LMFDB - Embedded newform 256.2.m.a.101.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.28
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32875 - 0.484175i) q^{2} +(-0.256946 + 0.0643616i) q^{3} +(1.53115 - 1.28669i) q^{4} +(2.70773 + 1.28066i) q^{5} +(-0.310255 + 0.209927i) q^{6} +(0.0816484 + 0.269159i) q^{7} +(1.41153 - 2.45104i) q^{8} +(-2.58388 + 1.38112i) q^{9} +O(q^{10})$	\(q+(1.32875 - 0.484175i) q^{2} +(-0.256946 + 0.0643616i) q^{3} +(1.53115 - 1.28669i) q^{4} +(2.70773 + 1.28066i) q^{5} +(-0.310255 + 0.209927i) q^{6} +(0.0816484 + 0.269159i) q^{7} +(1.41153 - 2.45104i) q^{8} +(-2.58388 + 1.38112i) q^{9} +(4.21796 + 0.390662i) q^{10} +(-3.27972 + 0.486501i) q^{11} +(-0.310609 + 0.429158i) q^{12} +(0.185108 - 0.517342i) q^{13} +(0.238810 + 0.318112i) q^{14} +(-0.778167 - 0.154787i) q^{15} +(0.688834 - 3.94024i) q^{16} +(2.69877 - 0.536818i) q^{17} +(-2.76463 + 3.08621i) q^{18} +(-2.75541 - 2.49736i) q^{19} +(5.79376 - 1.52314i) q^{20} +(-0.0383027 - 0.0639042i) q^{21} +(-4.12238 + 2.23440i) q^{22} +(1.52298 - 0.150000i) q^{23} +(-0.204934 + 0.720633i) q^{24} +(2.51976 + 3.07033i) q^{25} +(-0.00452213 - 0.777043i) q^{26} +(1.16383 - 1.05483i) q^{27} +(0.471341 + 0.307065i) q^{28} +(-0.870712 - 1.17402i) q^{29} +(-1.10893 + 0.171096i) q^{30} +(-6.89257 - 2.85500i) q^{31} +(-0.992480 - 5.56911i) q^{32} +(0.811400 - 0.336093i) q^{33} +(3.32607 - 2.01997i) q^{34} +(-0.123619 + 0.833374i) q^{35} +(-2.17924 + 5.43936i) q^{36} +(-0.295784 + 6.02081i) q^{37} +(-4.87041 - 1.98426i) q^{38} +(-0.0142658 + 0.144843i) q^{39} +(6.96099 - 4.82907i) q^{40} +(-4.03484 + 4.91647i) q^{41} +(-0.0818355 - 0.0663675i) q^{42} +(-1.64925 + 6.58418i) q^{43} +(-4.39576 + 4.96491i) q^{44} +(-8.76521 + 0.430607i) q^{45} +(1.95103 - 0.936700i) q^{46} +(-2.74054 - 1.83117i) q^{47} +(0.0766074 + 1.05676i) q^{48} +(5.75451 - 3.84504i) q^{49} +(4.83470 + 2.85970i) q^{50} +(-0.658887 + 0.311630i) q^{51} +(-0.382234 - 1.03031i) q^{52} +(-4.00873 + 5.40515i) q^{53} +(1.03571 - 1.96510i) q^{54} +(-9.50365 - 2.88290i) q^{55} +(0.774967 + 0.179801i) q^{56} +(0.868727 + 0.464344i) q^{57} +(-1.72539 - 1.13840i) q^{58} +(2.64993 + 7.40605i) q^{59} +(-1.39065 + 0.764261i) q^{60} +(-1.33165 + 2.22172i) q^{61} +(-10.5408 - 0.456363i) q^{62} +(-0.582709 - 0.582709i) q^{63} +(-4.01518 - 6.91942i) q^{64} +(1.16376 - 1.16376i) q^{65} +(0.915419 - 0.839443i) q^{66} +(7.38813 + 4.42827i) q^{67} +(3.44149 - 4.29444i) q^{68} +(-0.381669 + 0.136563i) q^{69} +(0.239240 + 1.16720i) q^{70} +(6.65865 - 12.4575i) q^{71} +(-0.262057 + 8.28268i) q^{72} +(3.77761 - 12.4531i) q^{73} +(2.52211 + 8.14336i) q^{74} +(-0.845053 - 0.626734i) q^{75} +(-7.43228 - 0.278456i) q^{76} +(-0.398730 - 0.843043i) q^{77} +(0.0511737 + 0.199367i) q^{78} +(1.45324 + 2.17492i) q^{79} +(6.91130 - 9.78696i) q^{80} +(4.65204 - 6.96227i) q^{81} +(-2.98086 + 8.48633i) q^{82} +(-0.239487 - 4.87486i) q^{83} +(-0.140872 - 0.0485630i) q^{84} +(7.99502 + 2.00265i) q^{85} +(0.996455 + 9.54724i) q^{86} +(0.299288 + 0.245619i) q^{87} +(-3.43698 + 8.72543i) q^{88} +(18.7205 + 1.84381i) q^{89} +(-11.4383 + 4.81607i) q^{90} +(0.154361 + 0.00758326i) q^{91} +(2.13890 - 2.18928i) q^{92} +(1.95477 + 0.289963i) q^{93} +(-4.52810 - 1.10627i) q^{94} +(-4.26265 - 10.2909i) q^{95} +(0.613451 + 1.36708i) q^{96} +(-3.53802 + 8.54153i) q^{97} +(5.78462 - 7.89528i) q^{98} +(7.80251 - 5.78674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	1.32875	−	0.484175i	0.939568	−	0.342364i
$2$	1.32875	−	0.484175i	0.939568	−	0.342364i
$3$	−0.256946	+	0.0643616i	−0.148348	+	0.0371592i	−0.316443	−	0.948612i	$-0.602489\pi$
$3$	−0.256946	+	0.0643616i	−0.148348	+	0.0371592i	0.168095	+	0.985771i	$0.446239\pi$
$4$	1.53115	−	1.28669i	0.765574	−	0.643347i
$5$	2.70773	+	1.28066i	1.21094	+	0.572730i	0.922955	−	0.384907i	$-0.125766\pi$
$5$	2.70773	+	1.28066i	1.21094	+	0.572730i	0.287980	+	0.957637i	$0.407016\pi$
$6$	−0.310255	+	0.209927i	−0.126661	+	0.0857025i
$7$	0.0816484	+	0.269159i	0.0308602	+	0.101732i	0.971018	−	0.239008i	$-0.0768223\pi$
$7$	0.0816484	+	0.269159i	0.0308602	+	0.101732i	−0.940157	+	0.340740i	$0.889322\pi$
$8$	1.41153	−	2.45104i	0.499050	−	0.866573i
$9$	−2.58388	+	1.38112i	−0.861295	+	0.460372i
$10$	4.21796	+	0.390662i	1.33384	+	0.123538i
$11$	−3.27972	+	0.486501i	−0.988873	+	0.146685i	−0.621522	−	0.783397i	$-0.713485\pi$
$11$	−3.27972	+	0.486501i	−0.988873	+	0.146685i	−0.367351	+	0.930082i	$0.619735\pi$
$12$	−0.310609	+	0.429158i	−0.0896651	+	0.123887i
$13$	0.185108	−	0.517342i	0.0513397	−	0.143485i	−0.913137	−	0.407653i	$-0.866347\pi$
$13$	0.185108	−	0.517342i	0.0513397	−	0.143485i	0.964477	+	0.264168i	$0.0850973\pi$
$14$	0.238810	+	0.318112i	0.0638247	+	0.0850190i
$15$	−0.778167	−	0.154787i	−0.200922	−	0.0399658i
$16$	0.688834	−	3.94024i	0.172208	−	0.985061i
$17$	2.69877	−	0.536818i	0.654547	−	0.130198i	0.143365	−	0.989670i	$-0.454208\pi$
$17$	2.69877	−	0.536818i	0.654547	−	0.130198i	0.511182	+	0.859472i	$0.329208\pi$
$18$	−2.76463	+	3.08621i	−0.651630	+	0.727426i
$19$	−2.75541	−	2.49736i	−0.632135	−	0.572934i	0.291327	−	0.956623i	$-0.405903\pi$
$19$	−2.75541	−	2.49736i	−0.632135	−	0.572934i	−0.923462	+	0.383690i	$0.874653\pi$
$20$	5.79376	−	1.52314i	1.29553	−	0.340585i
$21$	−0.0383027	−	0.0639042i	−0.00835834	−	0.0139450i
$22$	−4.12238	+	2.23440i	−0.878893	+	0.476375i
$23$	1.52298	−	0.150000i	0.317563	−	0.0312772i	0.0620198	−	0.998075i	$-0.480246\pi$
$23$	1.52298	−	0.150000i	0.317563	−	0.0312772i	0.255543	+	0.966798i	$0.417746\pi$
$24$	−0.204934	+	0.720633i	−0.0418319	+	0.147099i
$25$	2.51976	+	3.07033i	0.503951	+	0.614066i
$26$	−0.00452213	−	0.777043i	−0.000886863	−	0.152391i
$27$	1.16383	−	1.05483i	0.223979	−	0.203002i
$28$	0.471341	+	0.307065i	0.0890750	+	0.0580299i
$29$	−0.870712	−	1.17402i	−0.161687	−	0.218010i	0.714933	−	0.699193i	$-0.246457\pi$
$29$	−0.870712	−	1.17402i	−0.161687	−	0.218010i	−0.876620	+	0.481183i	$0.840207\pi$
$30$	−1.10893	+	0.171096i	−0.202463	+	0.0312377i
$31$	−6.89257	−	2.85500i	−1.23794	−	0.512773i	−0.334871	−	0.942264i	$-0.608693\pi$
$31$	−6.89257	−	2.85500i	−1.23794	−	0.512773i	−0.903071	+	0.429491i	$0.858693\pi$
$32$	−0.992480	−	5.56911i	−0.175447	−	0.984489i
$33$	0.811400	−	0.336093i	0.141247	−	0.0585062i
$34$	3.32607	−	2.01997i	0.570416	−	0.346422i
$35$	−0.123619	+	0.833374i	−0.0208955	+	0.140866i
$36$	−2.17924	+	5.43936i	−0.363206	+	0.906561i
$37$	−0.295784	+	6.02081i	−0.0486265	+	0.989816i	0.843246	+	0.537528i	$0.180642\pi$
$37$	−0.295784	+	6.02081i	−0.0486265	+	0.989816i	−0.891872	+	0.452287i	$0.850608\pi$
$38$	−4.87041	−	1.98426i	−0.790085	−	0.321890i
$39$	−0.0142658	+	0.144843i	−0.00228435	+	0.0231934i
$40$	6.96099	−	4.82907i	1.10063	−	0.763543i
$41$	−4.03484	+	4.91647i	−0.630137	+	0.767824i	−0.986006	−	0.166712i	$-0.946685\pi$
$41$	−4.03484	+	4.91647i	−0.630137	+	0.767824i	0.355869	+	0.934536i	$0.384185\pi$
$42$	−0.0818355	−	0.0663675i	−0.0126275	−	0.0102407i
$43$	−1.64925	+	6.58418i	−0.251508	+	1.00408i	0.704257	+	0.709946i	$0.251280\pi$
$43$	−1.64925	+	6.58418i	−0.251508	+	1.00408i	−0.955765	+	0.294132i	$0.904970\pi$
$44$	−4.39576	+	4.96491i	−0.662686	+	0.748488i
$45$	−8.76521	+	0.430607i	−1.30664	+	0.0641912i
$46$	1.95103	−	0.936700i	0.287663	−	0.138109i
$47$	−2.74054	−	1.83117i	−0.399749	−	0.267104i	0.339405	−	0.940640i	$-0.389774\pi$
$47$	−2.74054	−	1.83117i	−0.399749	−	0.267104i	−0.739154	+	0.673536i	$0.764774\pi$
$48$	0.0766074	+	1.05676i	0.0110573	+	0.152531i
$49$	5.75451	−	3.84504i	0.822072	−	0.549291i
$50$	4.83470	+	2.85970i	0.683730	+	0.404422i
$51$	−0.658887	+	0.311630i	−0.0922627	+	0.0436370i
$52$	−0.382234	−	1.03031i	−0.0530063	−	0.142878i
$53$	−4.00873	+	5.40515i	−0.550642	+	0.742454i	−0.987594	−	0.157030i	$-0.949808\pi$
$53$	−4.00873	+	5.40515i	−0.550642	+	0.742454i	0.436952	+	0.899485i	$0.356058\pi$
$54$	1.03571	−	1.96510i	0.140942	−	0.267417i
$55$	−9.50365	−	2.88290i	−1.28147	−	0.388730i
$56$	0.774967	+	0.179801i	0.103559	+	0.0240270i
$57$	0.868727	+	0.464344i	0.115066	+	0.0615039i
$58$	−1.72539	−	1.13840i	−0.226555	−	0.149479i
$59$	2.64993	+	7.40605i	0.344991	+	0.964186i	0.981255	+	0.192714i	$0.0617291\pi$
$59$	2.64993	+	7.40605i	0.344991	+	0.964186i	−0.636264	+	0.771472i	$0.719521\pi$
$60$	−1.39065	+	0.764261i	−0.179533	+	0.0986657i
$61$	−1.33165	+	2.22172i	−0.170500	+	0.284462i	−0.931104	−	0.364754i	$-0.881153\pi$
$61$	−1.33165	+	2.22172i	−0.170500	+	0.284462i	0.760604	+	0.649216i	$0.224903\pi$
$62$	−10.5408	−	0.456363i	−1.33869	−	0.0579581i
$63$	−0.582709	−	0.582709i	−0.0734144	−	0.0734144i
$64$	−4.01518	−	6.91942i	−0.501898	−	0.864927i
$65$	1.16376	−	1.16376i	0.144347	−	0.144347i
$66$	0.915419	−	0.839443i	0.112680	−	0.103328i
$67$	7.38813	+	4.42827i	0.902603	+	0.541000i	0.888488	−	0.458901i	$-0.151757\pi$
$67$	7.38813	+	4.42827i	0.902603	+	0.541000i	0.0141157	+	0.999900i	$0.495507\pi$
$68$	3.44149	−	4.29444i	0.417342	−	0.520777i
$69$	−0.381669	+	0.136563i	−0.0459475	+	0.0164403i
$70$	0.239240	+	1.16720i	0.0285946	+	0.139507i
$71$	6.65865	−	12.4575i	0.790237	−	1.47843i	−0.0858667	−	0.996307i	$-0.527366\pi$
$71$	6.65865	−	12.4575i	0.790237	−	1.47843i	0.876104	−	0.482123i	$-0.160134\pi$
$72$	−0.262057	+	8.28268i	−0.0308837	+	0.976124i
$73$	3.77761	−	12.4531i	0.442136	−	1.45753i	−0.399124	−	0.916897i	$-0.630686\pi$
$73$	3.77761	−	12.4531i	0.442136	−	1.45753i	0.841260	−	0.540630i	$-0.181814\pi$
$74$	2.52211	+	8.14336i	0.293189	+	0.946647i
$75$	−0.845053	−	0.626734i	−0.0975784	−	0.0723690i
$76$	−7.43228	−	0.278456i	−0.852542	−	0.0319411i
$77$	−0.398730	−	0.843043i	−0.0454395	−	0.0960737i
$78$	0.0511737	+	0.199367i	0.00579428	+	0.0225739i
$79$	1.45324	+	2.17492i	0.163502	+	0.244698i	0.904170	−	0.427174i	$-0.140491\pi$
$79$	1.45324	+	2.17492i	0.163502	+	0.244698i	−0.740668	+	0.671872i	$0.765491\pi$
$80$	6.91130	−	9.78696i	0.772707	−	1.09422i
$81$	4.65204	−	6.96227i	0.516893	−	0.773585i
$82$	−2.98086	+	8.48633i	−0.329181	+	0.937158i
$83$	−0.239487	−	4.87486i	−0.0262871	−	0.535086i	−0.975439	−	0.220268i	$-0.929307\pi$
$83$	−0.239487	−	4.87486i	−0.0262871	−	0.535086i	0.949152	−	0.314817i	$-0.101943\pi$
$84$	−0.140872	−	0.0485630i	−0.0153704	−	0.00529866i
$85$	7.99502	+	2.00265i	0.867182	+	0.217218i
$86$	0.996455	+	9.54724i	0.107450	+	1.02951i
$87$	0.299288	+	0.245619i	0.0320870	+	0.0263331i
$88$	−3.43698	+	8.72543i	−0.366384	+	0.930134i
$89$	18.7205	+	1.84381i	1.98437	+	0.195443i	0.999790	+	0.0204934i	$0.00652370\pi$
$89$	18.7205	+	1.84381i	1.98437	+	0.195443i	0.984577	+	0.174950i	$0.0559763\pi$
$90$	−11.4383	+	4.81607i	−1.20570	+	0.507658i
$91$	0.154361	+	0.00758326i	0.0161814	+	0.000794942i
$92$	2.13890	−	2.18928i	0.222996	−	0.228248i
$93$	1.95477	+	0.289963i	0.202700	+	0.0300678i
$94$	−4.52810	−	1.10627i	−0.467038	−	0.114103i
$95$	−4.26265	−	10.2909i	−0.437338	−	1.05583i
$96$	0.613451	+	1.36708i	0.0626101	+	0.139527i
$97$	−3.53802	+	8.54153i	−0.359231	+	0.867261i	0.636177	+	0.771543i	$0.280515\pi$
$97$	−3.53802	+	8.54153i	−0.359231	+	0.867261i	−0.995408	+	0.0957182i	$0.969485\pi$
$98$	5.78462	−	7.89528i	0.584335	−	0.797544i
$99$	7.80251	−	5.78674i	0.784182	−	0.581589i
$100$	7.80870	+	1.45898i	0.780870	+	0.145898i
$101$	1.65509	+	1.82612i	0.164688	+	0.181705i	0.817704	−	0.575639i	$-0.195247\pi$
$101$	1.65509	+	1.82612i	0.164688	+	0.181705i	−0.653016	+	0.757344i	$0.726497\pi$
$102$	−0.724612	+	0.733095i	−0.0717473	+	0.0725873i
$103$	−10.7522	+	8.82406i	−1.05944	+	0.869461i	−0.991743	−	0.128245i	$-0.959066\pi$
$103$	−10.7522	+	8.82406i	−1.05944	+	0.869461i	−0.0676987	+	0.997706i	$0.521566\pi$
$104$	−1.00674	−	1.18395i	−0.0987191	−	0.116096i
$105$	−0.0218738	−	0.222088i	−0.00213466	−	0.0216736i
$106$	−2.70956	+	9.12302i	−0.263176	+	0.886106i
$107$	−0.0362564	+	0.0217312i	−0.00350503	+	0.00210084i	−0.515854	−	0.856676i	$-0.672525\pi$
$107$	−0.0362564	+	0.0217312i	−0.00350503	+	0.00210084i	0.512349	+	0.858777i	$0.328775\pi$
$108$	0.424747	−	3.11259i	0.0408713	−	0.299510i
$109$	−4.09651	+	4.51980i	−0.392374	+	0.432918i	−0.904815	−	0.425804i	$-0.859991\pi$
$109$	−4.09651	+	4.51980i	−0.392374	+	0.432918i	0.512441	+	0.858722i	$0.328741\pi$
$110$	−14.0238	+	0.770779i	−1.33712	+	0.0734909i
$111$	−0.311509	−	1.56606i	−0.0295671	−	0.148644i
$112$	1.11679	−	0.136309i	0.105527	−	0.0128800i
$113$	3.07235	−	15.4457i	0.289022	−	1.45301i	−0.514373	−	0.857566i	$-0.671975\pi$
$113$	3.07235	−	15.4457i	0.289022	−	1.45301i	0.803395	−	0.595446i	$-0.203025\pi$
$114$	1.37914	+	0.196381i	0.129169	+	0.0183928i
$115$	4.31592	+	1.54426i	0.402461	+	0.144003i
$116$	−2.84379	−	0.677258i	−0.264040	−	0.0628818i
$117$	0.236211	+	1.59241i	0.0218378	+	0.147218i
$118$	7.10692	+	8.55776i	0.654245	+	0.787805i
$119$	0.364839	+	0.682566i	0.0334447	+	0.0625707i
$120$	−1.47779	+	1.68883i	−0.134903	+	0.154169i
$121$	−0.00645337	+	0.00195761i	−0.000586670	+	0.000177964i
$122$	−0.693724	+	3.59686i	−0.0628068	+	0.325644i
$123$	0.720305	−	1.52296i	0.0649477	−	0.137320i
$124$	−14.2271	+	4.49721i	−1.27763	+	0.403861i
$125$	−0.748242	−	2.98715i	−0.0669248	−	0.267179i
$126$	−1.05641	−	0.492141i	−0.0941122	−	0.0438434i
$127$		−	18.1104i		−	1.60703i	−0.595281	−	0.803517i	$-0.702959\pi$
$127$		−	18.1104i		−	1.60703i	0.595281	−	0.803517i	$-0.297041\pi$
$128$	−8.68538	−	7.25012i	−0.767686	−	0.640826i
$129$		−	1.79793i		−	0.158299i
$130$	0.982885	−	2.10982i	0.0862047	−	0.185043i
$131$	−0.617672	−	2.46588i	−0.0539662	−	0.215445i	0.937048	−	0.349200i	$-0.113547\pi$
$131$	−0.617672	−	2.46588i	−0.0539662	−	0.215445i	−0.991014	+	0.133755i	$0.957297\pi$
$132$	0.809925	−	1.55863i	0.0704949	−	0.135661i
$133$	0.447211	−	0.945548i	0.0387781	−	0.0819894i
$134$	11.9610	+	2.30692i	1.03328	+	0.199287i
$135$	4.50222	−	1.36573i	0.387489	−	0.117544i
$136$	2.49362	−	7.37252i	0.213826	−	0.632188i
$137$	−1.66755	−	3.11977i	−0.142469	−	0.266540i	0.800559	−	0.599254i	$-0.204536\pi$
$137$	−1.66755	−	3.11977i	−0.142469	−	0.266540i	−0.943028	+	0.332713i	$0.892036\pi$
$138$	−0.441022	+	0.366253i	−0.0375423	+	0.0311775i
$139$	2.56570	+	17.2965i	0.217620	+	1.46707i	0.772432	+	0.635098i	$0.219040\pi$
$139$	2.56570	+	17.2965i	0.217620	+	1.46707i	−0.554812	+	0.831976i	$0.687210\pi$
$140$	0.883018	+	1.43508i	0.0746286	+	0.121286i
$141$	0.822029	+	0.294127i	0.0692274	+	0.0247699i
$142$	2.81609	−	19.7768i	0.236321	−	1.65963i
$143$	−0.355415	+	1.78679i	−0.0297213	+	0.149419i
$144$	3.66206	+	11.1325i	0.305172	+	0.927708i
$145$	−0.854134	−	4.29402i	−0.0709319	−	0.356599i
$146$	−1.00999	−	18.3761i	−0.0835875	−	1.52082i
$147$	−1.23113	+	1.35834i	−0.101541	+	0.112034i
$148$	7.29406	+	9.59934i	0.599568	+	0.789061i
$149$	13.0771	−	7.83812i	1.07132	−	0.642124i	0.134137	−	0.990963i	$-0.457174\pi$
$149$	13.0771	−	7.83812i	1.07132	−	0.642124i	0.937183	+	0.348839i	$0.113424\pi$
$150$	−1.42631	−	0.423619i	−0.116458	−	0.0345883i
$151$	1.42732	+	14.4918i	0.116153	+	1.17933i	0.859756	+	0.510704i	$0.170615\pi$
$151$	1.42732	+	14.4918i	0.116153	+	1.17933i	−0.743603	+	0.668621i	$0.766885\pi$
$152$	−10.0105	+	3.22853i	−0.811956	+	0.261868i
$153$	−6.23190	+	5.11438i	−0.503819	+	0.413473i
$154$	−0.937992	−	0.927138i	−0.0755856	−	0.0747109i
$155$	−15.0070	−	16.5576i	−1.20539	−	1.32994i
$156$	0.164526	+	0.240132i	0.0131726	+	0.0192259i
$157$	−14.5231	+	10.7711i	−1.15907	+	0.859627i	−0.991990	−	0.126316i	$-0.959685\pi$
$157$	−14.5231	+	10.7711i	−1.15907	+	0.859627i	−0.167082	+	0.985943i	$0.553435\pi$
$158$	2.98403	+	2.18631i	0.237397	+	0.173933i
$159$	0.682144	−	1.64684i	0.0540975	−	0.130603i
$160$	4.44478	−	16.3507i	0.351391	−	1.29264i
$161$	0.164722	+	0.397675i	0.0129819	+	0.0313412i
$162$	2.81044	−	11.5035i	0.220809	−	0.903801i
$163$	22.2738	+	3.30401i	1.74462	+	0.258790i	0.941497	−	0.337023i	$-0.109420\pi$
$163$	22.2738	+	3.30401i	1.74462	+	0.258790i	0.803124	+	0.595813i	$0.203170\pi$
$164$	0.148051	+	12.7195i	0.0115608	+	0.993223i
$165$	2.62748	+	0.129080i	0.204549	+	0.0100488i
$166$	−2.67851	−	6.36152i	−0.207892	−	0.493749i
$167$	16.4595	+	1.62112i	1.27367	+	0.125446i	0.712157	−	0.702020i	$-0.247718\pi$
$167$	16.4595	+	1.62112i	1.27367	+	0.125446i	0.561516	+	0.827466i	$0.310218\pi$
$168$	−0.210697	+	0.00367889i	−0.0162556	+	0.000283833i
$169$	9.81576	+	8.05558i	0.755058	+	0.619660i
$170$	11.5930	−	1.20997i	0.889144	−	0.0928007i
$171$	10.5688	+	2.64735i	0.808217	+	0.202448i
$172$	5.94658	+	12.2034i	0.453422	+	0.930503i
$173$	−0.660018	−	13.4350i	−0.0501802	−	1.02144i	−0.883435	−	0.468553i	$-0.844775\pi$
$173$	−0.660018	−	13.4350i	−0.0501802	−	1.02144i	0.833255	−	0.552889i	$-0.186475\pi$
$174$	0.516601	+	0.181459i	0.0391634	+	0.0137563i
$175$	−0.620672	+	0.928902i	−0.0469184	+	0.0702184i
$176$	−0.342252	+	13.2580i	−0.0257982	+	0.999360i
$177$	−1.15755	−	1.73240i	−0.0870071	−	0.130215i
$178$	25.7676	−	6.61404i	1.93136	−	0.495743i
$179$	7.51799	+	15.8955i	0.561921	+	1.18808i	0.962365	+	0.271761i	$0.0876059\pi$
$179$	7.51799	+	15.8955i	0.561921	+	1.18808i	−0.400444	+	0.916321i	$0.631144\pi$
$180$	−12.8668	+	11.9375i	−0.959034	+	0.889767i
$181$	−11.1529	−	8.27156i	−0.828989	−	0.614820i	0.0957570	−	0.995405i	$-0.469473\pi$
$181$	−11.1529	−	8.27156i	−0.828989	−	0.614820i	−0.924746	+	0.380584i	$0.875723\pi$
$182$	0.208778	−	0.0646614i	0.0154757	−	0.00479302i
$183$	0.199168	−	0.656569i	0.0147229	−	0.0485350i
$184$	1.78207	−	3.94461i	0.131376	−	0.290800i
$185$	−8.51153	+	15.9240i	−0.625780	+	1.17075i
$186$	2.73779	−	0.561164i	0.200745	−	0.0411465i
$187$	−8.59004	+	3.07357i	−0.628166	+	0.224761i
$188$	−6.55234	+	0.722445i	−0.477879	+	0.0526897i
$189$	0.378942	+	0.227129i	0.0275639	+	0.0165212i
$190$	−10.6466	−	11.6102i	−0.772386	−	0.842293i
$191$	4.55704	−	4.55704i	0.329736	−	0.329736i	−0.522750	−	0.852486i	$-0.675094\pi$
$191$	4.55704	−	4.55704i	0.329736	−	0.329736i	0.852486	+	0.522750i	$0.175094\pi$
$192$	1.47703	+	1.51949i	0.106595	+	0.109660i
$193$	−8.74783	−	8.74783i	−0.629682	−	0.629682i	0.318306	−	0.947988i	$-0.396886\pi$
$193$	−8.74783	−	8.74783i	−0.629682	−	0.629682i	−0.947988	+	0.318306i	$0.896886\pi$
$194$	−0.565542	+	13.0626i	−0.0406035	+	0.937838i
$195$	−0.224123	+	0.373926i	−0.0160498	+	0.0267774i
$196$	3.86362	−	13.2916i	0.275973	−	0.949401i
$197$	−9.18327	−	25.6655i	−0.654281	−	1.82859i	−0.552014	−	0.833835i	$-0.686140\pi$
$197$	−9.18327	−	25.6655i	−0.654281	−	1.82859i	−0.102267	−	0.994757i	$-0.532610\pi$
$198$	7.56578	−	11.4669i	0.537677	−	0.814917i
$199$	12.4817	+	6.67159i	0.884801	+	0.472936i	0.850197	−	0.526465i	$-0.176483\pi$
$199$	12.4817	+	6.67159i	0.884801	+	0.472936i	0.0346045	+	0.999401i	$0.488983\pi$
$200$	11.0822	−	1.84216i	0.783631	−	0.130261i
$201$	−2.18336	−	0.662315i	−0.154002	−	0.0467161i
$202$	3.08337	+	1.62509i	0.216945	+	0.114341i
$203$	0.244905	−	0.330216i	0.0171890	−	0.0231766i
$204$	−0.607881	+	1.32494i	−0.0425602	+	0.0927643i
$205$	−17.2216	+	8.14522i	−1.20281	+	0.568887i
$206$	−10.0145	+	16.9309i	−0.697745	+	1.17963i
$207$	−3.72803	+	2.49099i	−0.259116	+	0.173136i
$208$	−1.91094	−	1.08573i	−0.132500	−	0.0752820i
$209$	10.2520	+	6.85013i	0.709142	+	0.473834i
$210$	−0.136595	−	0.284509i	−0.00942592	−	0.0196330i
$211$	13.2665	−	0.651740i	0.913301	−	0.0448676i	0.413012	−	0.910726i	$-0.364477\pi$
$211$	13.2665	−	0.651740i	0.913301	−	0.0448676i	0.500290	+	0.865858i	$0.333227\pi$
$212$	0.816811	+	13.4341i	0.0560988	+	0.922658i
$213$	−0.909132	+	3.62946i	−0.0622927	+	0.248686i
$214$	−0.0376539	+	0.0464298i	−0.00257397	+	0.00317387i
$215$	−12.8978	+	15.7161i	−0.879625	+	1.07183i
$216$	−0.942659	−	4.34151i	−0.0641398	−	0.295402i
$217$	0.205680	−	2.08830i	0.0139624	−	0.141763i
$218$	−3.25486	+	7.98911i	−0.220447	+	0.541091i
$219$	−0.169139	+	3.44291i	−0.0114294	+	0.232650i
$220$	−18.2609	+	7.81415i	−1.23115	+	0.526830i
$221$	0.221845	−	1.49556i	0.0149229	−	0.100602i
$222$	−1.17217	−	1.93008i	−0.0786706	−	0.129538i
$223$	5.07548	−	2.10233i	0.339879	−	0.140783i	−0.206214	−	0.978507i	$-0.566114\pi$
$223$	5.07548	−	2.10233i	0.339879	−	0.140783i	0.546093	+	0.837724i	$0.316114\pi$
$224$	1.41794	−	0.721843i	0.0947400	−	0.0482302i
$225$	−10.7512	−	4.45331i	−0.716750	−	0.296887i
$226$	−3.39606	−	22.0111i	−0.225903	−	1.46415i
$227$	−6.32744	−	8.53157i	−0.419967	−	0.566260i	0.541668	−	0.840593i	$-0.317793\pi$
$227$	−6.32744	−	8.53157i	−0.419967	−	0.566260i	−0.961635	+	0.274333i	$0.911543\pi$
$228$	1.92762	−	0.406806i	0.127660	−	0.0269414i
$229$	−18.1066	+	16.4108i	−1.19652	+	1.08446i	−0.202053	+	0.979375i	$0.564761\pi$
$229$	−18.1066	+	16.4108i	−1.19652	+	1.08446i	−0.994463	+	0.105084i	$0.966489\pi$
$230$	6.48246	−	0.0377258i	0.427441	−	0.00248756i
$231$	0.156712	+	0.190954i	0.0103109	+	0.0125638i
$232$	−4.10660	+	0.476989i	−0.269612	+	0.0313158i
$233$	−15.1730	+	1.49441i	−0.994016	+	0.0979021i	−0.581927	−	0.813241i	$-0.697701\pi$
$233$	−15.1730	+	1.49441i	−0.994016	+	0.0979021i	−0.412090	+	0.911143i	$0.635201\pi$
$234$	1.08487	+	2.00154i	0.0709202	+	0.130845i
$235$	−5.07555	−	8.46804i	−0.331092	−	0.552394i
$236$	13.5868	+	7.93012i	0.884423	+	0.516207i
$237$	−0.513385	−	0.465305i	−0.0333480	−	0.0302248i
$238$	0.815261	+	0.730313i	0.0528455	+	0.0473392i
$239$	10.3722	−	2.06316i	0.670921	−	0.133454i	0.152136	−	0.988359i	$-0.451385\pi$
$239$	10.3722	−	2.06316i	0.670921	−	0.133454i	0.518785	+	0.854905i	$0.326385\pi$
$240$	−1.14593	+	2.95954i	−0.0739692	+	0.191038i
$241$	−18.7370	−	3.72702i	−1.20696	−	0.240079i	−0.449690	−	0.893184i	$-0.648466\pi$
$241$	−18.7370	−	3.72702i	−1.20696	−	0.240079i	−0.757267	+	0.653106i	$0.773466\pi$
$242$	−0.00762709	+	0.00572574i	−0.000490288	+	0.000368064i
$243$	−2.33470	+	6.52505i	−0.149771	+	0.418582i
$244$	0.819724	+	5.11520i	0.0524774	+	0.327467i
$245$	20.5059	−	3.04176i	1.31007	−	0.194331i
$246$	0.219727	−	2.37238i	0.0140093	−	0.151258i
$247$	−1.80204	+	0.963210i	−0.114661	+	0.0612876i
$248$	−16.7268	+	12.8641i	−1.06215	+	0.816868i
$249$	0.375289	+	1.23716i	0.0237830	+	0.0784020i
$250$	−2.44053	−	3.60689i	−0.154353	−	0.228120i
$251$	−13.9802	−	6.61212i	−0.882420	−	0.417353i	−0.0680378	−	0.997683i	$-0.521674\pi$
$251$	−13.9802	−	6.61212i	−0.882420	−	0.417353i	−0.814382	+	0.580329i	$0.802924\pi$
$252$	−1.64198	−	0.142446i	−0.103435	−	0.00897323i
$253$	−4.92197	+	1.23289i	−0.309441	+	0.0775110i
$254$	−8.76859	−	24.0641i	−0.550190	−	1.50992i
$255$	−2.18318			−0.136716
$256$	−15.0510	−	5.42834i	−0.940689	−	0.339271i
$257$	15.6460			0.975973			0.487987	−	0.872851i	$-0.337731\pi$
$257$	15.6460			0.975973			0.487987	+	0.872851i	$0.337731\pi$
$258$	−0.870512	−	2.38899i	−0.0541957	−	0.148732i
$259$	−1.64470	+	0.411977i	−0.102197	+	0.0255990i
$260$	0.284487	−	3.27930i	0.0176431	−	0.203374i
$261$	3.87128	+	1.83098i	0.239626	+	0.113335i
$262$	−2.01465	−	2.97748i	−0.124466	−	0.183949i
$263$	3.11908	+	10.2822i	0.192331	+	0.634030i	0.999070	+	0.0431220i	$0.0137304\pi$
$263$	3.11908	+	10.2822i	0.192331	+	0.634030i	−0.806739	+	0.590908i	$0.798770\pi$
$264$	0.321536	−	2.46318i	0.0197892	−	0.151598i
$265$	−17.7767	+	9.50187i	−1.09202	+	0.583695i
$266$	0.136420	−	1.47292i	0.00836446	−	0.0903108i
$267$	−4.92883	+	0.731122i	−0.301639	+	0.0447440i
$268$	17.0102	−	2.72592i	1.03906	−	0.166512i
$269$	6.05469	−	16.9217i	0.369161	−	1.03174i	−0.603065	−	0.797692i	$-0.706054\pi$
$269$	6.05469	−	16.9217i	0.369161	−	1.03174i	0.972226	−	0.234044i	$-0.0751959\pi$
$270$	5.32106	−	3.99458i	0.323830	−	0.243102i
$271$	−20.3166	−	4.04122i	−1.23414	−	0.245487i	−0.465434	−	0.885083i	$-0.654102\pi$
$271$	−20.3166	−	4.04122i	−1.23414	−	0.245487i	−0.768711	+	0.639596i	$0.779102\pi$
$272$	−0.256192	−	11.0036i	−0.0155339	−	0.667190i
$273$	−0.0401505	+	0.00798643i	−0.00243002	+	0.000483361i
$274$	−3.72628	−	3.33801i	−0.225113	−	0.201657i
$275$	−9.75782	−	8.84397i	−0.588419	−	0.533312i
$276$	−0.408677	+	0.700190i	−0.0245994	+	0.0421465i
$277$	5.32076	+	8.87715i	0.319694	+	0.533376i	0.975062	−	0.221933i	$-0.0712366\pi$
$277$	5.32076	+	8.87715i	0.319694	+	0.533376i	−0.655368	+	0.755309i	$0.727487\pi$
$278$	11.7837	+	21.7405i	0.706741	+	1.30391i
$279$	21.7527	−	2.14245i	1.30230	−	0.128265i
$280$	1.86814	+	1.47933i	0.111643	+	0.0884066i
$281$	−2.57967	−	3.14334i	−0.153890	−	0.187516i	0.690358	−	0.723468i	$-0.257453\pi$
$281$	−2.57967	−	3.14334i	−0.153890	−	0.187516i	−0.844249	+	0.535952i	$0.819953\pi$
$282$	1.23468	−	0.00718543i	0.0735241	−	0.000427886i
$283$	−23.4777	+	21.2789i	−1.39560	+	1.26490i	−0.471972	+	0.881614i	$0.656458\pi$
$283$	−23.4777	+	21.2789i	−1.39560	+	1.26490i	−0.923630	+	0.383286i	$0.874792\pi$
$284$	−5.83356	−	27.6419i	−0.346158	−	1.64024i
$285$	1.75761	+	2.36987i	0.104112	+	0.140379i
$286$	0.392863	+	2.54628i	0.0232305	+	0.150565i
$287$	−1.65275	−	0.684591i	−0.0975586	−	0.0404101i
$288$	10.2560	+	13.0192i	0.604343	+	0.767164i
$289$	−8.71078	+	3.60812i	−0.512399	+	0.212243i
$290$	−3.21399	−	5.29212i	−0.188732	−	0.310764i
$291$	0.359333	−	2.42243i	0.0210645	−	0.142005i
$292$	−10.2393	−	23.9282i	−0.599208	−	1.40029i
$293$	−0.264648	+	5.38704i	−0.0154609	+	0.314714i	0.978592	+	0.205812i	$0.0659836\pi$
$293$	−0.264648	+	5.38704i	−0.0154609	+	0.314714i	−0.994052	+	0.108902i	$0.965266\pi$
$294$	−0.978183	+	2.40097i	−0.0570488	+	0.140027i
$295$	−2.30936	+	23.4473i	−0.134456	+	1.36515i
$296$	14.3397	+	9.22352i	0.833480	+	0.536106i
$297$	−3.30385	+	4.02576i	−0.191709	+	0.233598i
$298$	13.5812	−	16.7465i	0.786737	−	0.970100i
$299$	0.204314	−	0.815667i	0.0118158	−	0.0471712i
$300$	−2.10032	+	0.127702i	−0.121262	+	0.00737289i
$301$	−1.90685	+	0.0936773i	−0.109909	+	0.00539947i
$302$	8.91312	+	18.5649i	0.512892	+	1.06829i
$303$	−0.542802	−	0.362689i	−0.0311832	−	0.0208359i
$304$	−11.7382	+	9.13672i	−0.673233	+	0.524027i
$305$	−6.45102	+	4.31043i	−0.369384	+	0.246815i
$306$	−5.80437	+	9.81306i	−0.331814	+	0.560975i
$307$	−12.4224	+	5.87534i	−0.708982	+	0.335324i	−0.747801	−	0.663923i	$-0.768890\pi$
$307$	−12.4224	+	5.87534i	−0.708982	+	0.335324i	0.0388190	+	0.999246i	$0.487640\pi$
$308$	−1.69525	−	0.777781i	−0.0965960	−	0.0443182i
$309$	2.19479	−	2.95934i	0.124857	−	0.168351i
$310$	−27.9573	−	14.7349i	−1.58787	−	0.836888i
$311$	−20.7509	−	6.29471i	−1.17667	−	0.356940i	−0.359397	−	0.933185i	$-0.617017\pi$
$311$	−20.7509	−	6.29471i	−1.17667	−	0.356940i	−0.817277	+	0.576245i	$0.804517\pi$
$312$	0.334879	+	0.239416i	0.0189588	+	0.0135542i
$313$	4.53755	+	2.42537i	0.256478	+	0.137090i	0.594625	−	0.804003i	$-0.297300\pi$
$313$	4.53755	+	2.42537i	0.256478	+	0.137090i	−0.338148	+	0.941093i	$0.609800\pi$
$314$	−14.0825	+	21.3438i	−0.794722	+	1.20450i
$315$	−0.831567	−	2.32407i	−0.0468535	−	0.130947i
$316$	5.02359	+	1.46026i	0.282599	+	0.0821460i
$317$	−13.2376	+	22.0857i	−0.743500	+	1.24045i	0.220717	+	0.975338i	$0.429160\pi$
$317$	−13.2376	+	22.0857i	−0.743500	+	1.24045i	−0.964216	+	0.265116i	$0.914590\pi$
$318$	0.109039	−	2.51852i	0.00611458	−	0.141231i
$319$	3.42685	+	3.42685i	0.191867	+	0.191867i
$320$	−2.01061	−	23.8780i	−0.112396	−	1.33482i
$321$	0.00791727	−	0.00791727i	0.000441899	−	0.000441899i
$322$	0.411419	+	0.448656i	0.0229275	+	0.0250026i
$323$	−8.77684	−	5.26064i	−0.488357	−	0.292710i
$324$	−1.83535	−	16.6460i	−0.101964	−	0.924779i
$325$	2.05484	−	0.735233i	0.113982	−	0.0407834i
$326$	31.1960	−	6.39423i	1.72779	−	0.354144i
$327$	0.761680	−	1.42500i	0.0421210	−	0.0788029i
$328$	6.35517	+	16.8293i	0.350905	+	0.929242i
$329$	0.269115	−	0.887153i	0.0148368	−	0.0489103i
$330$	3.55375	−	1.10064i	0.195628	−	0.0605885i
$331$	21.2819	+	15.7838i	1.16976	+	0.867554i	0.993164	−	0.116729i	$-0.0372409\pi$
$331$	21.2819	+	15.7838i	1.16976	+	0.867554i	0.176597	+	0.984283i	$0.443491\pi$
$332$	−6.63915	−	7.15599i	−0.364371	−	0.392736i
$333$	−7.55117	−	15.9656i	−0.413801	−	0.874909i
$334$	22.6554	−	5.81522i	1.23965	−	0.318194i
$335$	14.3340	+	21.4523i	0.783147	+	1.17206i
$336$	−0.278182	+	0.106903i	−0.0151761	+	0.00583202i
$337$	7.83485	−	11.7257i	0.426792	−	0.638739i	−0.554292	−	0.832322i	$-0.687011\pi$
$337$	7.83485	−	11.7257i	0.426792	−	0.638739i	0.981084	+	0.193583i	$0.0620110\pi$
$338$	16.9430	+	5.95131i	0.921577	+	0.323708i
$339$	0.204685	+	4.16646i	0.0111170	+	0.226291i
$340$	14.8184	−	7.22080i	0.803639	−	0.391603i
$341$	23.9947	+	6.01035i	1.29938	+	0.325479i
$342$	15.3251	−	1.59949i	0.828685	−	0.0864906i
$343$	3.02674	+	2.48398i	0.163429	+	0.134123i
$344$	13.8101	+	13.3361i	0.744591	+	0.719035i
$345$	−1.20835	−	0.119012i	−0.0650553	−	0.00640739i
$346$	−7.38188	−	17.5322i	−0.396852	−	0.942534i
$347$	7.99296	+	0.392669i	0.429085	+	0.0210796i	0.262465	−	0.964942i	$-0.415465\pi$
$347$	7.99296	+	0.392669i	0.429085	+	0.0210796i	0.166620	+	0.986021i	$0.446715\pi$
$348$	0.774291	−	0.00901254i	0.0415064	−	0.000483123i
$349$	10.2145	+	1.51518i	0.546772	+	0.0811060i	0.414401	−	0.910094i	$-0.363991\pi$
$349$	10.2145	+	1.51518i	0.546772	+	0.0811060i	0.132371	+	0.991200i	$0.457741\pi$
$350$	−0.374967	+	1.53479i	−0.0200428	+	0.0820381i
$351$	−0.330275	−	0.797355i	−0.0176288	−	0.0425597i
$352$	5.96443	+	17.7823i	0.317905	+	0.947799i
$353$	−3.02856	+	7.31160i	−0.161194	+	0.389157i	−0.983754	−	0.179521i	$-0.942545\pi$
$353$	−3.02856	+	7.31160i	−0.161194	+	0.389157i	0.822560	+	0.568678i	$0.192545\pi$
$354$	−2.37689	−	1.74147i	−0.126330	−	0.0925581i
$355$	33.9837	−	25.2040i	1.80367	−	1.33769i
$356$	31.0363	−	21.2644i	1.64492	−	1.12701i
$357$	−0.137675	−	0.151901i	−0.00728654	−	0.00803945i
$358$	17.6857	+	17.4810i	0.934719	+	0.923902i
$359$	4.85347	−	3.98314i	0.256156	−	0.210222i	−0.497547	−	0.867437i	$-0.665766\pi$
$359$	4.85347	−	3.98314i	0.256156	−	0.210222i	0.753703	+	0.657215i	$0.228266\pi$
$360$	−11.3169	+	22.0917i	−0.596453	+	1.16433i
$361$	−0.506837	−	5.14600i	−0.0266756	−	0.270842i
$362$	−18.8243	−	5.59087i	−0.989383	−	0.293850i
$363$	0.00153217		0.000918350i	8.04183e−5		4.82009e-5i
$364$	0.246107	−	0.187004i	0.0128995	−	0.00980168i
$365$	26.1770	−	28.8819i	1.37017	−	1.51175i
$366$	−0.0532500	−	0.968848i	−0.00278342	−	0.0506425i
$367$	−1.42131	−	7.14539i	−0.0741916	−	0.372986i	0.925796	−	0.378024i	$-0.123396\pi$
$367$	−1.42131	−	7.14539i	−0.0741916	−	0.372986i	−0.999987	+	0.00503781i	$0.998396\pi$
$368$	0.458041	−	6.10422i	0.0238770	−	0.318205i
$369$	3.63536	−	18.2762i	0.189249	−	0.951420i
$370$	−3.59971	+	25.2800i	−0.187140	+	1.31425i
$371$	−1.78215	−	0.637663i	−0.0925245	−	0.0331058i
$372$	3.36614	−	2.07122i	0.174526	−	0.107388i
$373$	−0.215676	−	1.45397i	−0.0111673	−	0.0752837i	0.982876	−	0.184266i	$-0.0589908\pi$
$373$	−0.215676	−	1.45397i	−0.0111673	−	0.0752837i	−0.994044	+	0.108982i	$0.965241\pi$
$374$	−9.92587	+	8.24308i	−0.513254	+	0.426240i
$375$	0.384516	+	0.719378i	0.0198563	+	0.0371485i
$376$	−8.35663	+	4.13243i	−0.430960	+	0.213114i
$377$	−0.768546	+	0.233136i	−0.0395821	+	0.0120071i
$378$	0.613488	+	0.118323i	0.0315544	+	0.00608589i
$379$	10.5880	−	22.3865i	0.543870	−	1.14992i	−0.425646	−	0.904890i	$-0.639953\pi$
$379$	10.5880	−	22.3865i	0.543870	−	1.14992i	0.969516	−	0.245027i	$-0.0787967\pi$
$380$	−19.7680	−	10.2722i	−1.01408	−	0.526954i
$381$	1.16561	+	4.65339i	0.0597162	+	0.238400i
$382$	3.84875	−	8.26156i	0.196919	−	0.422698i
$383$			13.4306i			0.686273i	0.939286	+	0.343136i	$0.111489\pi$
$383$			13.4306i			0.686273i	−0.939286	+	0.343136i	$0.888511\pi$
$384$	2.69830	+	1.30388i	0.137697	+	0.0665386i
$385$		−	2.79337i		−	0.142364i
$386$	−15.8591	−	7.38819i	−0.807209	−	0.376049i
$387$	−4.83203	−	19.2906i	−0.245626	−	0.980594i
$388$	5.57311	+	17.6307i	0.282932	+	0.895064i
$389$	−5.32233	+	11.2531i	−0.269853	+	0.570556i	−0.992722	−	0.120429i	$-0.961573\pi$
$389$	−5.32233	+	11.2531i	−0.269853	+	0.570556i	0.722869	+	0.690985i	$0.242823\pi$
$390$	−0.116757	+	0.605369i	−0.00591223	+	0.0306541i
$391$	4.02964	−	1.22238i	0.203788	−	0.0618183i
$392$	−1.30170	−	19.5319i	−0.0657455	−	0.986510i
$393$	0.317417	+	0.593845i	0.0160116	+	0.0299555i
$394$	−24.6289	−	29.6567i	−1.24078	−	1.49408i
$395$	1.14964	+	7.75022i	0.0578445	+	0.389956i
$396$	4.50104	−	18.8998i	0.226186	−	0.949751i
$397$	−25.8455	−	9.24766i	−1.29715	−	0.464127i	−0.404357	−	0.914601i	$-0.632505\pi$
$397$	−25.8455	−	9.24766i	−1.29715	−	0.464127i	−0.892789	+	0.450474i	$0.851255\pi$
$398$	19.8152	+	2.82156i	0.993247	+	0.141432i
$399$	−0.0540521	+	0.271738i	−0.00270599	+	0.0136039i
$400$	13.8335	−	7.81350i	0.691677	−	0.390675i
$401$	1.30919	+	6.58176i	0.0653780	+	0.328677i	0.999608	−	0.0279934i	$-0.00891175\pi$
$401$	1.30919	+	6.58176i	0.0653780	+	0.328677i	−0.934230	+	0.356671i	$0.883912\pi$
$402$	−3.22182	+	0.177078i	−0.160690	+	0.00883186i
$403$	−2.75288	+	3.03734i	−0.137131	+	0.151300i
$404$	4.88385	+	0.666453i	0.242981	+	0.0331573i
$405$	21.5128	−	12.8943i	1.06898	−	0.640722i
$406$	0.165535	−	0.557352i	0.00821536	−	0.0276609i
$407$	−1.95904	−	19.8905i	−0.0971061	−	0.985935i
$408$	−0.166219	+	2.05483i	−0.00822906	+	0.101729i
$409$	9.74630	−	7.99858i	0.481924	−	0.395504i	−0.361822	−	0.932247i	$-0.617845\pi$
$409$	9.74630	−	7.99858i	0.481924	−	0.395504i	0.843746	+	0.536743i	$0.180345\pi$
$410$	−18.9395	+	19.1612i	−0.935355	+	0.946306i
$411$	0.629265	+	0.694287i	0.0310394	+	0.0342467i
$412$	−5.10927	+	27.3457i	−0.251716	+	1.34723i
$413$	−1.77704	+	1.31794i	−0.0874424	+	0.0648517i
$414$	−3.74754	+	5.11492i	−0.184182	+	0.251385i
$415$	5.59459	−	13.5065i	0.274628	−	0.663009i
$416$	−3.06485	−	0.517435i	−0.150267	−	0.0253693i
$417$	−1.77248	−	4.27915i	−0.0867987	−	0.209551i
$418$	16.9389	+	4.13837i	0.828510	+	0.202414i
$419$	−6.76946	−	1.00415i	−0.330710	−	0.0490561i	−0.0206890	−	0.999786i	$-0.506586\pi$
$419$	−6.76946	−	1.00415i	−0.330710	−	0.0490561i	−0.310021	+	0.950730i	$0.600336\pi$
$420$	−0.319252	−	0.311906i	−0.0155779	−	0.0152194i
$421$	1.13555	+	0.0557861i	0.0553434	+	0.00271885i	0.0767206	−	0.997053i	$-0.475555\pi$
$421$	1.13555	+	0.0557861i	0.0553434	+	0.00271885i	−0.0213771	+	0.999771i	$0.506805\pi$
$422$	17.3122	−	7.28929i	0.842747	−	0.354837i
$423$	9.61031	+	0.946533i	0.467269	+	0.0460220i
$424$	7.58980	+	17.4551i	0.368593	+	0.847693i
$425$	8.44845	+	6.93346i	0.409810	+	0.336322i
$426$	0.549285	+	5.26282i	0.0266130	+	0.254985i
$427$	−0.706721	−	0.177024i	−0.0342006	−	0.00856682i
$428$	−0.0275524	+	0.0799246i	−0.00133180	+	0.00386330i
$429$	−0.0236784	−	0.481985i	−0.00114320	−	0.0232704i
$430$	−9.52867	+	27.1275i	−0.459513	+	1.30820i
$431$	−17.3716	+	25.9984i	−0.836760	+	1.25230i	0.128683	+	0.991686i	$0.458925\pi$
$431$	−17.3716	+	25.9984i	−0.836760	+	1.25230i	−0.965443	+	0.260614i	$0.916075\pi$
$432$	−3.35461	−	5.31237i	−0.161399	−	0.255591i
$433$	4.98892	+	7.46644i	0.239752	+	0.358814i	0.931759	−	0.363076i	$-0.118274\pi$
$433$	4.98892	+	7.46644i	0.239752	+	0.358814i	−0.692008	+	0.721890i	$0.743274\pi$
$434$	−0.737807	−	2.87441i	−0.0354159	−	0.137976i
$435$	0.495836	+	1.04836i	0.0237735	+	0.0502649i
$436$	−0.456761	+	12.1914i	−0.0218749	+	0.583864i
$437$	−4.57103	−	3.39011i	−0.218662	−	0.162171i
$438$	1.44223	+	4.65666i	0.0689124	+	0.222504i
$439$	11.5033	−	37.9215i	0.549025	−	1.80989i	−0.0366263	−	0.999329i	$-0.511661\pi$
$439$	11.5033	−	37.9215i	0.549025	−	1.80989i	0.585651	−	0.810563i	$-0.300839\pi$
$440$	−20.4808	+	19.2245i	−0.976382	+	0.916494i
$441$	−9.55854	+	17.8828i	−0.455169	+	0.851561i
$442$	−0.429335	−	2.09463i	−0.0204214	−	0.0996314i
$443$	12.5098	−	4.47607i	0.594358	−	0.212665i	−0.0224900	−	0.999747i	$-0.507159\pi$
$443$	12.5098	−	4.47607i	0.594358	−	0.212665i	0.616848	+	0.787082i	$0.288409\pi$
$444$	−2.49201	−	1.99706i	−0.118266	−	0.0947761i
$445$	48.3288	+	28.9672i	2.29100	+	1.37317i
$446$	5.72615	−	5.25090i	0.271141	−	0.248637i
$447$	−2.85564	+	2.85564i	−0.135067	+	0.135067i
$448$	1.53459	−	1.64568i	0.0725024	−	0.0777510i
$449$	25.4923	+	25.4923i	1.20306	+	1.20306i	0.973232	+	0.229823i	$0.0738147\pi$
$449$	25.4923	+	25.4923i	1.20306	+	1.20306i	0.229823	+	0.973232i	$0.426185\pi$
$450$	−16.4419	−	0.711848i	−0.775078	−	0.0335569i
$451$	10.8413	−	18.0876i	0.510497	−	0.851712i
$452$	−15.1697	−	27.6029i	−0.713524	−	1.29833i
$453$	−1.29946	−	3.63175i	−0.0610539	−	0.170634i
$454$	−12.5384	−	8.27272i	−0.588454	−	0.388258i
$455$	0.408256	+	0.218218i	0.0191394	+	0.0102302i
$456$	2.36436	−	1.47385i	0.110721	−	0.0690193i
$457$	−15.4213	−	4.67799i	−0.721376	−	0.218827i	−0.0918130	−	0.995776i	$-0.529266\pi$
$457$	−15.4213	−	4.67799i	−0.721376	−	0.218827i	−0.629563	+	0.776949i	$0.716766\pi$
$458$	−16.1134	+	30.5726i	−0.752929	+	1.42857i
$459$	2.57465	−	3.47151i	0.120174	−	0.162036i
$460$	8.59530	−	3.18877i	0.400758	−	0.148677i
$461$	6.40516	−	3.02942i	0.298318	−	0.141094i	−0.272536	−	0.962146i	$-0.587862\pi$
$461$	6.40516	−	3.02942i	0.298318	−	0.141094i	0.570854	+	0.821052i	$0.306612\pi$
$462$	0.300686	+	0.177854i	0.0139892	+	0.00827450i
$463$	−18.9544	+	12.6650i	−0.880888	+	0.588590i	−0.911664	−	0.410936i	$-0.865202\pi$
$463$	−18.9544	+	12.6650i	−0.880888	+	0.588590i	0.0307765	+	0.999526i	$0.490202\pi$
$464$	−5.22570	+	2.62211i	−0.242597	+	0.121729i
$465$	4.92166	+	3.28855i	0.228236	+	0.152503i
$466$	−19.4376	+	9.33209i	−0.900428	+	0.432301i
$467$	−24.9009	+	1.22330i	−1.15228	+	0.0566078i	−0.616221	−	0.787574i	$-0.711337\pi$
$467$	−24.9009	+	1.22330i	−1.15228	+	0.0566078i	−0.536058	+	0.844181i	$0.680087\pi$
$468$	2.41062	+	2.13428i	0.111431	+	0.0986572i
$469$	−0.588679	+	2.35014i	−0.0271827	+	0.108519i
$470$	−10.8441	−	8.79445i	−0.500203	−	0.405658i
$471$	3.03842	−	3.70232i	0.140003	−	0.170594i
$472$	21.8930	+	3.95877i	1.00771	+	0.182217i
$473$	2.20588	−	22.3966i	0.101426	−	1.02980i
$474$	−0.907450	−	0.369706i	−0.0416806	−	0.0169811i
$475$	0.724757	−	14.7528i	0.0332541	−	0.676903i
$476$	1.43688	+	0.575674i	0.0658591	+	0.0263860i
$477$	2.89297	−	19.5028i	0.132460	−	0.892972i
$478$	12.7831	−	7.76337i	0.584686	−	0.355088i
$479$	8.85448	−	3.66765i	0.404572	−	0.167579i	−0.171112	−	0.985252i	$-0.554736\pi$
$479$	8.85448	−	3.66765i	0.404572	−	0.167579i	0.575684	+	0.817673i	$0.304736\pi$
$480$	−0.0897107	+	4.48732i	−0.00409471	+	0.204817i
$481$	3.06007	+	1.26752i	0.139527	+	0.0577940i
$482$	−26.7013	+	4.11972i	−1.21621	+	0.187648i
$483$	−0.0679198	−	0.0915793i	−0.00309046	−	0.00416700i
$484$	−0.00736223	+	0.0113009i	−0.000334647	+	0.000513678i
$485$	−20.5188	+	18.5972i	−0.931712	+	0.844455i
$486$	0.0570360	+	9.80056i	0.00258721	+	0.444562i
$487$	6.25355	+	7.61997i	0.283375	+	0.345294i	0.895172	−	0.445721i	$-0.147053\pi$
$487$	6.25355	+	7.61997i	0.283375	+	0.345294i	−0.611796	+	0.791015i	$0.709553\pi$
$488$	3.56586	+	6.39993i	0.161419	+	0.289711i
$489$	−5.93582	+	0.584627i	−0.268427	+	0.0264378i
$490$	25.7744	−	13.9702i	1.16437	−	0.631108i
$491$	−12.8774	−	21.4847i	−0.581150	−	0.969591i	−0.998157	−	0.0606874i	$-0.980671\pi$
$491$	−12.8774	−	21.4847i	−0.581150	−	0.969591i	0.417006	−	0.908904i	$-0.363079\pi$
$492$	−0.856686	−	3.25869i	−0.0386224	−	0.146913i
$493$	−2.98008	−	2.70099i	−0.134216	−	0.121646i
$494$	−1.92809	+	2.15237i	−0.0867491	+	0.0968395i
$495$	28.5380	−	5.67655i	1.28269	−	0.255142i
$496$	−15.9972	+	25.1918i	−0.718296	+	1.13114i
$497$	3.89670	+	0.775102i	0.174791	+	0.0347681i
$498$	1.09767	+	1.46217i	0.0491877	+	0.0655216i
$499$	−3.12387	+	8.73064i	−0.139844	+	0.390837i	−0.990963	−	0.134135i	$-0.957174\pi$
$499$	−3.12387	+	8.73064i	−0.139844	+	0.390837i	0.851119	+	0.524972i	$0.175924\pi$
$500$	−4.98922	−	3.61101i	−0.223125	−	0.161489i
$501$	−4.33354	+	0.642820i	−0.193608	+	0.0287191i
$502$	−21.7775	−	2.01701i	−0.971980	−	0.0900234i
$503$	−23.2503	+	12.4275i	−1.03668	+	0.554117i	−0.899723	−	0.436461i	$-0.856232\pi$
$503$	−23.2503	+	12.4275i	−1.03668	+	0.554117i	−0.136956	+	0.990577i	$0.543732\pi$
$504$	−2.25075	+	0.605733i	−0.100256	+	0.0269815i
$505$	2.14292	+	7.06425i	0.0953586	+	0.314355i
$506$	−5.94312	+	4.02129i	−0.264204	+	0.178768i
$507$	−3.04059	−	1.43809i	−0.135037	−	0.0638679i
$508$	−23.3025	−	27.7297i	−1.03388	−	1.23030i
$509$	5.47369	−	1.37109i	0.242617	−	0.0607724i	−0.119764	−	0.992802i	$-0.538214\pi$
$509$	5.47369	−	1.37109i	0.242617	−	0.0607724i	0.362381	+	0.932030i	$0.381964\pi$
$510$	−2.90090	+	1.05704i	−0.128454	+	0.0468067i
$511$	3.66030			0.161922
$512$	−22.6273	+	0.0744221i	−0.999995	+	0.00328902i
$513$	−5.84112			−0.257892
$514$	20.7897	−	7.57543i	0.916993	−	0.334138i
$515$	−40.4146	+	10.1233i	−1.78088	+	0.446087i
$516$	−2.31338	−	2.75289i	−0.101841	−	0.121189i
$517$	9.87909	+	4.67246i	0.434482	+	0.205495i
$518$	−1.98593	+	1.34374i	−0.0872567	+	0.0590405i
$519$	1.03429	+	3.40959i	0.0454001	+	0.149664i
$520$	−1.20975	−	4.49511i	−0.0530509	−	0.197124i
$521$	−14.7129	+	7.86422i	−0.644585	+	0.344538i	−0.761084	−	0.648653i	$-0.775333\pi$
$521$	−14.7129	+	7.86422i	−0.644585	+	0.344538i	0.116499	+	0.993191i	$0.462833\pi$
$522$	6.03047	+	0.558534i	0.263946	+	0.0244464i
$523$	28.6318	−	4.24712i	1.25198	−	0.185714i	0.512379	−	0.858759i	$-0.328764\pi$
$523$	28.6318	−	4.24712i	1.25198	−	0.185714i	0.739601	+	0.673046i	$0.235014\pi$
$524$	−4.11859	−	2.98088i	−0.179921	−	0.130220i
$525$	0.0996937	−	0.278625i	0.00435099	−	0.0121602i
$526$	9.12288	+	12.1523i	0.397777	+	0.529867i
$527$	−20.1341	−	4.00491i	−0.877053	−	0.174457i
$528$	−0.765367	−	3.42862i	−0.0333083	−	0.149212i
$529$	−20.2611	+	4.03018i	−0.880917	+	0.175225i
$530$	−19.0203	+	21.2327i	−0.826188	+	0.922288i
$531$	−17.0757	−	15.4765i	−0.741023	−	0.671624i
$532$	−0.531885	−	2.02320i	−0.0230601	−	0.0877168i
$533$	1.79662	+	2.99747i	0.0778201	+	0.129835i
$534$	−6.19518	+	3.35789i	−0.268092	+	0.145310i
$535$	−0.126003	+	0.0124102i	−0.00544758	+	0.000536540i
$536$	21.2824	−	11.8580i	0.919260	−	0.512186i
$537$	−2.95478	−	3.60040i	−0.127508	−	0.155369i
$538$	−0.147914	−	25.4163i	−0.00637703	−	1.09577i
$539$	−17.0026	+	15.4102i	−0.732352	+	0.663766i
$540$	5.13628	−	7.88412i	0.221030	−	0.339278i
$541$	−5.29594	−	7.14074i	−0.227690	−	0.307005i	0.674558	−	0.738222i	$-0.264334\pi$
$541$	−5.29594	−	7.14074i	−0.227690	−	0.307005i	−0.902248	+	0.431217i	$0.858084\pi$
$542$	−28.9523	+	4.46702i	−1.24361	+	0.191875i
$543$	3.39807	+	1.40753i	0.145825	+	0.0604027i
$544$	−5.66807	−	14.4969i	−0.243017	−	0.621552i
$545$	−16.8806	+	6.99217i	−0.723085	+	0.299512i
$546$	−0.0494831	+	0.0300518i	−0.00211768	+	0.00128610i
$547$	−2.17686	+	14.6752i	−0.0930759	+	0.627467i	0.891567	+	0.452888i	$0.149606\pi$
$547$	−2.17686	+	14.6752i	−0.0930759	+	0.627467i	−0.984643	+	0.174579i	$0.944144\pi$
$548$	−6.56747	−	2.63121i	−0.280548	−	0.112400i
$549$	0.372373	−	7.57982i	0.0158925	−	0.323499i
$550$	−17.2477	−	7.02693i	−0.735446	−	0.299629i
$551$	−0.532778	+	5.40939i	−0.0226971	+	0.230448i
$552$	−0.204014	+	1.12825i	−0.00868341	+	0.0480214i
$553$	−0.466745	+	0.568730i	−0.0198480	+	0.0241849i
$554$	11.3681	+	9.21933i	0.482982	+	0.391692i
$555$	1.16211	−	4.63942i	0.0493290	−	0.196932i
$556$	26.1838	+	23.1823i	1.11044	+	0.983149i
$557$	37.1456	−	1.82484i	1.57391	−	0.0773211i	0.756738	−	0.653718i	$-0.226792\pi$
$557$	37.1456	−	1.82484i	1.57391	−	0.0773211i	0.817170	+	0.576397i	$0.195542\pi$
$558$	27.8666	−	13.3789i	1.17969	−	0.566374i
$559$	3.10098	+	2.07201i	0.131158	+	0.0876367i
$560$	3.19854	+	1.06115i	0.135163	+	0.0448416i
$561$	2.00936	−	1.34261i	0.0848352	−	0.0566850i
$562$	−4.94966	−	2.92770i	−0.208789	−	0.123497i
$563$	−17.0828	+	8.07956i	−0.719954	+	0.340513i	−0.752171	−	0.658968i	$-0.770993\pi$
$563$	−17.0828	+	8.07956i	−0.719954	+	0.340513i	0.0322172	+	0.999481i	$0.489743\pi$
$564$	1.63710	−	0.607349i	0.0689344	−	0.0255740i
$565$	28.0999	−	37.8883i	1.18217	−	1.59397i
$566$	−20.8932	+	39.6416i	−0.878206	+	1.66626i
$567$	2.25379	+	0.683678i	0.0946501	+	0.0287118i
$568$	−21.1349	−	33.9047i	−0.886799	−	1.42261i
$569$	30.3499	+	16.2223i	1.27233	+	0.680076i	0.962646	−	0.270762i	$-0.0872758\pi$
$569$	30.3499	+	16.2223i	1.27233	+	0.680076i	0.309687	+	0.950839i	$0.399776\pi$
$570$	3.48286	+	2.29796i	0.145881	+	0.0962511i
$571$	−6.59125	−	18.4213i	−0.275835	−	0.770908i	−0.996946	−	0.0780886i	$-0.975118\pi$
$571$	−6.59125	−	18.4213i	−0.275835	−	0.770908i	0.721111	−	0.692819i	$-0.243632\pi$
$572$	1.75486	+	3.19316i	0.0733745	+	0.133513i
$573$	−0.877614	+	1.46421i	−0.0366629	+	0.0611683i
$574$	−2.52755	−	0.109430i	−0.105498	−	0.00456751i
$575$	4.29808	+	4.29808i	0.179242	+	0.179242i
$576$	19.9313	+	12.3335i	0.830470	+	0.513898i
$577$	2.44053	−	2.44053i	0.101601	−	0.101601i	−0.654479	−	0.756080i	$-0.727112\pi$
$577$	2.44053	−	2.44053i	0.101601	−	0.101601i	0.756080	+	0.654479i	$0.227112\pi$
$578$	−9.82748	+	9.01184i	−0.408769	+	0.374843i
$579$	2.81074	+	1.68470i	0.116811	+	0.0700135i
$580$	−6.83290	−	5.47577i	−0.283721	−	0.227369i
$581$	1.29256	−	0.462484i	0.0536243	−	0.0191871i
$582$	−0.695415	−	3.39278i	−0.0288259	−	0.140635i
$583$	10.5179	−	19.6776i	0.435608	−	0.814964i
$584$	−25.1909	−	26.8370i	−1.04241	−	1.11052i
$585$	−1.39974	+	4.61432i	−0.0578721	+	0.190779i
$586$	2.25662	+	7.28616i	0.0932201	+	0.300989i
$587$	3.18290	+	2.36060i	0.131372	+	0.0974325i	0.659390	−	0.751801i	$-0.270815\pi$
$587$	3.18290	+	2.36060i	0.131372	+	0.0974325i	−0.528018	+	0.849233i	$0.677065\pi$
$588$	−0.137271	+	3.66390i	−0.00566094	+	0.151097i
$589$	11.8619	+	25.0799i	0.488762	+	1.03340i
$590$	8.28404	+	32.2737i	0.341048	+	1.32869i
$591$	4.01148	+	6.00360i	0.165010	+	0.246955i
$592$	23.5197	+	5.31280i	0.966654	+	0.218355i
$593$	−1.02744	+	1.53768i	−0.0421920	+	0.0631449i	−0.851966	−	0.523597i	$-0.824590\pi$
$593$	−1.02744	+	1.53768i	−0.0421920	+	0.0631449i	0.809774	+	0.586742i	$0.199590\pi$
$594$	−2.44082	+	6.94887i	−0.100148	+	0.285115i
$595$	0.113750	+	2.31544i	0.00466331	+	0.0949239i
$596$	9.93774	−	28.8276i	0.407066	−	1.18082i
$597$	−3.63651	−	0.910898i	−0.148832	−	0.0372806i
$598$	−0.123444	−	1.18274i	−0.00504799	−	0.0483658i
$599$	−17.8664	−	14.6625i	−0.729999	−	0.599095i	0.194220	−	0.980958i	$-0.437783\pi$
$599$	−17.8664	−	14.6625i	−0.729999	−	0.599095i	−0.924219	+	0.381863i	$0.875283\pi$
$600$	−2.72897	+	1.18661i	−0.111410	+	0.0484430i
$601$	16.3037	+	1.60578i	0.665043	+	0.0655010i	0.424905	−	0.905238i	$-0.360307\pi$
$601$	16.3037	+	1.60578i	0.665043	+	0.0655010i	0.240138	+	0.970739i	$0.422807\pi$
$602$	−2.48836	+	1.04772i	−0.101418	+	0.0427019i
$603$	−25.2060	−	1.23829i	−1.02647	−	0.0504272i
$604$	20.8320	+	20.3526i	0.847640	+	0.828135i
$605$	−0.0199811	−	0.00296391i	−0.000812345	−	0.000120500i
$606$	−0.896852	−	0.219111i	−0.0364321	−	0.00890078i
$607$	−8.42150	−	20.3313i	−0.341818	−	0.825222i	−0.997532	−	0.0702125i	$-0.977632\pi$
$607$	−8.42150	−	20.3313i	−0.341818	−	0.825222i	0.655714	−	0.755009i	$-0.272368\pi$
$608$	−11.1734	+	17.8238i	−0.453140	+	0.722849i
$609$	−0.0416742	+	0.100610i	−0.00168872	+	0.00407694i
$610$	−6.48478	+	8.85090i	−0.262561	+	0.358363i
$611$	−1.45464	+	1.07883i	−0.0588484	+	0.0436450i
$612$	−2.96131	+	15.8494i	−0.119704	+	0.640675i
$613$	−8.00806	−	8.83553i	−0.323443	−	0.356864i	0.557424	−	0.830228i	$-0.311790\pi$
$613$	−8.00806	−	8.83553i	−0.323443	−	0.356864i	−0.880867	+	0.473364i	$0.843040\pi$
$614$	−13.6615	+	13.8215i	−0.551334	+	0.557789i
$615$	3.90079	−	3.20129i	0.157295	−	0.129089i
$616$	−2.62915	−	0.212676i	−0.105931	−	0.00856898i
$617$	−0.950550	−	9.65109i	−0.0382677	−	0.388538i	−0.995173	−	0.0981378i	$-0.968711\pi$
$617$	−0.950550	−	9.65109i	−0.0382677	−	0.388538i	0.956905	−	0.290401i	$-0.0937886\pi$
$618$	1.48349	−	4.99488i	0.0596748	−	0.200923i
$619$	−35.6762	+	21.3835i	−1.43395	+	0.859475i	−0.999157	−	0.0410568i	$-0.986928\pi$
$619$	−35.6762	+	21.3835i	−1.43395	+	0.859475i	−0.434790	+	0.900532i	$0.643178\pi$
$620$	−44.2825	−	6.04282i	−1.77843	−	0.242685i
$621$	1.61426	−	1.78106i	0.0647779	−	0.0714714i
$622$	−30.6204	+	1.68297i	−1.22777	+	0.0674809i
$623$	1.03222	+	5.18932i	0.0413550	+	0.207906i
$624$	0.560889	+	0.155983i	0.0224535	+	0.00624433i
$625$	5.67390	−	28.5246i	0.226956	−	1.14099i
$626$	7.20358	+	1.02574i	0.287913	+	0.0409969i
$627$	−3.07508	−	1.10028i	−0.122807	−	0.0439411i
$628$	−8.37798	+	35.1790i	−0.334318	+	1.40379i
$629$	2.43383	+	16.4076i	0.0970432	+	0.654212i
$630$	−2.23020	−	2.68549i	−0.0888534	−	0.106992i
$631$	12.1453	+	22.7222i	0.483497	+	0.904558i	0.998867	+	0.0475908i	$0.0151544\pi$
$631$	12.1453	+	22.7222i	0.483497	+	0.904558i	−0.515370	+	0.856968i	$0.672346\pi$
$632$	7.38211	−	0.491978i	0.293644	−	0.0195698i
$633$	−3.36682	+	1.02131i	−0.133819	+	0.0405936i
$634$	−6.89617	+	35.7556i	−0.273882	+	1.42004i
$635$	23.1933	−	49.0380i	0.920396	−	1.94601i
$636$	−1.07452	−	3.39927i	−0.0426074	−	0.134790i
$637$	−0.923996	−	3.68880i	−0.0366100	−	0.146155i
$638$	6.21263	+	2.89423i	0.245960	+	0.114584i
$639$			41.3850i			1.63717i
$640$	−14.2327	−	30.7544i	−0.562598	−	1.21568i
$641$			36.5837i			1.44497i	0.691386	+	0.722485i	$0.257000\pi$
$641$			36.5837i			1.44497i	−0.691386	+	0.722485i	$0.743000\pi$
$642$	0.00668672	−	0.0143534i	0.000263904	−	0.000566484i
$643$	−1.65156	−	6.59339i	−0.0651311	−	0.260018i	0.928714	−	0.370797i	$-0.120915\pi$
$643$	−1.65156	−	6.59339i	−0.0651311	−	0.260018i	−0.993845	+	0.110779i	$0.964665\pi$
$644$	0.763901	+	0.396952i	0.0301019	+	0.0156421i
$645$	2.30254	−	4.86831i	0.0906623	−	0.191689i
$646$	−14.2093	−	2.74054i	−0.559057	−	0.107825i
$647$	−12.3504	+	3.74644i	−0.485543	+	0.147288i	−0.523559	−	0.851989i	$-0.675396\pi$
$647$	−12.3504	+	3.74644i	−0.485543	+	0.147288i	0.0380165	+	0.999277i	$0.487896\pi$
$648$	−10.4983	−	21.2298i	−0.412413	−	0.833984i
$649$	−12.2941	−	23.0006i	−0.482585	−	0.902853i
$650$	2.37438	−	1.97184i	0.0931310	−	0.0773421i
$651$	0.0815579	+	0.549819i	0.00319651	+	0.0215491i
$652$	38.3558	−	23.6007i	1.50213	−	0.924274i
$653$	−12.7054	−	4.54605i	−0.497200	−	0.177901i	0.0763350	−	0.997082i	$-0.475678\pi$
$653$	−12.7054	−	4.54605i	−0.497200	−	0.177901i	−0.573535	+	0.819181i	$0.694428\pi$
$654$	0.322131	−	2.26226i	0.0125963	−	0.0884613i
$655$	1.48547	−	7.46799i	0.0580423	−	0.291798i
$656$	16.5927	+	19.2849i	0.647838	+	0.752948i
$657$	7.43828	+	37.3947i	0.290195	+	1.45891i
$658$	−0.0719512	−	1.30910i	−0.00280495	−	0.0510341i
$659$	32.0838	−	35.3990i	1.24981	−	1.37895i	0.353550	−	0.935416i	$-0.384974\pi$
$659$	32.0838	−	35.3990i	1.24981	−	1.37895i	0.896257	−	0.443535i	$-0.146276\pi$
$660$	4.18914	−	3.18312i	0.163062	−	0.123903i
$661$	0.0701765	−	0.0420622i	0.00272955	−	0.00163603i	−0.512737	−	0.858546i	$-0.671369\pi$
$661$	0.0701765	−	0.0420622i	0.00272955	−	0.00163603i	0.515467	+	0.856910i	$0.327619\pi$
$662$	35.9205	+	10.6685i	1.39609	+	0.414642i
$663$	0.0392543	+	0.398555i	0.00152451	+	0.0154786i
$664$	−12.2865	−	6.29401i	−0.476809	−	0.244255i
$665$	2.42186	−	1.98757i	0.0939155	−	0.0770745i
$666$	−17.7638	−	17.5582i	−0.688331	−	0.680366i
$667$	−1.50218	−	1.65740i	−0.0581646	−	0.0641747i
$668$	27.2878	−	18.6962i	1.05580	−	0.723376i
$669$	−1.16882	+	0.866853i	−0.0451890	+	0.0335145i
$670$	29.4329	+	21.5646i	1.13709	+	0.833111i
$671$	3.28656	−	7.93447i	0.126876	−	0.306307i
$672$	−0.317875	+	0.276736i	−0.0122623	+	0.0106753i
$673$	8.92188	+	21.5393i	0.343913	+	0.830280i	0.997312	+	0.0732662i	$0.0233423\pi$
$673$	8.92188	+	21.5393i	0.343913	+	0.830280i	−0.653399	+	0.757013i	$0.726658\pi$
$674$	4.73327	−	19.3739i	0.182319	−	0.746256i
$675$	6.17125	+	0.915418i	0.237531	+	0.0352344i
$676$	25.3945	−	0.295585i	0.976710	−	0.0113686i
$677$	9.89341	+	0.486032i	0.380235	+	0.0186797i	0.238288	−	0.971195i	$-0.423414\pi$
$677$	9.89341	+	0.486032i	0.380235	+	0.0186797i	0.141947	+	0.989874i	$0.454664\pi$
$678$	2.28927	+	5.43708i	0.0879190	+	0.208810i
$679$	−2.58790	−	0.254886i	−0.0993145	−	0.00978162i
$680$	16.1938	−	16.7693i	0.621003	−	0.643074i
$681$	2.17492	+	1.78491i	0.0833430	+	0.0683978i
$682$	34.7930	−	3.63137i	1.33229	−	0.139052i
$683$	−10.9045	−	2.73143i	−0.417248	−	0.104515i	0.0286699	−	0.999589i	$-0.490873\pi$
$683$	−10.9045	−	2.73143i	−0.417248	−	0.104515i	−0.445918	+	0.895074i	$0.647123\pi$
$684$	19.5887	−	9.54534i	0.748995	−	0.364975i
$685$	−0.519914	−	10.5831i	−0.0198649	−	0.404359i
$686$	5.22447	+	1.83512i	0.199471	+	0.0700651i
$687$	3.59618	−	5.38207i	0.137203	−	0.205339i
$688$	24.8072	+	11.0338i	0.945765	+	0.420661i
$689$	2.05426	+	3.07442i	0.0782612	+	0.117126i
$690$	−1.66322	+	0.426915i	−0.0633175	+	0.0162524i
$691$	−7.90009	−	16.7033i	−0.300534	−	0.635425i	0.696052	−	0.717991i	$-0.254938\pi$
$691$	−7.90009	−	16.7033i	−0.300534	−	0.635425i	−0.996586	+	0.0825664i	$0.973688\pi$
$692$	−18.2973	−	19.7217i	−0.695559	−	0.749707i
$693$	2.19461	+	1.62763i	0.0833664	+	0.0618287i
$694$	10.8108	−	3.34824i	0.410371	−	0.127097i
$695$	−15.2038	+	50.1202i	−0.576713	+	1.90117i
$696$	1.02448	−	0.386868i	0.0388326	−	0.0146642i
$697$	−8.24985	+	15.4344i	−0.312485	+	0.584619i
$698$	14.3062	−	2.93233i	0.541497	−	0.110990i
$699$	3.80246	−	1.36054i	0.143822	−	0.0514604i
$700$	0.244871	+	2.22090i	0.00925526	+	0.0839422i
$701$	36.2004	+	21.6977i	1.36727	+	0.819510i	0.994122	−	0.108262i	$-0.0345286\pi$
$701$	36.2004	+	21.6977i	1.36727	+	0.819510i	0.373147	+	0.927772i	$0.378279\pi$
$702$	−0.824912	−	0.899574i	−0.0311343	−	0.0339522i
$703$	15.8511	−	15.8511i	0.597837	−	0.597837i
$704$	16.5350	+	20.7404i	0.623185	+	0.781682i
$705$	1.84916	+	1.84916i	0.0696434	+	0.0696434i
$706$	−0.484107	+	11.1816i	−0.0182196	+	0.420826i
$707$	−0.356379	+	0.594582i	−0.0134030	+	0.0223616i
$708$	−4.00146	−	1.16315i	−0.150384	−	0.0437138i
$709$	−2.44230	−	6.82577i	−0.0917224	−	0.256347i	0.886918	−	0.461927i	$-0.152842\pi$
$709$	−2.44230	−	6.82577i	−0.0917224	−	0.256347i	−0.978640	+	0.205580i	$0.934092\pi$
$710$	32.9526	−	49.9439i	1.23669	−	1.87436i
$711$	−6.75882	−	3.61266i	−0.253476	−	0.135485i
$712$	30.9437	−	43.2820i	1.15966	−	1.62206i
$713$	−10.9255	−	3.31421i	−0.409162	−	0.124118i
$714$	−0.256482	−	0.135180i	−0.00959861	−	0.00505897i
$715$	−3.25065	+	4.38299i	−0.121567	+	0.163915i
$716$	31.9638	+	14.6649i	1.19454	+	0.548055i
$717$	−2.53231	+	1.19769i	−0.0945707	+	0.0447286i
$718$	4.52050	−	7.64252i	0.168704	−	0.285216i
$719$	−12.9709	+	8.66690i	−0.483734	+	0.323221i	−0.773412	−	0.633903i	$-0.781452\pi$
$719$	−12.9709	+	8.66690i	−0.483734	+	0.323221i	0.289678	+	0.957124i	$0.406452\pi$
$720$	−4.34108	+	34.8337i	−0.161782	+	1.29817i
$721$	−3.25297	−	2.17356i	−0.121147	−	0.0809478i
$722$	−3.16503	−	6.59235i	−0.117790	−	0.245342i
$723$	5.05428	−	0.248301i	0.187971	−	0.00923441i
$724$	−27.7197	+	1.68540i	−1.03020	+	0.0626373i
$725$	1.41065	−	5.63162i	0.0523901	−	0.209153i
$726$	0.00159123	−	0.00196210i	5.90562e−5	−	7.28203e-5i
$727$	−15.8340	+	19.2938i	−0.587251	+	0.715568i	−0.978853	−	0.204567i	$-0.934421\pi$
$727$	−15.8340	+	19.2938i	−0.587251	+	0.715568i	0.391601	+	0.920135i	$0.371921\pi$
$728$	0.236471	−	0.367640i	0.00876421	−	0.0136257i
$729$	−2.28230	+	23.1725i	−0.0845295	+	0.858242i
$730$	20.7988	−	51.0510i	0.769798	−	1.88948i
$731$	−0.916437	+	18.6545i	−0.0338956	+	0.689962i
$732$	−0.539848	−	1.26157i	−0.0199534	−	0.0466291i
$733$	3.49838	−	23.5841i	0.129216	−	0.871100i	−0.823517	−	0.567291i	$-0.807991\pi$
$733$	3.49838	−	23.5841i	0.129216	−	0.871100i	0.952733	−	0.303809i	$-0.0982586\pi$
$734$	−5.34818	−	8.80627i	−0.197405	−	0.325045i
$735$	−5.07313	+	2.10136i	−0.187125	+	0.0775098i
$736$	−2.34689	−	8.33276i	−0.0865076	−	0.307149i
$737$	−26.3854	−	10.9292i	−0.971917	−	0.402581i
$738$	−4.01839	−	26.0446i	−0.147919	−	0.958715i
$739$	−4.77106	−	6.43303i	−0.175506	−	0.236643i	0.706692	−	0.707522i	$-0.250187\pi$
$739$	−4.77106	−	6.43303i	−0.175506	−	0.236643i	−0.882198	+	0.470879i	$0.843937\pi$
$740$	7.45685	+	35.3337i	0.274119	+	1.29889i
$741$	0.401033	−	0.363475i	0.0147323	−	0.0133526i
$742$	−2.67677	+	0.0155779i	−0.0982673	+	0.000571883i
$743$	−12.6645	−	15.4318i	−0.464617	−	0.566137i	0.487009	−	0.873397i	$-0.338088\pi$
$743$	−12.6645	−	15.4318i	−0.464617	−	0.566137i	−0.951626	+	0.307260i	$0.900588\pi$
$744$	3.46992	−	4.38193i	0.127214	−	0.160649i
$745$	45.4473	−	4.47617i	1.66506	−	0.163994i
$746$	−0.990555	−	1.82754i	−0.0362668	−	0.0669108i
$747$	7.35155	+	12.2653i	0.268979	+	0.448765i
$748$	−9.19789	+	15.7588i	−0.336308	+	0.576201i
$749$	−0.00880942	−	0.00798439i	−0.000321889	−	0.000291743i
$750$	0.859230	+	0.769700i	0.0313746	+	0.0281055i
$751$	24.4105	−	4.85555i	0.890752	−	0.177182i	0.271560	−	0.962421i	$-0.412460\pi$
$751$	24.4105	−	4.85555i	0.890752	−	0.177182i	0.619192	+	0.785240i	$0.287460\pi$
$752$	−9.10304	+	9.53703i	−0.331954	+	0.347780i
$753$	4.01771	+	0.799173i	0.146414	+	0.0291235i
$754$	−0.908326	+	0.681890i	−0.0330793	+	0.0248330i
$755$	−14.6943	+	41.0678i	−0.534781	+	1.49461i
$756$	0.872461	−	0.139814i	0.0317311	−	0.00508499i
$757$	−43.4522	+	6.44552i	−1.57930	+	0.234267i	−0.878021	−	0.478623i	$-0.841136\pi$
$757$	−43.4522	+	6.44552i	−1.57930	+	0.234267i	−0.701276	+	0.712889i	$0.747386\pi$
$758$	3.22984	−	34.8725i	0.117313	−	1.26663i
$759$	1.18533	−	0.633572i	0.0430247	−	0.0229972i
$760$	−31.2403	−	4.07803i	−1.13321	−	0.147926i
$761$	−9.26464	−	30.5414i	−0.335843	−	1.10713i	−0.948500	−	0.316777i	$-0.897399\pi$
$761$	−9.26464	−	30.5414i	−0.335843	−	1.10713i	0.612657	−	0.790349i	$-0.290101\pi$
$762$	3.80186	+	5.61882i	0.137727	+	0.203549i
$763$	−1.55102	−	0.733576i	−0.0561506	−	0.0265572i
$764$	1.11399	−	12.8410i	0.0403026	−	0.464572i
$765$	−23.4241	+	5.86743i	−0.846901	+	0.212138i
$766$	6.50277	+	17.8459i	0.234955	+	0.644800i
$767$	4.32199			0.156058
$768$	4.21668	+	0.426083i	0.152156	+	0.0153750i
$769$	−15.3275			−0.552722			−0.276361	−	0.961054i	$-0.589129\pi$
$769$	−15.3275			−0.552722			−0.276361	+	0.961054i	$0.589129\pi$
$770$	−1.35248	−	3.71169i	−0.0487401	−	0.133760i
$771$	−4.02019	+	1.00701i	−0.144784	+	0.0362664i
$772$	−24.6500	−	2.13844i	−0.887173	−	0.0769642i
$773$	−19.4765	−	9.21171i	−0.700522	−	0.331322i	0.0438959	−	0.999036i	$-0.486023\pi$
$773$	−19.4765	−	9.21171i	−0.700522	−	0.331322i	−0.744418	+	0.667714i	$0.767273\pi$
$774$	−15.7606	−	23.2928i	−0.566502	−	0.837241i
$775$	−8.60182	−	28.3564i	−0.308986	−	1.01859i
$776$	15.9416	+	20.7284i	0.572271	+	0.744107i
$777$	0.396085	−	0.211712i	0.0142095	−	0.00759511i
$778$	−1.62356	+	17.5295i	−0.0582074	+	0.628463i
$779$	23.3958	−	3.47045i	0.838243	−	0.124342i
$780$	0.137964	+	0.860915i	0.00493989	+	0.0308257i
$781$	−15.7780	+	44.0965i	−0.564580	+	1.57790i
$782$	4.76253	−	3.57528i	0.170308	−	0.127852i
$783$	−2.25175	−	0.447901i	−0.0804710	−	0.0160067i
$784$	−11.1865	−	25.3227i	−0.399517	−	0.904384i
$785$	−53.1189	+	10.5660i	−1.89589	+	0.377117i
$786$	0.709292	+	0.635386i	0.0252996	+	0.0226635i
$787$	33.8148	+	30.6480i	1.20537	+	1.09248i	0.993340	+	0.115218i	$0.0367566\pi$
$787$	33.8148	+	30.6480i	1.20537	+	1.09248i	0.212027	+	0.977264i	$0.431993\pi$
$788$	−47.0846	−	27.4817i	−1.67732	−	0.978994i
$789$	−1.46322	−	2.44123i	−0.0520919	−	0.0869102i
$790$	5.28004	+	9.74147i	0.187855	+	0.346586i
$791$	4.40820	−	0.434170i	0.156738	−	0.0154373i
$792$	−3.17006	−	27.2924i	−0.112643	−	0.969793i
$793$	0.902890	+	1.10018i	0.0320626	+	0.0390684i
$794$	−38.8196	+	0.225917i	−1.37766	+	0.00801751i
$795$	3.95611	−	3.58561i	0.140309	−	0.127168i
$796$	27.6956	−	5.84489i	0.981644	−	0.207167i
$797$	−21.3905	−	28.8418i	−0.757691	−	1.02163i	−0.998693	−	0.0511037i	$-0.983726\pi$
$797$	−21.3905	−	28.8418i	−0.757691	−	1.02163i	0.241002	−	0.970525i	$-0.422524\pi$
$798$	0.0597472	+	0.387242i	0.00211503	+	0.0137082i
$799$	−8.37910	−	3.47074i	−0.296431	−	0.122786i
$800$	14.5982	−	17.0800i	0.516125	−	0.603871i
$801$	−50.9181	+	21.0910i	−1.79910	+	0.745212i
$802$	4.92631	+	8.11163i	0.173954	+	0.286432i
$803$	−6.33106	+	42.6806i	−0.223418	+	1.50616i
$804$	−4.19525	+	1.79522i	−0.147955	+	0.0633124i
$805$	−0.0632632	+	1.28775i	−0.00222973	+	0.0453873i
$806$	−2.18729	+	5.36873i	−0.0770438	+	0.189106i
$807$	−0.466619	+	4.73766i	−0.0164258	+	0.166774i
$808$	6.81209	−	1.47909i	0.239649	−	0.0520342i
$809$	18.1628	−	22.1315i	0.638572	−	0.778102i	−0.348685	−	0.937240i	$-0.613372\pi$
$809$	18.1628	−	22.1315i	0.638572	−	0.778102i	0.987256	+	0.159138i	$0.0508715\pi$
$810$	22.3420	−	27.5492i	0.785019	−	0.967981i
$811$	7.04579	−	28.1284i	0.247411	−	0.987721i	−0.711197	−	0.702993i	$-0.751847\pi$
$811$	7.04579	−	28.1284i	0.247411	−	0.987721i	0.958608	−	0.284728i	$-0.0919034\pi$
$812$	−0.0499014	−	0.820729i	−0.00175120	−	0.0288019i
$813$	5.48037	−	0.269233i	0.192205	−	0.00944242i
$814$	−12.2336	−	25.4810i	−0.428786	−	0.893107i
$815$	56.0802	+	37.4716i	1.96441	+	1.31257i
$816$	0.774036	+	2.81084i	0.0270967	+	0.0983990i
$817$	20.9874	−	14.0233i	0.734257	−	0.490615i
$818$	9.07768	−	15.3470i	0.317393	−	0.536596i
$819$	−0.409324	+	0.193596i	−0.0143029	+	0.00676479i
$820$	−15.8884	+	34.6305i	−0.554849	+	1.20935i
$821$	−23.5812	+	31.7956i	−0.822990	+	1.10967i	0.169279	+	0.985568i	$0.445856\pi$
$821$	−23.5812	+	31.7956i	−0.822990	+	1.10967i	−0.992269	+	0.124105i	$0.960394\pi$
$822$	1.17229	+	0.617859i	0.0408884	+	0.0215503i
$823$	−46.1150	−	13.9888i	−1.60747	−	0.487620i	−0.646184	−	0.763181i	$-0.723636\pi$
$823$	−46.1150	−	13.9888i	−1.60747	−	0.487620i	−0.961283	+	0.275561i	$0.911136\pi$
$824$	6.45117	+	38.8094i	0.224737	+	1.35199i
$825$	3.07645	+	1.64439i	0.107108	+	0.0572505i
$826$	−1.72313	+	2.61161i	−0.0599552	+	0.0908697i
$827$	6.12220	+	17.1104i	0.212890	+	0.594987i	0.999755	−	0.0221381i	$-0.00704735\pi$
$827$	6.12220	+	17.1104i	0.212890	+	0.594987i	−0.786865	+	0.617125i	$0.788297\pi$
$828$	−2.50303	+	8.61091i	−0.0869862	+	0.299250i
$829$	−1.52006	+	2.53607i	−0.0527940	+	0.0880815i	−0.882994	−	0.469384i	$-0.844476\pi$
$829$	−1.52006	+	2.53607i	−0.0527940	+	0.0880815i	0.830200	+	0.557465i	$0.188226\pi$
$830$	0.894278	−	20.6556i	0.0310408	−	0.716965i
$831$	−1.93850	−	1.93850i	−0.0672457	−	0.0672457i
$832$	−4.32295	+	0.796384i	−0.149871	+	0.0276096i
$833$	13.4660	−	13.4660i	0.466569	−	0.466569i
$834$	−4.42704	−	4.82772i	−0.153296	−	0.167170i
$835$	42.4918	+	25.4686i	1.47049	+	0.881377i
$836$	24.5113	−	2.70255i	0.847741	−	0.0934698i
$837$	−11.0333	+	3.94778i	−0.381367	+	0.136455i
$838$	−9.48110	+	1.94333i	−0.327519	+	0.0671314i
$839$	15.8872	−	29.7228i	0.548486	−	1.02615i	−0.443072	−	0.896486i	$-0.646112\pi$
$839$	15.8872	−	29.7228i	0.548486	−	1.02615i	0.991559	−	0.129660i	$-0.0413884\pi$
$840$	−0.575223	−	0.259870i	−0.0198471	−	0.00896638i
$841$	7.79807	−	25.7068i	0.268899	−	0.886442i
$842$	1.53587	−	0.475680i	0.0529297	−	0.0163930i
$843$	0.865147	+	0.641637i	0.0297972	+	0.0220991i
$844$	19.4743	−	18.0678i	0.670335	−	0.621919i
$845$	16.2620	+	34.3830i	0.559429	+	1.18281i
$846$	13.2280	−	3.39537i	0.454787	−	0.116735i
$847$	−0.00105381	−	0.00157715i	−3.62095e−5	−	5.41914e-5i
$848$	18.5362	+	19.5186i	0.636537	+	0.670272i
$849$	4.66295	−	6.97859i	0.160032	−	0.239505i
$850$	14.5829	+	5.12230i	0.500189	+	0.175694i
$851$	0.452651	+	9.21393i	0.0155167	+	0.315849i
$852$	3.27799	+	6.72702i	0.112302	+	0.230464i
$853$	−55.7301	−	13.9597i	−1.90816	−	0.477970i	−0.997963	−	0.0637979i	$-0.979679\pi$
$853$	−55.7301	−	13.9597i	−1.90816	−	0.477970i	−0.910199	−	0.414172i	$-0.864071\pi$
$854$	−1.02477	+	0.106956i	−0.0350668	+	0.00365995i
$855$	25.2272	+	20.7034i	0.862750	+	0.708041i
$856$	0.00208724	+	0.119540i	7.13403e−5	+	0.00408579i
$857$	6.49961	+	0.640156i	0.222023	+	0.0218673i	0.208417	−	0.978040i	$-0.433169\pi$
$857$	6.49961	+	0.640156i	0.222023	+	0.0218673i	0.0136059	+	0.999907i	$0.495669\pi$
$858$	−0.264828	−	0.628972i	−0.00904107	−	0.0214728i
$859$	42.8637	+	2.10576i	1.46249	+	0.0718476i	0.764669	−	0.644423i	$-0.222902\pi$
$859$	42.8637	+	2.10576i	1.46249	+	0.0718476i	0.697822	+	0.716271i	$0.254152\pi$
$860$	0.473262	+	40.6592i	0.0161381	+	1.38647i
$861$	0.468729	+	0.0695293i	0.0159742	+	0.00236955i
$862$	−10.4947	+	42.9563i	−0.357451	+	1.46310i
$863$	−13.9099	−	33.5814i	−0.473498	−	1.14313i	−0.962607	−	0.270903i	$-0.912678\pi$
$863$	−13.9099	−	33.5814i	−0.473498	−	1.14313i	0.489109	−	0.872223i	$-0.337322\pi$
$864$	−7.02955	−	5.43458i	−0.239150	−	0.184888i
$865$	15.4185	−	37.2236i	0.524245	−	1.26564i
$866$	10.2441	+	7.50552i	0.348108	+	0.255048i
$867$	2.00598	−	1.48773i	0.0681265	−	0.0505261i
$868$	−2.37208	−	3.46215i	−0.0805136	−	0.117513i
$869$	−5.82432	−	6.42614i	−0.197576	−	0.217992i
$870$	1.16643	+	1.15293i	0.0395457	+	0.0390881i
$871$	3.65853	−	3.00248i	0.123965	−	0.101735i
$872$	5.29587	+	16.4205i	0.179341	+	0.556069i
$873$	−2.65501	−	26.9568i	−0.0898584	−	0.912348i
$874$	−7.71516	−	2.29142i	−0.260969	−	0.0775086i
$875$	0.742924	−	0.445292i	0.0251154	−	0.0150536i
$876$	4.17100	+	5.48924i	0.140925	+	0.185464i
$877$	13.8588	−	15.2908i	0.467978	−	0.516335i	−0.460531	−	0.887644i	$-0.652341\pi$
$877$	13.8588	−	15.2908i	0.467978	−	0.516335i	0.928509	+	0.371309i	$0.121091\pi$
$878$	−3.07556	−	55.9577i	−0.103795	−	1.88848i
$879$	−0.278719	−	1.40121i	−0.00940094	−	0.0472617i
$880$	−17.9058	+	35.4609i	−0.603603	+	1.19539i
$881$	3.22188	−	16.1975i	0.108548	−	0.545708i	−0.887793	−	0.460243i	$-0.847762\pi$
$881$	3.22188	−	16.1975i	0.108548	−	0.545708i	0.996341	−	0.0854650i	$-0.0272376\pi$
$882$	−4.04251	+	28.3897i	−0.136118	+	0.955932i
$883$	15.7674	+	5.64165i	0.530614	+	0.189857i	0.588546	−	0.808464i	$-0.299701\pi$
$883$	15.7674	+	5.64165i	0.530614	+	0.189857i	−0.0579320	+	0.998321i	$0.518451\pi$
$884$	−1.58465	−	2.57536i	−0.0532974	−	0.0866189i
$885$	−0.915726	−	6.17332i	−0.0307818	−	0.207514i
$886$	14.4552	−	12.0045i	0.485631	−	0.403299i
$887$	−26.3408	−	49.2802i	−0.884438	−	1.65467i	−0.747677	−	0.664062i	$-0.768831\pi$
$887$	−26.3408	−	49.2802i	−0.884438	−	1.65467i	−0.136760	−	0.990604i	$-0.543669\pi$
$888$	−4.27818	−	1.44702i	−0.143566	−	0.0485587i
$889$	4.87456	−	1.47868i	0.163487	−	0.0495934i
$890$	78.2420	+	15.0905i	2.62268	+	0.505834i
$891$	−11.8702	+	25.0975i	−0.397668	+	0.840799i
$892$	5.06626	−	9.74958i	0.169631	−	0.326440i
$893$	2.97823	+	11.8898i	0.0996627	+	0.397876i
$894$	−2.41180	+	5.17706i	−0.0806627	+	0.173147i
$895$			52.6686i			1.76052i
$896$	1.24228	−	2.92970i	0.0415018	−	0.0978746i
$897$			0.222732i			0.00743682i
$898$	46.2156	+	21.5301i	1.54223	+	0.718469i
$899$	2.64962	+	10.5779i	0.0883699	+	0.352793i
$900$	−22.1918	+	7.01489i	−0.739727	+	0.233830i
$901$	−7.91705	+	16.7392i	−0.263755	+	0.557664i
$902$	5.64779	−	29.2830i	0.188051	−	0.975016i
$903$	0.483927	−	0.146798i	0.0161041	−	0.00488512i
$904$	−33.5214	−	29.3325i	−1.11490	−	0.975585i
$905$	−19.6060	−	36.6803i	−0.651726	−	1.21929i
$906$	−3.48506	−	4.19651i	−0.115783	−	0.139420i
$907$	6.23198	+	42.0126i	0.206930	+	1.39501i	0.804863	+	0.593460i	$0.202239\pi$
$907$	6.23198	+	42.0126i	0.206930	+	1.39501i	−0.597934	+	0.801545i	$0.704011\pi$
$908$	−20.6658	−	4.92161i	−0.685818	−	0.163329i
$909$	−6.79865	−	2.43260i	−0.225497	−	0.0806841i
$910$	0.648126	+	0.0922889i	0.0214852	+	0.00305935i
$911$	0.831610	−	4.18079i	0.0275525	−	0.138516i	−0.964561	−	0.263861i	$-0.915004\pi$
$911$	0.831610	−	4.18079i	0.0275525	−	0.138516i	0.992113	+	0.125345i	$0.0400039\pi$
$912$	2.42804	−	3.10314i	0.0804003	−	0.102755i
$913$	3.15707	+	15.8717i	0.104484	+	0.525276i
$914$	−22.7560	+	1.25072i	−0.752700	+	0.0413701i
$915$	1.38014	−	1.52275i	0.0456259	−	0.0503404i
$916$	−6.60812	+	48.4251i	−0.218338	+	1.60001i
$917$	0.613282	−	0.367587i	0.0202524	−	0.0121388i
$918$	1.74024	−	5.85934i	0.0574365	−	0.193387i
$919$	−2.28262	−	23.1758i	−0.0752966	−	0.764500i	−0.956494	−	0.291751i	$-0.905762\pi$
$919$	−2.28262	−	23.1758i	−0.0752966	−	0.764500i	0.881198	−	0.472748i	$-0.156738\pi$
$920$	9.87707	−	8.39871i	0.325637	−	0.276897i
$921$	2.81373	−	2.30917i	0.0927157	−	0.0760898i
$922$	7.04408	−	7.12655i	0.231985	−	0.234701i
$923$	−5.21220	−	5.75078i	−0.171562	−	0.189289i
$924$	0.485648	+	0.0907385i	0.0159767	+	0.00298508i
$925$	−19.2312	+	14.2628i	−0.632318	+	0.468959i
$926$	−19.0536	+	26.0058i	−0.626142	+	0.854604i
$927$	15.5953	−	37.6503i	0.512216	−	1.23660i
$928$	−5.67408	+	6.01428i	−0.186261	+	0.197428i
$929$	10.1369	+	24.4727i	0.332581	+	0.802922i	0.998386	+	0.0567958i	$0.0180884\pi$
$929$	10.1369	+	24.4727i	0.332581	+	0.802922i	−0.665805	+	0.746126i	$0.731912\pi$
$930$	8.13188	+	1.98671i	0.266655	+	0.0651467i
$931$	−25.4585	−	3.77641i	−0.834368	−	0.123767i
$932$	−21.3093	+	21.8112i	−0.698009	+	0.714449i
$933$	5.73699	+	0.281840i	0.187821	+	0.00922704i
$934$	−32.4948	+	13.6819i	−1.06326	+	0.447685i
$935$	−27.1957	−	2.67855i	−0.889396	−	0.0875978i
$936$	4.23647	+	1.66876i	0.138473	+	0.0545453i
$937$	24.1788	+	19.8430i	0.789887	+	0.648243i	0.940287	−	0.340382i	$-0.110556\pi$
$937$	24.1788	+	19.8430i	0.789887	+	0.648243i	−0.150400	+	0.988625i	$0.548056\pi$
$938$	0.355672	+	3.40777i	0.0116131	+	0.111268i
$939$	−1.32201	−	0.331146i	−0.0431421	−	0.0108065i
$940$	−18.6672	−	6.43515i	−0.608857	−	0.209891i
$941$	2.18266	+	44.4290i	0.0711526	+	1.44834i	0.723448	+	0.690379i	$0.242556\pi$
$941$	2.18266	+	44.4290i	0.0711526	+	1.44834i	−0.652295	+	0.757965i	$0.726194\pi$
$942$	2.24472	−	6.39058i	0.0731370	−	0.208216i
$943$	−5.40750	+	8.09290i	−0.176093	+	0.263541i
$944$	31.0070	−	5.33982i	1.00919	−	0.173796i
$945$	0.735197	+	1.10030i	0.0239160	+	0.0357928i
$946$	−7.91283	−	30.8275i	−0.257268	−	1.00229i
$947$	−9.78085	−	20.6799i	−0.317835	−	0.672006i	0.680308	−	0.732927i	$-0.261846\pi$
$947$	−9.78085	−	20.6799i	−0.317835	−	0.672006i	−0.998143	+	0.0609210i	$0.980596\pi$
$948$	−1.38478	−	0.0518816i	−0.0449754	−	0.00168504i
$949$	−5.74326	−	4.25949i	−0.186434	−	0.138269i
$950$	−6.17990	−	19.9536i	−0.200503	−	0.647382i
$951$	1.97989	−	6.52682i	0.0642023	−	0.211647i
$952$	2.18798	+	0.0692257i	0.0709127	+	0.00224362i
$953$	22.2593	−	41.6442i	0.721050	−	1.34899i	−0.207667	−	0.978200i	$-0.566587\pi$
$953$	22.2593	−	41.6442i	0.721050	−	1.34899i	0.928717	−	0.370790i	$-0.120913\pi$
$954$	−5.59874	−	27.3150i	−0.181266	−	0.884357i
$955$	18.1753	−	6.50321i	0.588138	−	0.210439i
$956$	13.2267	−	16.5048i	0.427782	−	0.533805i
$957$	−1.10107	−	0.659959i	−0.0355927	−	0.0213334i
$958$	9.98960	−	9.16050i	0.322749	−	0.295962i
$959$	0.703561	−	0.703561i	0.0227192	−	0.0227192i
$960$	2.05345	+	6.00596i	0.0662747	+	0.193842i
$961$	17.4362	+	17.4362i	0.562459	+	0.562459i
$962$	4.67977	+	0.202610i	0.150882	+	0.00653240i
$963$	0.0636689	−	0.106225i	0.00205170	−	0.00342306i
$964$	−33.4847	+	18.4022i	−1.07847	+	0.592695i
$965$	−12.4838	−	34.8898i	−0.401867	−	1.12314i
$966$	−0.134589	−	0.0888008i	−0.00433032	−	0.00285712i
$967$	11.3288	+	6.05538i	0.364310	+	0.194728i	0.643387	−	0.765541i	$-0.277528\pi$
$967$	11.3288	+	6.05538i	0.364310	+	0.194728i	−0.279077	+	0.960269i	$0.590028\pi$
$968$	−0.00431094	+	0.0185807i	−0.000138559	+	0.000597206i
$969$	2.59376	+	0.786808i	0.0833235	+	0.0252759i
$970$	−18.2601	+	34.6457i	−0.586296	+	1.11241i
$971$	18.0582	−	24.3486i	0.579515	−	0.781385i	−0.412027	−	0.911171i	$-0.635179\pi$
$971$	18.0582	−	24.3486i	0.579515	−	0.781385i	0.991542	+	0.129787i	$0.0414292\pi$
$972$	4.82097	+	12.9949i	0.154633	+	0.416811i
$973$	−4.44603	+	2.10281i	−0.142533	+	0.0674131i
$974$	11.9988	+	7.09722i	0.384466	+	0.227410i
$975$	−0.480662	+	0.321168i	−0.0153935	+	0.0102856i
$976$	7.83683	+	6.77741i	0.250851	+	0.216939i
$977$	32.9127	+	21.9915i	1.05297	+	0.703571i	0.956490	−	0.291764i	$-0.0942420\pi$
$977$	32.9127	+	21.9915i	1.05297	+	0.703571i	0.0964787	+	0.995335i	$0.469242\pi$
$978$	−7.60416	+	3.65080i	−0.243154	+	0.116740i
$979$	−62.2950	+	3.06036i	−1.99096	+	0.0978094i
$980$	27.4837	−	31.0422i	0.877935	−	0.991606i
$981$	4.34254	−	17.3364i	0.138647	−	0.553509i
$982$	−27.5132	−	22.3128i	−0.877983	−	0.712031i
$983$	13.9154	−	16.9559i	0.443832	−	0.540811i	−0.502257	−	0.864719i	$-0.667497\pi$
$983$	13.9154	−	16.9559i	0.443832	−	0.540811i	0.946089	+	0.323908i	$0.104997\pi$
$984$	−2.71610	−	3.91519i	−0.0865860	−	0.124812i
$985$	8.00302	−	81.2560i	0.254997	−	2.58903i
$986$	−5.26754	−	2.14606i	−0.167753	−	0.0683444i
$987$	−0.0120494	+	0.245271i	−0.000383537	+	0.00780707i
$988$	−1.51983	+	3.79349i	−0.0483523	+	0.120687i
$989$	−1.52414	+	10.2749i	−0.0484649	+	0.326724i
$990$	35.1714	−	21.3601i	1.11782	−	0.678868i
$991$	−55.8515	+	23.1344i	−1.77418	+	0.734890i	−0.780175	+	0.625561i	$0.784870\pi$
$991$	−55.8515	+	23.1344i	−1.77418	+	0.734890i	−0.994006	+	0.109329i	$0.965130\pi$
$992$	−9.05905	+	41.2190i	−0.287625	+	1.30871i
$993$	−6.48418	−	2.68584i	−0.205769	−	0.0852324i
$994$	5.55303	−	0.856770i	0.176131	−	0.0271751i
$995$	25.2530	+	34.0497i	0.800572	+	1.07945i
$996$	2.16648	+	1.41140i	0.0686474	+	0.0447219i
$997$	−17.6760	+	16.0206i	−0.559806	+	0.507378i	−0.901701	−	0.432360i	$-0.857681\pi$
$997$	−17.6760	+	16.0206i	−0.559806	+	0.507378i	0.341896	+	0.939738i	$0.388931\pi$
$998$	0.0763152	+	13.1133i	0.00241572	+	0.415095i
$999$	6.00670	+	7.31919i	0.190044	+	0.231569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.28	✓	992
256.109	even	64	inner	256.2.m.a.109.28	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.28	✓	992	1.1	even	1	trivial
256.2.m.a.109.28	yes	992	256.109	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32875 - 0.484175i) q^{2} +(-0.256946 + 0.0643616i) q^{3} +(1.53115 - 1.28669i) q^{4} +(2.70773 + 1.28066i) q^{5} +(-0.310255 + 0.209927i) q^{6} +(0.0816484 + 0.269159i) q^{7} +(1.41153 - 2.45104i) q^{8} +(-2.58388 + 1.38112i) q^{9} +O(q^{10})\)	\(q+(1.32875 - 0.484175i) q^{2} +(-0.256946 + 0.0643616i) q^{3} +(1.53115 - 1.28669i) q^{4} +(2.70773 + 1.28066i) q^{5} +(-0.310255 + 0.209927i) q^{6} +(0.0816484 + 0.269159i) q^{7} +(1.41153 - 2.45104i) q^{8} +(-2.58388 + 1.38112i) q^{9} +(4.21796 + 0.390662i) q^{10} +(-3.27972 + 0.486501i) q^{11} +(-0.310609 + 0.429158i) q^{12} +(0.185108 - 0.517342i) q^{13} +(0.238810 + 0.318112i) q^{14} +(-0.778167 - 0.154787i) q^{15} +(0.688834 - 3.94024i) q^{16} +(2.69877 - 0.536818i) q^{17} +(-2.76463 + 3.08621i) q^{18} +(-2.75541 - 2.49736i) q^{19} +(5.79376 - 1.52314i) q^{20} +(-0.0383027 - 0.0639042i) q^{21} +(-4.12238 + 2.23440i) q^{22} +(1.52298 - 0.150000i) q^{23} +(-0.204934 + 0.720633i) q^{24} +(2.51976 + 3.07033i) q^{25} +(-0.00452213 - 0.777043i) q^{26} +(1.16383 - 1.05483i) q^{27} +(0.471341 + 0.307065i) q^{28} +(-0.870712 - 1.17402i) q^{29} +(-1.10893 + 0.171096i) q^{30} +(-6.89257 - 2.85500i) q^{31} +(-0.992480 - 5.56911i) q^{32} +(0.811400 - 0.336093i) q^{33} +(3.32607 - 2.01997i) q^{34} +(-0.123619 + 0.833374i) q^{35} +(-2.17924 + 5.43936i) q^{36} +(-0.295784 + 6.02081i) q^{37} +(-4.87041 - 1.98426i) q^{38} +(-0.0142658 + 0.144843i) q^{39} +(6.96099 - 4.82907i) q^{40} +(-4.03484 + 4.91647i) q^{41} +(-0.0818355 - 0.0663675i) q^{42} +(-1.64925 + 6.58418i) q^{43} +(-4.39576 + 4.96491i) q^{44} +(-8.76521 + 0.430607i) q^{45} +(1.95103 - 0.936700i) q^{46} +(-2.74054 - 1.83117i) q^{47} +(0.0766074 + 1.05676i) q^{48} +(5.75451 - 3.84504i) q^{49} +(4.83470 + 2.85970i) q^{50} +(-0.658887 + 0.311630i) q^{51} +(-0.382234 - 1.03031i) q^{52} +(-4.00873 + 5.40515i) q^{53} +(1.03571 - 1.96510i) q^{54} +(-9.50365 - 2.88290i) q^{55} +(0.774967 + 0.179801i) q^{56} +(0.868727 + 0.464344i) q^{57} +(-1.72539 - 1.13840i) q^{58} +(2.64993 + 7.40605i) q^{59} +(-1.39065 + 0.764261i) q^{60} +(-1.33165 + 2.22172i) q^{61} +(-10.5408 - 0.456363i) q^{62} +(-0.582709 - 0.582709i) q^{63} +(-4.01518 - 6.91942i) q^{64} +(1.16376 - 1.16376i) q^{65} +(0.915419 - 0.839443i) q^{66} +(7.38813 + 4.42827i) q^{67} +(3.44149 - 4.29444i) q^{68} +(-0.381669 + 0.136563i) q^{69} +(0.239240 + 1.16720i) q^{70} +(6.65865 - 12.4575i) q^{71} +(-0.262057 + 8.28268i) q^{72} +(3.77761 - 12.4531i) q^{73} +(2.52211 + 8.14336i) q^{74} +(-0.845053 - 0.626734i) q^{75} +(-7.43228 - 0.278456i) q^{76} +(-0.398730 - 0.843043i) q^{77} +(0.0511737 + 0.199367i) q^{78} +(1.45324 + 2.17492i) q^{79} +(6.91130 - 9.78696i) q^{80} +(4.65204 - 6.96227i) q^{81} +(-2.98086 + 8.48633i) q^{82} +(-0.239487 - 4.87486i) q^{83} +(-0.140872 - 0.0485630i) q^{84} +(7.99502 + 2.00265i) q^{85} +(0.996455 + 9.54724i) q^{86} +(0.299288 + 0.245619i) q^{87} +(-3.43698 + 8.72543i) q^{88} +(18.7205 + 1.84381i) q^{89} +(-11.4383 + 4.81607i) q^{90} +(0.154361 + 0.00758326i) q^{91} +(2.13890 - 2.18928i) q^{92} +(1.95477 + 0.289963i) q^{93} +(-4.52810 - 1.10627i) q^{94} +(-4.26265 - 10.2909i) q^{95} +(0.613451 + 1.36708i) q^{96} +(-3.53802 + 8.54153i) q^{97} +(5.78462 - 7.89528i) q^{98} +(7.80251 - 5.78674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more