LMFDB - Embedded newform 256.2.m.a.101.8

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			101.8
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04211 + 0.956032i) q^{2} +(-0.576868 + 0.144498i) q^{3} +(0.172006 - 1.99259i) q^{4} +(-0.652101 - 0.308421i) q^{5} +(0.463018 - 0.702088i) q^{6} +(0.308398 + 1.01665i) q^{7} +(1.72573 + 2.24095i) q^{8} +(-2.33387 + 1.24748i) q^{9} +O(q^{10})$	\(q+(-1.04211 + 0.956032i) q^{2} +(-0.576868 + 0.144498i) q^{3} +(0.172006 - 1.99259i) q^{4} +(-0.652101 - 0.308421i) q^{5} +(0.463018 - 0.702088i) q^{6} +(0.308398 + 1.01665i) q^{7} +(1.72573 + 2.24095i) q^{8} +(-2.33387 + 1.24748i) q^{9} +(0.974424 - 0.302020i) q^{10} +(-0.325772 + 0.0483237i) q^{11} +(0.188701 + 1.17432i) q^{12} +(-1.33897 + 3.74217i) q^{13} +(-1.29334 - 0.764629i) q^{14} +(0.420743 + 0.0836909i) q^{15} +(-3.94083 - 0.685473i) q^{16} +(-6.24026 + 1.24127i) q^{17} +(1.23953 - 3.53127i) q^{18} +(5.69816 + 5.16451i) q^{19} +(-0.726721 + 1.24632i) q^{20} +(-0.324809 - 0.541911i) q^{21} +(0.293292 - 0.361807i) q^{22} +(-5.60713 + 0.552254i) q^{23} +(-1.31933 - 1.04337i) q^{24} +(-2.84185 - 3.46281i) q^{25} +(-2.18228 - 5.17987i) q^{26} +(2.48798 - 2.25498i) q^{27} +(2.07881 - 0.439640i) q^{28} +(-1.42124 - 1.91633i) q^{29} +(-0.518473 + 0.315028i) q^{30} +(-1.25771 - 0.520961i) q^{31} +(4.76213 - 3.05322i) q^{32} +(0.180945 - 0.0749497i) q^{33} +(5.31638 - 7.25943i) q^{34} +(0.112450 - 0.758076i) q^{35} +(2.08427 + 4.86501i) q^{36} +(-0.549622 + 11.1878i) q^{37} +(-10.8756 + 0.0656108i) q^{38} +(0.231673 - 2.35222i) q^{39} +(-0.434195 - 1.99358i) q^{40} +(-1.34401 + 1.63768i) q^{41} +(0.856572 + 0.254206i) q^{42} +(1.60903 - 6.42361i) q^{43} +(0.0402547 + 0.657441i) q^{44} +(1.90667 - 0.0936685i) q^{45} +(5.31530 - 5.93610i) q^{46} +(8.16939 + 5.45861i) q^{47} +(2.37239 - 0.174014i) q^{48} +(4.88182 - 3.26193i) q^{49} +(6.27209 + 0.891741i) q^{50} +(3.42045 - 1.61775i) q^{51} +(7.22631 + 3.31169i) q^{52} +(-6.50207 + 8.76703i) q^{53} +(-0.436934 + 4.72854i) q^{54} +(0.227340 + 0.0689629i) q^{55} +(-1.74605 + 2.44557i) q^{56} +(-4.03335 - 2.15587i) q^{57} +(3.31317 + 0.638277i) q^{58} +(0.392752 + 1.09767i) q^{59} +(0.239132 - 0.823972i) q^{60} +(3.16695 - 5.28374i) q^{61} +(1.80873 - 0.659511i) q^{62} +(-1.98801 - 1.98801i) q^{63} +(-2.04371 + 7.73455i) q^{64} +(2.02731 - 2.02731i) q^{65} +(-0.116911 + 0.251095i) q^{66} +(9.67755 + 5.80050i) q^{67} +(1.39997 + 12.6478i) q^{68} +(3.15477 - 1.12880i) q^{69} +(0.607559 + 0.897507i) q^{70} +(2.14155 - 4.00655i) q^{71} +(-6.82316 - 3.07727i) q^{72} +(1.49238 - 4.91972i) q^{73} +(-10.1231 - 12.1844i) q^{74} +(2.13974 + 1.58694i) q^{75} +(11.2709 - 10.4658i) q^{76} +(-0.149596 - 0.316293i) q^{77} +(2.00737 + 2.67277i) q^{78} +(-2.44276 - 3.65585i) q^{79} +(2.35840 + 1.66243i) q^{80} +(3.30129 - 4.94073i) q^{81} +(-0.165063 - 2.99156i) q^{82} +(-0.136740 - 2.78340i) q^{83} +(-1.13567 + 0.553999i) q^{84} +(4.45211 + 1.11520i) q^{85} +(4.46438 + 8.23242i) q^{86} +(1.09678 + 0.900101i) q^{87} +(-0.670485 - 0.646644i) q^{88} +(-3.19358 - 0.314540i) q^{89} +(-1.89741 + 1.92045i) q^{90} +(-4.21742 - 0.207189i) q^{91} +(0.135958 + 11.2677i) q^{92} +(0.800811 + 0.118789i) q^{93} +(-13.7321 + 2.12170i) q^{94} +(-2.12293 - 5.12522i) q^{95} +(-2.30594 + 2.44942i) q^{96} +(3.06875 - 7.40863i) q^{97} +(-1.96891 + 8.06647i) q^{98} +(0.700025 - 0.519174i) 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 $

$2$	−1.04211	+	0.956032i	−0.736886	+	0.676017i
$2$	−1.04211	+	0.956032i	−0.736886	+	0.676017i
$3$	−0.576868	+	0.144498i	−0.333055	+	0.0834259i	−0.405900	−	0.913917i	$-0.633042\pi$
$3$	−0.576868	+	0.144498i	−0.333055	+	0.0834259i	0.0728454	+	0.997343i	$0.476792\pi$
$4$	0.172006	−	1.99259i	0.0860028	−	0.996295i
$5$	−0.652101	−	0.308421i	−0.291629	−	0.137930i	0.276142	−	0.961117i	$-0.410944\pi$
$5$	−0.652101	−	0.308421i	−0.291629	−	0.137930i	−0.567771	+	0.823187i	$0.692194\pi$
$6$	0.463018	−	0.702088i	0.189026	−	0.286626i
$7$	0.308398	+	1.01665i	0.116563	+	0.384258i	0.995736	−	0.0922448i	$-0.0294042\pi$
$7$	0.308398	+	1.01665i	0.116563	+	0.384258i	−0.879173	+	0.476503i	$0.841904\pi$
$8$	1.72573	+	2.24095i	0.610138	+	0.792295i
$9$	−2.33387	+	1.24748i	−0.777956	+	0.415826i
$10$	0.974424	−	0.302020i	0.308140	−	0.0955070i
$11$	−0.325772	+	0.0483237i	−0.0982239	+	0.0145701i	−0.195661	−	0.980672i	$-0.562685\pi$
$11$	−0.325772	+	0.0483237i	−0.0982239	+	0.0145701i	0.0974376	+	0.995242i	$0.468935\pi$
$12$	0.188701	+	1.17432i	0.0544732	+	0.338996i
$13$	−1.33897	+	3.74217i	−0.371364	+	1.03789i	0.599939	+	0.800046i	$0.295191\pi$
$13$	−1.33897	+	3.74217i	−0.371364	+	1.03789i	−0.971303	+	0.237846i	$0.923559\pi$
$14$	−1.29334	−	0.764629i	−0.345659	−	0.204356i
$15$	0.420743	+	0.0836909i	0.108635	+	0.0216089i
$16$	−3.94083	−	0.685473i	−0.985207	−	0.171368i
$17$	−6.24026	+	1.24127i	−1.51349	+	0.301051i	−0.880849	−	0.473398i	$-0.843027\pi$
$17$	−6.24026	+	1.24127i	−1.51349	+	0.301051i	−0.632637	+	0.774449i	$0.718027\pi$
$18$	1.23953	−	3.53127i	0.292160	−	0.832327i
$19$	5.69816	+	5.16451i	1.30725	+	1.18482i	0.969918	+	0.243434i	$0.0782739\pi$
$19$	5.69816	+	5.16451i	1.30725	+	1.18482i	0.337330	+	0.941386i	$0.390476\pi$
$20$	−0.726721	+	1.24632i	−0.162500	+	0.278686i
$21$	−0.324809	−	0.541911i	−0.0708791	−	0.118255i
$22$	0.293292	−	0.361807i	0.0625302	−	0.0771375i
$23$	−5.60713	+	0.552254i	−1.16917	+	0.115153i	−0.663908	−	0.747815i	$-0.731103\pi$
$23$	−5.60713	+	0.552254i	−1.16917	+	0.115153i	−0.505259	+	0.862968i	$0.668603\pi$
$24$	−1.31933	−	1.04337i	−0.269307	−	0.212977i
$25$	−2.84185	−	3.46281i	−0.568371	−	0.692562i
$26$	−2.18228	−	5.17987i	−0.427980	−	1.01586i
$27$	2.48798	−	2.25498i	0.478813	−	0.433971i
$28$	2.07881	−	0.439640i	0.392859	−	0.0830842i
$29$	−1.42124	−	1.91633i	−0.263919	−	0.355853i	0.651293	−	0.758826i	$-0.274227\pi$
$29$	−1.42124	−	1.91633i	−0.263919	−	0.355853i	−0.915212	+	0.402973i	$0.867977\pi$
$30$	−0.518473	+	0.315028i	−0.0946598	+	0.0575160i
$31$	−1.25771	−	0.520961i	−0.225892	−	0.0935673i	0.266867	−	0.963733i	$-0.414011\pi$
$31$	−1.25771	−	0.520961i	−0.225892	−	0.0935673i	−0.492759	+	0.870166i	$0.664011\pi$
$32$	4.76213	−	3.05322i	0.841833	−	0.539737i
$33$	0.180945	−	0.0749497i	0.0314984	−	0.0130471i
$34$	5.31638	−	7.25943i	0.911751	−	1.24498i
$35$	0.112450	−	0.758076i	0.0190075	−	0.128138i
$36$	2.08427	+	4.86501i	0.347379	+	0.810835i
$37$	−0.549622	+	11.1878i	−0.0903574	+	1.83927i	0.344522	+	0.938778i	$0.388041\pi$
$37$	−0.549622	+	11.1878i	−0.0903574	+	1.83927i	−0.434880	+	0.900489i	$0.643209\pi$
$38$	−10.8756	+	0.0656108i	−1.76425	+	0.0106435i
$39$	0.231673	−	2.35222i	0.0370974	−	0.376657i
$40$	−0.434195	−	1.99358i	−0.0686522	−	0.315212i
$41$	−1.34401	+	1.63768i	−0.209899	+	0.255762i	−0.867309	−	0.497771i	$-0.834152\pi$
$41$	−1.34401	+	1.63768i	−0.209899	+	0.255762i	0.657410	+	0.753533i	$0.271652\pi$
$42$	0.856572	+	0.254206i	0.132172	+	0.0392248i
$43$	1.60903	−	6.42361i	0.245375	−	0.979591i	−0.714606	−	0.699527i	$-0.753394\pi$
$43$	1.60903	−	6.42361i	0.245375	−	0.979591i	0.959981	−	0.280064i	$-0.0903558\pi$
$44$	0.0402547	+	0.657441i	0.00606862	+	0.0991130i
$45$	1.90667	−	0.0936685i	0.284229	−	0.0139633i
$46$	5.31530	−	5.93610i	0.783698	−	0.875231i
$47$	8.16939	+	5.45861i	1.19163	+	0.796221i	0.983327	−	0.181844i	$-0.0582066\pi$
$47$	8.16939	+	5.45861i	1.19163	+	0.796221i	0.208301	+	0.978065i	$0.433207\pi$
$48$	2.37239	−	0.174014i	0.342425	−	0.0251167i
$49$	4.88182	−	3.26193i	0.697402	−	0.465989i
$50$	6.27209	+	0.891741i	0.887008	+	0.126111i
$51$	3.42045	−	1.61775i	0.478959	−	0.226531i
$52$	7.22631	+	3.31169i	1.00211	+	0.459249i
$53$	−6.50207	+	8.76703i	−0.893128	+	1.20424i	0.0850292	+	0.996378i	$0.472902\pi$
$53$	−6.50207	+	8.76703i	−0.893128	+	1.20424i	−0.978157	+	0.207866i	$0.933348\pi$
$54$	−0.436934	+	4.72854i	−0.0594592	+	0.643473i
$55$	0.227340	+	0.0689629i	0.0306545	+	0.00929895i
$56$	−1.74605	+	2.44557i	−0.233326	+	0.326803i
$57$	−4.03335	−	2.15587i	−0.534230	−	0.285552i
$58$	3.31317	+	0.638277i	0.435040	+	0.0838098i
$59$	0.392752	+	1.09767i	0.0511320	+	0.142904i	0.964395	−	0.264466i	$-0.0851958\pi$
$59$	0.392752	+	1.09767i	0.0511320	+	0.142904i	−0.913263	+	0.407371i	$0.866446\pi$
$60$	0.239132	−	0.823972i	0.0308718	−	0.106374i
$61$	3.16695	−	5.28374i	0.405486	−	0.676513i	−0.585471	−	0.810694i	$-0.699090\pi$
$61$	3.16695	−	5.28374i	0.405486	−	0.676513i	0.990957	+	0.134181i	$0.0428402\pi$
$62$	1.80873	−	0.659511i	0.229709	−	0.0837580i
$63$	−1.98801	−	1.98801i	−0.250466	−	0.250466i
$64$	−2.04371	+	7.73455i	−0.255464	+	0.966819i
$65$	2.02731	−	2.02731i	0.251457	−	0.251457i
$66$	−0.116911	+	0.251095i	−0.0143907	+	0.0309077i
$67$	9.67755	+	5.80050i	1.18230	+	0.708644i	0.963652	−	0.267160i	$-0.0860852\pi$
$67$	9.67755	+	5.80050i	1.18230	+	0.708644i	0.218649	+	0.975804i	$0.429835\pi$
$68$	1.39997	+	12.6478i	0.169772	+	1.53377i
$69$	3.15477	−	1.12880i	0.379790	−	0.135891i
$70$	0.607559	+	0.897507i	0.0726172	+	0.107273i
$71$	2.14155	−	4.00655i	0.254155	−	0.475490i	−0.722194	−	0.691690i	$-0.756866\pi$
$71$	2.14155	−	4.00655i	0.254155	−	0.475490i	0.976349	+	0.216200i	$0.0693664\pi$
$72$	−6.82316	−	3.07727i	−0.804117	−	0.362660i
$73$	1.49238	−	4.91972i	0.174670	−	0.575810i	−0.825269	−	0.564740i	$-0.808976\pi$
$73$	1.49238	−	4.91972i	0.174670	−	0.575810i	0.999939	−	0.0110697i	$-0.00352368\pi$
$74$	−10.1231	−	12.1844i	−1.17679	−	1.41641i
$75$	2.13974	+	1.58694i	0.247076	+	0.183244i
$76$	11.2709	−	10.4658i	1.29286	−	1.20051i
$77$	−0.149596	−	0.316293i	−0.0170480	−	0.0360450i
$78$	2.00737	+	2.67277i	0.227290	+	0.302632i
$79$	−2.44276	−	3.65585i	−0.274832	−	0.411315i	0.668218	−	0.743965i	$-0.267057\pi$
$79$	−2.44276	−	3.65585i	−0.274832	−	0.411315i	−0.943050	+	0.332650i	$0.892057\pi$
$80$	2.35840	+	1.66243i	0.263678	+	0.185866i
$81$	3.30129	−	4.94073i	0.366810	−	0.548970i
$82$	−0.165063	−	2.99156i	−0.0182281	−	0.330363i
$83$	−0.136740	−	2.78340i	−0.0150091	−	0.305518i	−0.994549	−	0.104268i	$-0.966750\pi$
$83$	−0.136740	−	2.78340i	−0.0150091	−	0.305518i	0.979540	−	0.201249i	$-0.0645001\pi$
$84$	−1.13567	+	0.553999i	−0.123912	+	0.0604463i
$85$	4.45211	+	1.11520i	0.482900	+	0.120960i
$86$	4.46438	+	8.23242i	0.481407	+	0.887725i
$87$	1.09678	+	0.900101i	0.117587	+	0.0965009i
$88$	−0.670485	−	0.646644i	−0.0714739	−	0.0689325i
$89$	−3.19358	−	0.314540i	−0.338518	−	0.0333411i	−0.0726701	−	0.997356i	$-0.523152\pi$
$89$	−3.19358	−	0.314540i	−0.338518	−	0.0333411i	−0.265848	+	0.964015i	$0.585652\pi$
$90$	−1.89741	+	1.92045i	−0.200005	+	0.202433i
$91$	−4.21742	−	0.207189i	−0.442106	−	0.0217193i
$92$	0.135958	+	11.2677i	0.0141746	+	1.17474i
$93$	0.800811	+	0.118789i	0.0830403	+	0.0123179i
$94$	−13.7321	+	2.12170i	−1.41635	+	0.218837i
$95$	−2.12293	−	5.12522i	−0.217808	−	0.525836i
$96$	−2.30594	+	2.44942i	−0.235349	+	0.249993i
$97$	3.06875	−	7.40863i	0.311585	−	0.752232i	−0.688062	−	0.725652i	$-0.741538\pi$
$97$	3.06875	−	7.40863i	0.311585	−	0.752232i	0.999647	−	0.0265802i	$-0.00846173\pi$
$98$	−1.96891	+	8.06647i	−0.198890	+	0.814837i
$99$	0.700025	−	0.519174i	0.0703552	−	0.0521789i
$100$	−7.38877	+	5.06703i	−0.738877	+	0.506703i
$101$	−0.824208	−	0.909373i	−0.0820117	−	0.0904860i	0.698563	−	0.715549i	$-0.253823\pi$
$101$	−0.824208	−	0.909373i	−0.0820117	−	0.0904860i	−0.780574	+	0.625063i	$0.785073\pi$
$102$	−2.01788	+	4.95594i	−0.199800	+	0.490711i
$103$	−12.0088	+	9.85535i	−1.18326	+	0.971077i	−0.999928	−	0.0119741i	$-0.996188\pi$
$103$	−12.0088	+	9.85535i	−1.18326	+	0.971077i	−0.183332	+	0.983051i	$0.558688\pi$
$104$	−10.6967	+	3.45741i	−1.04890	+	0.339027i
$105$	0.0446716	+	0.453559i	0.00435950	+	0.0442628i
$106$	−1.60566	−	15.3524i	−0.155955	−	1.49116i
$107$	8.50489	−	5.09763i	0.822198	−	0.492807i	−0.0401070	−	0.999195i	$-0.512770\pi$
$107$	8.50489	−	5.09763i	0.822198	−	0.492807i	0.862305	+	0.506389i	$0.169020\pi$
$108$	−4.06530	−	5.34540i	−0.391184	−	0.514362i
$109$	−3.05106	+	3.36633i	−0.292239	+	0.322436i	−0.869319	−	0.494252i	$-0.835442\pi$
$109$	−3.05106	+	3.36633i	−0.292239	+	0.322436i	0.577080	+	0.816688i	$0.304192\pi$
$110$	−0.302845	+	0.145477i	−0.0288752	+	0.0138707i
$111$	−1.29956	−	6.53332i	−0.123349	−	0.620115i
$112$	−0.518455	−	4.21785i	−0.0489894	−	0.398549i
$113$	0.0343575	−	0.172727i	0.00323208	−	0.0162488i	−0.979136	−	0.203208i	$-0.934863\pi$
$113$	0.0343575	−	0.172727i	0.00323208	−	0.0162488i	0.982368	+	0.186959i	$0.0598632\pi$
$114$	6.26429	−	1.60935i	0.586705	−	0.150729i
$115$	3.82674	+	1.36923i	0.356845	+	0.127681i
$116$	−4.06291	+	2.50234i	−0.377232	+	0.232336i
$117$	−1.54330	−	10.4041i	−0.142678	−	0.961857i
$118$	−1.45870	−	0.768413i	−0.134284	−	0.0707382i
$119$	−3.18642	−	5.96137i	−0.292098	−	0.546477i
$120$	0.538541	+	1.08729i	0.0491618	+	0.0992556i
$121$	−10.4226	+	3.16165i	−0.947505	+	0.287422i
$122$	1.75110	+	8.53396i	0.158537	+	0.772629i
$123$	0.538674	−	1.13893i	0.0485706	−	0.102694i
$124$	−1.25439	+	2.41649i	−0.112648	+	0.217008i
$125$	1.66155	+	6.63330i	0.148614	+	0.593300i
$126$	3.97233	+	0.171133i	0.353884	+	0.0152457i
$127$			8.35539i			0.741421i	0.928748	+	0.370711i	$0.120886\pi$
$127$			8.35539i			0.741421i	−0.928748	+	0.370711i	$0.879114\pi$
$128$	−5.26469	−	10.0141i	−0.465338	−	0.885133i
$129$			3.93808i			0.346728i
$130$	−0.174516	+	4.05086i	−0.0153061	+	0.355284i
$131$	−2.48630	−	9.92585i	−0.217229	−	0.867226i	−0.976336	−	0.216260i	$-0.930614\pi$
$131$	−2.48630	−	9.92585i	−0.217229	−	0.867226i	0.759107	−	0.650966i	$-0.225636\pi$
$132$	−0.118221	−	0.373440i	−0.0102898	−	0.0325038i
$133$	−3.49321	+	7.38576i	−0.302899	+	0.640427i
$134$	−15.6306	+	3.20726i	−1.35028	+	0.277065i
$135$	−2.31790	+	0.703127i	−0.199493	+	0.0605156i
$136$	−13.5506	−	11.8420i	−1.16196	−	1.01545i
$137$	0.558646	+	1.04515i	0.0477283	+	0.0892934i	0.904655	−	0.426146i	$-0.140129\pi$
$137$	0.558646	+	1.04515i	0.0477283	+	0.0892934i	−0.856926	+	0.515439i	$0.827629\pi$
$138$	−2.20847	+	4.19240i	−0.187997	+	0.356881i
$139$	−1.17331	−	7.90978i	−0.0995184	−	0.670899i	−0.980320	−	0.197414i	$-0.936746\pi$
$139$	−1.17331	−	7.90978i	−0.0995184	−	0.670899i	0.880802	−	0.473485i	$-0.157004\pi$
$140$	−1.49119	−	0.354460i	−0.126029	−	0.0299573i
$141$	−5.50142	−	1.96844i	−0.463303	−	0.165773i
$142$	1.59865	+	6.22267i	0.134156	+	0.522195i
$143$	0.255363	−	1.28380i	0.0213546	−	0.107357i
$144$	10.0525	−	3.31629i	0.837707	−	0.276358i
$145$	0.335760	+	1.68798i	0.0278834	+	0.140179i
$146$	3.14818	+	6.55368i	0.260545	+	0.542386i
$147$	−2.34482	+	2.58711i	−0.193398	+	0.213382i
$148$	22.1982	+	3.01954i	1.82468	+	0.248205i
$149$	−3.81437	+	2.28624i	−0.312485	+	0.187296i	−0.661744	−	0.749730i	$-0.730183\pi$
$149$	−3.81437	+	2.28624i	−0.312485	+	0.187296i	0.349259	+	0.937026i	$0.386433\pi$
$150$	−3.74703	+	0.391888i	−0.305943	+	0.0319975i
$151$	1.91860	+	19.4798i	0.156133	+	1.58525i	0.679848	+	0.733353i	$0.262046\pi$
$151$	1.91860	+	19.4798i	0.156133	+	1.58525i	−0.523715	+	0.851894i	$0.675454\pi$
$152$	−1.73992	+	21.6818i	−0.141127	+	1.75863i
$153$	13.0155	−	10.6815i	1.05224	−	0.863551i
$154$	0.458282	+	0.186596i	0.0369294	+	0.0150363i
$155$	0.659480	+	0.727624i	0.0529707	+	0.0584441i
$156$	−4.64716	−	0.866225i	−0.372070	−	0.0693535i
$157$	15.8676	−	11.7682i	1.26637	−	0.939204i	0.266672	−	0.963787i	$-0.414076\pi$
$157$	15.8676	−	11.7682i	1.26637	−	0.939204i	0.999698	+	0.0245833i	$0.00782589\pi$
$158$	6.04074	+	1.47446i	0.480576	+	0.117301i
$159$	2.48402	−	5.99696i	0.196996	−	0.475590i
$160$	−4.04707	+	0.522266i	−0.319949	+	0.0412887i
$161$	−2.29067	−	5.53018i	−0.180530	−	0.435839i
$162$	1.28317	+	8.30494i	0.100816	+	0.652498i
$163$	−8.17850	−	1.21317i	−0.640589	−	0.0950224i	−0.181469	−	0.983397i	$-0.558085\pi$
$163$	−8.17850	−	1.21317i	−0.640589	−	0.0950224i	−0.459120	+	0.888374i	$0.651835\pi$
$164$	3.03205	+	2.95975i	0.236763	+	0.231117i
$165$	−0.141110	−	0.00693230i	−0.0109854	−	0.000539679i
$166$	2.80352	+	2.76989i	0.217595	+	0.214985i
$167$	−4.02301	−	0.396232i	−0.311310	−	0.0306614i	−0.0588442	−	0.998267i	$-0.518742\pi$
$167$	−4.02301	−	0.396232i	−0.311310	−	0.0306614i	−0.252466	+	0.967606i	$0.581242\pi$
$168$	0.653863	−	1.66307i	0.0504466	−	0.128309i
$169$	−2.16188	−	1.77421i	−0.166299	−	0.136478i
$170$	−5.70578	+	3.09420i	−0.437613	+	0.237314i
$171$	−19.7414	−	4.94495i	−1.50966	−	0.378150i
$172$	−12.5229	−	4.31103i	−0.954859	−	0.328713i
$173$	−0.143174	−	2.91438i	−0.0108853	−	0.221576i	−0.998075	−	0.0620232i	$-0.980245\pi$
$173$	−0.143174	−	2.91438i	−0.0108853	−	0.221576i	0.987189	−	0.159553i	$-0.0510053\pi$
$174$	−2.00349	+	0.110545i	−0.151884	+	0.00838038i
$175$	2.64405	−	3.95710i	0.199871	−	0.299128i
$176$	1.31693	+	0.0328726i	0.0992677	+	0.00247786i
$177$	−0.385177	−	0.576459i	−0.0289517	−	0.0433293i
$178$	3.62878	−	2.72537i	0.271989	−	0.204275i
$179$	7.43390	+	15.7177i	0.555636	+	1.17479i	0.964958	+	0.262403i	$0.0845151\pi$
$179$	7.43390	+	15.7177i	0.555636	+	1.17479i	−0.409323	+	0.912390i	$0.634235\pi$
$180$	0.141314	−	3.81531i	0.0105330	−	0.284377i
$181$	3.16556	+	2.34774i	0.235294	+	0.174506i	0.706922	−	0.707292i	$-0.250083\pi$
$181$	3.16556	+	2.34774i	0.235294	+	0.174506i	−0.471627	+	0.881798i	$0.656333\pi$
$182$	4.59311	−	3.81607i	0.340464	−	0.282866i
$183$	−1.06342	+	3.50564i	−0.0786105	+	0.259144i
$184$	−10.9140	−	11.6122i	−0.804588	−	0.856066i
$185$	3.80897	−	7.12608i	0.280041	−	0.523920i
$186$	−0.948103	+	0.641809i	−0.0695183	+	0.0470597i
$187$	1.97292	−	0.705921i	0.144274	−	0.0516221i
$188$	12.2820	−	15.3393i	0.895754	−	1.11874i
$189$	3.05981	+	1.83398i	0.222569	+	0.133403i
$190$	7.11221	+	3.31147i	0.515974	+	0.240239i
$191$	−13.2396	+	13.2396i	−0.957981	+	0.957981i	−0.999152	−	0.0411710i	$-0.986891\pi$
$191$	−13.2396	+	13.2396i	−0.957981	+	0.957981i	0.0411710	+	0.999152i	$0.486891\pi$
$192$	0.0613259	−	4.75713i	0.00442581	−	0.343316i
$193$	16.8480	+	16.8480i	1.21275	+	1.21275i	0.970120	+	0.242626i	$0.0780087\pi$
$193$	16.8480	+	16.8480i	1.21275	+	1.21275i	0.242626	+	0.970120i	$0.421991\pi$
$194$	3.88489	+	10.6545i	0.278919	+	0.764946i
$195$	−0.876548	+	1.46243i	−0.0627709	+	0.104727i
$196$	−5.65998	−	10.2885i	−0.404284	−	0.734895i
$197$	8.55457	+	23.9084i	0.609488	+	1.70340i	0.706127	+	0.708085i	$0.250441\pi$
$197$	8.55457	+	23.9084i	0.609488	+	1.70340i	−0.0966393	+	0.995319i	$0.530809\pi$
$198$	−0.233159	+	1.21028i	−0.0165699	+	0.0860112i
$199$	−17.1241	−	9.15301i	−1.21389	−	0.648840i	−0.264943	−	0.964264i	$-0.585353\pi$
$199$	−17.1241	−	9.15301i	−1.21389	−	0.648840i	−0.948951	+	0.315424i	$0.897853\pi$
$200$	2.85571	−	12.3443i	0.201929	−	0.872876i
$201$	−6.42083	−	1.94774i	−0.452890	−	0.137383i
$202$	1.72831	+	0.159702i	0.121603	+	0.0112366i
$203$	1.50993	−	2.03590i	0.105976	−	0.142892i
$204$	−2.63518	−	7.09381i	−0.184499	−	0.496666i
$205$	1.38152	−	0.653412i	0.0964898	−	0.0456363i
$206$	3.09249	−	21.7512i	0.215464	−	1.51548i
$207$	12.3974	−	8.28365i	0.861676	−	0.575754i
$208$	7.84181	−	13.8294i	0.543732	−	0.958899i
$209$	−2.10587	−	1.40710i	−0.145666	−	0.0973308i
$210$	−0.480169	−	0.429952i	−0.0331348	−	0.0296695i
$211$	23.1057	−	1.13511i	1.59066	−	0.0781443i	0.765650	−	0.643257i	$-0.222417\pi$
$211$	23.1057	−	1.13511i	1.59066	−	0.0781443i	0.825014	+	0.565113i	$0.191167\pi$
$212$	16.3507	+	14.4639i	1.12297	+	0.993387i
$213$	−0.656451	+	2.62070i	−0.0449793	+	0.179567i
$214$	−3.98957	+	13.4433i	−0.272721	+	0.918962i
$215$	−3.03043	+	3.69258i	−0.206673	+	0.251832i
$216$	9.34688	+	1.68397i	0.635975	+	0.114579i
$217$	0.141760	−	1.43932i	0.00962332	−	0.0977072i
$218$	−0.0387612	−	6.42501i	−0.00262524	−	0.435157i
$219$	−0.150018	+	3.05368i	−0.0101372	+	0.206348i
$220$	0.176519	−	0.441134i	0.0119009	−	0.0297412i
$221$	3.71050	−	25.0142i	0.249595	−	1.68263i
$222$	7.60035	+	5.56605i	0.510102	+	0.373569i
$223$	−1.24324	+	0.514968i	−0.0832537	+	0.0344848i	−0.423922	−	0.905699i	$-0.639347\pi$
$223$	−1.24324	+	0.514968i	−0.0832537	+	0.0344848i	0.340668	+	0.940184i	$0.389347\pi$
$224$	4.57269	+	3.89982i	0.305525	+	0.260568i
$225$	10.9523	+	4.53658i	0.730152	+	0.302439i
$226$	0.129328	+	0.212848i	0.00860277	+	0.0141584i
$227$	6.99292	+	9.42886i	0.464136	+	0.625815i	0.971819	−	0.235729i	$-0.0757478\pi$
$227$	6.99292	+	9.42886i	0.464136	+	0.625815i	−0.507683	+	0.861544i	$0.669498\pi$
$228$	−4.98952	+	7.66599i	−0.330439	+	0.507692i
$229$	−8.54546	+	7.74516i	−0.564700	+	0.511814i	−0.903239	−	0.429138i	$-0.858817\pi$
$229$	−8.54546	+	7.74516i	−0.564700	+	0.511814i	0.338539	+	0.940952i	$0.390067\pi$
$230$	−5.29693	+	2.23159i	−0.349269	+	0.147147i
$231$	0.132001	+	0.160843i	0.00868500	+	0.0105827i
$232$	1.84171	−	6.49200i	0.120914	−	0.426221i
$233$	−18.3476	+	1.80709i	−1.20199	+	0.118386i	−0.679122	−	0.734025i	$-0.737639\pi$
$233$	−18.3476	+	1.80709i	−1.20199	+	0.118386i	−0.522872	+	0.852411i	$0.675139\pi$
$234$	11.5549	+	9.36679i	0.755369	+	0.612326i
$235$	−3.64372	−	6.07918i	−0.237690	−	0.396562i
$236$	2.25476	−	0.593789i	0.146772	−	0.0386524i
$237$	1.93741	+	1.75597i	0.125848	+	0.114062i
$238$	9.01987	+	3.16611i	0.584671	+	0.205228i
$239$	24.2293	−	4.81950i	1.56726	−	0.311748i	0.666312	−	0.745673i	$-0.267872\pi$
$239$	24.2293	−	4.81950i	1.56726	−	0.311748i	0.900949	+	0.433925i	$0.142872\pi$
$240$	−1.60071	−	0.618219i	−0.103325	−	0.0399059i
$241$	−5.11541	−	1.01752i	−0.329512	−	0.0655441i	0.0275618	−	0.999620i	$-0.491226\pi$
$241$	−5.11541	−	1.01752i	−0.329512	−	0.0655441i	−0.357074	+	0.934076i	$0.616226\pi$
$242$	7.83886	−	13.2591i	0.503901	−	0.852327i
$243$	−4.58414	+	12.8118i	−0.294072	+	0.821877i
$244$	−9.98359	−	7.21926i	−0.639134	−	0.462166i
$245$	−4.18948	+	0.621451i	−0.267656	+	0.0397031i
$246$	0.527494	+	1.70189i	0.0336318	+	0.108508i
$247$	−26.9562	+	14.4084i	−1.71518	+	0.916783i
$248$	−1.00302	−	3.71750i	−0.0636920	−	0.236062i
$249$	0.481076	+	1.58590i	0.0304870	+	0.100502i
$250$	−8.07317	−	5.32415i	−0.510592	−	0.336729i
$251$	−2.30786	−	1.09154i	−0.145671	−	0.0688972i	0.353330	−	0.935499i	$-0.385049\pi$
$251$	−2.30786	−	1.09154i	−0.145671	−	0.0688972i	−0.499001	+	0.866602i	$0.666299\pi$
$252$	−4.30323	+	3.61934i	−0.271078	+	0.227997i
$253$	1.79996	−	0.450866i	0.113162	−	0.0283457i
$254$	−7.98802	−	8.70728i	−0.501213	−	0.546343i
$255$	−2.72943			−0.170923
$256$	15.0603	+	5.40267i	0.941266	+	0.337667i
$257$	25.2172			1.57301			0.786504	−	0.617585i	$-0.211889\pi$
$257$	25.2172			1.57301			0.786504	+	0.617585i	$0.211889\pi$
$258$	−3.76493	−	4.10393i	−0.234394	−	0.255499i
$259$	−11.5436	+	2.89152i	−0.717285	+	0.179671i
$260$	−3.69089	−	4.38830i	−0.228899	−	0.272151i
$261$	5.70757	+	2.69948i	0.353290	+	0.167094i
$262$	12.0804	+	7.96690i	0.746332	+	0.492197i
$263$	−1.94264	−	6.40401i	−0.119788	−	0.394888i	0.876456	−	0.481483i	$-0.159902\pi$
$263$	−1.94264	−	6.40401i	−0.119788	−	0.394888i	−0.996244	+	0.0865944i	$0.972402\pi$
$264$	0.480220	+	0.276145i	0.0295555	+	0.0169955i
$265$	6.94394	−	3.71162i	0.426563	−	0.228003i
$266$	−3.42071	−	11.0364i	−0.209737	−	0.676687i
$267$	1.88772	−	0.280017i	0.115527	−	0.0171368i
$268$	13.2226	−	18.2857i	0.807699	−	1.11697i
$269$	−3.43951	+	9.61278i	−0.209710	+	0.586101i	−0.999633	−	0.0271058i	$-0.991371\pi$
$269$	−3.43951	+	9.61278i	−0.209710	+	0.586101i	0.789922	+	0.613207i	$0.210121\pi$
$270$	1.74331	−	2.94873i	0.106094	−	0.179454i
$271$	−5.94335	−	1.18221i	−0.361033	−	0.0718139i	0.0112412	−	0.999937i	$-0.496422\pi$
$271$	−5.94335	−	1.18221i	−0.361033	−	0.0718139i	−0.372274	+	0.928123i	$0.621422\pi$
$272$	25.4427	−	0.614080i	1.54269	−	0.0372341i
$273$	2.46283	−	0.489888i	0.149057	−	0.0296494i
$274$	−1.58137	−	0.555086i	−0.0955342	−	0.0335339i
$275$	1.09313	+	0.990756i	0.0659183	+	0.0597449i
$276$	−1.70659	−	6.48033i	−0.102725	−	0.390070i
$277$	−2.11161	−	3.52300i	−0.126874	−	0.211677i	0.787737	−	0.616012i	$-0.211253\pi$
$277$	−2.11161	−	3.52300i	−0.126874	−	0.211677i	−0.914611	+	0.404335i	$0.867503\pi$
$278$	8.78472	+	7.12118i	0.526873	+	0.427100i
$279$	3.58522	−	0.353113i	0.214641	−	0.0211403i
$280$	1.89287	−	1.05624i	0.113120	−	0.0631224i
$281$	−0.508347	−	0.619423i	−0.0303255	−	0.0369517i	0.757627	−	0.652688i	$-0.226359\pi$
$281$	−0.508347	−	0.619423i	−0.0303255	−	0.0369517i	−0.787952	+	0.615736i	$0.788859\pi$
$282$	7.61500	−	3.20820i	0.453467	−	0.191045i
$283$	−21.7039	+	19.6713i	−1.29016	+	1.16934i	−0.314696	+	0.949193i	$0.601903\pi$
$283$	−21.7039	+	19.6713i	−1.29016	+	1.16934i	−0.975467	+	0.220144i	$0.929347\pi$
$284$	−7.61505	−	4.95637i	−0.451870	−	0.294107i
$285$	1.96524	+	2.64981i	0.116411	+	0.156961i
$286$	0.961234	+	1.58200i	0.0568390	+	0.0935456i
$287$	−2.07944	−	0.861331i	−0.122745	−	0.0508428i
$288$	−7.30535	+	13.0664i	−0.430472	+	0.769948i
$289$	21.6942	−	8.98602i	1.27613	−	0.528589i
$290$	−1.96366	−	1.43807i	−0.115310	−	0.0844465i
$291$	−0.699735	+	4.71723i	−0.0410192	+	0.276529i
$292$	−9.54629	−	3.81992i	−0.558655	−	0.223544i
$293$	0.245412	−	4.99547i	0.0143371	−	0.291838i	−0.980910	−	0.194460i	$-0.937704\pi$
$293$	0.245412	−	4.99547i	0.0143371	−	0.291838i	0.995247	−	0.0973780i	$-0.0310456\pi$
$294$	−0.0297890	−	4.93780i	−0.00173733	−	0.287978i
$295$	0.0824299	−	0.836925i	0.00479925	−	0.0487276i
$296$	−26.0198	+	18.0755i	−1.51237	+	1.05062i
$297$	−0.701546	+	0.854837i	−0.0407078	+	0.0496026i
$298$	1.78928	−	6.02918i	0.103650	−	0.349261i
$299$	5.44115	−	21.7223i	0.314670	−	1.25623i
$300$	3.53017	−	3.99067i	0.203815	−	0.230401i
$301$	7.02679	−	0.345204i	0.405017	−	0.0198972i
$302$	−20.6227	−	18.4660i	−1.18671	−	1.06260i
$303$	0.606862	+	0.405492i	0.0348633	+	0.0232949i
$304$	−18.9153	−	24.2584i	−1.08487	−	1.39131i
$305$	−3.69479	+	2.46878i	−0.211563	+	0.141362i
$306$	−3.35174	+	23.5746i	−0.191606	+	1.34767i
$307$	−14.9546	+	7.07301i	−0.853505	+	0.403678i	−0.803667	−	0.595079i	$-0.797121\pi$
$307$	−14.9546	+	7.07301i	−0.853505	+	0.403678i	−0.0498384	+	0.998757i	$0.515871\pi$
$308$	−0.655974	+	0.243678i	−0.0373776	+	0.0138849i
$309$	5.50341	−	7.42048i	0.313078	−	0.422137i
$310$	−1.38288	−	0.127784i	−0.0785426	−	0.00725762i
$311$	21.2245	+	6.43837i	1.20353	+	0.365087i	0.827471	−	0.561509i	$-0.189779\pi$
$311$	21.2245	+	6.43837i	1.20353	+	0.365087i	0.376059	+	0.926596i	$0.377279\pi$
$312$	5.67101	−	3.54013i	0.321058	−	0.200420i
$313$	−24.5416	−	13.1178i	−1.38717	−	0.741460i	−0.402427	−	0.915452i	$-0.631833\pi$
$313$	−24.5416	−	13.1178i	−1.38717	−	0.741460i	−0.984747	+	0.173992i	$0.944333\pi$
$314$	−5.28506	+	27.4337i	−0.298253	+	1.54817i
$315$	0.683239	+	1.90953i	0.0384962	+	0.107590i
$316$	−7.70477	+	4.23859i	−0.433427	+	0.238439i
$317$	−3.62347	+	6.04540i	−0.203514	+	0.339543i	−0.942516	−	0.334160i	$-0.891547\pi$
$317$	−3.62347	+	6.04540i	−0.203514	+	0.339543i	0.739002	+	0.673703i	$0.235297\pi$
$318$	3.14465	+	8.62432i	0.176343	+	0.483628i
$319$	0.555605	+	0.555605i	0.0311079	+	0.0311079i
$320$	3.71820	−	4.41338i	0.207854	−	0.246716i
$321$	−4.16960	+	4.16960i	−0.232724	+	0.232724i
$322$	7.67417	+	3.57312i	0.427665	+	0.199122i
$323$	−41.9685	−	25.1550i	−2.33519	−	1.39966i
$324$	−9.27701	−	7.42795i	−0.515389	−	0.412664i
$325$	16.7636	−	5.99811i	0.929877	−	0.332715i
$326$	9.68276	−	6.55465i	0.536278	−	0.363028i
$327$	1.27363	−	2.38280i	0.0704321	−	0.131769i
$328$	−5.98935	−	0.185664i	−0.330707	−	0.0102516i
$329$	−3.03008	+	9.98885i	−0.167054	+	0.550703i
$330$	0.153681	−	0.127682i	0.00845984	−	0.00702865i
$331$	3.87246	+	2.87201i	0.212850	+	0.157860i	0.696872	−	0.717196i	$-0.254575\pi$
$331$	3.87246	+	2.87201i	0.212850	+	0.157860i	−0.484022	+	0.875056i	$0.660825\pi$
$332$	−5.56969	−	0.206294i	−0.305676	−	0.0113219i
$333$	−12.6738	−	26.7965i	−0.694521	−	1.46844i
$334$	4.57125	−	3.43321i	0.250128	−	0.187857i
$335$	−4.52175	−	6.76727i	−0.247049	−	0.369736i
$336$	0.908550	+	2.35823i	0.0495655	+	0.128652i
$337$	−17.3699	+	25.9959i	−0.946199	+	1.41609i	−0.0371915	+	0.999308i	$0.511841\pi$
$337$	−17.3699	+	25.9959i	−0.946199	+	1.41609i	−0.909008	+	0.416779i	$0.863159\pi$
$338$	3.94913	−	0.217897i	0.214804	−	0.0118521i
$339$	0.00513893	+	0.104605i	0.000279108	+	0.00568138i
$340$	2.98792	−	8.67942i	0.162043	−	0.470707i
$341$	0.434901	+	0.108937i	0.0235512	+	0.00589928i
$342$	25.3003	−	13.7202i	1.36808	−	0.741901i
$343$	10.5705	+	8.67498i	0.570753	+	0.468405i
$344$	17.1717	−	7.47966i	0.925838	−	0.403276i
$345$	−2.40538	−	0.236909i	−0.129501	−	0.0127547i
$346$	2.93544	+	2.90024i	0.157810	+	0.155918i
$347$	−15.2429	−	0.748833i	−0.818279	−	0.0401995i	−0.364378	−	0.931251i	$-0.618718\pi$
$347$	−15.2429	−	0.748833i	−0.818279	−	0.0401995i	−0.453902	+	0.891052i	$0.649968\pi$
$348$	1.98218	−	2.03060i	0.106256	−	0.108852i
$349$	−5.36570	−	0.795926i	−0.287219	−	0.0426050i	0.00156620	−	0.999999i	$-0.499501\pi$
$349$	−5.36570	−	0.795926i	−0.287219	−	0.0426050i	−0.288786	+	0.957394i	$0.593251\pi$
$350$	1.02771	+	6.65154i	0.0549334	+	0.355540i
$351$	5.10718	+	12.3298i	0.272601	+	0.658117i
$352$	−1.40382	+	1.22477i	−0.0748241	+	0.0652807i
$353$	−11.3530	+	27.4086i	−0.604261	+	1.45881i	0.264896	+	0.964277i	$0.414662\pi$
$353$	−11.3530	+	27.4086i	−0.604261	+	1.45881i	−0.869156	+	0.494537i	$0.835338\pi$
$354$	0.952512	+	0.232494i	0.0506254	+	0.0123569i
$355$	−2.63221	+	1.95218i	−0.139703	+	0.103611i
$356$	−1.17606	+	6.30938i	−0.0623311	+	0.334397i
$357$	2.69955	+	2.97849i	0.142875	+	0.157638i
$358$	−22.7736	−	9.27256i	−1.20362	−	0.490070i
$359$	6.72062	−	5.51547i	0.354701	−	0.291095i	−0.440121	−	0.897939i	$-0.645064\pi$
$359$	6.72062	−	5.51547i	0.354701	−	0.291095i	0.794822	+	0.606843i	$0.207564\pi$
$360$	3.50030	+	4.11109i	0.184482	+	0.216674i
$361$	3.93453	+	39.9479i	0.207080	+	2.10252i
$362$	−5.54339	+	0.579763i	−0.291354	+	0.0304717i
$363$	5.55559	−	3.32989i	0.291593	−	0.174774i
$364$	−1.13826	+	8.36795i	−0.0596611	+	0.438600i
$365$	−2.49053	+	2.74788i	−0.130360	+	0.143830i
$366$	−2.24329	−	4.66994i	−0.117259	−	0.244102i
$367$	5.72076	+	28.7602i	0.298621	+	1.50127i	0.780568	+	0.625070i	$0.214930\pi$
$367$	5.72076	+	28.7602i	0.298621	+	1.50127i	−0.481947	+	0.876200i	$0.660070\pi$
$368$	22.4753	+	1.66720i	1.17160	+	0.0869088i
$369$	1.09377	−	5.49874i	0.0569393	−	0.286253i
$370$	2.84338	+	11.0677i	0.147820	+	0.575382i
$371$	−10.9182	−	3.90661i	−0.566846	−	0.202821i
$372$	0.374442	−	1.57526i	0.0194139	−	0.0816732i
$373$	0.299198	+	2.01703i	0.0154919	+	0.104438i	0.995543	−	0.0943070i	$-0.0300635\pi$
$373$	0.299198	+	2.01703i	0.0154919	+	0.104438i	−0.980051	+	0.198745i	$0.936314\pi$
$374$	−1.38112	+	2.62182i	−0.0714162	+	0.135571i
$375$	−1.91700	−	3.58645i	−0.0989932	−	0.185203i
$376$	1.86569	+	27.7273i	0.0962155	+	1.42993i
$377$	9.07423	−	2.75264i	0.467347	−	0.141768i
$378$	−4.94202	+	1.01406i	−0.254190	+	0.0521577i
$379$	−11.5965	+	24.5188i	−0.595674	+	1.25945i	0.350734	+	0.936475i	$0.385932\pi$
$379$	−11.5965	+	24.5188i	−0.595674	+	1.25945i	−0.946408	+	0.322972i	$0.895318\pi$
$380$	−10.5776	+	3.34857i	−0.542620	+	0.171778i
$381$	−1.20734	−	4.81996i	−0.0618538	−	0.246934i
$382$	1.13970	−	26.4546i	0.0583119	−	1.35353i
$383$		−	29.6476i		−	1.51492i	−0.652881	−	0.757461i	$-0.726440\pi$
$383$		−	29.6476i		−	1.51492i	0.652881	−	0.757461i	$-0.273560\pi$
$384$	4.48406	+	5.01610i	0.228826	+	0.255977i
$385$			0.252394i			0.0128632i
$386$	−33.6648	−	1.45032i	−1.71349	−	0.0738193i
$387$	4.25805	+	16.9991i	0.216449	+	0.864111i
$388$	−14.2345	−	7.38909i	−0.722648	−	0.375124i
$389$	12.4803	−	26.3874i	0.632777	−	1.33789i	−0.291646	−	0.956526i	$-0.594203\pi$
$389$	12.4803	−	26.3874i	0.632777	−	1.33789i	0.924423	−	0.381368i	$-0.124547\pi$
$390$	−0.484668	−	2.36203i	−0.0245421	−	0.119606i
$391$	34.3044	−	10.4061i	1.73485	−	0.526261i
$392$	15.7345	+	5.31070i	0.794713	+	0.268231i
$393$	2.86853	+	5.36664i	0.144698	+	0.270711i
$394$	−31.7721	−	16.7369i	−1.60065	−	0.843191i
$395$	0.465386	+	3.13738i	0.0234161	+	0.157859i
$396$	−0.914092	−	1.48416i	−0.0459349	−	0.0745820i
$397$	−4.63496	−	1.65842i	−0.232622	−	0.0832335i	0.217998	−	0.975949i	$-0.430047\pi$
$397$	−4.63496	−	1.65842i	−0.232622	−	0.0832335i	−0.450620	+	0.892716i	$0.648797\pi$
$398$	26.5958	−	6.83268i	1.33313	−	0.342491i
$399$	0.947892	−	4.76537i	0.0474539	−	0.238567i
$400$	8.82559	+	15.5944i	0.441280	+	0.779718i
$401$	−0.743304	−	3.73684i	−0.0371188	−	0.186609i	0.957778	−	0.287510i	$-0.0928274\pi$
$401$	−0.743304	−	3.73684i	−0.0371188	−	0.186609i	−0.994896	+	0.100901i	$0.967827\pi$
$402$	8.55334	−	4.10875i	0.426602	−	0.204926i
$403$	3.63356	−	4.00902i	0.181001	−	0.199704i
$404$	−1.95378	+	1.48589i	−0.0972040	+	0.0739258i
$405$	−3.67660	+	2.20367i	−0.182692	+	0.109501i
$406$	0.372869	+	3.56518i	0.0185052	+	0.176937i
$407$	−0.361585	−	3.67124i	−0.0179231	−	0.181976i
$408$	9.52807	+	4.87325i	0.471710	+	0.241262i
$409$	22.4235	−	18.4025i	1.10877	−	0.909943i	0.112281	−	0.993676i	$-0.464184\pi$
$409$	22.4235	−	18.4025i	1.10877	−	0.909943i	0.996488	+	0.0837330i	$0.0266843\pi$
$410$	−0.815023	+	2.00171i	−0.0402511	+	0.0988575i
$411$	−0.473287	−	0.522192i	−0.0233455	−	0.0257578i
$412$	17.5721	+	25.6238i	0.865715	+	1.26239i
$413$	−0.994823	+	0.737811i	−0.0489520	+	0.0363053i
$414$	−5.00004	+	20.4848i	−0.245738	+	1.00677i
$415$	−0.769290	+	1.85723i	−0.0377630	+	0.0911679i
$416$	5.04931	+	21.9089i	0.247563	+	1.07417i
$417$	1.81979	+	4.39336i	0.0891155	+	0.215144i
$418$	3.53978	−	0.546922i	0.173136	−	0.0267508i
$419$	22.8983	+	3.39664i	1.11865	+	0.165937i	0.680348	−	0.732889i	$-0.261829\pi$
$419$	22.8983	+	3.39664i	1.11865	+	0.165937i	0.438306	+	0.898826i	$0.355579\pi$
$420$	0.911440	−	0.0109976i	0.0444737	−	0.000536627i
$421$	1.06033	+	0.0520904i	0.0516771	+	0.00253873i	0.0748898	−	0.997192i	$-0.476139\pi$
$421$	1.06033	+	0.0520904i	0.0516771	+	0.00253873i	−0.0232127	+	0.999731i	$0.507389\pi$
$422$	−22.9936	+	23.2727i	−1.11931	+	1.13290i
$423$	−25.8758	−	2.54854i	−1.25812	−	0.123914i
$424$	−30.8673	+	0.558708i	−1.49905	+	0.0271333i
$425$	22.0322	+	18.0813i	1.06872	+	0.877074i
$426$	−1.82138	−	3.35866i	−0.0882460	−	0.162728i
$427$	6.34840	+	1.59019i	0.307220	+	0.0769547i
$428$	−8.69460	−	17.8236i	−0.420269	−	0.861535i
$429$	0.0381952	+	0.777482i	0.00184408	+	0.0375372i
$430$	−0.372178	−	6.74528i	−0.0179480	−	0.325286i
$431$	11.7697	−	17.6147i	0.566928	−	0.848468i	−0.431635	−	0.902048i	$-0.642063\pi$
$431$	11.7697	−	17.6147i	0.566928	−	0.848468i	0.998564	+	0.0535800i	$0.0170632\pi$
$432$	−11.3504	+	7.18103i	−0.546099	+	0.345498i
$433$	−7.64799	−	11.4460i	−0.367539	−	0.550061i	0.600896	−	0.799327i	$-0.294811\pi$
$433$	−7.64799	−	11.4460i	−0.367539	−	0.550061i	−0.968435	+	0.249266i	$0.919811\pi$
$434$	1.22830	+	1.63546i	0.0589604	+	0.0785046i
$435$	−0.437599	−	0.925225i	−0.0209813	−	0.0443612i
$436$	6.18291	+	6.65854i	0.296108	+	0.318886i
$437$	−34.8024	−	25.8112i	−1.66483	−	1.23472i
$438$	−2.76308	−	3.32570i	−0.132025	−	0.158908i
$439$	2.35804	−	7.77342i	0.112543	−	0.371005i	−0.882517	−	0.470281i	$-0.844153\pi$
$439$	2.35804	−	7.77342i	0.112543	−	0.371005i	0.995060	+	0.0992759i	$0.0316526\pi$
$440$	0.237785	+	0.628469i	0.0113360	+	0.0299611i
$441$	−7.32433	+	13.7029i	−0.348778	+	0.652517i
$442$	20.0476	+	29.6150i	0.953566	+	1.40864i
$443$	19.4965	−	6.97594i	0.926304	−	0.331437i	0.169840	−	0.985472i	$-0.445675\pi$
$443$	19.4965	−	6.97594i	0.926304	−	0.331437i	0.756465	+	0.654035i	$0.226925\pi$
$444$	−13.2418	+	1.46572i	−0.628426	+	0.0695599i
$445$	1.98552	+	1.19008i	0.0941229	+	0.0564151i
$446$	0.803276	−	1.72524i	0.0380362	−	0.0816923i
$447$	1.87003	−	1.87003i	0.0884493	−	0.0884493i
$448$	−8.49361	+	0.307575i	−0.401286	+	0.0145316i
$449$	−11.7529	−	11.7529i	−0.554654	−	0.554654i	0.373126	−	0.927781i	$-0.378286\pi$
$449$	−11.7529	−	11.7529i	−0.554654	−	0.554654i	−0.927781	+	0.373126i	$0.878286\pi$
$450$	−15.7507	+	5.74309i	−0.742493	+	0.270732i
$451$	0.358701	−	0.598457i	0.0168906	−	0.0281802i
$452$	−0.338264	−	0.0981705i	−0.0159106	−	0.00461755i
$453$	−3.92157	−	10.9601i	−0.184252	−	0.514949i
$454$	−16.3017	−	3.14050i	−0.765077	−	0.147391i
$455$	2.68628	+	1.43585i	0.125935	+	0.0673136i
$456$	−2.12927	−	12.7590i	−0.0997124	−	0.597494i
$457$	−27.9361	−	8.47432i	−1.30679	−	0.396412i	−0.441313	−	0.897353i	$-0.645487\pi$
$457$	−27.9361	−	8.47432i	−1.30679	−	0.396412i	−0.865481	+	0.500941i	$0.832987\pi$
$458$	1.50073	−	16.2411i	0.0701247	−	0.758896i
$459$	−12.7266	+	17.1599i	−0.594029	+	0.800956i
$460$	3.38653	−	7.38961i	0.157898	−	0.344542i
$461$	−26.8506	+	12.6994i	−1.25055	+	0.591468i	−0.934057	−	0.357125i	$-0.883757\pi$
$461$	−26.8506	+	12.6994i	−1.25055	+	0.591468i	−0.316498	+	0.948593i	$0.602507\pi$
$462$	−0.291331	−	0.0414203i	−0.0135539	−	0.00192704i
$463$	7.88351	−	5.26760i	0.366378	−	0.244806i	−0.358730	−	0.933442i	$-0.616790\pi$
$463$	7.88351	−	5.26760i	0.366378	−	0.244806i	0.725108	+	0.688636i	$0.241790\pi$
$464$	4.28729	+	8.52614i	0.199032	+	0.395816i
$465$	−0.485573	−	0.324449i	−0.0225179	−	0.0150460i
$466$	17.3927	−	19.4241i	0.805702	−	0.899805i
$467$	25.2452	−	1.24022i	1.16821	−	0.0573905i	0.544303	−	0.838889i	$-0.316794\pi$
$467$	25.2452	−	1.24022i	1.16821	−	0.0573905i	0.623907	+	0.781499i	$0.285544\pi$
$468$	−20.9965	+	1.28560i	−0.970563	+	0.0594269i
$469$	−2.91255	+	11.6276i	−0.134489	+	0.536910i
$470$	9.60907	+	2.85169i	0.443233	+	0.131539i
$471$	−7.45302	+	9.08153i	−0.343417	+	0.418455i
$472$	−1.78204	+	2.77442i	−0.0820249	+	0.127703i
$473$	−0.213764	+	2.17038i	−0.00982889	+	0.0997944i
$474$	−3.69777	+	0.0223081i	−0.169844	+	0.00102465i
$475$	1.69038	−	34.4084i	0.0775598	−	1.57877i
$476$	−12.4266	+	5.32383i	−0.569574	+	0.244017i
$477$	4.23830	−	28.5723i	0.194058	−	1.30823i
$478$	−20.6421	+	28.1864i	−0.944147	+	1.28922i
$479$	12.4172	−	5.14337i	0.567356	−	0.235007i	−0.0805192	−	0.996753i	$-0.525658\pi$
$479$	12.4172	−	5.14337i	0.567356	−	0.235007i	0.647875	+	0.761746i	$0.275658\pi$
$480$	2.25916	−	0.886071i	0.103116	−	0.0404434i
$481$	−41.1308	−	17.0370i	−1.87540	−	0.776818i
$482$	6.30362	−	3.83012i	0.287122	−	0.174457i
$483$	2.12052	+	2.85919i	0.0964869	+	0.130097i
$484$	4.50713	+	21.3117i	0.204869	+	0.968713i
$485$	−4.28611	+	3.88471i	−0.194622	+	0.176395i
$486$	−7.47130	−	17.7339i	−0.338905	−	0.804428i
$487$	−0.424061	−	0.516719i	−0.0192160	−	0.0234148i	0.763314	−	0.646028i	$-0.223571\pi$
$487$	−0.424061	−	0.516719i	−0.0192160	−	0.0234148i	−0.782530	+	0.622613i	$0.786071\pi$
$488$	17.3059	−	2.02133i	0.783401	−	0.0915012i
$489$	4.89321	−	0.481940i	0.221279	−	0.0217941i
$490$	3.77180	−	4.65291i	0.170392	−	0.210197i
$491$	−4.52492	−	7.54938i	−0.204207	−	0.340699i	0.738539	−	0.674211i	$-0.235516\pi$
$491$	−4.52492	−	7.54938i	−0.204207	−	0.340699i	−0.942746	+	0.333512i	$0.891766\pi$
$492$	−2.17677	−	1.26926i	−0.0981363	−	0.0572226i
$493$	11.2476	+	10.1942i	0.506567	+	0.459125i
$494$	14.3166	−	40.7861i	0.644132	−	1.83505i
$495$	−0.616611	+	0.122652i	−0.0277146	+	0.00551278i
$496$	4.59932	+	2.91514i	0.206515	+	0.130894i
$497$	4.73371	+	0.941594i	0.212336	+	0.0422363i
$498$	−2.01750	−	1.19276i	−0.0904065	−	0.0534489i
$499$	4.18745	−	11.7031i	0.187456	−	0.523904i	−0.810643	−	0.585541i	$-0.800882\pi$
$499$	4.18745	−	11.7031i	0.187456	−	0.523904i	0.998099	+	0.0616370i	$0.0196321\pi$
$500$	13.5032	−	2.16983i	0.603883	−	0.0970378i
$501$	2.37800	−	0.352743i	0.106241	−	0.0157594i
$502$	3.44860	−	1.06888i	0.153919	−	0.0477066i
$503$	35.3633	−	18.9021i	1.57677	−	0.842803i	0.577115	−	0.816663i	$-0.304178\pi$
$503$	35.3633	−	18.9021i	1.57677	−	0.842803i	0.999658	−	0.0261402i	$-0.00832163\pi$
$504$	1.02426	−	7.88579i	0.0456242	−	0.351261i
$505$	0.256997	+	0.847206i	0.0114362	+	0.0377002i
$506$	−1.44472	+	2.19067i	−0.0642256	+	0.0973871i
$507$	1.50349	+	0.711098i	0.0667723	+	0.0315810i
$508$	16.6489	+	1.43718i	0.738674	+	0.0637643i
$509$	−0.793086	+	0.198658i	−0.0351529	+	0.00880535i	−0.260517	−	0.965469i	$-0.583893\pi$
$509$	−0.793086	+	0.198658i	−0.0351529	+	0.00880535i	0.225364	+	0.974275i	$0.427643\pi$
$510$	2.84438	−	2.60942i	0.125951	−	0.115547i
$511$	5.46189			0.241620
$512$	−20.8596	+	8.76789i	−0.921874	+	0.387490i
$513$	25.8228			1.14010
$514$	−26.2792	+	24.1085i	−1.15913	+	1.06338i
$515$	10.8705	−	2.72293i	0.479013	−	0.119987i
$516$	7.84697	+	0.677371i	0.345444	+	0.0298196i
$517$	−2.92514	−	1.38349i	−0.128647	−	0.0608457i
$518$	9.26538	−	14.0494i	0.407097	−	0.617294i
$519$	0.503715	+	1.66052i	0.0221106	+	0.0728889i
$520$	8.04169	+	1.04451i	0.352651	+	0.0458048i
$521$	5.89916	−	3.15317i	0.258447	−	0.138143i	−0.337086	−	0.941474i	$-0.609441\pi$
$521$	5.89916	−	3.15317i	0.258447	−	0.138143i	0.595532	+	0.803331i	$0.296941\pi$
$522$	−8.52873	+	2.64345i	−0.373292	+	0.115701i
$523$	3.17629	−	0.471159i	0.138890	−	0.0206023i	−0.0769236	−	0.997037i	$-0.524510\pi$
$523$	3.17629	−	0.471159i	0.138890	−	0.0206023i	0.215813	+	0.976435i	$0.430760\pi$
$524$	−20.2058	+	3.24687i	−0.882695	+	0.141840i
$525$	−0.953474	+	2.66478i	−0.0416130	+	0.116301i
$526$	8.14689	+	4.81649i	0.355221	+	0.210009i
$527$	8.49510	+	1.68978i	0.370052	+	0.0736080i
$528$	−0.764448	+	0.171331i	−0.0332683	+	0.00745624i
$529$	8.57683	−	1.70604i	0.372906	−	0.0741755i
$530$	−3.68796	+	10.5066i	−0.160195	+	0.456376i
$531$	−2.28595	−	2.07186i	−0.0992018	−	0.0899112i
$532$	14.1159	+	8.23092i	0.612004	+	0.356856i
$533$	−4.32889	−	7.22232i	−0.187505	−	0.312833i
$534$	−1.69952	+	2.09653i	−0.0735453	+	0.0907259i
$535$	−7.11826	+	0.701088i	−0.307749	+	0.0303107i
$536$	3.70221	+	31.6970i	0.159911	+	1.36910i
$537$	−6.55955	−	7.99283i	−0.283065	−	0.344916i
$538$	−5.60576	−	13.3059i	−0.241682	−	0.573658i
$539$	−1.43273	+	1.29855i	−0.0617120	+	0.0559325i
$540$	1.00235	+	4.73957i	0.0431344	+	0.203958i
$541$	−4.03203	−	5.43656i	−0.173350	−	0.233736i	0.707985	−	0.706228i	$-0.249605\pi$
$541$	−4.03203	−	5.43656i	−0.173350	−	0.233736i	−0.881335	+	0.472492i	$0.843355\pi$
$542$	7.32387	−	4.45004i	0.314587	−	0.191145i
$543$	−2.16535	−	0.896919i	−0.0929243	−	0.0384905i
$544$	−25.9271	+	24.9639i	−1.11161	+	1.07032i
$545$	3.02785	−	1.25418i	0.129699	−	0.0537230i
$546$	−2.09821	+	2.86507i	−0.0897949	+	0.122614i
$547$	4.83376	−	32.5865i	0.206676	−	1.39330i	−0.598908	−	0.800818i	$-0.704398\pi$
$547$	4.83376	−	32.5865i	0.206676	−	1.39330i	0.805584	−	0.592481i	$-0.201852\pi$
$548$	2.17865	−	0.933380i	0.0930673	−	0.0398720i
$549$	−0.799895	+	16.2822i	−0.0341387	+	0.694909i
$550$	−2.08636	+	0.0125867i	−0.0889628	+	0.000536700i
$551$	1.79841	−	18.2596i	0.0766149	−	0.777884i
$552$	7.97386	+	5.12169i	0.339390	+	0.217994i
$553$	2.96338	−	3.61089i	0.126016	−	0.153551i
$554$	5.56864	+	1.65261i	0.236589	+	0.0702126i
$555$	−1.16757	+	4.66120i	−0.0495605	+	0.197857i
$556$	−15.9628	+	0.977389i	−0.676972	+	0.0414505i
$557$	1.20983	−	0.0594352i	0.0512622	−	0.00251835i	−0.0234204	−	0.999726i	$-0.507456\pi$
$557$	1.20983	−	0.0594352i	0.0512622	−	0.00251835i	0.0746826	+	0.997207i	$0.476206\pi$
$558$	−3.39862	+	3.79557i	−0.143875	+	0.160679i
$559$	21.8838	+	14.6223i	0.925586	+	0.618457i
$560$	−0.962786	+	2.91036i	−0.0406852	+	0.122985i
$561$	−1.03611	+	0.692306i	−0.0437446	+	0.0292292i
$562$	1.12194	+	0.159513i	0.0473264	+	0.00672867i
$563$	−16.3503	+	7.73311i	−0.689082	+	0.325912i	−0.739824	−	0.672800i	$-0.765091\pi$
$563$	−16.3503	+	7.73311i	−0.689082	+	0.325912i	0.0507420	+	0.998712i	$0.483841\pi$
$564$	−4.86857	+	10.6235i	−0.205004	+	0.447330i
$565$	−0.0756772	+	0.102039i	−0.00318376	+	0.00429281i
$566$	3.81159	−	41.2494i	0.160213	−	1.73384i
$567$	6.04111	+	1.83255i	0.253703	+	0.0769599i
$568$	12.6742	−	2.11513i	0.531798	−	0.0887488i
$569$	14.2142	+	7.59766i	0.595892	+	0.318511i	0.741627	−	0.670813i	$-0.234055\pi$
$569$	14.2142	+	7.59766i	0.595892	+	0.318511i	−0.145735	+	0.989324i	$0.546555\pi$
$570$	−4.58131	−	0.882581i	−0.191890	−	0.0369673i
$571$	3.37759	+	9.43973i	0.141348	+	0.395040i	0.991267	−	0.131873i	$-0.0420992\pi$
$571$	3.37759	+	9.43973i	0.141348	+	0.395040i	−0.849919	+	0.526914i	$0.823349\pi$
$572$	−2.51416	−	0.729655i	−0.105122	−	0.0305084i
$573$	5.72439	−	9.55057i	0.239140	−	0.398981i
$574$	2.99047	−	1.09040i	0.124820	−	0.0455125i
$575$	17.8470	+	17.8470i	0.744271	+	0.744271i
$576$	−4.87893	−	20.6009i	−0.203289	−	0.858370i
$577$	21.4270	−	21.4270i	0.892017	−	0.892017i	−0.102696	−	0.994713i	$-0.532747\pi$
$577$	21.4270	−	21.4270i	0.892017	−	0.892017i	0.994713	+	0.102696i	$0.0327468\pi$
$578$	−14.0169	+	30.1048i	−0.583026	+	1.25219i
$579$	−12.1536	−	7.28457i	−0.505085	−	0.302737i
$580$	3.42121	−	0.378690i	0.142058	−	0.0157243i
$581$	2.78757	−	0.997410i	0.115648	−	0.0413795i
$582$	−3.78062	−	5.58486i	−0.156712	−	0.231500i
$583$	1.69454	−	3.17025i	0.0701805	−	0.131298i
$584$	13.6003	−	5.14576i	0.562784	−	0.212933i
$585$	−2.20245	+	7.26049i	−0.0910599	+	0.300184i
$586$	4.52008	+	5.44047i	0.186723	+	0.224744i
$587$	25.1426	+	18.6470i	1.03775	+	0.769645i	0.973592	−	0.228295i	$-0.0733149\pi$
$587$	25.1426	+	18.6470i	1.03775	+	0.769645i	0.0641546	+	0.997940i	$0.479565\pi$
$588$	4.75173	+	5.11727i	0.195958	+	0.211033i
$589$	−4.47613	−	9.46398i	−0.184436	−	0.389957i
$590$	0.714225	+	0.950977i	0.0294042	+	0.0391511i
$591$	−8.38958	−	12.5559i	−0.345101	−	0.516480i
$592$	9.83492	−	43.7125i	0.404213	−	1.79657i
$593$	−21.7525	+	32.5549i	−0.893267	+	1.33687i	0.0478732	+	0.998853i	$0.484756\pi$
$593$	−21.7525	+	32.5549i	−0.893267	+	1.33687i	−0.941141	+	0.338016i	$0.890244\pi$
$594$	−0.0861595	−	1.56154i	−0.00353517	−	0.0640707i
$595$	0.239256	+	4.87017i	0.00980855	+	0.199658i
$596$	3.89945	+	7.99371i	0.159728	+	0.327435i
$597$	11.2009	+	2.80569i	0.458423	+	0.114829i
$598$	15.0969	+	27.8390i	0.617358	+	1.13842i
$599$	25.3799	+	20.8288i	1.03700	+	0.851041i	0.989016	−	0.147807i	$-0.0472215\pi$
$599$	25.3799	+	20.8288i	1.03700	+	0.851041i	0.0479804	+	0.998848i	$0.484722\pi$
$600$	0.136362	+	7.53369i	0.00556697	+	0.307562i
$601$	−0.305905	−	0.0301290i	−0.0124781	−	0.00122899i	0.0917761	−	0.995780i	$-0.470746\pi$
$601$	−0.305905	−	0.0301290i	−0.0124781	−	0.00122899i	−0.104254	+	0.994551i	$0.533246\pi$
$602$	−6.99269	+	7.07758i	−0.285001	+	0.288461i
$603$	−29.8221	−	1.46507i	−1.21445	−	0.0596621i
$604$	39.1453	−	0.472334i	1.59280	−	0.0192190i
$605$	7.77168	+	1.15282i	0.315964	+	0.0468688i
$606$	−1.02008	+	0.157610i	−0.0414380	+	0.00640247i
$607$	−9.85237	−	23.7857i	−0.399895	−	0.965433i	−0.987690	−	0.156423i	$-0.950004\pi$
$607$	−9.85237	−	23.7857i	−0.399895	−	0.965433i	0.587795	−	0.809010i	$-0.299996\pi$
$608$	42.9037	+	7.19636i	1.73998	+	0.291851i
$609$	−0.576845	+	1.39263i	−0.0233749	+	0.0564321i
$610$	1.49016	−	6.10508i	0.0603348	−	0.247188i
$611$	−31.3657	+	23.2624i	−1.26892	+	0.941094i
$612$	−19.0452	−	27.7718i	−0.769856	−	1.12261i
$613$	12.3570	+	13.6338i	0.499094	+	0.550665i	0.937443	−	0.348140i	$-0.113187\pi$
$613$	12.3570	+	13.6338i	0.499094	+	0.550665i	−0.438349	+	0.898805i	$0.644437\pi$
$614$	8.82241	−	21.6680i	0.356043	−	0.874449i
$615$	−0.702540	+	0.576560i	−0.0283292	+	0.0232491i
$616$	0.450636	−	0.881073i	0.0181566	−	0.0354994i
$617$	2.28717	+	23.2221i	0.0920782	+	0.934885i	0.924612	+	0.380911i	$0.124389\pi$
$617$	2.28717	+	23.2221i	0.0920782	+	0.934885i	−0.832534	+	0.553974i	$0.813111\pi$
$618$	1.35904	+	12.9944i	0.0546686	+	0.522713i
$619$	38.1018	−	22.8373i	1.53144	−	0.917910i	0.534071	−	0.845440i	$-0.320662\pi$
$619$	38.1018	−	22.8373i	1.53144	−	0.917910i	0.997371	−	0.0724705i	$-0.0230883\pi$
$620$	1.56329	−	1.18892i	0.0627832	−	0.0477481i
$621$	−12.7051	+	14.0179i	−0.509839	+	0.562521i
$622$	−28.2736	+	13.5818i	−1.13367	+	0.544579i
$623$	−0.665114	−	3.34376i	−0.0266472	−	0.133965i
$624$	−2.52537	+	9.11089i	−0.101096	+	0.364727i
$625$	−3.40733	+	17.1298i	−0.136293	+	0.685192i
$626$	38.1162	−	9.79235i	1.52343	−	0.391381i
$627$	1.41813	+	0.507415i	0.0566347	+	0.0202642i
$628$	−20.7199	−	33.6418i	−0.826813	−	1.34245i
$629$	−10.4573	−	70.4972i	−0.416959	−	2.81091i
$630$	−2.53758	−	1.33675i	−0.101100	−	0.0532573i
$631$	−0.841703	−	1.57472i	−0.0335077	−	0.0626885i	0.864610	−	0.502443i	$-0.167565\pi$
$631$	−0.841703	−	1.57472i	−0.0335077	−	0.0626885i	−0.898118	+	0.439755i	$0.855065\pi$
$632$	3.97703	−	11.7831i	0.158198	−	0.468707i
$633$	−13.1649	+	3.99354i	−0.523259	+	0.158729i
$634$	−2.00352	−	9.76415i	−0.0795699	−	0.387784i
$635$	2.57698	−	5.44856i	0.102264	−	0.216220i
$636$	−11.5222	−	5.98114i	−0.456885	−	0.237168i
$637$	5.67008	+	22.6362i	0.224657	+	0.896880i
$638$	−1.11018	−	0.0478279i	−0.0439525	−	0.00189353i
$639$			12.0223i			0.475594i
$640$	0.344543	+	8.15397i	0.0136193	+	0.322314i
$641$			45.0056i			1.77761i	0.458282	+	0.888807i	$0.348465\pi$
$641$			45.0056i			1.77761i	−0.458282	+	0.888807i	$0.651535\pi$
$642$	0.358930	−	8.33147i	0.0141658	−	0.328817i
$643$	−9.31597	−	37.1914i	−0.367386	−	1.46669i	−0.818648	−	0.574296i	$-0.805276\pi$
$643$	−9.31597	−	37.1914i	−0.367386	−	1.46669i	0.451262	−	0.892392i	$-0.350974\pi$
$644$	−11.4134	+	3.61315i	−0.449750	+	0.142378i
$645$	1.21459	−	2.56802i	0.0478242	−	0.101116i
$646$	67.7850	−	13.9089i	2.66696	−	0.547238i
$647$	19.4303	−	5.89413i	0.763885	−	0.231722i	0.115782	−	0.993275i	$-0.463063\pi$
$647$	19.4303	−	5.89413i	0.763885	−	0.231722i	0.648103	+	0.761552i	$0.275563\pi$
$648$	16.7691	−	1.12834i	0.658751	−	0.0443254i
$649$	−0.180991	−	0.338610i	−0.00710452	−	0.0132916i
$650$	−11.7352	+	22.2772i	−0.460292	+	0.873785i
$651$	0.126201	+	0.850780i	0.00494622	+	0.0333447i
$652$	−3.82409	+	16.0877i	−0.149763	+	0.630044i
$653$	13.9730	+	4.99963i	0.546807	+	0.195651i	0.595778	−	0.803149i	$-0.296844\pi$
$653$	13.9730	+	4.99963i	0.546807	+	0.195651i	−0.0489703	+	0.998800i	$0.515594\pi$
$654$	0.950761	+	3.70078i	0.0371777	+	0.144712i
$655$	−1.44002	+	7.23949i	−0.0562664	+	0.282870i
$656$	6.41909	−	5.53253i	0.250623	−	0.216009i
$657$	2.65423	+	13.3437i	0.103551	+	0.520587i
$658$	−6.39196	−	13.3064i	−0.249185	−	0.518737i
$659$	2.89694	−	3.19628i	0.112849	−	0.124510i	−0.681907	−	0.731439i	$-0.738849\pi$
$659$	2.89694	−	3.19628i	0.112849	−	0.124510i	0.794756	+	0.606930i	$0.207599\pi$
$660$	−0.0380850	+	0.279983i	−0.00148246	+	0.0108983i
$661$	7.57580	−	4.54076i	0.294664	−	0.176615i	−0.359129	−	0.933288i	$-0.616926\pi$
$661$	7.57580	−	4.54076i	0.294664	−	0.176615i	0.653794	+	0.756673i	$0.273176\pi$
$662$	−6.78129	+	0.709230i	−0.263562	+	0.0275650i
$663$	1.47403	+	14.9660i	0.0572464	+	0.581232i
$664$	6.00148	−	5.10982i	0.232903	−	0.198299i
$665$	4.55585	−	3.73889i	0.176668	−	0.144988i
$666$	38.8259	+	15.8085i	1.50447	+	0.612566i
$667$	9.02740	+	9.96020i	0.349542	+	0.385660i
$668$	−1.48151	+	7.94806i	−0.0573213	+	0.307520i
$669$	0.642776	−	0.476715i	0.0248511	−	0.0184309i
$670$	11.1819	+	2.72934i	0.431995	+	0.105444i
$671$	−0.776373	+	1.87433i	−0.0299715	+	0.0723577i
$672$	−3.20135	−	1.58894i	−0.123495	−	0.0612946i
$673$	−14.2976	−	34.5175i	−0.551133	−	1.33055i	−0.916628	−	0.399740i	$-0.869100\pi$
$673$	−14.2976	−	34.5175i	−0.551133	−	1.33055i	0.365495	−	0.930813i	$-0.380900\pi$
$674$	−6.75148	−	43.6969i	−0.260057	−	1.68314i
$675$	−14.8790	−	2.20710i	−0.572695	−	0.0849512i
$676$	−3.90713	+	4.00257i	−0.150274	+	0.153945i
$677$	−48.4236	−	2.37890i	−1.86107	−	0.0914285i	−0.912707	−	0.408615i	$-0.866012\pi$
$677$	−48.4236	−	2.37890i	−1.86107	−	0.0914285i	−0.948363	+	0.317187i	$0.897262\pi$
$678$	−0.105361	−	0.104098i	−0.00404638	−	0.00399785i
$679$	8.47839	+	0.835048i	0.325371	+	0.0320462i
$680$	5.18405	+	11.9015i	0.198799	+	0.456401i
$681$	−5.39644	−	4.42874i	−0.206792	−	0.169710i
$682$	−0.557364	+	0.302255i	−0.0213426	+	0.0115739i
$683$	−20.9314	−	5.24305i	−0.800918	−	0.200620i	−0.179151	−	0.983822i	$-0.557335\pi$
$683$	−20.9314	−	5.24305i	−0.800918	−	0.200620i	−0.621767	+	0.783202i	$0.713585\pi$
$684$	−13.2489	+	38.4859i	−0.506584	+	1.47154i
$685$	−0.0419466	−	0.853843i	−0.00160270	−	0.0326237i
$686$	−19.3092	+	1.06541i	−0.737230	+	0.0406774i
$687$	3.81045	−	5.70274i	0.145378	−	0.217573i
$688$	−10.7441	+	24.2114i	−0.409616	+	0.923050i
$689$	−24.1017	−	36.0707i	−0.918200	−	1.37418i
$690$	2.73317	−	2.05273i	0.104050	−	0.0781461i
$691$	12.0418	+	25.4602i	0.458092	+	0.968554i	0.992376	+	0.123249i	$0.0393313\pi$
$691$	12.0418	+	25.4602i	0.458092	+	0.968554i	−0.534284	+	0.845305i	$0.679419\pi$
$692$	−5.83179	−	0.216002i	−0.221691	−	0.00821117i
$693$	0.743705	+	0.551569i	0.0282510	+	0.0209524i
$694$	16.6007	−	13.7923i	0.630154	−	0.523548i
$695$	−1.67443	+	5.51985i	−0.0635147	+	0.209380i
$696$	−0.124341	+	4.01115i	−0.00471315	+	0.152042i
$697$	6.35417	−	11.8878i	0.240681	−	0.450283i
$698$	6.35261	−	4.30033i	0.240450	−	0.162770i
$699$	10.3231	−	3.69365i	0.390454	−	0.139707i
$700$	−7.43008	−	5.94914i	−0.280831	−	0.224857i
$701$	−6.70686	−	4.01994i	−0.253315	−	0.151831i	0.381809	−	0.924241i	$-0.375301\pi$
$701$	−6.70686	−	4.01994i	−0.253315	−	0.151831i	−0.635124	+	0.772410i	$0.719051\pi$
$702$	−17.1100	−	7.96646i	−0.645774	−	0.300675i
$703$	−60.9115	+	60.9115i	−2.29732	+	2.29732i
$704$	0.292022	−	2.61846i	0.0110060	−	0.0986868i
$705$	2.98038	+	2.98038i	0.112247	+	0.112247i
$706$	−14.3724	−	39.4168i	−0.540911	−	1.48347i
$707$	0.670331	−	1.11838i	0.0252104	−	0.0420610i
$708$	−1.21490	+	0.668346i	−0.0456587	+	0.0251180i
$709$	12.3483	+	34.5113i	0.463751	+	1.29610i	0.914911	+	0.403655i	$0.132260\pi$
$709$	12.3483	+	34.5113i	0.463751	+	1.29610i	−0.451160	+	0.892443i	$0.648990\pi$
$710$	0.876717	−	4.55087i	0.0329026	−	0.170791i
$711$	10.2617	+	5.48497i	0.384842	+	0.205703i
$712$	−4.80638	−	7.69945i	−0.180127	−	0.288549i
$713$	7.33985	+	2.22652i	0.274879	+	0.0833838i
$714$	−5.66077	−	0.523076i	−0.211849	−	0.0195756i
$715$	−0.562473	+	0.758407i	−0.0210353	+	0.0283628i
$716$	32.5975	−	12.1092i	1.21823	−	0.452541i
$717$	−13.2807	+	6.28130i	−0.495976	+	0.234579i
$718$	−1.73069	+	12.1729i	−0.0645888	+	0.454288i
$719$	−30.4992	+	20.3789i	−1.13743	+	0.760006i	−0.974000	−	0.226548i	$-0.927256\pi$
$719$	−30.4992	+	20.3789i	−1.13743	+	0.760006i	−0.163430	+	0.986555i	$0.552256\pi$
$720$	−7.57805	−	0.937837i	−0.282417	−	0.0349511i
$721$	−13.7229	−	9.16937i	−0.511069	−	0.341485i
$722$	−42.2917	−	37.8688i	−1.57393	−	1.40933i
$723$	3.09795	−	0.152192i	0.115214	−	0.00566009i
$724$	5.22258	−	5.90384i	0.194096	−	0.219414i
$725$	−2.59690	+	10.3674i	−0.0964466	+	0.385036i
$726$	−2.60608	+	8.78145i	−0.0967206	+	0.325910i
$727$	9.47309	−	11.5430i	0.351337	−	0.428106i	−0.567114	−	0.823639i	$-0.691940\pi$
$727$	9.47309	−	11.5430i	0.351337	−	0.428106i	0.918452	+	0.395533i	$0.129440\pi$
$728$	−6.81383	−	9.80858i	−0.252537	−	0.363530i
$729$	−0.954139	+	9.68753i	−0.0353385	+	0.358798i
$730$	−0.0316401	−	5.24463i	−0.00117105	−	0.194112i
$731$	−2.06737	+	42.0822i	−0.0764643	+	1.55647i
$732$	6.80238	+	2.72196i	0.251423	+	0.100606i
$733$	−4.13763	+	27.8936i	−0.152827	+	1.03027i	0.768041	+	0.640400i	$0.221232\pi$
$733$	−4.13763	+	27.8936i	−0.152827	+	1.03027i	−0.920868	+	0.389874i	$0.872518\pi$
$734$	−33.4574	−	24.5022i	−1.23493	−	0.904393i
$735$	2.32698	−	0.963868i	0.0858320	−	0.0355528i
$736$	−25.0157	+	19.7497i	−0.922091	+	0.727983i
$737$	−3.43297	−	1.42198i	−0.126455	−	0.0523795i
$738$	4.11714	+	6.77600i	0.151554	+	0.249428i
$739$	7.68005	+	10.3553i	0.282515	+	0.380928i	0.921556	−	0.388245i	$-0.126919\pi$
$739$	7.68005	+	10.3553i	0.282515	+	0.380928i	−0.639041	+	0.769173i	$0.720669\pi$
$740$	−13.5442	−	8.81544i	−0.497894	−	0.324062i
$741$	13.4682	−	12.2068i	0.494766	−	0.448430i
$742$	15.1129	−	6.36705i	0.554812	−	0.233742i
$743$	−17.5603	−	21.3973i	−0.644227	−	0.784993i	0.343838	−	0.939029i	$-0.388273\pi$
$743$	−17.5603	−	21.3973i	−0.644227	−	0.784993i	−0.988065	+	0.154036i	$0.950773\pi$
$744$	1.11578	+	1.99958i	0.0409066	+	0.0733080i
$745$	3.19248	−	0.314432i	0.116963	−	0.0115199i
$746$	−2.24014	−	1.81593i	−0.0820173	−	0.0664859i
$747$	3.79136	+	6.32550i	0.138719	+	0.231438i
$748$	−1.06726	−	4.05264i	−0.0390228	−	0.148179i
$749$	7.80540	+	7.07440i	0.285203	+	0.258493i
$750$	5.42649	+	1.90478i	0.198147	+	0.0695527i
$751$	−2.51941	+	0.501142i	−0.0919345	+	0.0182869i	−0.240843	−	0.970564i	$-0.577424\pi$
$751$	−2.51941	+	0.501142i	−0.0919345	+	0.0182869i	0.148909	+	0.988851i	$0.452424\pi$
$752$	−28.4524	−	27.1114i	−1.03755	−	0.988650i
$753$	1.48906	+	0.296192i	0.0542643	+	0.0107938i
$754$	−6.82478	+	11.5438i	−0.248544	+	0.420401i
$755$	4.75687	−	13.2946i	0.173120	−	0.483839i
$756$	4.18068	−	5.78150i	0.152050	−	0.210271i
$757$	−30.0441	+	4.45662i	−1.09197	+	0.161979i	−0.668340	−	0.743856i	$-0.732995\pi$
$757$	−30.0441	+	4.45662i	−1.09197	+	0.161979i	−0.423632	+	0.905835i	$0.639245\pi$
$758$	−11.3559	−	36.6381i	−0.412463	−	1.33076i
$759$	−0.973188	+	0.520180i	−0.0353245	+	0.0188813i
$760$	7.82174	−	13.6021i	0.283724	−	0.493401i
$761$	−2.45210	−	8.08350i	−0.0888887	−	0.293027i	0.901213	−	0.433375i	$-0.142678\pi$
$761$	−2.45210	−	8.08350i	−0.0888887	−	0.293027i	−0.990102	+	0.140349i	$0.955178\pi$
$762$	5.86622	+	3.86870i	0.212511	+	0.140148i
$763$	−4.36332	−	2.06370i	−0.157963	−	0.0747109i
$764$	24.1037	+	28.6583i	0.872043	+	1.03682i
$765$	−11.7818	+	2.95119i	−0.425973	+	0.106701i
$766$	28.3441	+	30.8962i	1.02411	+	1.11633i
$767$	−4.63355			−0.167308
$768$	−9.46845	−	0.940450i	−0.341663	−	0.0339356i
$769$	−13.2861			−0.479108			−0.239554	−	0.970883i	$-0.577001\pi$
$769$	−13.2861			−0.479108			−0.239554	+	0.970883i	$0.577001\pi$
$770$	−0.241296	−	0.263023i	−0.00869572	−	0.00947869i
$771$	−14.5470	+	3.64384i	−0.523898	+	0.131230i
$772$	36.4691	−	30.6732i	1.31255	−	1.10395i
$773$	12.6853	+	5.99970i	0.456259	+	0.215794i	0.641846	−	0.766833i	$-0.278169\pi$
$773$	12.6853	+	5.99970i	0.456259	+	0.215794i	−0.185587	+	0.982628i	$0.559419\pi$
$774$	−20.6890	−	13.6442i	−0.743652	−	0.490429i
$775$	1.77024	+	5.83571i	0.0635890	+	0.209625i
$776$	21.8982	−	5.90837i	0.786100	−	0.212098i
$777$	6.24132	−	3.33606i	0.223906	−	0.119680i
$778$	12.2213	+	39.4303i	0.438154	+	1.41364i
$779$	−16.1162	+	2.39061i	−0.577422	+	0.0856525i
$780$	2.76326	+	1.99815i	0.0989404	+	0.0715451i
$781$	−0.504044	+	1.40871i	−0.0180361	+	0.0504075i
$782$	−25.8006	+	43.6405i	−0.922626	+	1.56058i
$783$	−7.85731	−	1.56292i	−0.280797	−	0.0558541i
$784$	−21.4744	+	9.50833i	−0.766942	+	0.339583i
$785$	−13.9768	+	2.78016i	−0.498854	+	0.0992282i
$786$	−8.12002	−	2.85025i	−0.289632	−	0.101665i
$787$	−10.8566	−	9.83985i	−0.386996	−	0.350753i	0.454757	−	0.890616i	$-0.349726\pi$
$787$	−10.8566	−	9.83985i	−0.386996	−	0.350753i	−0.841753	+	0.539863i	$0.818476\pi$
$788$	49.1111	−	12.9334i	1.74951	−	0.460732i
$789$	2.04601	+	3.41356i	0.0728399	+	0.121526i
$790$	−3.48442	−	2.82459i	−0.123970	−	0.100494i
$791$	0.186199	−	0.0183390i	0.00662047	−	0.000652059i
$792$	2.37150	+	0.672767i	0.0842675	+	0.0239057i
$793$	15.5322	+	18.9260i	0.551565	+	0.672083i
$794$	6.41566	−	2.70291i	0.227683	−	0.0959227i
$795$	−3.46942	+	3.14450i	−0.123048	+	0.111524i
$796$	−21.1836	+	32.5469i	−0.750834	+	1.15359i
$797$	−2.63918	−	3.55852i	−0.0934845	−	0.126049i	0.753989	−	0.656887i	$-0.228127\pi$
$797$	−2.63918	−	3.55852i	−0.0934845	−	0.126049i	−0.847473	+	0.530838i	$0.821877\pi$
$798$	3.56804	+	5.87228i	0.126307	+	0.207876i
$799$	−57.7547	−	23.9228i	−2.04322	−	0.846328i
$800$	−24.1060	−	7.81355i	−0.852275	−	0.276251i
$801$	7.84576	−	3.24982i	0.277216	−	0.114827i
$802$	4.34715	+	3.18359i	0.153503	+	0.112417i
$803$	−0.248437	+	1.67482i	−0.00876714	+	0.0591033i
$804$	−4.98546	+	12.4591i	−0.175824	+	0.439397i
$805$	−0.211871	+	4.31273i	−0.00746746	+	0.152004i
$806$	0.0461614	+	7.65166i	0.00162597	+	0.269518i
$807$	0.595115	−	6.04231i	0.0209490	−	0.212699i
$808$	0.615499	−	3.41634i	0.0216532	−	0.120186i
$809$	1.01624	−	1.23829i	0.0357290	−	0.0435359i	−0.754839	−	0.655910i	$-0.772285\pi$
$809$	1.01624	−	1.23829i	0.0357290	−	0.0435359i	0.790568	+	0.612374i	$0.209785\pi$
$810$	1.72466	−	5.81142i	0.0605984	−	0.204193i
$811$	−2.80126	+	11.1833i	−0.0983655	+	0.392697i	−0.999134	−	0.0416020i	$-0.986754\pi$
$811$	−2.80126	+	11.1833i	−0.0983655	+	0.392697i	0.900769	+	0.434299i	$0.143004\pi$
$812$	−3.79700	−	3.35885i	−0.133249	−	0.117873i
$813$	3.59935	−	0.176825i	0.126235	−	0.00620152i
$814$	3.88663	+	3.48016i	0.136226	+	0.121980i
$815$	4.95904	+	3.31353i	0.173708	+	0.116068i
$816$	−14.5883	+	4.03065i	−0.510693	+	0.141101i
$817$	42.3433	−	28.2929i	1.48140	−	0.989843i
$818$	−5.77448	+	40.6150i	−0.201900	+	1.42007i
$819$	10.1014	−	4.77759i	0.352970	−	0.166942i
$820$	−1.06435	−	2.86520i	−0.0371688	−	0.100057i
$821$	−13.3367	+	17.9825i	−0.465454	+	0.627592i	−0.972101	−	0.234561i	$-0.924635\pi$
$821$	−13.3367	+	17.9825i	−0.465454	+	0.627592i	0.506647	+	0.862153i	$0.330885\pi$
$822$	0.992452	+	0.0917062i	0.0346157	+	0.00319862i
$823$	−34.4707	−	10.4566i	−1.20157	−	0.364493i	−0.374841	−	0.927089i	$-0.622303\pi$
$823$	−34.4707	−	10.4566i	−1.20157	−	0.364493i	−0.826732	+	0.562596i	$0.809803\pi$
$824$	−42.8093	−	9.90340i	−1.49133	−	0.345001i
$825$	−0.773755	−	0.413581i	−0.0269387	−	0.0143990i
$826$	0.331349	−	1.71997i	0.0115291	−	0.0598453i
$827$	10.4727	+	29.2691i	0.364170	+	1.01779i	0.974254	+	0.225451i	$0.0723856\pi$
$827$	10.4727	+	29.2691i	0.364170	+	1.01779i	−0.610084	+	0.792337i	$0.708864\pi$
$828$	−14.3735	−	26.1277i	−0.499514	−	0.908000i
$829$	5.58421	−	9.31668i	0.193947	−	0.323582i	−0.745358	−	0.666665i	$-0.767721\pi$
$829$	5.58421	−	9.31668i	0.193947	−	0.323582i	0.939305	+	0.343083i	$0.111471\pi$
$830$	−0.973883	−	2.67091i	−0.0338040	−	0.0927087i
$831$	1.72719	+	1.72719i	0.0599154	+	0.0599154i
$832$	−26.2075	−	18.0043i	−0.908583	−	0.624185i
$833$	−26.4149	+	26.4149i	−0.915222	+	0.915222i
$834$	−6.09662	−	2.83861i	−0.211109	−	0.0982930i
$835$	2.50120	+	1.49916i	0.0865578	+	0.0518807i
$836$	−3.16599	+	3.95410i	−0.109498	+	0.136755i
$837$	−4.30392	+	1.53997i	−0.148765	+	0.0532291i
$838$	−27.1099	+	18.3518i	−0.936496	+	0.633952i
$839$	16.6697	−	31.1868i	0.575502	−	1.07669i	−0.410798	−	0.911726i	$-0.634750\pi$
$839$	16.6697	−	31.1868i	0.575502	−	1.07669i	0.986300	−	0.164962i	$-0.0527502\pi$
$840$	−0.939311	+	0.882826i	−0.0324093	+	0.0304604i
$841$	6.76588	−	22.3041i	0.233306	−	0.769108i
$842$	−1.15478	+	0.959421i	−0.0397964	+	0.0330638i
$843$	0.382755	+	0.283870i	0.0131828	+	0.00977701i
$844$	1.71250	−	46.2355i	0.0589468	−	1.59149i
$845$	0.862562	+	1.82373i	0.0296730	+	0.0627383i
$846$	29.4020	−	22.0822i	1.01086	−	0.759202i
$847$	−6.42858	−	9.62105i	−0.220889	−	0.330583i
$848$	31.6331	−	30.0924i	1.08629	−	1.03338i
$849$	9.67784	−	14.4839i	0.332142	−	0.497086i
$850$	−40.2464	+	2.22064i	−1.38044	+	0.0761672i
$851$	−3.09671	−	63.0351i	−0.106154	−	2.16081i
$852$	5.10907	+	1.75881i	0.175034	+	0.0602559i
$853$	21.2704	+	5.32796i	0.728285	+	0.182426i	0.589353	−	0.807876i	$-0.299383\pi$
$853$	21.2704	+	5.32796i	0.728285	+	0.182426i	0.138933	+	0.990302i	$0.455633\pi$
$854$	−8.13603	+	4.41211i	−0.278409	+	0.150979i
$855$	11.3482	+	9.31326i	0.388102	+	0.318507i
$856$	26.1007	+	10.2619i	0.892103	+	0.350744i
$857$	47.3516	+	4.66372i	1.61750	+	0.159310i	0.865867	−	0.500274i	$-0.166767\pi$
$857$	47.3516	+	4.66372i	1.61750	+	0.159310i	0.751631	+	0.659584i	$0.229267\pi$
$858$	−0.783101	−	0.773709i	−0.0267346	−	0.0264140i
$859$	−30.7934	−	1.51278i	−1.05066	−	0.0516154i	−0.483595	−	0.875292i	$-0.660669\pi$
$859$	−30.7934	−	1.51278i	−1.05066	−	0.0516154i	−0.567060	+	0.823676i	$0.691919\pi$
$860$	6.83655	+	6.67354i	0.233125	+	0.227566i
$861$	1.32402	+	0.196400i	0.0451225	+	0.00669330i
$862$	4.57476	+	29.6087i	0.155817	+	1.00848i
$863$	16.5649	+	39.9913i	0.563877	+	1.36132i	0.906643	+	0.421899i	$0.138636\pi$
$863$	16.5649	+	39.9913i	0.563877	+	1.36132i	−0.342765	+	0.939421i	$0.611364\pi$
$864$	4.96317	−	18.3349i	0.168850	−	0.623764i
$865$	−0.805492	+	1.94463i	−0.0273875	+	0.0661194i
$866$	18.9128	+	4.61635i	0.642685	+	0.156870i
$867$	−11.2162	+	8.31851i	−0.380923	+	0.282511i
$868$	−2.84358	−	0.530041i	−0.0965175	−	0.0179908i
$869$	0.972446	+	1.07293i	0.0329880	+	0.0363966i
$870$	1.34057	+	0.545832i	0.0454497	+	0.0185054i
$871$	−34.6644	+	28.4484i	−1.17456	+	0.963936i
$872$	−12.8091	−	1.02790i	−0.433770	−	0.0348092i
$873$	2.08004	+	21.1190i	0.0703985	+	0.714768i
$874$	60.9445	−	6.37397i	2.06148	−	0.215603i
$875$	−6.23133	+	3.73491i	−0.210657	+	0.126263i
$876$	6.05892	+	0.824173i	0.204712	+	0.0278462i
$877$	−14.5178	+	16.0180i	−0.490232	+	0.540888i	−0.934949	−	0.354783i	$-0.884555\pi$
$877$	−14.5178	+	16.0180i	−0.490232	+	0.540888i	0.444716	+	0.895672i	$0.353305\pi$
$878$	4.97429	+	10.3552i	0.167874	+	0.349469i
$879$	0.580265	+	2.91719i	0.0195718	+	0.0983943i
$880$	−0.848636	−	0.427606i	−0.0286075	−	0.0144146i
$881$	−2.94017	+	14.7812i	−0.0990567	+	0.497992i	0.899124	+	0.437695i	$0.144205\pi$
$881$	−2.94017	+	14.7812i	−0.0990567	+	0.497992i	−0.998180	+	0.0602973i	$0.980795\pi$
$882$	−5.46758	−	21.2822i	−0.184103	−	0.716610i
$883$	9.69183	+	3.46779i	0.326156	+	0.116701i	0.494876	−	0.868963i	$-0.335213\pi$
$883$	9.69183	+	3.46779i	0.326156	+	0.116701i	−0.168720	+	0.985664i	$0.553963\pi$
$884$	−49.2047	−	11.6961i	−1.65493	−	0.393382i
$885$	0.0733827	+	0.494706i	0.00246673	+	0.0166294i
$886$	−13.6483	+	25.9090i	−0.458524	+	0.870429i
$887$	−25.7854	−	48.2412i	−0.865790	−	1.61978i	−0.781985	−	0.623297i	$-0.785793\pi$
$887$	−25.7854	−	48.2412i	−0.865790	−	1.61978i	−0.0838051	−	0.996482i	$-0.526707\pi$
$888$	12.3982	−	14.1870i	0.416055	−	0.476084i
$889$	−8.49452	+	2.57678i	−0.284897	+	0.0864226i
$890$	−3.20690	+	0.658028i	−0.107495	+	0.0220571i
$891$	−0.836713	+	1.76908i	−0.0280309	+	0.0592664i
$892$	0.812276	+	2.56585i	0.0271970	+	0.0859111i
$893$	18.3594	+	73.2950i	0.614375	+	2.45272i
$894$	−0.160977	+	3.73659i	−0.00538387	+	0.124970i
$895$		−	12.5423i		−	0.419242i
$896$	8.55727	−	8.44069i	0.285878	−	0.281984i
$897$			13.3171i			0.444646i
$898$	23.4840	+	1.01172i	0.783672	+	0.0337616i
$899$	0.789184	+	3.15060i	0.0263207	+	0.105078i
$900$	10.9234	−	21.0431i	0.364114	−	0.701436i
$901$	29.6924	−	62.7793i	0.989198	−	2.09148i
$902$	0.198336	+	0.966590i	0.00660387	+	0.0321839i
$903$	−4.00365	+	1.21449i	−0.133233	+	0.0404158i
$904$	0.446364	−	0.221087i	0.0148459	−	0.00735323i
$905$	−1.34017	−	2.50729i	−0.0445489	−	0.0833451i
$906$	14.5649	+	7.67249i	0.483887	+	0.254902i
$907$	−2.17666	−	14.6739i	−0.0722750	−	0.487238i	−0.994845	−	0.101408i	$-0.967665\pi$
$907$	−2.17666	−	14.6739i	−0.0722750	−	0.487238i	0.922570	−	0.385830i	$-0.126085\pi$
$908$	19.9907	−	12.3122i	0.663413	−	0.408595i
$909$	3.05801	+	1.09417i	0.101428	+	0.0362915i
$910$	−4.17213	+	1.07185i	−0.138305	+	0.0355316i
$911$	−9.33506	+	46.9305i	−0.309285	+	1.55488i	0.443294	+	0.896376i	$0.353810\pi$
$911$	−9.33506	+	46.9305i	−0.309285	+	1.55488i	−0.752579	+	0.658502i	$0.771190\pi$
$912$	14.4169	+	11.2607i	0.477393	+	0.372878i
$913$	0.179050	+	0.900145i	0.00592569	+	0.0297904i
$914$	37.2143	−	17.8766i	1.23094	−	0.591304i
$915$	1.77467	−	1.95805i	0.0586688	−	0.0647311i
$916$	13.9631	+	18.3598i	0.461352	+	0.606625i
$917$	9.32436	−	5.58881i	0.307918	−	0.184559i
$918$	−3.14279	−	30.0497i	−0.103727	−	0.991787i
$919$	4.40703	+	44.7453i	0.145374	+	1.47601i	0.740325	+	0.672249i	$0.234672\pi$
$919$	4.40703	+	44.7453i	0.145374	+	1.47601i	−0.594950	+	0.803762i	$0.702828\pi$
$920$	3.53555	+	10.9385i	0.116564	+	0.360630i
$921$	7.60481	−	6.24111i	0.250587	−	0.205651i
$922$	15.8404	−	38.9042i	0.521674	−	1.28124i
$923$	12.1257	+	13.3787i	0.399124	+	0.440365i
$924$	0.343199	−	0.235357i	0.0112904	−	0.00774268i
$925$	40.3032	−	29.8909i	1.32516	−	0.982807i
$926$	−3.17954	+	13.0263i	−0.104486	+	0.428072i
$927$	15.7326	−	37.9818i	0.516725	−	1.24748i
$928$	−12.6191	−	4.78643i	−0.414243	−	0.157122i
$929$	−10.2155	−	24.6624i	−0.335160	−	0.809147i	−0.998166	−	0.0605331i	$-0.980720\pi$
$929$	−10.2155	−	24.6624i	−0.335160	−	0.809147i	0.663007	−	0.748613i	$-0.269280\pi$
$930$	0.816207	−	0.126110i	0.0267645	−	0.00413530i
$931$	44.6636	+	6.62522i	1.46379	+	0.217133i
$932$	0.444881	+	36.8702i	0.0145726	+	1.20772i
$933$	−13.1741	−	0.647200i	−0.431299	−	0.0211884i
$934$	−25.1227	+	25.4277i	−0.822041	+	0.832019i
$935$	−1.50426	−	0.148157i	−0.0491947	−	0.00484525i
$936$	20.6517	−	21.4131i	0.675021	−	0.699908i
$937$	−15.8308	−	12.9920i	−0.517171	−	0.424431i	0.339260	−	0.940693i	$-0.389823\pi$
$937$	−15.8308	−	12.9920i	−0.517171	−	0.424431i	−0.856431	+	0.516261i	$0.827323\pi$
$938$	−8.08110	−	14.9017i	−0.263857	−	0.486559i
$939$	16.0528	+	4.02101i	0.523862	+	0.131221i
$940$	−12.7401	+	6.21479i	−0.415535	+	0.202704i
$941$	−0.781548	−	15.9088i	−0.0254777	−	0.518611i	−0.977287	−	0.211920i	$-0.932028\pi$
$941$	−0.781548	−	15.9088i	−0.0254777	−	0.518611i	0.951809	−	0.306691i	$-0.0992218\pi$
$942$	−0.915333	−	16.5893i	−0.0298232	−	0.540509i
$943$	6.63161	−	9.92491i	0.215955	−	0.323199i
$944$	−0.795346	−	4.59495i	−0.0258863	−	0.149553i
$945$	−1.42967	−	2.13965i	−0.0465072	−	0.0696029i
$946$	−1.85219	−	2.46615i	−0.0602199	−	0.0801816i
$947$	4.65208	+	9.83600i	0.151172	+	0.319627i	0.965337	−	0.261007i	$-0.0840546\pi$
$947$	4.65208	+	9.83600i	0.151172	+	0.319627i	−0.814165	+	0.580634i	$0.802805\pi$
$948$	3.83217	−	3.55843i	0.124463	−	0.115573i
$949$	16.4122	+	12.1721i	0.532763	+	0.395124i
$950$	31.1340	+	37.4736i	1.01012	+	1.21580i
$951$	1.21672	−	4.01098i	0.0394548	−	0.130065i
$952$	7.86023	−	17.4283i	0.254751	−	0.564855i
$953$	11.6444	−	21.7851i	0.377198	−	0.705689i	−0.619662	−	0.784869i	$-0.712730\pi$
$953$	11.6444	−	21.7851i	0.377198	−	0.705689i	0.996860	+	0.0791803i	$0.0252303\pi$
$954$	22.8992	+	33.8275i	0.741389	+	1.09521i
$955$	12.7169	−	4.55018i	0.411509	−	0.147240i
$956$	−5.43572	−	49.1080i	−0.175804	−	1.58827i
$957$	−0.400795	−	0.240227i	−0.0129559	−	0.00776544i
$958$	−8.02291	+	17.2312i	−0.259209	+	0.556715i
$959$	−0.890270	+	0.890270i	−0.0287483	+	0.0287483i
$960$	−1.50719	+	3.08321i	−0.0486443	+	0.0995103i
$961$	−20.6099	−	20.6099i	−0.664835	−	0.664835i
$962$	59.1509	−	21.5679i	1.90710	−	0.695378i
$963$	−13.4901	+	22.5068i	−0.434712	+	0.725273i
$964$	−2.90737	+	10.0179i	−0.0936402	+	0.322655i
$965$	−5.79033	−	16.1829i	−0.186397	−	0.520945i
$966$	−4.94329	−	0.952317i	−0.159048	−	0.0306403i
$967$	−15.2793	−	8.16694i	−0.491348	−	0.262631i	0.207063	−	0.978328i	$-0.433609\pi$
$967$	−15.2793	−	8.16694i	−0.491348	−	0.262631i	−0.698411	+	0.715697i	$0.746109\pi$
$968$	−25.0716	−	17.9003i	−0.805832	−	0.575336i
$969$	27.8452	+	8.44674i	0.894515	+	0.271348i
$970$	0.752717	−	8.14597i	0.0241683	−	0.261551i
$971$	0.0349805	−	0.0471658i	0.00112258	−	0.00151362i	−0.802646	−	0.596456i	$-0.796575\pi$
$971$	0.0349805	−	0.0471658i	0.00112258	−	0.00151362i	0.803768	+	0.594942i	$0.202825\pi$
$972$	24.7402	+	11.3380i	0.793541	+	0.363667i
$973$	7.67964	−	3.63220i	0.246198	−	0.116443i
$974$	0.935920	+	0.133065i	0.0299888	+	0.00426369i
$975$	−8.80367	+	5.88242i	−0.281943	+	0.188388i
$976$	−16.1023	+	18.6514i	−0.515421	+	0.597018i
$977$	−37.0263	−	24.7402i	−1.18458	−	0.791508i	−0.202369	−	0.979309i	$-0.564864\pi$
$977$	−37.0263	−	24.7402i	−1.18458	−	0.791508i	−0.982207	+	0.187801i	$0.939864\pi$
$978$	−4.63854	+	5.18031i	−0.148324	+	0.165648i
$979$	1.05558	−	0.0518571i	0.0337364	−	0.00165736i
$980$	0.517683	+	8.45482i	0.0165368	+	0.270079i
$981$	2.92135	−	11.6627i	0.0932716	−	0.372361i
$982$	11.9329	+	3.54135i	0.380795	+	0.113009i
$983$	22.8288	−	27.8170i	0.728127	−	0.887225i	−0.268987	−	0.963144i	$-0.586689\pi$
$983$	22.8288	−	27.8170i	0.728127	−	0.887225i	0.997114	+	0.0759184i	$0.0241888\pi$
$984$	3.48189	−	0.758346i	0.110999	−	0.0241752i
$985$	1.79541	−	18.2291i	0.0572066	−	0.580828i
$986$	−21.4673	+	0.129509i	−0.683659	+	0.00412442i
$987$	0.304591	−	6.20009i	0.00969523	−	0.197351i
$988$	24.0734	+	56.1909i	0.765876	+	1.78767i
$989$	−5.47457	+	36.9066i	−0.174081	+	1.17356i
$990$	0.525321	−	0.717317i	0.0166958	−	0.0227978i
$991$	30.6750	−	12.7060i	0.974423	−	0.403619i	0.162066	−	0.986780i	$-0.448184\pi$
$991$	30.6750	−	12.7060i	0.974423	−	0.403619i	0.812357	+	0.583161i	$0.198184\pi$
$992$	−7.57999	+	1.35918i	−0.240665	+	0.0431540i
$993$	−2.64890	−	1.09721i	−0.0840603	−	0.0348189i
$994$	−5.83326	+	3.54433i	−0.185020	+	0.112419i
$995$	8.34365	+	11.2501i	0.264512	+	0.356653i
$996$	3.24279	−	0.685804i	0.102752	−	0.0217305i
$997$	27.6614	−	25.0708i	0.876045	−	0.794001i	−0.103625	−	0.994616i	$-0.533044\pi$
$997$	27.6614	−	25.0708i	0.876045	−	0.794001i	0.979670	+	0.200615i	$0.0642942\pi$
$998$	6.82477	+	16.1993i	0.216034	+	0.512781i
$999$	23.8608	+	29.0745i	0.754924	+	0.919877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.8	✓	992
256.109	even	64	inner	256.2.m.a.109.8	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.8	✓	992	1.1	even	1	trivial
256.2.m.a.109.8	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)

\(f(q)\)	\(=\)	\(q+(-1.04211 + 0.956032i) q^{2} +(-0.576868 + 0.144498i) q^{3} +(0.172006 - 1.99259i) q^{4} +(-0.652101 - 0.308421i) q^{5} +(0.463018 - 0.702088i) q^{6} +(0.308398 + 1.01665i) q^{7} +(1.72573 + 2.24095i) q^{8} +(-2.33387 + 1.24748i) q^{9} +O(q^{10})\)	\(q+(-1.04211 + 0.956032i) q^{2} +(-0.576868 + 0.144498i) q^{3} +(0.172006 - 1.99259i) q^{4} +(-0.652101 - 0.308421i) q^{5} +(0.463018 - 0.702088i) q^{6} +(0.308398 + 1.01665i) q^{7} +(1.72573 + 2.24095i) q^{8} +(-2.33387 + 1.24748i) q^{9} +(0.974424 - 0.302020i) q^{10} +(-0.325772 + 0.0483237i) q^{11} +(0.188701 + 1.17432i) q^{12} +(-1.33897 + 3.74217i) q^{13} +(-1.29334 - 0.764629i) q^{14} +(0.420743 + 0.0836909i) q^{15} +(-3.94083 - 0.685473i) q^{16} +(-6.24026 + 1.24127i) q^{17} +(1.23953 - 3.53127i) q^{18} +(5.69816 + 5.16451i) q^{19} +(-0.726721 + 1.24632i) q^{20} +(-0.324809 - 0.541911i) q^{21} +(0.293292 - 0.361807i) q^{22} +(-5.60713 + 0.552254i) q^{23} +(-1.31933 - 1.04337i) q^{24} +(-2.84185 - 3.46281i) q^{25} +(-2.18228 - 5.17987i) q^{26} +(2.48798 - 2.25498i) q^{27} +(2.07881 - 0.439640i) q^{28} +(-1.42124 - 1.91633i) q^{29} +(-0.518473 + 0.315028i) q^{30} +(-1.25771 - 0.520961i) q^{31} +(4.76213 - 3.05322i) q^{32} +(0.180945 - 0.0749497i) q^{33} +(5.31638 - 7.25943i) q^{34} +(0.112450 - 0.758076i) q^{35} +(2.08427 + 4.86501i) q^{36} +(-0.549622 + 11.1878i) q^{37} +(-10.8756 + 0.0656108i) q^{38} +(0.231673 - 2.35222i) q^{39} +(-0.434195 - 1.99358i) q^{40} +(-1.34401 + 1.63768i) q^{41} +(0.856572 + 0.254206i) q^{42} +(1.60903 - 6.42361i) q^{43} +(0.0402547 + 0.657441i) q^{44} +(1.90667 - 0.0936685i) q^{45} +(5.31530 - 5.93610i) q^{46} +(8.16939 + 5.45861i) q^{47} +(2.37239 - 0.174014i) q^{48} +(4.88182 - 3.26193i) q^{49} +(6.27209 + 0.891741i) q^{50} +(3.42045 - 1.61775i) q^{51} +(7.22631 + 3.31169i) q^{52} +(-6.50207 + 8.76703i) q^{53} +(-0.436934 + 4.72854i) q^{54} +(0.227340 + 0.0689629i) q^{55} +(-1.74605 + 2.44557i) q^{56} +(-4.03335 - 2.15587i) q^{57} +(3.31317 + 0.638277i) q^{58} +(0.392752 + 1.09767i) q^{59} +(0.239132 - 0.823972i) q^{60} +(3.16695 - 5.28374i) q^{61} +(1.80873 - 0.659511i) q^{62} +(-1.98801 - 1.98801i) q^{63} +(-2.04371 + 7.73455i) q^{64} +(2.02731 - 2.02731i) q^{65} +(-0.116911 + 0.251095i) q^{66} +(9.67755 + 5.80050i) q^{67} +(1.39997 + 12.6478i) q^{68} +(3.15477 - 1.12880i) q^{69} +(0.607559 + 0.897507i) q^{70} +(2.14155 - 4.00655i) q^{71} +(-6.82316 - 3.07727i) q^{72} +(1.49238 - 4.91972i) q^{73} +(-10.1231 - 12.1844i) q^{74} +(2.13974 + 1.58694i) q^{75} +(11.2709 - 10.4658i) q^{76} +(-0.149596 - 0.316293i) q^{77} +(2.00737 + 2.67277i) q^{78} +(-2.44276 - 3.65585i) q^{79} +(2.35840 + 1.66243i) q^{80} +(3.30129 - 4.94073i) q^{81} +(-0.165063 - 2.99156i) q^{82} +(-0.136740 - 2.78340i) q^{83} +(-1.13567 + 0.553999i) q^{84} +(4.45211 + 1.11520i) q^{85} +(4.46438 + 8.23242i) q^{86} +(1.09678 + 0.900101i) q^{87} +(-0.670485 - 0.646644i) q^{88} +(-3.19358 - 0.314540i) q^{89} +(-1.89741 + 1.92045i) q^{90} +(-4.21742 - 0.207189i) q^{91} +(0.135958 + 11.2677i) q^{92} +(0.800811 + 0.118789i) q^{93} +(-13.7321 + 2.12170i) q^{94} +(-2.12293 - 5.12522i) q^{95} +(-2.30594 + 2.44942i) q^{96} +(3.06875 - 7.40863i) q^{97} +(-1.96891 + 8.06647i) q^{98} +(0.700025 - 0.519174i) 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

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