
$182$	1.41542	−	0.415603i	0.104918	−	0.0308066i
$183$	−9.94014			−0.734797
$184$	−1.45500	−	4.56979i	−0.107264	−	0.336889i
$185$	−12.3736			−0.909723
$186$	6.89460	−	2.02444i	0.505536	−	0.148439i
$187$	−20.5981	−	23.7714i	−1.50628	−	1.73834i
$188$	5.86572	−	3.76967i	0.427801	−	0.274931i
$189$	−0.467774	−	3.25344i	−0.0340256	−	0.236653i
$190$	0.280042	+	0.179972i	0.0203164	+	0.0130566i
$191$	−3.93085	+	8.60736i	−0.284426	+	0.622807i	−0.996882	−	0.0789105i	$-0.974856\pi$
$191$	−3.93085	+	8.60736i	−0.284426	+	0.622807i	0.712455	+	0.701718i	$0.247583\pi$
$192$	0.712591	−	0.822373i	0.0514268	−	0.0593497i
$193$	−3.63769	+	25.3007i	−0.261847	+	1.82118i	0.257108	+	0.966383i	$0.417230\pi$
$193$	−3.63769	+	25.3007i	−0.261847	+	1.82118i	−0.518955	+	0.854801i	$0.673679\pi$
$194$	4.23073	+	9.26401i	0.303749	+	0.665117i
$195$	3.01722	+	0.885937i	0.216068	+	0.0634432i
$196$	6.33899	+	1.86129i	0.452785	+	0.132950i
$197$	2.18904	+	4.79334i	0.155963	+	0.341511i	0.971443	−	0.237274i	$-0.0762540\pi$
$197$	2.18904	+	4.79334i	0.155963	+	0.341511i	−0.815480	+	0.578786i	$0.803527\pi$
$198$	1.52226	−	10.5875i	0.108182	−	0.752424i
$199$	16.3820	−	18.9058i	1.16129	−	1.34020i	0.231178	−	0.972911i	$-0.425742\pi$
$199$	16.3820	−	18.9058i	1.16129	−	1.34020i	0.930108	−	0.367285i	$-0.119713\pi$
$200$	−1.44991	+	3.17487i	−0.102524	+	0.224497i
$201$	5.67009	+	3.64394i	0.399937	+	0.257024i
$202$	2.02588	+	14.0903i	0.142541	+	0.991392i
$203$	−1.04626	+	0.672388i	−0.0734328	+	0.0471924i
$204$	3.80518	+	4.39141i	0.266416	+	0.307460i
$205$	12.7474	−	3.74297i	0.890317	−	0.261421i
$206$	−0.753717			−0.0525139
$207$	6.70916	+	5.55256i	0.466319	+	0.385929i
$208$	−2.35194			−0.163078
$209$	1.53120	−	0.449602i	0.105915	−	0.0310996i
$210$	−0.549167	−	0.633773i	−0.0378961	−	0.0437345i
$211$	−7.45882	+	4.79349i	−0.513487	+	0.329998i	−0.771591	−	0.636119i	$-0.780539\pi$
$211$	−7.45882	+	4.79349i	−0.513487	+	0.329998i	0.258104	+	0.966117i	$0.416902\pi$
$212$	0.375276	+	2.61010i	0.0257741	+	0.179263i
$213$	8.29579	+	5.33138i	0.568418	+	0.365300i
$214$	0.246356	−	0.539445i	0.0168406	−	0.0368757i
$215$	3.69909	−	4.26898i	0.252276	−	0.291142i
$216$	−0.745796	+	5.18713i	−0.0507450	+	0.352939i
$217$	1.72058	+	3.76754i	0.116800	+	0.255757i
$218$	6.58427	+	1.93332i	0.445943	+	0.130941i
$219$	−6.20028	−	1.82057i	−0.418976	−	0.123022i
$220$	−3.00658	−	6.58350i	−0.202704	−	0.443859i
$221$	1.78736	−	12.4313i	0.120231	−	0.836222i
$222$	7.17607	−	8.28163i	0.481626	−	0.555827i
$223$	−7.05499	+	15.4483i	−0.472437	+	1.03449i	0.512037	+	0.858963i	$0.328891\pi$
$223$	−7.05499	+	15.4483i	−0.472437	+	1.03449i	−0.984474	+	0.175530i	$0.943836\pi$
$224$	0.527646	+	0.339098i	0.0352549	+	0.0226569i
$225$	−0.901999	−	6.27354i	−0.0601333	−	0.418236i
$226$	−1.04844	+	0.673792i	−0.0697412	+	0.0448199i
$227$	11.7844	+	13.5999i	0.782155	+	0.902655i	0.997263	−	0.0739349i	$-0.0235557\pi$
$227$	11.7844	+	13.5999i	0.782155	+	0.902655i	−0.215108	+	0.976590i	$0.569010\pi$
$228$	−0.282866	+	0.0830570i	−0.0187333	+	0.00550059i
$229$	7.49653			0.495385			0.247692	−	0.968839i	$-0.420328\pi$
$229$	7.49653			0.495385			0.247692	+	0.968839i	$0.420328\pi$
$230$	5.85019	+	0.706312i	0.385750	+	0.0465728i
$231$	−4.02022			−0.264511
$232$	1.90255	−	0.558640i	0.124909	−	0.0366765i
$233$	−3.61684	−	4.17406i	−0.236947	−	0.273452i	0.624805	−	0.780781i	$-0.285178\pi$
$233$	−3.61684	−	4.17406i	−0.236947	−	0.273452i	−0.861753	+	0.507329i	$0.830633\pi$
$234$	3.59293	−	2.30904i	0.234877	−	0.150946i
$235$	1.21925	+	8.48007i	0.0795351	+	0.553179i
$236$	1.38745	+	0.891662i	0.0903156	+	0.0580423i
$237$	2.71545	−	5.94600i	0.176387	−	0.386234i
$238$	−2.19331	+	2.53121i	−0.142171	+	0.164074i
$239$	−0.742743	+	5.16589i	−0.0480440	+	0.334153i	0.951597	+	0.307350i	$0.0994421\pi$
$239$	−0.742743	+	5.16589i	−0.0480440	+	0.334153i	−0.999641	+	0.0268040i	$0.991467\pi$
$240$	0.555420	+	1.21620i	0.0358522	+	0.0785054i
$241$	1.49095	+	0.437783i	0.0960407	+	0.0282001i	0.329400	−	0.944191i	$-0.393154\pi$
$241$	1.49095	+	0.437783i	0.0960407	+	0.0282001i	−0.233359	+	0.972391i	$0.574972\pi$
$242$	−22.7366	−	6.67606i	−1.46156	−	0.429153i
$243$	−6.41578	−	14.0486i	−0.411572	−	0.901217i
$244$	−1.30003	+	9.04187i	−0.0832256	+	0.578847i
$245$	−5.31589	+	6.13486i	−0.339619	+	0.391942i
$246$	−4.88770	+	10.7026i	−0.311628	+	0.682371i
$247$	0.536045	+	0.344495i	0.0341077	+	0.0219197i
$248$	−0.939780	−	6.53631i	−0.0596761	−	0.415056i
$249$	1.78785	−	1.14898i	0.113300	−	0.0728137i
$250$	−6.83155	−	7.88403i	−0.432065	−	0.498630i
$251$	8.56499	−	2.51491i	0.540617	−	0.158740i	−1.28787e−5	−	1.00000i	$-0.500004\pi$
$251$	8.56499	−	2.51491i	0.540617	−	0.158740i	0.540630	+	0.841260i	$0.318186\pi$
$252$	−1.13897			−0.0717483
$253$	20.9249	−	18.9780i	1.31554	−	1.19314i
$254$	−7.18567			−0.450869
$255$	−6.85041	+	2.01146i	−0.428989	+	0.125963i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−3.06431	+	1.96932i	−0.191147	+	0.122843i	−0.632714	−	0.774386i	$-0.718059\pi$
$257$	−3.06431	+	1.96932i	−0.191147	+	0.122843i	0.441567	+	0.897228i	$0.354423\pi$
$258$	0.711933	+	4.95160i	0.0443230	+	0.308273i
$259$	5.31361	+	3.41485i	0.330172	+	0.212188i
$260$	1.20048	−	2.62869i	0.0744509	−	0.163025i
$261$	−2.35798	+	2.72125i	−0.145955	+	0.168441i
$262$	0.0936773	−	0.651540i	0.00578740	−	0.0402523i
$263$	6.70351	+	14.6786i	0.413356	+	0.905124i	0.995740	+	0.0922095i	$0.0293929\pi$
$263$	6.70351	+	14.6786i	0.413356	+	0.905124i	−0.582384	+	0.812914i	$0.697880\pi$
$264$	6.15000	+	1.80580i	0.378507	+	0.111140i
$265$	−3.10879	−	0.912822i	−0.190971	−	0.0560742i
$266$	−0.0705905	−	0.154572i	−0.00432818	−	0.00947740i
$267$	0.710880	−	4.94428i	0.0435052	−	0.302585i
$268$	4.05621	−	4.68112i	0.247773	−	0.285945i
$269$	−1.86684	+	4.08782i	−0.113823	+	0.249239i	−0.957967	−	0.286879i	$-0.907382\pi$
$269$	−1.86684	+	4.08782i	−0.113823	+	0.249239i	0.844143	+	0.536117i	$0.180110\pi$
$270$	−5.41683	−	3.48119i	−0.329658	−	0.211858i
$271$	0.498456	+	3.46684i	0.0302791	+	0.210595i	0.999344	−	0.0362095i	$-0.0115284\pi$
$271$	0.498456	+	3.46684i	0.0302791	+	0.210595i	−0.969065	+	0.246805i	$0.920619\pi$
$272$	4.49223	−	2.88698i	0.272381	−	0.175049i
$273$	−1.05119	−	1.21314i	−0.0636210	−	0.0734226i
$274$	12.0168	−	3.52845i	0.725960	−	0.213161i
$275$	−20.5590			−1.23976
$276$	−3.86556	+	3.50590i	−0.232679	+	0.211031i
$277$	−12.0692			−0.725166			−0.362583	−	0.931951i	$-0.618105\pi$
$277$	−12.0692			−0.725166			−0.362583	+	0.931951i	$0.618105\pi$
$278$	−16.3692	+	4.80642i	−0.981758	+	0.288270i
$279$	7.85273	+	9.06254i	0.470131	+	0.542560i
$280$	−0.648323	+	0.416652i	−0.0387447	+	0.0248997i
$281$	0.891748	+	6.20224i	0.0531972	+	0.369995i	0.998978	+	0.0451902i	$0.0143894\pi$
$281$	0.891748	+	6.20224i	0.0531972	+	0.369995i	−0.945781	+	0.324804i	$0.894702\pi$
$282$	−6.38281	−	4.10199i	−0.380091	−	0.244270i
$283$	13.1398	−	28.7722i	0.781080	−	1.71033i	0.0804995	−	0.996755i	$-0.474348\pi$
$283$	13.1398	−	28.7722i	0.781080	−	1.71033i	0.700581	−	0.713573i	$-0.252924\pi$
$284$	5.93456	−	6.84885i	0.352152	−	0.406405i
$285$	0.0515511	−	0.358546i	0.00305362	−	0.0212384i
$286$	−5.75507	−	12.6018i	−0.340304	−	0.745163i
$287$	−6.50712	−	1.91066i	−0.384103	−	0.112783i
$288$	1.74236	+	0.511603i	0.102670	+	0.0301465i
$289$	4.78341	+	10.4742i	0.281377	+	0.616130i
$290$	−0.346732	+	2.41157i	−0.0203608	+	0.141613i
$291$	7.25727	−	8.37534i	0.425429	−	0.490971i
$292$	−2.46695	+	5.40187i	−0.144367	+	0.316120i
$293$	5.70182	+	3.66434i	0.333104	+	0.214073i	0.696491	−	0.717565i	$-0.254744\pi$
$293$	5.70182	+	3.66434i	0.333104	+	0.214073i	−0.363387	+	0.931638i	$0.618380\pi$
$294$	−1.02310	−	7.11584i	−0.0596686	−	0.415004i
$295$	−1.70477	+	1.09559i	−0.0992558	+	0.0637878i
$296$	−6.59471	−	7.61070i	−0.383310	−	0.442363i
$297$	−29.6179	+	8.69660i	−1.71860	+	0.504628i
$298$	−18.4139			−1.06669
$299$	11.1982	+	1.35199i	0.647608	+	0.0781877i
$300$	3.79797			0.219276
$301$	−2.76666	+	0.812365i	−0.159468	+	0.0468239i
$302$	7.53111	+	8.69136i	0.433366	+	0.500132i
$303$	13.0311	−	8.37460i	0.748619	−	0.481108i
$304$	0.0385566	+	0.268167i	0.00221137	+	0.0153804i
$305$	−9.44228	−	6.06819i	−0.540663	−	0.347463i
$306$	−4.02822	+	8.82057i	−0.230278	+	0.504238i
$307$	3.97728	−	4.59002i	0.226995	−	0.261966i	−0.630815	−	0.775933i	$-0.717279\pi$
$307$	3.97728	−	4.59002i	0.226995	−	0.261966i	0.857810	+	0.513967i	$0.171825\pi$
$308$	−0.525785	+	3.65692i	−0.0299594	+	0.208372i
$309$	0.340707	+	0.746045i	0.0193822	+	0.0424410i
$310$	7.78514	+	2.28592i	0.442166	+	0.129832i
$311$	−9.81498	−	2.88194i	−0.556556	−	0.163420i	−0.00865482	−	0.999963i	$-0.502755\pi$
$311$	−9.81498	−	2.88194i	−0.556556	−	0.163420i	−0.547901	+	0.836543i	$0.684573\pi$
$312$	1.06316	+	2.32800i	0.0601897	+	0.131797i
$313$	−0.572129	+	3.97924i	−0.0323386	+	0.224920i	−0.999581	−	0.0289333i	$-0.990789\pi$
$313$	−0.572129	+	3.97924i	−0.0323386	+	0.224920i	0.967243	+	0.253853i	$0.0816981\pi$
$314$	−2.11398	+	2.43966i	−0.119299	+	0.137678i
$315$	0.581357	−	1.27299i	0.0327557	−	0.0717251i
$316$	−5.05353	−	3.24771i	−0.284283	−	0.182698i
$317$	−0.710583	−	4.94221i	−0.0399103	−	0.277582i	0.960087	−	0.279700i	$-0.0902350\pi$
$317$	−0.710583	−	4.94221i	−0.0399103	−	0.277582i	−0.999998	+	0.00211768i	$0.999326\pi$
$318$	2.41390	−	1.55132i	0.135365	−	0.0869936i
$319$	7.64868	+	8.82705i	0.428244	+	0.494220i
$320$	1.17894	−	0.346167i	0.0659045	−	0.0193513i
$321$	−0.645316			−0.0360180
$322$	−2.31733	−	1.91784i	−0.129140	−	0.106877i
$323$	−1.44672			−0.0804974
$324$	0.244379	−	0.0717563i	0.0135766	−	0.00398646i
$325$	−5.37570	−	6.20389i	−0.298190	−	0.344130i
$326$	9.30738	−	5.98149i	0.515488	−	0.331284i
$327$	−1.06269	−	7.39118i	−0.0587670	−	0.408733i
$328$	9.09616	+	5.84575i	0.502251	+	0.322777i
$329$	1.81674	−	3.97810i	0.100160	−	0.219320i
$330$	−5.15740	+	5.95196i	−0.283906	+	0.327645i
$331$	−0.698720	+	4.85970i	−0.0384051	+	0.267113i	−0.999972	−	0.00745672i	$-0.997626\pi$
$331$	−0.698720	+	4.85970i	−0.0384051	+	0.267113i	0.961567	+	0.274570i	$0.0885355\pi$
$332$	−0.811325	−	1.77655i	−0.0445273	−	0.0975011i
$333$	17.5463	+	5.15205i	0.961529	+	0.282330i
$334$	21.0433	+	6.17887i	1.15144	+	0.338093i
$335$	3.16157	+	6.92286i	0.172735	+	0.378237i
$336$	0.0971309	−	0.675560i	0.00529892	−	0.0368548i
$337$	−19.4055	+	22.3951i	−1.05708	+	1.21994i	−0.0823405	+	0.996604i	$0.526239\pi$
$337$	−19.4055	+	22.3951i	−1.05708	+	1.21994i	−0.974742	+	0.223334i	$0.928306\pi$
$338$	−3.10248	+	6.79348i	−0.168753	+	0.369517i
$339$	1.14087	+	0.733190i	0.0619634	+	0.0398214i
$340$	0.933756	+	6.49442i	0.0506401	+	0.352209i
$341$	32.7224	−	21.0294i	1.77202	−	1.13881i
$342$	−0.322176	−	0.371811i	−0.0174213	−	0.0201052i
$343$	8.18856	−	2.40438i	0.442141	−	0.129824i
$344$	4.59725			0.247867
$345$	−1.94538	−	6.10992i	−0.104736	−	0.328947i
$346$	11.0953			0.596488
$347$	12.3371	−	3.62249i	0.662288	−	0.194465i	0.0667221	−	0.997772i	$-0.478746\pi$
$347$	12.3371	−	3.62249i	0.662288	−	0.194465i	0.595566	+	0.803306i	$0.296928\pi$
$348$	−1.41298	−	1.63066i	−0.0757436	−	0.0874127i
$349$	−19.8005	+	12.7250i	−1.05990	+	0.681156i	−0.949830	−	0.312768i	$-0.898744\pi$
$349$	−19.8005	+	12.7250i	−1.05990	+	0.681156i	−0.110070	+	0.993924i	$0.535107\pi$
$350$	0.311549	+	2.16687i	0.0166530	+	0.115824i
$351$	−10.3687	−	6.66354i	−0.553439	−	0.355673i
$352$	2.44695	−	5.35807i	0.130423	−	0.285586i
$353$	−5.44378	+	6.28246i	−0.289743	+	0.334382i	−0.881896	−	0.471444i	$-0.843733\pi$
$353$	−5.44378	+	6.28246i	−0.289743	+	0.334382i	0.592153	+	0.805826i	$0.298278\pi$
$354$	0.255407	−	1.77640i	0.0135747	−	0.0944144i
$355$	4.62563	+	10.1287i	0.245503	+	0.537576i
$356$	−4.40450	−	1.29328i	−0.233438	−	0.0685437i
$357$	3.49691	+	1.02678i	0.185076	+	0.0543432i
$358$	−7.28542	−	15.9528i	−0.385046	−	0.843134i
$359$	2.75167	−	19.1383i	0.145228	−	1.01008i	−0.778668	−	0.627436i	$-0.784104\pi$
$359$	2.75167	−	19.1383i	0.145228	−	1.01008i	0.923896	−	0.382645i	$-0.124987\pi$
$360$	−1.46115	+	1.68625i	−0.0770091	+	0.0888732i
$361$	−7.86239	+	17.2162i	−0.413810	+	0.906118i
$362$	17.1666	+	11.0323i	0.902256	+	0.579845i
$363$	3.66965	+	25.5230i	0.192606	+	1.33961i
$364$	−1.24099	+	0.797537i	−0.0650456	+	0.0418023i
$365$	−4.77832	−	5.51448i	−0.250109	−	0.288641i
$366$	9.53750	−	2.80046i	0.498533	−	0.146383i
$367$	30.4419			1.58906			0.794528	−	0.607228i	$-0.207718\pi$
$367$	30.4419			1.58906			0.794528	+	0.607228i	$0.207718\pi$
$368$	2.68352	+	3.97476i	0.139888	+	0.207199i
$369$	−19.6348			−1.02215
$370$	11.8724	−	3.48604i	0.617215	−	0.181231i
$371$	1.08309	+	1.24996i	0.0562314	+	0.0648945i
$372$	−6.04497	+	3.88486i	−0.313417	+	0.201421i
$373$	−2.74614	−	19.0998i	−0.142190	−	0.988951i	−0.928557	−	0.371191i	$-0.878949\pi$
$373$	−2.74614	−	19.0998i	−0.142190	−	0.988951i	0.786367	−	0.617760i	$-0.211960\pi$
$374$	26.4609	+	17.0054i	1.36826	+	0.879327i
$375$	−4.71567	+	10.3259i	−0.243516	+	0.533226i
$376$	−4.56608	+	5.26953i	−0.235477	+	0.271755i
$377$	−0.663699	+	4.61613i	−0.0341823	+	0.237743i
$378$	1.36543	+	2.98987i	0.0702300	+	0.153782i
$379$	−31.0238	−	9.10940i	−1.59358	−	0.467918i	−0.639832	−	0.768515i	$-0.720996\pi$
$379$	−31.0238	−	9.10940i	−1.59358	−	0.467918i	−0.953751	+	0.300596i	$0.902814\pi$
$380$	−0.319403	−	0.0937851i	−0.0163850	−	0.00481107i
$381$	3.24818	+	7.11253i	0.166409	+	0.364386i
$382$	1.34665	−	9.36615i	0.0689006	−	0.479214i
$383$	4.70842	−	5.43380i	0.240589	−	0.277654i	−0.622595	−	0.782544i	$-0.713922\pi$
$383$	4.70842	−	5.43380i	0.240589	−	0.277654i	0.863184	+	0.504890i	$0.168467\pi$
$384$	−0.452036	+	0.989821i	−0.0230679	+	0.0505116i
$385$	−3.81886	−	2.45423i	−0.194627	−	0.125079i
$386$	−3.63769	−	25.3007i	−0.185154	−	1.28777i
$387$	−7.02297	+	4.51339i	−0.356998	+	0.229428i
$388$	−6.66933	−	7.69682i	−0.338584	−	0.390747i
$389$	−25.2205	+	7.40541i	−1.27873	+	0.375469i	−0.849434	−	0.527695i	$-0.823056\pi$
$389$	−25.2205	+	7.40541i	−1.27873	+	0.375469i	−0.429296	+	0.903164i	$0.641238\pi$
$390$	−3.14460			−0.159233
$391$	−23.0482	+	11.1633i	−1.16560	+	0.564554i
$392$	−6.60660			−0.333684
$393$	−0.687254	+	0.201796i	−0.0346674	+	0.0101793i
$394$	−3.45081	−	3.98245i	−0.173849	−	0.200633i
$395$	6.20931	−	3.99048i	0.312424	−	0.200783i
$396$	1.52226	+	10.5875i	0.0764964	+	0.532044i
$397$	−7.79986	−	5.01267i	−0.391464	−	0.251579i	0.330072	−	0.943956i	$-0.392927\pi$
$397$	−7.79986	−	5.01267i	−0.391464	−	0.251579i	−0.721536	+	0.692377i	$0.756563\pi$
$398$	−10.3920	+	22.7553i	−0.520904	+	1.14062i
$399$	−0.121089	+	0.139744i	−0.00606203	+	0.00699595i
$400$	0.496718	−	3.45475i	0.0248359	−	0.172738i
$401$	−11.6450	−	25.4989i	−0.581522	−	1.27336i	−0.940432	−	0.339983i	$-0.889579\pi$
$401$	−11.6450	−	25.4989i	−0.581522	−	1.27336i	0.358910	−	0.933372i	$-0.383149\pi$
$402$	−6.46703	−	1.89889i	−0.322546	−	0.0947080i
$403$	14.9020	+	4.37561i	0.742320	+	0.217965i
$404$	−5.91352	−	12.9488i	−0.294209	−	0.644227i
$405$	−0.0445371	+	0.309762i	−0.00221306	+	0.0153922i
$406$	0.814442	−	0.939916i	0.0404201	−	0.0466473i
$407$	24.6417	−	53.9579i	1.22145	−	2.67459i
$408$	−4.88825	−	3.14148i	−0.242004	−	0.155527i
$409$	−0.00630601	−	0.0438593i	−0.000311812	−	0.00216870i	0.989665	−	0.143399i	$-0.0458033\pi$
$409$	−0.00630601	−	0.0438593i	−0.000311812	−	0.00216870i	−0.989977	+	0.141230i	$0.954894\pi$
$410$	−11.1765	+	7.18271i	−0.551969	+	0.354729i
$411$	−8.92455	−	10.2995i	−0.440216	−	0.508036i
$412$	0.723186	−	0.212347i	0.0356288	−	0.0104616i
$413$	1.03445			0.0509017
$414$	−8.00173	−	3.43745i	−0.393263	−	0.168942i
$415$	2.39972			0.117798
$416$	2.25667	−	0.662618i	0.110642	−	0.0324875i
$417$	12.1570	+	14.0299i	0.595329	+	0.687046i
$418$	−1.34251	+	0.862779i	−0.0656643	+	0.0421999i
$419$	−1.75577	−	12.2117i	−0.0857752	−	0.596579i	−0.986694	−	0.162591i	$-0.948015\pi$
$419$	−1.75577	−	12.2117i	−0.0857752	−	0.596579i	0.900918	−	0.433989i	$-0.142894\pi$
$420$	0.705476	+	0.453382i	0.0344237	+	0.0221228i
$421$	1.15963	−	2.53923i	0.0565167	−	0.123754i	−0.879267	−	0.476330i	$-0.841967\pi$
$421$	1.15963	−	2.53923i	0.0565167	−	0.123754i	0.935783	+	0.352576i	$0.114694\pi$
$422$	5.80620	−	6.70072i	0.282642	−	0.326186i
$423$	1.80194	−	12.5328i	0.0876133	−	0.609364i
$424$	−1.09543	−	2.39865i	−0.0531986	−	0.116489i
$425$	17.8829	+	5.25088i	0.867446	+	0.254705i
$426$	−9.46178	−	2.77823i	−0.458425	−	0.134606i
$427$	2.38012	+	5.21175i	0.115182	+	0.252214i
$428$	−0.0843979	+	0.587000i	−0.00407953	+	0.0283737i
$429$	−9.87207	+	11.3930i	−0.476628	+	0.550058i
$430$	−2.34654	+	5.13821i	−0.113160	+	0.247787i
$431$	2.94160	+	1.89045i	0.141692	+	0.0910597i	0.609566	−	0.792735i	$-0.291344\pi$
$431$	2.94160	+	1.89045i	0.141692	+	0.0910597i	−0.467874	+	0.883795i	$0.654980\pi$
$432$	−0.745796	−	5.18713i	−0.0358821	−	0.249566i
$433$	−7.93237	+	5.09782i	−0.381205	+	0.244986i	−0.717184	−	0.696884i	$-0.754569\pi$
$433$	−7.93237	+	5.09782i	−0.381205	+	0.244986i	0.335979	+	0.941870i	$0.390933\pi$
$434$	−2.71232	−	3.13018i	−0.130196	−	0.150254i
$435$	2.54376	−	0.746916i	0.121964	−	0.0358119i
$436$	−6.86224			−0.328642
$437$	−0.0294243	−	1.29898i	−0.00140756	−	0.0621384i
$438$	6.46203			0.308768
$439$	−21.6681	+	6.36232i	−1.03416	+	0.303657i	−0.754402	−	0.656413i	$-0.772073\pi$
$439$	−21.6681	+	6.36232i	−1.03416	+	0.303657i	−0.279759	+	0.960070i	$0.590255\pi$
$440$	4.73958	+	5.46977i	0.225951	+	0.260761i
$441$	10.0926	−	6.48609i	0.480598	−	0.308861i
$442$	1.78736	+	12.4313i	0.0850159	+	0.591298i
$443$	−5.11530	−	3.28740i	−0.243035	−	0.156189i	0.413453	−	0.910525i	$-0.364323\pi$
$443$	−5.11530	−	3.28740i	−0.243035	−	0.156189i	−0.656488	+	0.754336i	$0.727959\pi$
$444$	−4.55219	+	9.96790i	−0.216037	+	0.473056i
$445$	3.69362	−	4.26267i	0.175095	−	0.202070i
$446$	2.41693	−	16.8101i	0.114445	−	0.795983i
$447$	8.32377	+	18.2265i	0.393701	+	0.862084i
$448$	−0.601808	−	0.176707i	−0.0284327	−	0.00834861i
$449$	11.5754	+	3.39884i	0.546276	+	0.160401i	0.543214	−	0.839594i	$-0.317207\pi$
$449$	11.5754	+	3.39884i	0.546276	+	0.160401i	0.00306173	+	0.999995i	$0.499025\pi$
$450$	2.63292	+	5.76530i	0.124117	+	0.271779i
$451$	−9.06408	+	63.0421i	−0.426811	+	2.96853i
$452$	0.816142	−	0.941878i	0.0383881	−	0.0443022i
$453$	5.19856	−	11.3833i	0.244250	−	0.534832i
$454$	−15.1385	−	9.72895i	−0.710487	−	0.456602i
$455$	−0.257953	−	1.79410i	−0.0120930	−	0.0841088i
$456$	0.248008	−	0.159385i	0.0116141	−	0.00746390i
$457$	13.2021	+	15.2360i	0.617566	+	0.712709i	0.975243	−	0.221136i	$-0.0709765\pi$
$457$	13.2021	+	15.2360i	0.617566	+	0.712709i	−0.357677	+	0.933845i	$0.616431\pi$
$458$	−7.19287	+	2.11202i	−0.336101	+	0.0986881i
$459$	27.9837			1.30617
$460$	−5.81221	+	0.970488i	−0.270996	+	0.0452492i
$461$	34.1368			1.58991			0.794954	−	0.606670i	$-0.207495\pi$
$461$	34.1368			1.58991			0.794954	+	0.606670i	$0.207495\pi$
$462$	3.85737	−	1.13263i	0.179461	−	0.0526945i
$463$	−7.64326	−	8.82079i	−0.355212	−	0.409937i	0.549818	−	0.835285i	$-0.314697\pi$
$463$	−7.64326	−	8.82079i	−0.355212	−	0.409937i	−0.905030	+	0.425348i	$0.860152\pi$
$464$	−1.66810	+	1.07202i	−0.0774396	+	0.0497674i
$465$	−1.25651	−	8.73921i	−0.0582692	−	0.405271i
$466$	4.64631	+	2.98600i	0.215236	+	0.138324i
$467$	1.97120	−	4.31632i	0.0912162	−	0.199736i	−0.858525	−	0.512772i	$-0.828619\pi$
$467$	1.97120	−	4.31632i	0.0912162	−	0.199736i	0.949741	+	0.313036i	$0.101346\pi$
$468$	−2.79686	+	3.22775i	−0.129285	+	0.149203i
$469$	0.552889	−	3.84543i	0.0255300	−	0.177565i
$470$	−3.55897	−	7.79307i	−0.164163	−	0.359467i
$471$	3.37043	+	0.989647i	0.155301	+	0.0456005i
$472$	−1.58246	−	0.464653i	−0.0728387	−	0.0213874i
$473$	11.2492	+	24.6324i	0.517240	+	1.13260i
$474$	−0.930270	+	6.47017i	−0.0427287	+	0.297185i
$475$	−0.619238	+	0.714638i	−0.0284126	+	0.0327899i
$476$	1.39134	−	3.04661i	0.0637719	−	0.139641i
$477$	4.02832	+	2.58884i	0.184444	+	0.118535i
$478$	−0.742743	−	5.16589i	−0.0339723	−	0.236282i
$479$	−25.0307	+	16.0862i	−1.14368	+	0.734999i	−0.968371	−	0.249514i	$-0.919729\pi$
$479$	−25.0307	+	16.0862i	−1.14368	+	0.734999i	−0.175310	+	0.984513i	$0.556093\pi$
$480$	−0.875565	−	1.01046i	−0.0399639	−	0.0461208i
$481$	22.7256	−	6.67283i	1.03620	−	0.304255i
$482$	−1.55390			−0.0707780
$483$	−0.850805	+	3.16068i	−0.0387130	+	0.143816i
$484$	23.6964			1.07711
$485$	12.0067	−	3.52549i	0.545196	−	0.160084i
$486$	10.1138	+	11.6720i	0.458773	+	0.529452i
$487$	−7.33075	+	4.71119i	−0.332188	+	0.213484i	−0.696093	−	0.717952i	$-0.745080\pi$
$487$	−7.33075	+	4.71119i	−0.332188	+	0.213484i	0.363905	+	0.931436i	$0.381443\pi$
$488$	−1.30003	−	9.04187i	−0.0588494	−	0.409306i
$489$	−10.1279	−	6.50879i	−0.457998	−	0.294338i
$490$	3.37217	−	7.38401i	0.152339	−	0.333576i
$491$	−9.86350	+	11.3831i	−0.445134	+	0.513712i	−0.933329	−	0.359023i	$-0.883110\pi$
$491$	−9.86350	+	11.3831i	−0.445134	+	0.513712i	0.488195	+	0.872735i	$0.337655\pi$
$492$	1.67445	−	11.6461i	0.0754901	−	0.525045i
$493$	−4.39858	−	9.63154i	−0.198102	−	0.433783i
$494$	−0.611387	−	0.179519i	−0.0275076	−	0.00807696i
$495$	−12.6104	−	3.70275i	−0.566795	−	0.166426i
$496$	2.74320	+	6.00678i	0.123173	+	0.269712i
$497$	0.808921	−	5.62617i	0.0362851	−	0.252368i
$498$	−1.39172	+	1.60613i	−0.0623646	+	0.0719726i
$499$	13.1268	−	28.7438i	0.587638	−	1.28675i	−0.349221	−	0.937040i	$-0.613554\pi$
$499$	13.1268	−	28.7438i	0.587638	−	1.28675i	0.936859	−	0.349707i	$-0.113719\pi$
$500$	8.77601	+	5.64000i	0.392475	+	0.252229i
$501$	−3.39636	−	23.6222i	−0.151738	−	1.05536i
$502$	−7.50951	+	4.82607i	−0.335166	+	0.215398i
$503$	21.8882	+	25.2604i	0.975947	+	1.12630i	0.991975	+	0.126432i	$0.0403525\pi$
$503$	21.8882	+	25.2604i	0.975947	+	1.12630i	−0.0160278	+	0.999872i	$0.505102\pi$
$504$	1.09283	−	0.320885i	0.0486786	−	0.0142933i
$505$	17.4909			0.778336
$506$	−14.7306	+	24.1045i	−0.654854	+	1.07158i
$507$	8.12677			0.360922
$508$	6.89460	−	2.02444i	0.305898	−	0.0898198i
$509$	11.7336	+	13.5414i	0.520085	+	0.600210i	0.953652	−	0.300911i	$-0.0972908\pi$
$509$	11.7336	+	13.5414i	0.520085	+	0.600210i	−0.433567	+	0.901121i	$0.642745\pi$
$510$	6.00622	−	3.85997i	0.265960	−	0.170922i
$511$	0.530084	+	3.68681i	0.0234495	+	0.163095i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−0.589794	+	1.29147i	−0.0260401	+	0.0570198i
$514$	2.38537	−	2.75286i	0.105214	−	0.121424i
$515$	−0.131797	+	0.916671i	−0.00580769	+	0.0403934i
$516$	−2.07812	−	4.55045i	−0.0914843	−	0.200323i
$517$	−39.4074	−	11.5711i	−1.73314	−	0.508895i
$518$	−6.06045	−	1.77951i	−0.266281	−	0.0781871i
$519$	−5.01548	−	10.9824i	−0.220155	−	0.482073i
$520$	−0.411268	+	2.86043i	−0.0180353	+	0.125438i
$521$	−5.37419	+	6.20215i	−0.235448	+	0.271721i	−0.861161	−	0.508332i	$-0.830262\pi$
$521$	−5.37419	+	6.20215i	−0.235448	+	0.271721i	0.625714	+	0.780053i	$0.284808\pi$
$522$	1.49580	−	3.27534i	0.0654694	−	0.143358i
$523$	−5.46786	−	3.51398i	−0.239093	−	0.153656i	0.415608	−	0.909544i	$-0.363569\pi$
$523$	−5.46786	−	3.51398i	−0.239093	−	0.153656i	−0.654701	+	0.755888i	$0.727205\pi$
$524$	0.0936773	+	0.651540i	0.00409231	+	0.0284627i
$525$	2.00398	−	1.28788i	0.0874610	−	0.0562078i
$526$	−10.5674	−	12.1955i	−0.460761	−	0.531747i
$527$	−33.8339	+	9.93454i	−1.47383	+	0.432755i
$528$	−6.40964			−0.278944
$529$	−10.4921	−	20.4674i	−0.456178	−	0.889889i
$530$	3.24003			0.140738
$531$	2.87362	−	0.843771i	0.124704	−	0.0366165i
$532$	0.111279	+	0.128423i	0.00482456	+	0.00556784i
$533$	−21.3936	+	13.7488i	−0.926660	+	0.595528i
$534$	0.710880	+	4.94428i	0.0307628	+	0.213960i
$535$	−0.612995	−	0.393948i	−0.0265021	−	0.0170318i
$536$	−2.57308	+	5.63427i	−0.111140	+	0.243363i
$537$	−12.4972	+	14.4225i	−0.539294	+	0.622378i
$538$	0.639552	−	4.44818i	0.0275730	−	0.191775i
$539$	−16.1660	−	35.3986i	−0.696319	−	1.52473i
$540$	6.17818	+	1.81408i	0.265866	+	0.0780654i
$541$	25.2892	+	7.42559i	1.08727	+	0.319251i	0.775783	−	0.631000i	$-0.217355\pi$
$541$	25.2892	+	7.42559i	1.08727	+	0.319251i	0.311486	+	0.950251i	$0.399173\pi$
$542$	−1.45499	−	3.18598i	−0.0624970	−	0.136849i
$543$	3.16008	−	21.9789i	0.135612	−	0.943203i
$544$	−3.49691	+	4.03564i	−0.149929	+	0.173027i
$545$	3.50265	−	7.66973i	0.150037	−	0.328535i
$546$	1.35039	+	0.867845i	0.0577915	+	0.0371403i
$547$	2.88152	+	20.0414i	0.123205	+	0.856910i	0.953888	+	0.300164i	$0.0970413\pi$
$547$	2.88152	+	20.0414i	0.123205	+	0.856910i	−0.830683	+	0.556746i	$0.812050\pi$
$548$	−10.5359	+	6.77104i	−0.450073	+	0.289244i
$549$	10.8629	+	12.5365i	0.463618	+	0.535044i
$550$	19.7262	−	5.79215i	0.841130	−	0.246978i
$551$	0.537209			0.0228859
$552$	2.72125	−	4.45294i	0.115824	−	0.189530i
$553$	−3.76777			−0.160222
$554$	11.5803	−	3.40028i	0.491999	−	0.144464i
$555$	−8.81729	−	10.1757i	−0.374273	−	0.431934i
$556$	14.3520	−	9.22346i	0.608660	−	0.391162i
$557$	−1.16082	−	8.07369i	−0.0491856	−	0.342093i	−0.999523	−	0.0308728i	$-0.990171\pi$
$557$	−1.16082	−	8.07369i	−0.0491856	−	0.342093i	0.950338	−	0.311220i	$-0.100738\pi$
$558$	−10.0879	−	6.48307i	−0.427053	−	0.274450i
$559$	−4.49165	+	9.83535i	−0.189977	+	0.415991i
$560$	0.504677	−	0.582428i	0.0213265	−	0.0246121i
$561$	4.87101	−	33.8786i	0.205654	−	1.43036i
$562$	−2.60300	−	5.69977i	−0.109801	−	0.240430i
$563$	−30.1773	−	8.86085i	−1.27182	−	0.373440i	−0.424940	−	0.905222i	$-0.639705\pi$
$563$	−30.1773	−	8.86085i	−1.27182	−	0.373440i	−0.846882	+	0.531781i	$0.821523\pi$
$564$	7.27993	+	2.13758i	0.306540	+	0.0900083i
$565$	0.636132	+	1.39294i	0.0267623	+	0.0586012i
$566$	−4.50150	+	31.3086i	−0.189212	+	1.31600i
$567$	0.104614	−	0.120730i	0.00439336	−	0.00507020i
$568$	−3.76463	+	8.24338i	−0.157960	+	0.345885i
$569$	−22.4600	−	14.4342i	−0.941573	−	0.605112i	−0.0227328	−	0.999742i	$-0.507237\pi$
$569$	−22.4600	−	14.4342i	−0.941573	−	0.605112i	−0.918840	+	0.394629i	$0.870873\pi$
$570$	0.0515511	+	0.358546i	0.00215924	+	0.0150178i
$571$	−24.2752	+	15.6007i	−1.01589	+	0.652870i	−0.938910	−	0.344163i	$-0.888163\pi$
$571$	−24.2752	+	15.6007i	−1.01589	+	0.652870i	−0.0769759	+	0.997033i	$0.524526\pi$
$572$	9.07230	+	10.4700i	0.379332	+	0.437772i
$573$	−9.87955	+	2.90090i	−0.412724	+	0.121187i
$574$	6.78183			0.283068
$575$	−4.35094	+	16.1634i	−0.181447	+	0.674061i
$576$	−1.81592			−0.0756632
$577$	26.9449	−	7.91174i	1.12173	−	0.329370i	0.332278	−	0.943181i	$-0.392183\pi$
$577$	26.9449	−	7.91174i	1.12173	−	0.329370i	0.789453	+	0.613811i	$0.210364\pi$
$578$	−7.54057	−	8.70228i	−0.313646	−	0.361967i
$579$	−23.3988	+	15.0375i	−0.972421	+	0.624937i
$580$	−0.346732	−	2.41157i	−0.0143973	−	0.100135i
$581$	−1.03052	−	0.662274i	−0.0427531	−	0.0274758i
$582$	−4.60370	+	10.0807i	−0.190829	+	0.417858i
$583$	10.1717	−	11.7387i	0.421267	−	0.486168i
$584$	0.845139	−	5.87807i	0.0349721	−	0.243236i
$585$	−2.17998	−	4.77349i	−0.0901311	−	0.197360i
$586$	−6.50322	−	1.90952i	−0.268645	−	0.0788814i
$587$	26.9043	+	7.89980i	1.11046	+	0.326060i	0.784999	−	0.619497i	$-0.212663\pi$
$587$	26.9043	+	7.89980i	1.11046	+	0.326060i	0.325458	+	0.945556i	$0.394481\pi$
$588$	2.98642	+	6.53936i	0.123158	+	0.269679i
$589$	0.254609	−	1.77085i	0.0104910	−	0.0729665i
$590$	1.32706	−	1.53150i	0.0546340	−	0.0630510i
$591$	−2.38202	+	5.21590i	−0.0979833	+	0.214553i
$592$	8.47176	+	5.44447i	0.348187	+	0.223766i
$593$	1.07775	+	7.49592i	0.0442579	+	0.307821i	0.999911	+	0.0133265i	$0.00424207\pi$
$593$	1.07775	+	7.49592i	0.0442579	+	0.307821i	−0.955653	+	0.294494i	$0.904849\pi$
$594$	25.9681	−	16.6887i	1.06548	−	0.684744i
$595$	2.69494	+	3.11012i	0.110482	+	0.127503i
$596$	17.6680	−	5.18781i	0.723711	−	0.212501i
$597$	27.2213			1.11409
$598$	−11.1255	+	1.85767i	−0.454955	+	0.0759656i
$599$	−12.5238			−0.511708			−0.255854	−	0.966715i	$-0.582357\pi$
$599$	−12.5238			−0.511708			−0.255854	+	0.966715i	$0.582357\pi$
$600$	−3.64412	+	1.07001i	−0.148771	+	0.0436830i
$601$	11.9356	+	13.7745i	0.486865	+	0.561872i	0.945025	−	0.326997i	$-0.106037\pi$
$601$	11.9356	+	13.7745i	0.486865	+	0.561872i	−0.458160	+	0.888870i	$0.651491\pi$
$602$	2.42572	−	1.55892i	0.0988650	−	0.0635367i
$603$	−1.60073	−	11.1333i	−0.0651867	−	0.453384i
$604$	−9.67468	−	6.21754i	−0.393657	−	0.252988i
$605$	−12.0952	+	26.4848i	−0.491740	+	1.07676i
$606$	−10.1439	+	11.7067i	−0.412067	+	0.475551i
$607$	1.26113	−	8.77135i	0.0511877	−	0.356018i	−0.948089	−	0.318004i	$-0.896988\pi$
$607$	1.26113	−	8.77135i	0.0511877	−	0.356018i	0.999277	−	0.0380146i	$-0.0121033\pi$
$608$	−0.112546	−	0.246442i	−0.00456435	−	0.00999453i
$609$	−1.29851	−	0.381276i	−0.0526181	−	0.0154501i
$610$	10.7694	+	3.16218i	0.436041	+	0.128033i
$611$	−6.81243	−	14.9171i	−0.275602	−	0.603483i
$612$	1.38001	−	9.59815i	0.0557834	−	0.387982i
$613$	13.9575	−	16.1078i	0.563736	−	0.650586i	−0.400292	−	0.916388i	$-0.631091\pi$
$613$	13.9575	−	16.1078i	0.563736	−	0.650586i	0.964028	+	0.265802i	$0.0856366\pi$
$614$	−2.52301	+	5.52462i	−0.101820	+	0.222956i
$615$	12.1618	+	7.81591i	0.490411	+	0.315168i
$616$	−0.525785	−	3.65692i	−0.0211845	−	0.147341i
$617$	30.0653	−	19.3218i	1.21038	−	0.777866i	0.229661	−	0.973271i	$-0.426238\pi$
$617$	30.0653	−	19.3218i	1.21038	−	0.777866i	0.980723	+	0.195404i	$0.0626020\pi$
$618$	−0.537092	−	0.619837i	−0.0216050	−	0.0249335i
$619$	7.07491	−	2.07738i	0.284365	−	0.0834970i	−0.136440	−	0.990648i	$-0.543566\pi$
$619$	7.07491	−	2.07738i	0.284365	−	0.0834970i	0.420804	+	0.907151i	$0.361748\pi$
$620$	−8.11380			−0.325858
$621$	0.569152	+	25.1260i	0.0228393	+	1.00827i
$622$	10.2293			0.410159
$623$	−2.76257	+	0.811163i	−0.110680	+	0.0324986i
$624$	−1.67597	−	1.93417i	−0.0670925	−	0.0774288i
$625$	3.89789	−	2.50502i	0.155916	−	0.100201i
$626$	−0.572129	−	3.97924i	−0.0228669	−	0.159043i
$627$	1.46086	+	0.938838i	0.0583411	+	0.0374936i
$628$	1.34102	−	2.93642i	0.0535124	−	0.117176i
$629$	−35.2152	+	40.6406i	−1.40412	+	1.62044i
$630$	−0.199164	+	1.38522i	−0.00793488	+	0.0551883i
$631$	−7.98638	−	17.4877i	−0.317933	−	0.696176i	0.681429	−	0.731884i	$-0.261359\pi$
$631$	−7.98638	−	17.4877i	−0.317933	−	0.696176i	−0.999362	+	0.0357081i	$0.988631\pi$
$632$	5.76381	+	1.69241i	0.229272	+	0.0673204i
$633$	−9.25713	−	2.71814i	−0.367938	−	0.108036i
$634$	2.07418	+	4.54182i	0.0823763	+	0.180379i
$635$	−1.25651	+	8.73921i	−0.0498630	+	0.346805i
$636$	−1.87906	+	2.16855i	−0.0745096	+	0.0859887i
$637$	6.45485	−	14.1342i	0.255751	−	0.560016i
$638$	−9.82572	−	6.31461i	−0.389004	−	0.249998i
$639$	−2.34199	−	16.2889i	−0.0926479	−	0.644380i
$640$	−1.03365	+	0.664289i	−0.0408588	+	0.0262583i
$641$	−10.1695	−	11.7363i	−0.401673	−	0.463555i	0.518494	−	0.855081i	$-0.326493\pi$
$641$	−10.1695	−	11.7363i	−0.401673	−	0.463555i	−0.920167	+	0.391526i	$0.871947\pi$
$642$	0.619176	−	0.181807i	0.0244369	−	0.00717533i
$643$	12.8573			0.507043			0.253522	−	0.967330i	$-0.418411\pi$
$643$	12.8573			0.507043			0.253522	+	0.967330i	$0.418411\pi$
$644$	2.76378	+	1.18729i	0.108908	+	0.0467858i
$645$	6.14664			0.242024
$646$	1.38811	−	0.407587i	0.0546146	−	0.0160363i
$647$	23.0648	+	26.6182i	0.906771	+	1.04647i	0.998714	+	0.0507053i	$0.0161469\pi$
$647$	23.0648	+	26.6182i	0.906771	+	1.04647i	−0.0919425	+	0.995764i	$0.529308\pi$
$648$	−0.214264	+	0.137699i	−0.00841710	+	0.00540934i
$649$	−1.38256	−	9.61592i	−0.0542703	−	0.377458i
$650$	6.90578	+	4.43808i	0.270867	+	0.174076i
$651$	−1.87226	+	4.09967i	−0.0733795	+	0.160679i
$652$	−7.24518	+	8.36139i	−0.283743	+	0.327457i
$653$	−4.09454	+	28.4782i	−0.160232	+	1.11444i	0.737964	+	0.674840i	$0.235787\pi$
$653$	−4.09454	+	28.4782i	−0.160232	+	1.11444i	−0.898196	+	0.439596i	$0.855122\pi$
$654$	3.10198	+	6.79239i	0.121297	+	0.265604i
$655$	−0.776023	−	0.227861i	−0.0303217	−	0.00890326i
$656$	−10.3746	−	3.04627i	−0.405062	−	0.118937i
$657$	4.47978	+	9.80934i	0.174773	+	0.382699i
$658$	−0.622387	+	4.32879i	−0.0242632	+	0.168754i
$659$	−1.97220	+	2.27605i	−0.0768262	+	0.0886621i	−0.792861	−	0.609402i	$-0.791410\pi$
$659$	−1.97220	+	2.27605i	−0.0768262	+	0.0886621i	0.716035	+	0.698064i	$0.245955\pi$
$660$	3.27163	−	7.16387i	0.127348	−	0.278853i
$661$	8.06392	+	5.18236i	0.313650	+	0.201571i	0.687989	−	0.725721i	$-0.258494\pi$
$661$	8.06392	+	5.18236i	0.313650	+	0.201571i	−0.374339	+	0.927292i	$0.622130\pi$
$662$	−0.698720	−	4.85970i	−0.0271565	−	0.188878i
$663$	11.4969	−	7.38858i	0.446501	−	0.286949i
$664$	1.27897	+	1.47602i	0.0496338	+	0.0572805i
$665$	−0.200334	+	0.0588234i	−0.00776862	+	0.00228107i
$666$	−18.2870			−0.708607
$667$	8.55850	−	4.14528i	0.331386	−	0.160506i
$668$	−21.9317			−0.848563
$669$	−17.7316	+	5.20646i	−0.685542	+	0.201293i
$670$	−4.98390	−	5.75172i	−0.192545	−	0.222208i
$671$	45.2659	−	29.0906i	1.74747	−	1.12303i
$672$	0.0971309	+	0.675560i	0.00374691	+	0.0260603i
$673$	13.4283	+	8.62986i	0.517624	+	0.332657i	0.773231	−	0.634124i	$-0.218639\pi$
$673$	13.4283	+	8.62986i	0.517624	+	0.332657i	−0.255607	+	0.966781i	$0.582275\pi$
$674$	12.3100	−	26.9551i	0.474162	−	1.03827i
$675$	11.9779	−	13.8232i	0.461028	−	0.532055i
$676$	1.06286	−	7.39237i	0.0408793	−	0.284322i
$677$	10.8453	+	23.7479i	0.416819	+	0.912706i	0.995284	+	0.0969993i	$0.0309244\pi$
$677$	10.8453	+	23.7479i	0.416819	+	0.912706i	−0.578466	+	0.815707i	$0.696348\pi$
$678$	−1.30122	−	0.382072i	−0.0499729	−	0.0146734i
$679$	−6.12902	−	1.79964i	−0.235210	−	0.0690640i
$680$	−2.72562	−	5.96828i	−0.104523	−	0.228873i
$681$	−2.78675	+	19.3823i	−0.106789	+	0.742731i
$682$	−25.4722	+	29.3965i	−0.975383	+	1.12565i
$683$	−17.1908	+	37.6427i	−0.657789	+	1.44036i	0.226779	+	0.973946i	$0.427181\pi$
$683$	−17.1908	+	37.6427i	−0.657789	+	1.44036i	−0.884568	+	0.466411i	$0.845547\pi$
$684$	0.413877	+	0.265983i	0.0158250	+	0.0101701i
$685$	−2.19000	−	15.2318i	−0.0836758	−	0.581978i
$686$	−7.17947	+	4.61397i	−0.274114	+	0.176162i
$687$	5.34196	+	6.16495i	0.203808	+	0.235207i
$688$	−4.41103	+	1.29519i	−0.168169	+	0.0493788i
$689$	6.20193			0.236275
$690$	3.58794	+	5.31435i	0.136590	+	0.202314i
$691$	40.6203			1.54527			0.772635	−	0.634850i	$-0.218938\pi$
$691$	40.6203			1.54527			0.772635	+	0.634850i	$0.218938\pi$
$692$	−10.6459	+	3.12591i	−0.404695	+	0.118829i
$693$	4.39343	+	5.07028i	0.166892	+	0.192604i
$694$	−10.8168	+	6.95151i	−0.410598	+	0.263876i
$695$	2.98321	+	20.7487i	0.113160	+	0.787042i
$696$	1.81515	+	1.16653i	0.0688032	+	0.0442171i
$697$	23.9855	−	52.5209i	0.908515	−	1.98937i
$698$	15.4134	−	17.7880i	0.583407	−	0.673287i
$699$	0.855307	−	5.94879i	0.0323507	−	0.225004i
$700$	−0.909407	−	1.99132i	−0.0343723	−	0.0752649i
$701$	−1.52463	−	0.447673i	−0.0575846	−	0.0169084i	0.252813	−	0.967515i	$-0.418644\pi$
$701$	−1.52463	−	0.447673i	−0.0575846	−	0.0169084i	−0.310398	+	0.950607i	$0.600462\pi$
$702$	11.8260	+	3.47243i	0.446344	+	0.131058i
$703$	−1.13338	−	2.48177i	−0.0427464	−	0.0936016i
$704$	−0.838287	+	5.83041i	−0.0315941	+	0.219742i
$705$	−6.10496	+	7.04550i	−0.229926	+	0.265349i
$706$	3.45330	−	7.56167i	0.129967	−	0.284587i
$707$	−7.51116	−	4.82713i	−0.282486	−	0.181543i
$708$	0.255407	+	1.77640i	0.00959879	+	0.0667610i
$709$	−3.64246	+	2.34087i	−0.136796	+	0.0879131i	−0.607249	−	0.794512i	$-0.707727\pi$
$709$	−3.64246	+	2.34087i	−0.136796	+	0.0879131i	0.470453	+	0.882425i	$0.344090\pi$
$710$	−7.29184	−	8.41523i	−0.273658	−	0.315818i
$711$	−10.4666	+	3.07327i	−0.392528	+	0.115257i
$712$	4.59045			0.172034
$713$	−9.60815	−	30.1767i	−0.359828	−	1.13013i
$714$	−3.64453			−0.136393
$715$	−16.3327	+	4.79572i	−0.610809	+	0.179350i
$716$	11.4847	+	13.2541i	0.429205	+	0.495329i
$717$	−4.77756	+	3.07035i	−0.178421	+	0.114664i
$718$	2.75167	+	19.1383i	0.102691	+	0.714235i
$719$	−21.8293	−	14.0289i	−0.814096	−	0.523188i	0.0660915	−	0.997814i	$-0.478947\pi$
$719$	−21.8293	−	14.0289i	−0.814096	−	0.523188i	−0.880188	+	0.474626i	$0.842583\pi$
$720$	0.926887	−	2.02960i	0.0345430	−	0.0756387i
$721$	0.309580	−	0.357275i	0.0115294	−	0.0133056i
$722$	2.69354	−	18.7340i	0.100243	−	0.697206i
$723$	0.702417	+	1.53808i	0.0261232	+	0.0572018i
$724$	−19.5794	−	5.74903i	−0.727662	−	0.213661i
$725$	−6.64044	−	1.94981i	−0.246620	−	0.0724141i
$726$	−10.7116	−	23.4552i	−0.397546	−	0.870505i
$727$	−2.47161	+	17.1904i	−0.0916670	+	0.637558i	0.891251	+	0.453511i	$0.149829\pi$
$727$	−2.47161	+	17.1904i	−0.0916670	+	0.637558i	−0.982918	+	0.184047i	$0.941080\pi$
$728$	0.966031	−	1.11486i	0.0358035	−	0.0413194i
$729$	7.29878	−	15.9821i	0.270325	−	0.591929i
$730$	6.13838	+	3.94489i	0.227191	+	0.146007i
$731$	−3.49368	−	24.2991i	−0.129218	−	0.898734i
$732$	−8.36218	+	5.37405i	−0.309075	+	0.198631i
$733$	−30.9021	−	35.6630i	−1.14140	−	1.31724i	−0.941341	−	0.337457i	$-0.890433\pi$
$733$	−30.9021	−	35.6630i	−1.14140	−	1.31724i	−0.200055	−	0.979785i	$-0.564112\pi$
$734$	−29.2088	+	8.57648i	−1.07812	+	0.316564i
$735$	−8.83319			−0.325817
$736$	−3.69464	−	3.05772i	−0.136186	−	0.112709i
$737$	−36.4850			−1.34394
$738$	18.8395	−	5.53177i	0.693491	−	0.203627i
$739$	−9.88757	−	11.4109i	−0.363720	−	0.419755i	0.544163	−	0.838980i	$-0.316847\pi$
$739$	−9.88757	−	11.4109i	−0.363720	−	0.419755i	−0.907883	+	0.419224i	$0.862302\pi$
$740$	−10.4093	+	6.68966i	−0.382654	+	0.245917i
$741$	0.0986769	+	0.686313i	0.00362499	+	0.0252123i
$742$	−1.39137	−	0.894181i	−0.0510789	−	0.0328264i
$743$	−4.94255	+	10.8227i	−0.181324	+	0.397045i	−0.978367	−	0.206878i	$-0.933670\pi$
$743$	−4.94255	+	10.8227i	−0.181324	+	0.397045i	0.797042	+	0.603924i	$0.206397\pi$
$744$	4.70561	−	5.43056i	0.172516	−	0.199094i
$745$	−3.21992	+	22.3950i	−0.117969	+	0.820491i
$746$	8.01594	+	17.5525i	0.293484	+	0.642641i
$747$	−3.40291	−	0.999185i	−0.124506	−	0.0365583i
$748$	−30.1800	−	8.86165i	−1.10349	−	0.324014i
$749$	0.154518	+	0.338348i	0.00564597	+	0.0123630i
$750$	1.61552	−	11.2362i	0.0589904	−	0.410287i
$751$	−5.20597	+	6.00801i	−0.189969	+	0.219235i	−0.842742	−	0.538318i	$-0.819060\pi$
$751$	−5.20597	+	6.00801i	−0.189969	+	0.219235i	0.652773	+	0.757553i	$0.273605\pi$
$752$	2.89652	−	6.34249i	0.105625	−	0.231287i
$753$	8.17152	+	5.25152i	0.297787	+	0.191376i
$754$	−0.663699	−	4.61613i	−0.0241705	−	0.168110i
$755$	11.8874	−	7.63954i	0.432625	−	0.278031i
$756$	−2.15246	−	2.48407i	−0.0782842	−	0.0903448i
$757$	−21.3067	+	6.25622i	−0.774406	+	0.227386i	−0.644977	−	0.764202i	$-0.723133\pi$
$757$	−21.3067	+	6.25622i	−0.774406	+	0.227386i	−0.129430	+	0.991589i	$0.541315\pi$
$758$	32.3335			1.17441
$759$	30.5179	+	3.68452i	1.10773	+	0.133740i
$760$	0.332887			0.0120751
$761$	−3.25541	+	0.955875i	−0.118009	+	0.0346504i	−0.340204	−	0.940352i	$-0.610496\pi$
$761$	−3.25541	+	0.955875i	−0.118009	+	0.0346504i	0.222195	+	0.975002i	$0.428678\pi$
$762$	−5.12044	−	5.90930i	−0.185494	−	0.214071i
$763$	−3.62084	+	2.32697i	−0.131083	+	0.0842420i
$764$	1.34665	+	9.36615i	0.0487201	+	0.338856i
$765$	10.0232	+	6.44152i	0.362389	+	0.232894i
$766$	−2.98681	+	6.54021i	−0.107918	+	0.236307i
$767$	2.54019	−	2.93154i	0.0917210	−	0.105852i
$768$	0.154861	−	1.07708i	0.00558806	−	0.0388658i
$769$	1.72530	+	3.77789i	0.0622160	+	0.136234i	0.938186	−	0.346132i	$-0.112505\pi$
$769$	1.72530	+	3.77789i	0.0622160	+	0.136234i	−0.875970	+	0.482366i	$0.839778\pi$
$770$	4.35561	+	1.27892i	0.156965	+	0.0460891i
$771$	−3.80311	−	1.11670i	−0.136966	−	0.0402168i
$772$	10.6184	+	23.2510i	0.382163	+	0.836821i
$773$	4.01918	−	27.9540i	0.144560	−	1.00544i	−0.780375	−	0.625311i	$-0.784972\pi$
$773$	4.01918	−	27.9540i	0.144560	−	1.00544i	0.924935	−	0.380125i	$-0.124119\pi$
$774$	5.46692	−	6.30916i	0.196504	−	0.226778i
$775$	−9.57454	+	20.9653i	−0.343928	+	0.753097i
$776$	8.56762	+	5.50608i	0.307560	+	0.197657i
$777$	0.978147	+	6.80316i	0.0350908	+	0.244062i
$778$	22.1125	−	14.2109i	0.792773	−	0.509484i
$779$	1.91835	+	2.21390i	0.0687321	+	0.0793211i
$780$	3.01722	−	0.885937i	0.108034	−	0.0317216i
$781$	−53.3804			−1.91010
$782$	18.9695	−	17.2046i	0.678349	−	0.615234i
$783$	−10.3912			−0.371351
$784$	6.33899	−	1.86129i	0.226392	−	0.0664748i
$785$	2.59746	+	2.99763i	0.0927075	+	0.106990i
$786$	0.602563	−	0.387244i	0.0214927	−	0.0138125i
$787$	−3.11544	−	21.6684i	−0.111053	−	0.772393i	−0.966899	−	0.255161i	$-0.917871\pi$
$787$	−3.11544	−	21.6684i	−0.111053	−	0.772393i	0.855845	−	0.517232i	$-0.173038\pi$
$788$	4.43302	+	2.84893i	0.157920	+	0.101489i
$789$	−7.29446	+	15.9726i	−0.259690	+	0.568641i
$790$	−4.83354	+	5.57820i	−0.171970	+	0.198464i
$791$	0.111246	−	0.773730i	0.00395544	−	0.0275107i
$792$	−4.44345	−	9.72980i	−0.157891	−	0.345733i
$793$	20.6143	+	6.05291i	0.732036	+	0.214945i
$794$	8.89615	+	2.61214i	0.315712	+	0.0927015i
$795$	−1.46461	−	3.20705i	−0.0519444	−	0.113742i
$796$	3.56014	−	24.7613i	0.126186	−	0.877642i
$797$	7.02444	−	8.10663i	0.248818	−	0.287152i	−0.617577	−	0.786510i	$-0.711886\pi$
$797$	7.02444	−	8.10663i	0.248818	−	0.287152i	0.866395	+	0.499359i	$0.166431\pi$
$798$	0.0768135	−	0.168198i	0.00271917	−	0.00595415i
$799$	31.3225	+	20.1297i	1.10811	+	0.712139i
$800$	0.496718	+	3.45475i	0.0175616	+	0.122144i
$801$	−7.01258	+	4.50671i	−0.247777	+	0.159237i
$802$	18.3571	+	21.1853i	0.648213	+	0.748078i
$803$	33.5631	−	9.85502i	1.18442	−	0.347776i
$804$	6.74004			0.237703
$805$	−2.73770	+	2.48298i	−0.0964912	+	0.0875136i
$806$	−15.5311			−0.547059
$807$	−4.69201	+	1.37770i	−0.165166	+	0.0484972i
$808$	9.32209	+	10.7583i	0.327950	+	0.378474i
$809$	28.3453	−	18.2164i	0.996568	−	0.640456i	0.0626850	−	0.998033i	$-0.480034\pi$
$809$	28.3453	−	18.2164i	0.996568	−	0.640456i	0.933883	+	0.357578i	$0.116397\pi$
$810$	−0.0445371	−	0.309762i	−0.00156487	−	0.0108839i
$811$	29.2735	+	18.8129i	1.02793	+	0.660611i	0.941973	−	0.335688i	$-0.108969\pi$
$811$	29.2735	+	18.8129i	1.02793	+	0.660611i	0.0859572	+	0.996299i	$0.472605\pi$
$812$	−0.516646	+	1.13130i	−0.0181307	+	0.0397008i
$813$	−2.49584	+	2.88035i	−0.0875330	+	0.101018i
$814$	−8.44188	+	58.7146i	−0.295888	+	2.05795i
$815$	−5.64717	−	12.3656i	−0.197812	−	0.433147i
$816$	5.57530	+	1.63705i	0.195174	+	0.0573084i
$817$	1.19506	+	0.350900i	0.0418097	+	0.0122764i
$818$	0.0184072	+	0.0403061i	0.000643591	+	0.00140927i
$819$	−0.381231	+	2.65152i	−0.0133213	+	0.0926516i
$820$	8.70019	−	10.0406i	0.303824	−	0.350631i
$821$	−9.90154	+	21.6813i	−0.345566	+	0.756684i	0.654434	+	0.756119i	$0.272907\pi$
$821$	−9.90154	+	21.6813i	−0.345566	+	0.756684i	−1.00000		0.000564668i	$0.999820\pi$
$822$	11.4647	+	7.36794i	0.399879	+	0.256987i
$823$	3.38486	+	23.5422i	0.117989	+	0.820630i	0.959765	+	0.280804i	$0.0906010\pi$
$823$	3.38486	+	23.5422i	0.117989	+	0.820630i	−0.841776	+	0.539826i	$0.818490\pi$
$824$	−0.634067	+	0.407490i	−0.0220888	+	0.0141956i
$825$	−14.6502	−	16.9072i	−0.510053	−	0.588633i
$826$	−0.992543	+	0.291437i	−0.0345350	+	0.0101404i
$827$	30.8236			1.07184			0.535921	−	0.844268i	$-0.319965\pi$
$827$	30.8236			1.07184			0.535921	+	0.844268i	$0.319965\pi$
$828$	8.64604	+	1.04386i	0.300471	+	0.0362768i
$829$	−30.9416			−1.07465			−0.537324	−	0.843376i	$-0.680565\pi$
$829$	−30.9416			−1.07465			−0.537324	+	0.843376i	$0.680565\pi$
$830$	−2.30252	+	0.676081i	−0.0799216	+	0.0234671i
$831$	−8.60038	−	9.92537i	−0.298344	−	0.344307i
$832$	−1.97858	+	1.27155i	−0.0685948	+	0.0440832i
$833$	5.02069	+	34.9197i	0.173957	+	1.20989i
$834$	−15.6172	−	10.0366i	−0.540779	−	0.347538i
$835$	11.1945	−	24.5124i	0.387400	−	0.848288i
$836$	1.04506	−	1.20606i	0.0361440	−	0.0417124i
$837$	−4.92489	+	34.2533i	−0.170229	+	1.18397i
$838$	5.12508	+	11.2224i	0.177043	+	0.387670i
$839$	37.7321	+	11.0791i	1.30266	+	0.382494i	0.858204	−	0.513308i	$-0.171580\pi$
$839$	37.7321	+	11.0791i	1.30266	+	0.382494i	0.444452	+	0.895803i	$0.353398\pi$
$840$	−0.804632	−	0.236261i	−0.0277624	−	0.00815179i
$841$	−10.4137	−	22.8028i	−0.359093	−	0.786305i
$842$	−0.397270	+	2.76307i	−0.0136908	+	0.0952218i
$843$	−4.46511	+	5.15301i	−0.153786	+	0.177479i
$844$	−3.68320	+	8.06509i	−0.126781	+	0.277612i
$845$	7.71973	+	4.96117i	0.265567	+	0.170669i
$846$	1.80194	+	12.5328i	0.0619520	+	0.430885i
$847$	12.5033	−	8.03540i	0.429620	−	0.276100i
$848$	1.72683	+	1.99287i	0.0592996	+	0.0684354i
$849$	33.0248	−	9.69695i	1.13341	−	0.332798i
$850$	−18.6378			−0.639272
$851$	−37.2065	−	30.7924i	−1.27542	−	1.05555i
$852$	9.86123			0.337840
$853$	5.57235	−	1.63619i	0.190794	−	0.0560220i	−0.184940	−	0.982750i	$-0.559209\pi$
$853$	5.57235	−	1.63619i	0.190794	−	0.0560220i	0.375733	+	0.926728i	$0.377391\pi$
$854$	−3.75203	−	4.33008i	−0.128392	−	0.148172i
$855$	−0.508534	+	0.326815i	−0.0173915	+	0.0111768i
$856$	−0.0843979	−	0.587000i	−0.00288466	−	0.0200633i
$857$	−17.8082	−	11.4446i	−0.608316	−	0.390941i	0.199909	−	0.979814i	$-0.435935\pi$
$857$	−17.8082	−	11.4446i	−0.608316	−	0.390941i	−0.808225	+	0.588873i	$0.799572\pi$
$858$	6.26241	−	13.7128i	0.213795	−	0.468146i
$859$	−1.76327	+	2.03492i	−0.0601620	+	0.0694306i	−0.785033	−	0.619454i	$-0.787354\pi$
$859$	−1.76327	+	2.03492i	−0.0601620	+	0.0694306i	0.724871	+	0.688885i	$0.241899\pi$
$860$	0.803890	−	5.59118i	0.0274124	−	0.190658i
$861$	−3.06564	−	6.71280i	−0.104477	−	0.228772i
$862$	−3.35504	−	0.985129i	−0.114273	−	0.0335536i
$863$	−19.3770	−	5.68960i	−0.659601	−	0.193676i	−0.0652336	−	0.997870i	$-0.520779\pi$
$863$	−19.3770	−	5.68960i	−0.659601	−	0.193676i	−0.594367	+	0.804194i	$0.702597\pi$
$864$	2.17697	+	4.76690i	0.0740620	+	0.162173i
$865$	1.94016	−	13.4941i	0.0659675	−	0.458814i
$866$	6.17483	−	7.12613i	0.209829	−	0.242156i
$867$	−5.20509	+	11.3976i	−0.176774	+	0.387082i
$868$	3.48433	+	2.23924i	0.118266	+	0.0760048i
$869$	5.03571	+	35.0241i	0.170825	+	1.18811i
$870$	−2.23029	+	1.43332i	−0.0756140	+	0.0485942i
$871$	−9.53996	−	11.0097i	−0.323249	−	0.373049i
$872$	6.58427	−	1.93332i	0.222972	−	0.0654703i
$873$	−18.4939			−0.625925
$874$	0.394196	+	1.23807i	0.0133339	+	0.0418783i
$875$	6.54314			0.221199
$876$	−6.20028	+	1.82057i	−0.209488	+	0.0615112i
$877$	−13.7744	−	15.8966i	−0.465130	−	0.536789i	0.473921	−	0.880568i	$-0.342838\pi$
$877$	−13.7744	−	15.8966i	−0.465130	−	0.536789i	−0.939051	+	0.343779i	$0.888293\pi$
$878$	18.9979	−	12.2092i	0.641148	−	0.412041i
$879$	1.04961	+	7.30020i	0.0354025	+	0.246229i
$880$	−6.08860	−	3.91291i	−0.205247	−	0.131904i
$881$	−10.2339	+	22.4090i	−0.344787	+	0.754979i	−1.00000		0.000465480i	$-0.999852\pi$
$881$	−10.2339	+	22.4090i	−0.344787	+	0.754979i	0.655212	+	0.755445i	$0.272579\pi$
$882$	−7.85639	+	9.06676i	−0.264538	+	0.305294i
$883$	0.165923	−	1.15402i	0.00558376	−	0.0388359i	−0.986839	−	0.161705i	$-0.948301\pi$
$883$	0.165923	−	1.15402i	0.00558376	−	0.0388359i	0.992423	+	0.122870i	$0.0392097\pi$
$884$	−5.21727	−	11.4242i	−0.175476	−	0.384238i
$885$	−2.11579	−	0.621253i	−0.0711216	−	0.0208832i
$886$	5.83426	+	1.71309i	0.196006	+	0.0575525i
$887$	−4.22870	−	9.25957i	−0.141986	−	0.310906i	0.825257	−	0.564757i	$-0.191030\pi$
$887$	−4.22870	−	9.25957i	−0.141986	−	0.310906i	−0.967243	+	0.253851i	$0.918303\pi$
$888$	1.55951	−	10.8466i	0.0523337	−	0.363989i
$889$	2.95143	−	3.40613i	0.0989877	−	0.114238i
$890$	−2.34307	+	5.13062i	−0.0785400	+	0.171979i
$891$	−1.26210	−	0.811100i	−0.0422818	−	0.0271729i
$892$	2.41693	+	16.8101i	0.0809249	+	0.562845i
$893$	−1.58917	+	1.02130i	−0.0531794	+	0.0341763i
$894$	−13.1216	−	15.1431i	−0.438852	−	0.506462i
$895$	−20.6758	+	6.07097i	−0.691116	+	0.202930i
$896$	0.627214			0.0209538
$897$	6.86788	+	10.1725i	0.229312	+	0.339650i
$898$	−12.0641			−0.402583
$899$	12.5636	−	3.68900i	0.419018	−	0.123035i
$900$	−4.15054	−	4.78998i	−0.138351	−	0.159666i
$901$	−11.8457	+	7.61280i	−0.394639	+	0.253619i
$902$	−9.06408	−	63.0421i	−0.301801	−	2.09907i
$903$	−2.63956	−	1.69634i	−0.0878392	−	0.0564508i
$904$	−0.517725	+	1.13366i	−0.0172193	+	0.0377049i
$905$	16.4193	−	18.9489i	0.545796	−	0.629882i
$906$	−1.78095	+	12.3868i	−0.0591680	+	0.411523i
$907$	8.16401	+	17.8767i	0.271082	+	0.593586i	0.995392	−	0.0958881i	$-0.0305691\pi$
$907$	8.16401	+	17.8767i	0.271082	+	0.593586i	−0.724311	+	0.689474i	$0.757842\pi$
$908$	17.2663	+	5.06984i	0.573002	+	0.168248i
$909$	−24.8029	−	7.28278i	−0.822659	−	0.241555i
$910$	0.752961	+	1.64876i	0.0249604	+	0.0546557i
$911$	6.81180	−	47.3771i	0.225685	−	1.56967i	−0.490298	−	0.871555i	$-0.663112\pi$
$911$	6.81180	−	47.3771i	0.225685	−	1.56967i	0.715983	−	0.698118i	$-0.245979\pi$
$912$	−0.193058	+	0.222801i	−0.00639280	+	0.00737768i
$913$	−4.77901	+	10.4646i	−0.158162	+	0.346326i
$914$	−16.9598	−	10.8994i	−0.560979	−	0.360519i
$915$	−1.73817	−	12.0892i	−0.0574620	−	0.399657i
$916$	6.30648	−	4.05293i	0.208372	−	0.133913i
$917$	0.270364	+	0.312017i	0.00892821	+	0.0103037i
$918$	−26.8502	+	7.88392i	−0.886187	+	0.260208i
$919$	−35.7413			−1.17900			−0.589499	−	0.807769i	$-0.700675\pi$
$919$	−35.7413			−1.17900			−0.589499	+	0.807769i	$0.700675\pi$
$920$	5.30335	−	2.56866i	0.174846	−	0.0846864i
$921$	6.60888			0.217770
$922$	−32.7540	+	9.61744i	−1.07870	+	0.316733i
$923$	−13.9577	−	16.1081i	−0.459424	−	0.530204i
$924$	−3.38202	+	2.17349i	−0.111260	+	0.0715027i
$925$	5.00215	+	34.7907i	0.164470	+	1.14391i
$926$	9.81876	+	6.31013i	0.322664	+	0.207364i
$927$	0.568573	−	1.24500i	0.0186744	−	0.0408912i
$928$	1.29851	−	1.49856i	0.0426256	−	0.0491925i
$929$	3.26383	−	22.7004i	0.107083	−	0.744777i	−0.863559	−	0.504247i	$-0.831770\pi$
$929$	3.26383	−	22.7004i	0.107083	−	0.744777i	0.970642	−	0.240529i	$-0.0773210\pi$
$930$	3.66773	+	8.03121i	0.120270	+	0.263354i
$931$	−1.71739	−	0.504270i	−0.0562851	−	0.0165268i
$932$	−5.29935	−	1.55603i	−0.173586	−	0.0509695i
$933$	−4.62403	−	10.1252i	−0.151384	−	0.331485i
$934$	−0.675303	+	4.69683i	−0.0220966	+	0.153685i
$935$	25.3090	−	29.2081i	0.827692	−	0.955208i
$936$	1.77421	−	3.88497i	0.0579917	−	0.126984i
$937$	−16.5521	−	10.6374i	−0.540735	−	0.347509i	0.241591	−	0.970378i	$-0.422331\pi$
$937$	−16.5521	−	10.6374i	−0.540735	−	0.347509i	−0.782326	+	0.622869i	$0.785967\pi$
$938$	0.552889	+	3.84543i	0.0180525	+	0.125558i
$939$	−3.68012	+	2.36507i	−0.120096	+	0.0771811i
$940$	5.61037	+	6.47471i	0.182990	+	0.211182i
$941$	50.1716	−	14.7317i	1.63555	−	0.480240i	0.670413	−	0.741989i	$-0.266117\pi$
$941$	50.1716	−	14.7317i	1.63555	−	0.480240i	0.965136	+	0.261748i	$0.0842989\pi$
$942$	−3.51272			−0.114451
$943$	47.6452	+	20.4678i	1.55154	+	0.666524i
$944$	1.64927			0.0536792
$945$	3.87504	−	1.13781i	0.126055	−	0.0370131i
$946$	−17.7333	−	20.4653i	−0.576559	−	0.665385i
$947$	−22.1851	+	14.2575i	−0.720917	+	0.463305i	−0.848956	−	0.528464i	$-0.822768\pi$
$947$	−22.1851	+	14.2575i	−0.720917	+	0.463305i	0.128038	+	0.991769i	$0.459132\pi$
$948$	−0.930270	−	6.47017i	−0.0302138	−	0.210141i
$949$	11.7498	+	7.55115i	0.381415	+	0.245121i
$950$	0.392817	−	0.860150i	0.0127447	−	0.0279069i
$951$	3.55799	−	4.10614i	0.115376	−	0.133151i
$952$	−0.476652	+	3.31519i	−0.0154484	+	0.107446i
$953$	17.2026	+	37.6685i	0.557247	+	1.22020i	0.953314	+	0.301980i	$0.0976474\pi$
$953$	17.2026	+	37.6685i	0.557247	+	1.22020i	−0.396067	+	0.918222i	$0.629625\pi$
$954$	−4.59450	−	1.34907i	−0.148752	−	0.0436777i
$955$	−11.1556	−	3.27559i	−0.360988	−	0.105996i
$956$	2.16805	+	4.74738i	0.0701199	+	0.153541i
$957$	−1.80875	+	12.5801i	−0.0584686	+	0.406658i
$958$	19.4848	−	22.4866i	0.629524	−	0.726509i
$959$	−3.26321	+	7.14543i	−0.105374	+	0.230738i
$960$	1.12478	+	0.722850i	0.0363020	+	0.0233299i
$961$	−1.79410	−	12.4782i	−0.0578742	−	0.402524i
$962$	−19.9251	+	12.8051i	−0.642410	+	0.412852i
$963$	0.705223	+	0.813870i	0.0227255	+	0.0262266i
$964$	1.49095	−	0.437783i	0.0480203	−	0.0141000i
$965$	−31.4068			−1.01102
$966$	−0.0741251	−	3.27235i	−0.00238494	−	0.105286i
$967$	−24.8632			−0.799546			−0.399773	−	0.916614i	$-0.630911\pi$
$967$	−24.8632			−0.799546			−0.399773	+	0.916614i	$0.630911\pi$
$968$	−22.7366	+	6.67606i	−0.730781	+	0.214577i
$969$	−1.03092	−	1.18974i	−0.0331178	−	0.0382200i
$970$	−10.5271	+	6.76536i	−0.338005	+	0.217222i
$971$	7.51378	+	52.2595i	0.241129	+	1.67709i	0.646484	+	0.762928i	$0.276239\pi$
$971$	7.51378	+	52.2595i	0.241129	+	1.67709i	−0.405355	+	0.914159i	$0.632852\pi$
$972$	−12.9925	−	8.34979i	−0.416736	−	0.267820i
$973$	4.44512	−	9.73345i	0.142504	−	0.312040i
$974$	5.70651	−	6.58566i	0.182848	−	0.211018i
$975$	1.27124	−	8.84166i	0.0407122	−	0.283160i
$976$	3.79475	+	8.30935i	0.121467	+	0.265976i
$977$	12.6033	+	3.70065i	0.403214	+	0.118394i	0.477050	−	0.878876i	$-0.341706\pi$
$977$	12.6033	+	3.70065i	0.403214	+	0.118394i	−0.0738363	+	0.997270i	$0.523524\pi$
$978$	11.5514	+	3.39179i	0.369372	+	0.108457i
$979$	11.2326	+	24.5959i	0.358995	+	0.786090i
$980$	−1.15525	+	8.03496i	−0.0369032	+	0.256667i
$981$	−8.16039	+	9.41759i	−0.260541	+	0.300680i
$982$	6.25698	−	13.7009i	0.199668	−	0.437212i
$983$	−45.2576	−	29.0853i	−1.44349	−	0.927677i	−0.999499	−	0.0316476i	$-0.989925\pi$
$983$	−45.2576	−	29.0853i	−1.44349	−	0.927677i	−0.443995	−	0.896029i	$-0.646439\pi$
$984$	1.67445	+	11.6461i	0.0533795	+	0.371263i
$985$	−5.44688	+	3.50050i	−0.173552	+	0.111535i
$986$	6.93393	+	8.00218i	0.220821	+	0.254841i
$987$	4.56608	−	1.34072i	0.145340	−	0.0426756i
$988$	0.637198			0.0202720
$989$	21.7466	−	3.63111i	0.691500	−	0.115463i
$990$	13.1428			0.417705
$991$	41.8902	−	12.3001i	1.33069	−	0.390725i	0.462348	−	0.886698i	$-0.347007\pi$
$991$	41.8902	−	12.3001i	1.33069	−	0.390725i	0.868337	+	0.495974i	$0.165189\pi$
$992$	−4.32439	−	4.99061i	−0.137300	−	0.158452i
$993$	−4.49439	+	2.88837i	−0.142625	+	0.0916596i
$994$	0.808921	+	5.62617i	0.0256574	+	0.178451i
$995$	25.8579	+	16.6178i	0.819749	+	0.526821i
$996$	0.882849	−	1.93317i	0.0279741	−	0.0612548i
$997$	34.9557	−	40.3411i	1.10706	−	1.27761i	0.149695	−	0.988732i	$-0.452171\pi$
$997$	34.9557	−	40.3411i	1.10706	−	1.27761i	0.957365	−	0.288882i	$-0.0932836\pi$
$998$	−4.49705	+	31.2777i	−0.142352	+	0.990078i
$999$	21.9230	+	48.0046i	0.693612	+	1.51880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.2.c.a.9.1	✓	10
3.2	odd	2		414.2.i.f.55.1		10
4.3	odd	2		368.2.m.b.193.1		10
23.8	even	11		1058.2.a.m.1.2		5
23.15	odd	22		1058.2.a.l.1.2		5
23.18	even	11	inner	46.2.c.a.41.1	yes	10
69.8	odd	22		9522.2.a.bp.1.5		5
69.38	even	22		9522.2.a.bu.1.1		5
69.41	odd	22		414.2.i.f.271.1		10
92.15	even	22		8464.2.a.bw.1.4		5
92.31	odd	22		8464.2.a.bx.1.4		5
92.87	odd	22		368.2.m.b.225.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.9.1	✓	10	1.1	even	1	trivial
46.2.c.a.41.1	yes	10	23.18	even	11	inner
368.2.m.b.193.1		10	4.3	odd	2
368.2.m.b.225.1		10	92.87	odd	22
414.2.i.f.55.1		10	3.2	odd	2
414.2.i.f.271.1		10	69.41	odd	22
1058.2.a.l.1.2		5	23.15	odd	22
1058.2.a.m.1.2		5	23.8	even	11
8464.2.a.bw.1.4		5	92.15	even	22
8464.2.a.bx.1.4		5	92.31	odd	22
9522.2.a.bp.1.5		5	69.8	odd	22
9522.2.a.bu.1.1		5	69.38	even	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.712591 + 0.822373i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.174863 + 1.21620i) q^{5} +(-0.915415 - 0.588302i) q^{6} +(0.260554 - 0.570534i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.258432 - 1.79743i) q^{9} +(-0.510424 - 1.11767i) q^{10} +(-5.65177 - 1.65951i) q^{11} +(1.04408 + 0.306569i) q^{12} +(-0.977031 - 2.13940i) q^{13} +(-0.0892619 + 0.620830i) q^{14} +(-0.875565 + 1.01046i) q^{15} +(0.415415 - 0.909632i) q^{16} +(4.49223 + 2.88698i) q^{17} +(0.258432 + 1.79743i) q^{18} +(-0.227916 + 0.146473i) q^{19} +(0.804632 + 0.928595i) q^{20} +(0.654861 - 0.192284i) q^{21} +5.89037 q^{22} +(-2.50079 + 4.09219i) q^{23} -1.08816 q^{24} +(3.34890 - 0.983325i) q^{25} +(1.54019 + 1.77748i) q^{26} +(4.40856 - 2.83321i) q^{27} +(-0.0892619 - 0.620830i) q^{28} +(-1.66810 - 1.07202i) q^{29} +(0.555420 - 1.21620i) q^{30} +(-4.32439 + 4.99061i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-2.66266 - 5.83041i) q^{33} +(-5.12362 - 1.50443i) q^{34} +(0.739446 + 0.217121i) q^{35} +(-0.754359 - 1.65182i) q^{36} +(-1.43317 + 9.96790i) q^{37} +(0.177418 - 0.204751i) q^{38} +(1.06316 - 2.32800i) q^{39} +(-1.03365 - 0.664289i) q^{40} +(-1.53880 - 10.7026i) q^{41} +(-0.574161 + 0.368991i) q^{42} +(-3.01056 - 3.47437i) q^{43} +(-5.65177 + 1.65951i) q^{44} +2.23123 q^{45} +(1.24659 - 4.63098i) q^{46} +6.97259 q^{47} +(1.04408 - 0.306569i) q^{48} +(4.32640 + 4.99294i) q^{49} +(-2.93621 + 1.88699i) q^{50} +(0.826944 + 5.75152i) q^{51} +(-1.97858 - 1.27155i) q^{52} +(-1.09543 + 2.39865i) q^{53} +(-3.43178 + 3.96048i) q^{54} +(1.03001 - 7.16387i) q^{55} +(0.260554 + 0.570534i) q^{56} +(-0.282866 - 0.0830570i) q^{57} +(1.90255 + 0.558640i) q^{58} +(0.685131 + 1.50023i) q^{59} +(-0.190279 + 1.32342i) q^{60} +(-5.98206 + 6.90366i) q^{61} +(2.74320 - 6.00678i) q^{62} +(-0.958162 - 0.615773i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(2.43109 - 1.56237i) q^{65} +(4.19742 + 4.84408i) q^{66} +(5.94311 - 1.74505i) q^{67} +5.33992 q^{68} +(-5.14735 + 0.859474i) q^{69} -0.770663 q^{70} +(8.69524 - 2.55315i) q^{71} +(1.18917 + 1.37238i) q^{72} +(-4.99580 + 3.21061i) q^{73} +(-1.43317 - 9.96790i) q^{74} +(3.19505 + 2.05334i) q^{75} +(-0.112546 + 0.246442i) q^{76} +(-2.41940 + 2.79213i) q^{77} +(-0.364223 + 2.53323i) q^{78} +(-2.49546 - 5.46429i) q^{79} +(1.17894 + 0.346167i) q^{80} +(0.244379 + 0.0717563i) q^{81} +(4.49173 + 9.83551i) q^{82} +(0.277948 - 1.93317i) q^{83} +(0.446947 - 0.515804i) q^{84} +(-2.72562 + 5.96828i) q^{85} +(3.86745 + 2.48546i) q^{86} +(-0.307069 - 2.13571i) q^{87} +(4.95529 - 3.18457i) q^{88} +(-3.00611 - 3.46923i) q^{89} +(-2.14085 + 0.628610i) q^{90} -1.47517 q^{91} +(0.108607 + 4.79460i) q^{92} -7.18567 q^{93} +(-6.69015 + 1.96441i) q^{94} +(-0.217995 - 0.251579i) q^{95} +(-0.915415 + 0.588302i) q^{96} +(-1.44938 - 10.0807i) q^{97} +(-5.55783 - 3.57180i) q^{98} +(-4.44345 + 9.72980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20}+ \cdots + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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