LMFDB - Embedded newform 256.2.m.a.5.14

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			5.14
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.408395 + 1.35396i) q^{2} +(-0.0625001 + 0.421342i) q^{3} +(-1.66643 - 1.10590i) q^{4} +(1.29990 + 0.0638600i) q^{5} +(-0.544956 - 0.256697i) q^{6} +(3.11690 + 1.66602i) q^{7} +(2.17791 - 1.80463i) q^{8} +(2.69720 + 0.818186i) q^{9} +O(q^{10})$	\(q+(-0.408395 + 1.35396i) q^{2} +(-0.0625001 + 0.421342i) q^{3} +(-1.66643 - 1.10590i) q^{4} +(1.29990 + 0.0638600i) q^{5} +(-0.544956 - 0.256697i) q^{6} +(3.11690 + 1.66602i) q^{7} +(2.17791 - 1.80463i) q^{8} +(2.69720 + 0.818186i) q^{9} +(-0.617338 + 1.73394i) q^{10} +(-2.31496 - 3.86227i) q^{11} +(0.570115 - 0.633016i) q^{12} +(-2.64400 + 2.91721i) q^{13} +(-3.52865 + 3.53977i) q^{14} +(-0.108151 + 0.543711i) q^{15} +(1.55395 + 3.68581i) q^{16} +(1.18057 + 5.93512i) q^{17} +(-2.20932 + 3.31776i) q^{18} +(-0.252525 - 0.533919i) q^{19} +(-2.09557 - 1.54398i) q^{20} +(-0.896768 + 1.20915i) q^{21} +(6.17478 - 1.55703i) q^{22} +(1.15881 + 0.951011i) q^{23} +(0.624247 + 1.03044i) q^{24} +(-3.29026 - 0.324062i) q^{25} +(-2.86999 - 4.77125i) q^{26} +(-1.05967 + 2.24047i) q^{27} +(-3.35162 - 6.22328i) q^{28} +(9.83069 - 2.46246i) q^{29} +(-0.691996 - 0.368481i) q^{30} +(-7.54570 - 3.12553i) q^{31} +(-5.62508 + 0.598726i) q^{32} +(1.77202 - 0.733995i) q^{33} +(-8.51807 - 0.825430i) q^{34} +(3.94526 + 2.36470i) q^{35} +(-3.58985 - 4.34629i) q^{36} +(-1.58781 - 4.43762i) q^{37} +(0.826036 - 0.123859i) q^{38} +(-1.06389 - 1.29635i) q^{39} +(2.94631 - 2.20676i) q^{40} +(4.89071 - 0.481693i) q^{41} +(-1.27091 - 1.70800i) q^{42} +(1.76370 - 0.261620i) q^{43} +(-0.413595 + 8.99630i) q^{44} +(3.45384 + 1.23580i) q^{45} +(-1.76089 + 1.18060i) q^{46} +(2.18071 - 3.26366i) q^{47} +(-1.65011 + 0.424382i) q^{48} +(3.05044 + 4.56531i) q^{49} +(1.78249 - 4.32254i) q^{50} +(-2.57450 + 0.126477i) q^{51} +(7.63218 - 1.93730i) q^{52} +(8.81849 + 2.20892i) q^{53} +(-2.60075 - 2.34975i) q^{54} +(-2.76257 - 5.16840i) q^{55} +(9.79487 - 1.99641i) q^{56} +(0.240745 - 0.0730293i) q^{57} +(-0.680731 + 14.3160i) q^{58} +(-7.94867 - 8.77000i) q^{59} +(0.781518 - 0.786450i) q^{60} +(-6.52032 - 8.79163i) q^{61} +(7.31348 - 8.94014i) q^{62} +(7.04378 + 7.04378i) q^{63} +(1.48661 - 7.86066i) q^{64} +(-3.62323 + 3.62323i) q^{65} +(0.270116 + 2.69901i) q^{66} +(-6.31339 + 4.68233i) q^{67} +(4.59634 - 11.1960i) q^{68} +(-0.473126 + 0.428817i) q^{69} +(-4.81294 + 4.37600i) q^{70} +(-0.929458 - 3.06401i) q^{71} +(7.35079 - 3.08551i) q^{72} +(-12.7277 + 6.80310i) q^{73} +(6.65683 - 0.337526i) q^{74} +(0.342183 - 1.36607i) q^{75} +(-0.169649 + 1.16901i) q^{76} +(-0.780873 - 15.8950i) q^{77} +(2.18970 - 0.911042i) q^{78} +(13.0736 - 8.73553i) q^{79} +(1.78461 + 4.89043i) q^{80} +(6.15288 + 4.11122i) q^{81} +(-1.34515 + 6.81856i) q^{82} +(-0.489707 + 1.36864i) q^{83} +(2.83160 - 1.02322i) q^{84} +(1.15561 + 7.79046i) q^{85} +(-0.366064 + 2.49483i) q^{86} +(0.423117 + 4.29598i) q^{87} +(-12.0117 - 4.23404i) q^{88} +(-6.21422 + 5.09988i) q^{89} +(-3.08376 + 4.17167i) q^{90} +(-13.1012 + 4.68768i) q^{91} +(-0.879346 - 2.86632i) q^{92} +(1.78852 - 2.98397i) q^{93} +(3.52828 + 4.28546i) q^{94} +(-0.294161 - 0.710168i) q^{95} +(0.0993002 - 2.40750i) q^{96} +(4.62792 - 11.1728i) q^{97} +(-7.42704 + 2.26573i) q^{98} +(-3.08384 - 12.3114i) 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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.408395	+	1.35396i	−0.288779	+	0.957396i
$2$	−0.408395	+	1.35396i	−0.288779	+	0.957396i
$3$	−0.0625001	+	0.421342i	−0.0360845	+	0.243262i	−0.999712	−	0.0239861i	$-0.992364\pi$
$3$	−0.0625001	+	0.421342i	−0.0360845	+	0.243262i	0.963628	+	0.267248i	$0.0861142\pi$
$4$	−1.66643	−	1.10590i	−0.833213	−	0.552952i
$5$	1.29990	+	0.0638600i	0.581333	+	0.0285591i	0.337611	−	0.941286i	$-0.390381\pi$
$5$	1.29990	+	0.0638600i	0.581333	+	0.0285591i	0.243723	+	0.969845i	$0.421631\pi$
$6$	−0.544956	−	0.256697i	−0.222477	−	0.104796i
$7$	3.11690	+	1.66602i	1.17808	+	0.629695i	0.939874	−	0.341521i	$-0.110942\pi$
$7$	3.11690	+	1.66602i	1.17808	+	0.629695i	0.238202	+	0.971216i	$0.423442\pi$
$8$	2.17791	−	1.80463i	0.770008	−	0.638034i
$9$	2.69720	+	0.818186i	0.899066	+	0.272729i
$10$	−0.617338	+	1.73394i	−0.195219	+	0.548319i
$11$	−2.31496	−	3.86227i	−0.697985	−	1.16452i	−0.978812	−	0.204760i	$-0.934359\pi$
$11$	−2.31496	−	3.86227i	−0.697985	−	1.16452i	0.280827	−	0.959758i	$-0.409391\pi$
$12$	0.570115	−	0.633016i	0.164578	−	0.182736i
$13$	−2.64400	+	2.91721i	−0.733314	+	0.809087i	−0.987425	−	0.158088i	$-0.949467\pi$
$13$	−2.64400	+	2.91721i	−0.733314	+	0.809087i	0.254111	+	0.967175i	$0.418217\pi$
$14$	−3.52865	+	3.53977i	−0.943071	+	0.946042i
$15$	−0.108151	+	0.543711i	−0.0279244	+	0.140386i
$16$	1.55395	+	3.68581i	0.388489	+	0.921454i
$17$	1.18057	+	5.93512i	0.286330	+	1.43948i	0.809435	+	0.587210i	$0.199774\pi$
$17$	1.18057	+	5.93512i	0.286330	+	1.43948i	−0.523105	+	0.852268i	$0.675226\pi$
$18$	−2.20932	+	3.31776i	−0.520741	+	0.782004i
$19$	−0.252525	−	0.533919i	−0.0579332	−	0.122489i	0.872946	−	0.487817i	$-0.162207\pi$
$19$	−0.252525	−	0.533919i	−0.0579332	−	0.122489i	−0.930879	+	0.365328i	$0.880957\pi$
$20$	−2.09557	−	1.54398i	−0.468583	−	0.345245i
$21$	−0.896768	+	1.20915i	−0.195691	+	0.263859i
$22$	6.17478	−	1.55703i	1.31647	−	0.331960i
$23$	1.15881	+	0.951011i	0.241629	+	0.198300i	0.747412	−	0.664361i	$-0.231296\pi$
$23$	1.15881	+	0.951011i	0.241629	+	0.198300i	−0.505783	+	0.862661i	$0.668796\pi$
$24$	0.624247	+	1.03044i	0.127424	+	0.210337i
$25$	−3.29026	−	0.324062i	−0.658052	−	0.0648125i
$26$	−2.86999	−	4.77125i	−0.562851	−	0.935719i
$27$	−1.05967	+	2.24047i	−0.203933	+	0.431179i
$28$	−3.35162	−	6.22328i	−0.633398	−	1.17609i
$29$	9.83069	−	2.46246i	1.82551	−	0.457267i	0.830501	−	0.557018i	$-0.188054\pi$
$29$	9.83069	−	2.46246i	1.82551	−	0.457267i	0.995012	+	0.0997506i	$0.0318045\pi$
$30$	−0.691996	−	0.368481i	−0.126341	−	0.0672752i
$31$	−7.54570	−	3.12553i	−1.35525	−	0.561362i	−0.417499	−	0.908677i	$-0.637093\pi$
$31$	−7.54570	−	3.12553i	−1.35525	−	0.561362i	−0.937748	+	0.347315i	$0.887093\pi$
$32$	−5.62508	+	0.598726i	−0.994383	+	0.105841i
$33$	1.77202	−	0.733995i	0.308469	−	0.127772i
$34$	−8.51807	−	0.825430i	−1.46084	−	0.141560i
$35$	3.94526	+	2.36470i	0.666871	+	0.399707i
$36$	−3.58985	−	4.34629i	−0.598308	−	0.724381i
$37$	−1.58781	−	4.43762i	−0.261034	−	0.729541i	−0.998531	−	0.0541902i	$-0.982742\pi$
$37$	−1.58781	−	4.43762i	−0.261034	−	0.729541i	0.737497	−	0.675351i	$-0.236008\pi$
$38$	0.826036	−	0.123859i	0.134001	−	0.0200926i
$39$	−1.06389	−	1.29635i	−0.170359	−	0.207583i
$40$	2.94631	−	2.20676i	0.465853	−	0.348920i
$41$	4.89071	−	0.481693i	0.763801	−	0.0752278i	0.291388	−	0.956605i	$-0.405883\pi$
$41$	4.89071	−	0.481693i	0.763801	−	0.0752278i	0.472413	+	0.881377i	$0.343383\pi$
$42$	−1.27091	−	1.70800i	−0.196106	−	0.263550i
$43$	1.76370	−	0.261620i	0.268962	−	0.0398967i	−0.0108871	−	0.999941i	$-0.503466\pi$
$43$	1.76370	−	0.261620i	0.268962	−	0.0398967i	0.279849	+	0.960044i	$0.409716\pi$
$44$	−0.413595	+	8.99630i	−0.0623518	+	1.35624i
$45$	3.45384	+	1.23580i	0.514868	+	0.184223i
$46$	−1.76089	+	1.18060i	−0.259628	+	0.174069i
$47$	2.18071	−	3.26366i	0.318089	−	0.476054i	−0.637626	−	0.770346i	$-0.720084\pi$
$47$	2.18071	−	3.26366i	0.318089	−	0.476054i	0.955716	+	0.294292i	$0.0950837\pi$
$48$	−1.65011	+	0.424382i	−0.238173	+	0.0612542i
$49$	3.05044	+	4.56531i	0.435777	+	0.652187i
$50$	1.78249	−	4.32254i	0.252083	−	0.611300i
$51$	−2.57450	+	0.126477i	−0.360502	+	0.0177103i
$52$	7.63218	−	1.93730i	1.05839	−	0.268655i
$53$	8.81849	+	2.20892i	1.21131	+	0.303418i	0.795456	−	0.606012i	$-0.207232\pi$
$53$	8.81849	+	2.20892i	1.21131	+	0.303418i	0.415857	+	0.909430i	$0.363482\pi$
$54$	−2.60075	−	2.34975i	−0.353918	−	0.319760i
$55$	−2.76257	−	5.16840i	−0.372505	−	0.696907i
$56$	9.79487	−	1.99641i	1.30889	−	0.266782i
$57$	0.240745	−	0.0730293i	0.0318875	−	0.00967297i
$58$	−0.680731	+	14.3160i	−0.0893844	+	1.87979i
$59$	−7.94867	−	8.77000i	−1.03483	−	1.14176i	−0.989755	−	0.142774i	$-0.954398\pi$
$59$	−7.94867	−	8.77000i	−1.03483	−	1.14176i	−0.0450732	−	0.998984i	$-0.514352\pi$
$60$	0.781518	−	0.786450i	0.100893	−	0.101530i
$61$	−6.52032	−	8.79163i	−0.834841	−	1.12565i	−0.990455	−	0.137835i	$-0.955985\pi$
$61$	−6.52032	−	8.79163i	−0.834841	−	1.12565i	0.155614	−	0.987818i	$-0.450265\pi$
$62$	7.31348	−	8.94014i	0.928813	−	1.13540i
$63$	7.04378	+	7.04378i	0.887432	+	0.887432i
$64$	1.48661	−	7.86066i	0.185826	−	0.982583i
$65$	−3.62323	+	3.62323i	−0.449407	+	0.449407i
$66$	0.270116	+	2.69901i	0.0332490	+	0.332225i
$67$	−6.31339	+	4.68233i	−0.771304	+	0.572038i	−0.908195	−	0.418548i	$-0.862539\pi$
$67$	−6.31339	+	4.68233i	−0.771304	+	0.572038i	0.136891	+	0.990586i	$0.456289\pi$
$68$	4.59634	−	11.1960i	0.557388	−	1.35772i
$69$	−0.473126	+	0.428817i	−0.0569577	+	0.0516235i
$70$	−4.81294	+	4.37600i	−0.575257	+	0.523033i
$71$	−0.929458	−	3.06401i	−0.110306	−	0.363631i	0.884356	−	0.466813i	$-0.154598\pi$
$71$	−0.929458	−	3.06401i	−0.110306	−	0.363631i	−0.994663	+	0.103181i	$0.967098\pi$
$72$	7.35079	−	3.08551i	0.866299	−	0.363631i
$73$	−12.7277	+	6.80310i	−1.48966	+	0.796242i	−0.997249	−	0.0741182i	$-0.976386\pi$
$73$	−12.7277	+	6.80310i	−1.48966	+	0.796242i	−0.492415	+	0.870360i	$0.663886\pi$
$74$	6.65683	−	0.337526i	0.773841	−	0.0392366i
$75$	0.342183	−	1.36607i	0.0395118	−	0.157740i
$76$	−0.169649	+	1.16901i	−0.0194601	+	0.134094i
$77$	−0.780873	−	15.8950i	−0.0889888	−	1.81141i
$78$	2.18970	−	0.911042i	0.247935	−	0.103155i
$79$	13.0736	−	8.73553i	1.47090	−	0.982824i	0.476274	−	0.879297i	$-0.341987\pi$
$79$	13.0736	−	8.73553i	1.47090	−	0.982824i	0.994627	−	0.103527i	$-0.0330128\pi$
$80$	1.78461	+	4.89043i	0.199525	+	0.546767i
$81$	6.15288	+	4.11122i	0.683653	+	0.456802i
$82$	−1.34515	+	6.81856i	−0.148547	+	0.752984i
$83$	−0.489707	+	1.36864i	−0.0537523	+	0.150228i	−0.965419	−	0.260702i	$-0.916046\pi$
$83$	−0.489707	+	1.36864i	−0.0537523	+	0.150228i	0.911667	+	0.410930i	$0.134796\pi$
$84$	2.83160	−	1.02322i	0.308953	−	0.111643i
$85$	1.15561	+	7.79046i	0.125343	+	0.844994i
$86$	−0.366064	+	2.49483i	−0.0394736	+	0.269024i
$87$	0.423117	+	4.29598i	0.0453629	+	0.460578i
$88$	−12.0117	−	4.23404i	−1.28046	−	0.451350i
$89$	−6.21422	+	5.09988i	−0.658706	+	0.540586i	−0.903284	−	0.429043i	$-0.858851\pi$
$89$	−6.21422	+	5.09988i	−0.658706	+	0.540586i	0.244578	+	0.969630i	$0.421351\pi$
$90$	−3.08376	+	4.17167i	−0.325057	+	0.439733i
$91$	−13.1012	+	4.68768i	−1.37338	+	0.491402i
$92$	−0.879346	−	2.86632i	−0.0916781	−	0.298835i
$93$	1.78852	−	2.98397i	0.185461	−	0.309423i
$94$	3.52828	+	4.28546i	0.363915	+	0.442012i
$95$	−0.294161	−	0.710168i	−0.0301803	−	0.0728617i
$96$	0.0993002	−	2.40750i	0.0101348	−	0.245715i
$97$	4.62792	−	11.1728i	0.469894	−	1.13442i	−0.494316	−	0.869282i	$-0.664581\pi$
$97$	4.62792	−	11.1728i	0.469894	−	1.13442i	0.964210	−	0.265141i	$-0.0854186\pi$
$98$	−7.42704	+	2.26573i	−0.750244	+	0.228873i
$99$	−3.08384	−	12.3114i	−0.309937	−	1.23734i
$100$	5.12459	+	4.17874i	0.512459	+	0.417874i
$101$	−2.97133	−	1.40533i	−0.295658	−	0.139836i	0.273971	−	0.961738i	$-0.411663\pi$
$101$	−2.97133	−	1.40533i	−0.295658	−	0.139836i	−0.569629	+	0.821902i	$0.692913\pi$
$102$	0.880169	−	3.53743i	0.0871497	−	0.350257i
$103$	−0.0635972	+	0.645714i	−0.00626642	+	0.0636241i	−0.997809	−	0.0661550i	$-0.978927\pi$
$103$	−0.0635972	+	0.645714i	−0.00626642	+	0.0636241i	0.991543	+	0.129779i	$0.0414268\pi$
$104$	−0.493919	+	11.1249i	−0.0484328	+	1.09088i
$105$	−1.24293	+	1.51451i	−0.121297	+	0.147801i
$106$	−6.59222	+	11.0378i	−0.640293	+	1.07208i
$107$	−7.42190	−	5.50446i	−0.717503	−	0.532136i	0.174227	−	0.984706i	$-0.444257\pi$
$107$	−7.42190	−	5.50446i	−0.717503	−	0.532136i	−0.891729	+	0.452569i	$0.850507\pi$
$108$	4.24360	−	2.56170i	0.408341	−	0.246499i
$109$	5.50729	−	2.60475i	0.527503	−	0.249490i	−0.145201	−	0.989402i	$-0.546383\pi$
$109$	5.50729	−	2.60475i	0.527503	−	0.249490i	0.672704	+	0.739912i	$0.265133\pi$
$110$	8.12604	−	1.62966i	0.774787	−	0.155382i
$111$	1.96899	−	0.391657i	0.186889	−	0.0371745i
$112$	−1.29711	+	14.0772i	−0.122565	+	1.33017i
$113$	−3.40974	−	0.678240i	−0.320762	−	0.0638035i	0.0320835	−	0.999485i	$-0.489786\pi$
$113$	−3.40974	−	0.678240i	−0.320762	−	0.0638035i	−0.352845	+	0.935682i	$0.614786\pi$
$114$	0.000559619		0.355785i	5.24131e−5		0.0333223i
$115$	1.44561	+	1.31022i	0.134804	+	0.122179i
$116$	−19.1054	−	6.76829i	−1.77389	−	0.628420i
$117$	−9.51821	+	5.70500i	−0.879959	+	0.527427i
$118$	15.1205	−	7.18057i	1.39195	−	0.661025i
$119$	−6.20829	+	20.4660i	−0.569113	+	1.87611i
$120$	0.745656	+	1.37933i	0.0680687	+	0.125915i
$121$	−4.37274	+	8.18083i	−0.397522	+	0.743711i
$122$	14.5664	−	5.23780i	1.31878	−	0.474208i
$123$	−0.102713	+	2.09077i	−0.00926130	+	0.188518i
$124$	9.11782	+	13.5533i	0.818804	+	1.21712i
$125$	−10.6932	−	1.58619i	−0.956431	−	0.141873i
$126$	−12.4136	+	6.66036i	−1.10590	+	0.593352i
$127$		−	7.97233i		−	0.707430i	−0.935353	−	0.353715i	$-0.884918\pi$
$127$		−	7.97233i		−	0.707430i	0.935353	−	0.353715i	$-0.115082\pi$
$128$	10.0359	+	5.22306i	0.887058	+	0.461658i
$129$			0.759472i			0.0668678i
$130$	−3.42601	−	6.38543i	−0.300481	−	0.560039i
$131$	2.47641	+	0.367340i	0.216365	+	0.0320947i	0.254033	−	0.967196i	$-0.418243\pi$
$131$	2.47641	+	0.367340i	0.216365	+	0.0320947i	−0.0376679	+	0.999290i	$0.511993\pi$
$132$	−3.76467	−	0.736535i	−0.327672	−	0.0641072i
$133$	0.102424	−	2.08488i	0.00888126	−	0.180782i
$134$	−3.76134	−	10.4603i	−0.324930	−	0.903636i
$135$	−1.52054	+	2.84472i	−0.130867	+	0.244835i
$136$	13.2819	+	10.7957i	1.13891	+	0.925722i
$137$	1.56455	−	5.15764i	0.133669	−	0.440647i	−0.864397	−	0.502809i	$-0.832300\pi$
$137$	1.56455	−	5.15764i	0.133669	−	0.440647i	0.998066	+	0.0621627i	$0.0197998\pi$
$138$	−0.387379	−	0.815722i	−0.0329759	−	0.0694389i
$139$	−11.1381	+	6.67590i	−0.944718	+	0.566242i	−0.901479	−	0.432823i	$-0.857518\pi$
$139$	−11.1381	+	6.67590i	−0.944718	+	0.566242i	−0.0432389	+	0.999065i	$0.513768\pi$
$140$	−3.95936	−	8.30368i	−0.334627	−	0.701789i
$141$	1.23882	+	1.12280i	0.104328	+	0.0945571i
$142$	4.52814	−	0.00712238i	0.379993	−	0.000597697i
$143$	17.3878	+	3.45864i	1.45404	+	0.289226i
$144$	1.17564	+	11.2128i	0.0979700	+	0.934400i
$145$	12.9362	−	2.57316i	1.07429	−	0.213690i
$146$	−4.01320	−	20.0112i	−0.332135	−	1.65614i
$147$	−2.11421	+	0.999945i	−0.174377	+	0.0824741i
$148$	−2.26162	+	9.15094i	−0.185904	+	0.752202i
$149$	−7.14812	−	5.30140i	−0.585596	−	0.434308i	0.261911	−	0.965092i	$-0.415647\pi$
$149$	−7.14812	−	5.30140i	−0.585596	−	0.434308i	−0.847507	+	0.530784i	$0.821897\pi$
$150$	1.70986	+	1.02120i	0.139610	+	0.0833805i
$151$	−10.3441	+	12.6043i	−0.841789	+	1.02572i	0.157482	+	0.987522i	$0.449663\pi$
$151$	−10.3441	+	12.6043i	−0.841789	+	1.02572i	−0.999270	+	0.0382004i	$0.987837\pi$
$152$	−1.51351	−	0.707115i	−0.122761	−	0.0573546i
$153$	−1.67181	+	16.9741i	−0.135157	+	1.37228i
$154$	21.8402	+	5.43419i	1.75993	+	0.437899i
$155$	−9.60906	−	4.54475i	−0.771819	−	0.365043i
$156$	0.339252	+	3.33684i	0.0271619	+	0.267161i
$157$	2.52270	+	10.0712i	0.201333	+	0.803767i	0.983531	+	0.180737i	$0.0578484\pi$
$157$	2.52270	+	10.0712i	0.201333	+	0.803767i	−0.782198	+	0.623030i	$0.785902\pi$
$158$	6.48836	+	21.2688i	0.516186	+	1.69205i
$159$	−1.48187	+	3.57754i	−0.117520	+	0.283717i
$160$	−7.35028	+	0.419066i	−0.581091	+	0.0331301i
$161$	2.02749	+	4.89480i	0.159789	+	0.385764i
$162$	−8.07924	+	6.65176i	−0.634765	+	0.522612i
$163$	−2.42289	+	4.04235i	−0.189775	+	0.316621i	−0.937880	−	0.346960i	$-0.887214\pi$
$163$	−2.42289	+	4.04235i	−0.189775	+	0.316621i	0.748105	+	0.663581i	$0.230964\pi$
$164$	−8.68272	−	4.60595i	−0.678007	−	0.359664i
$165$	2.35032	−	0.840959i	0.182972	−	0.0654686i
$166$	−1.65309	−	1.22199i	−0.128305	−	0.0948449i
$167$	12.8003	−	10.5049i	0.990518	−	0.812897i	0.00817144	−	0.999967i	$-0.497399\pi$
$167$	12.8003	−	10.5049i	0.990518	−	0.812897i	0.982347	+	0.187069i	$0.0598989\pi$
$168$	0.228992	+	4.25176i	0.0176671	+	0.328031i
$169$	−0.245124	−	2.48879i	−0.0188557	−	0.191445i
$170$	−11.0199	−	1.61694i	−0.845190	−	0.124014i
$171$	−0.244265	−	1.64670i	−0.0186794	−	0.125926i
$172$	−3.22841	−	1.51451i	−0.246164	−	0.115481i
$173$	3.31419	−	9.26254i	0.251973	−	0.704218i	−0.747240	−	0.664554i	$-0.768621\pi$
$173$	3.31419	−	9.26254i	0.251973	−	0.704218i	0.999213	−	0.0396634i	$-0.0126286\pi$
$174$	−5.98940	−	1.18157i	−0.454055	−	0.0895749i
$175$	−9.71550	−	6.49169i	−0.734423	−	0.490726i
$176$	10.6383	−	14.5343i	0.801890	−	1.09556i
$177$	4.19196	−	2.80098i	0.315087	−	0.210534i
$178$	−4.36719	−	10.4966i	−0.327334	−	0.786753i
$179$	1.05017	+	21.3767i	0.0784936	+	1.59777i	0.638724	+	0.769436i	$0.279463\pi$
$179$	1.05017	+	21.3767i	0.0784936	+	1.59777i	−0.560230	+	0.828337i	$0.689287\pi$
$180$	−4.38889	−	5.87899i	−0.327129	−	0.438194i
$181$	0.0320761	−	0.128055i	0.00238420	−	0.00951826i	−0.968827	−	0.247736i	$-0.920313\pi$
$181$	0.0320761	−	0.128055i	0.00238420	−	0.00951826i	0.971212	+	0.238218i	$0.0765633\pi$
$182$	−0.996476	−	19.6529i	−0.0738637	−	1.45677i
$183$	4.11180	−	2.19780i	0.303953	−	0.162466i
$184$	4.24001	−	0.0200077i	0.312578	−	0.00147499i
$185$	−1.78061	−	5.86987i	−0.130913	−	0.431561i
$186$	3.30976	+	3.64023i	0.242683	+	0.266915i
$187$	20.1901	−	18.2992i	1.47644	−	1.33817i
$188$	−7.24329	+	3.02700i	−0.528271	+	0.220767i
$189$	−7.03553	+	5.21790i	−0.511759	+	0.379547i
$190$	1.08168	−	0.108254i	0.0784730	−	0.00785356i
$191$	14.9987	−	14.9987i	1.08527	−	1.08527i	0.0892609	−	0.996008i	$-0.471550\pi$
$191$	14.9987	−	14.9987i	1.08527	−	1.08527i	0.996008	−	0.0892609i	$-0.0284505\pi$
$192$	3.21911	+	1.11766i	0.232319	+	0.0806602i
$193$	−8.07013	−	8.07013i	−0.580900	−	0.580900i	0.354250	−	0.935151i	$-0.384736\pi$
$193$	−8.07013	−	8.07013i	−0.580900	−	0.580900i	−0.935151	+	0.354250i	$0.884736\pi$
$194$	13.2375	+	10.8289i	0.950397	+	0.777472i
$195$	−1.30017	−	1.75307i	−0.0931068	−	0.125540i
$196$	−0.0345452	−	10.9812i	−0.00246751	−	0.784374i
$197$	−5.37182	−	5.92689i	−0.382726	−	0.422274i	0.518869	−	0.854854i	$-0.326353\pi$
$197$	−5.37182	−	5.92689i	−0.382726	−	0.422274i	−0.901595	+	0.432580i	$0.857603\pi$
$198$	17.9286	+	0.852507i	1.27413	+	0.0605851i
$199$	−8.50508	+	2.57999i	−0.602909	+	0.182890i	−0.576959	−	0.816773i	$-0.695761\pi$
$199$	−8.50508	+	2.57999i	−0.602909	+	0.182890i	−0.0259496	+	0.999663i	$0.508261\pi$
$200$	−7.75071	+	5.23193i	−0.548058	+	0.369953i
$201$	−1.57827	−	2.95274i	−0.111323	−	0.208270i
$202$	3.11624	−	3.44913i	0.219258	−	0.242680i
$203$	34.7437	+	8.70285i	2.43853	+	0.610820i
$204$	4.43009	+	2.63638i	0.310168	+	0.184584i
$205$	6.38820	−	0.313832i	0.446172	−	0.0219190i
$206$	−0.848299	−	0.349815i	−0.0591038	−	0.0243727i
$207$	2.34744	+	3.51319i	0.163158	+	0.244183i
$208$	−14.8609	−	5.21209i	−1.03042	−	0.361394i
$209$	−1.47756	+	2.21132i	−0.102205	+	0.152960i
$210$	−1.54298	−	2.30139i	−0.106476	−	0.158811i
$211$	23.6989	+	8.47959i	1.63150	+	0.583759i	0.983978	−	0.178289i	$-0.0570562\pi$
$211$	23.6989	+	8.47959i	1.63150	+	0.583759i	0.647520	+	0.762048i	$0.275806\pi$
$212$	−12.2525	−	13.4334i	−0.841506	−	0.922609i
$213$	1.34909	−	0.200118i	0.0924379	−	0.0137119i
$214$	10.4839	−	7.80098i	0.716665	−	0.533264i
$215$	2.30934	−	0.227451i	0.157496	−	0.0155120i
$216$	1.73537	+	6.79186i	0.118077	+	0.462128i
$217$	−18.3120	−	22.3132i	−1.24310	−	1.51472i
$218$	1.27759	+	8.52043i	0.0865291	+	0.577076i
$219$	−2.07095	−	5.78791i	−0.139942	−	0.391110i
$220$	−1.11214	+	11.6679i	−0.0749803	+	0.786649i
$221$	−20.4354	−	12.2485i	−1.37463	−	0.823923i
$222$	−0.273839	+	2.82589i	−0.0183789	+	0.189662i
$223$	0.398798	−	0.165187i	0.0267055	−	0.0110618i	−0.369291	−	0.929314i	$-0.620399\pi$
$223$	0.398798	−	0.165187i	0.0267055	−	0.0110618i	0.395996	+	0.918252i	$0.370399\pi$
$224$	−18.5303	−	7.50531i	−1.23811	−	0.501469i
$225$	−8.60934	−	3.56611i	−0.573956	−	0.237740i
$226$	2.31083	−	4.33967i	0.153714	−	0.288671i
$227$	7.81087	−	1.95652i	0.518425	−	0.129859i	0.0250685	−	0.999686i	$-0.492020\pi$
$227$	7.81087	−	1.95652i	0.518425	−	0.129859i	0.493357	+	0.869827i	$0.335770\pi$
$228$	−0.481948	−	0.144543i	−0.0319178	−	0.00957261i
$229$	−5.41024	+	11.4390i	−0.357519	+	0.755910i	−0.999946	−	0.0104372i	$-0.996678\pi$
$229$	−5.41024	+	11.4390i	−0.357519	+	0.755910i	0.642427	+	0.766347i	$0.277928\pi$
$230$	−2.36437	+	1.42221i	−0.155902	+	0.0937777i
$231$	6.74605	+	0.664428i	0.443857	+	0.0437161i
$232$	16.9665	−	23.1038i	1.11391	−	1.51684i
$233$	−10.9618	−	8.99609i	−0.718130	−	0.589354i	0.202736	−	0.979233i	$-0.435017\pi$
$233$	−10.9618	−	8.99609i	−0.718130	−	0.589354i	−0.920866	+	0.389880i	$0.872517\pi$
$234$	−3.83716	−	15.2172i	−0.250843	−	0.994779i
$235$	3.04312	−	4.10318i	0.198512	−	0.267662i
$236$	3.54709	+	23.4050i	0.230896	+	1.52354i
$237$	2.86354	+	6.05444i	0.186007	+	0.393278i
$238$	−25.1747	−	16.7640i	−1.63184	−	1.08665i
$239$	5.51384	+	27.7200i	0.356661	+	1.79306i	0.576046	+	0.817417i	$0.304595\pi$
$239$	5.51384	+	27.7200i	0.356661	+	1.79306i	−0.219385	+	0.975638i	$0.570405\pi$
$240$	−2.17208	+	0.446278i	−0.140207	+	0.0288071i
$241$	−0.949166	+	4.77178i	−0.0611411	+	0.307377i	−0.999240	−	0.0389916i	$-0.987585\pi$
$241$	−0.949166	+	4.77178i	−0.0611411	+	0.307377i	0.938098	+	0.346369i	$0.112585\pi$
$242$	−9.29072	−	9.26154i	−0.597230	−	0.595354i
$243$	−7.11002	+	7.84470i	−0.456108	+	0.503238i
$244$	1.14293	+	21.8615i	0.0731688	+	1.39954i
$245$	3.67373	+	6.12925i	0.234706	+	0.391583i
$246$	−2.78887	−	0.992929i	−0.177812	−	0.0633068i
$247$	2.22523	+	0.675016i	0.141588	+	0.0429502i
$248$	−22.0743	+	6.81008i	−1.40172	+	0.432440i
$249$	−0.546058	−	0.291874i	−0.0346050	−	0.0184968i
$250$	6.51471	−	13.8304i	0.412026	−	0.874713i
$251$	−9.02196	−	0.443220i	−0.569461	−	0.0279758i	−0.237699	−	0.971339i	$-0.576393\pi$
$251$	−9.02196	−	0.443220i	−0.569461	−	0.0279758i	−0.331762	+	0.943363i	$0.607643\pi$
$252$	−3.94820	−	19.5277i	−0.248713	−	1.23013i
$253$	0.990467	−	6.67719i	0.0622701	−	0.419791i
$254$	10.7942	+	3.25586i	0.677291	+	0.204291i
$255$	−3.35467			−0.210078
$256$	−11.1705	+	11.4552i	−0.698153	+	0.715948i
$257$	24.3349			1.51797			0.758984	−	0.651109i	$-0.225696\pi$
$257$	24.3349			1.51797			0.758984	+	0.651109i	$0.225696\pi$
$258$	−1.02830	−	0.310165i	−0.0640190	−	0.0193100i
$259$	2.44412	−	16.4769i	0.151870	−	1.02383i
$260$	10.0448	−	2.03090i	0.622952	−	0.125951i
$261$	28.5301	+	1.40159i	1.76597	+	0.0867564i
$262$	−1.50872	+	3.20294i	−0.0932089	+	0.197878i
$263$	4.82403	+	2.57850i	0.297463	+	0.158997i	0.613376	−	0.789791i	$-0.289811\pi$
$263$	4.82403	+	2.57850i	0.297463	+	0.158997i	−0.315914	+	0.948788i	$0.602311\pi$
$264$	2.53471	−	4.79642i	0.156001	−	0.295199i
$265$	11.3221	+	3.43452i	0.695511	+	0.210981i
$266$	2.78102	+	0.990134i	0.170515	+	0.0607090i
$267$	−1.76040	−	2.93705i	−0.107735	−	0.179745i
$268$	15.6990	−	0.820757i	0.958970	−	0.0501357i
$269$	7.43921	−	8.20790i	0.453577	−	0.500445i	−0.470634	−	0.882329i	$-0.655975\pi$
$269$	7.43921	−	8.20790i	0.453577	−	0.500445i	0.924210	+	0.381884i	$0.124725\pi$
$270$	−3.23067	−	3.22052i	−0.196612	−	0.195995i
$271$	−1.03271	+	5.19180i	−0.0627329	+	0.315380i	−0.999392	−	0.0348625i	$-0.988901\pi$
$271$	−1.03271	+	5.19180i	−0.0627329	+	0.315380i	0.936659	+	0.350242i	$0.113901\pi$
$272$	−20.0412	+	13.5743i	−1.21518	+	0.823061i
$273$	−1.15629	−	5.81306i	−0.0699818	−	0.351822i
$274$	6.34429	+	4.22470i	0.383273	+	0.255223i
$275$	6.36519	+	13.4581i	0.383835	+	0.811551i
$276$	1.26266	−	0.191359i	0.0760032	−	0.0115185i
$277$	−5.02752	+	6.77883i	−0.302074	+	0.407300i	−0.927999	−	0.372584i	$-0.878472\pi$
$277$	−5.02752	+	6.77883i	−0.302074	+	0.407300i	0.625924	+	0.779884i	$0.284722\pi$
$278$	−4.49018	−	17.8069i	−0.269303	−	1.06799i
$279$	−17.7950	−	14.6040i	−1.06536	−	0.874316i
$280$	12.8599	−	1.96964i	0.768523	−	0.117709i
$281$	−7.23035	−	0.712127i	−0.431327	−	0.0424820i	−0.119975	−	0.992777i	$-0.538282\pi$
$281$	−7.23035	−	0.712127i	−0.431327	−	0.0424820i	−0.311351	+	0.950295i	$0.600782\pi$
$282$	−2.02616	+	1.21877i	−0.120656	+	0.0725768i
$283$	−2.76666	+	5.84960i	−0.164461	+	0.347723i	−0.969343	−	0.245712i	$-0.920978\pi$
$283$	−2.76666	+	5.84960i	−0.164461	+	0.347723i	0.804882	+	0.593434i	$0.202228\pi$
$284$	−1.83963	+	6.13384i	−0.109162	+	0.363976i
$285$	0.317609	−	0.0795568i	0.0188135	−	0.00471254i
$286$	−11.7840	+	22.1299i	−0.696800	+	1.30857i
$287$	16.0464	+	6.64662i	0.947186	+	0.392337i
$288$	−15.6618	−	2.98748i	−0.922882	−	0.176039i
$289$	−18.1260	+	7.50802i	−1.06623	+	0.441648i
$290$	−1.79911	+	18.5660i	−0.105647	+	1.09023i
$291$	4.41831	+	2.64823i	0.259006	+	0.155242i
$292$	28.7333	+	2.73875i	1.68149	+	0.160273i
$293$	−0.127593	−	0.356597i	−0.00745404	−	0.0208326i	0.937759	−	0.347286i	$-0.112897\pi$
$293$	−0.127593	−	0.356597i	−0.00745404	−	0.0208326i	−0.945213	+	0.326453i	$0.894147\pi$
$294$	−0.490456	−	3.27093i	−0.0286040	−	0.190764i
$295$	−9.77243	−	11.9077i	−0.568973	−	0.693295i
$296$	−11.4664	−	6.79935i	−0.666470	−	0.395204i
$297$	11.1064	−	1.09388i	0.644458	−	0.0634736i
$298$	10.0972	−	7.51321i	0.584913	−	0.435229i
$299$	−5.83819	+	0.866014i	−0.337631	+	0.0500829i
$300$	−2.08096	+	1.89803i	−0.120144	+	0.109583i
$301$	5.93314	+	2.12291i	0.341980	+	0.122363i
$302$	−12.8413	−	19.1530i	−0.738931	−	1.10213i
$303$	0.777833	−	1.16411i	0.0446854	−	0.0668764i
$304$	1.57551	−	1.76045i	0.0903620	−	0.100969i
$305$	−7.91434	−	11.8446i	−0.453174	−	0.678222i
$306$	−22.2996	−	9.19571i	−1.27478	−	0.525684i
$307$	−6.25100	+	0.307092i	−0.356764	+	0.0175267i	−0.226661	−	0.973974i	$-0.572781\pi$
$307$	−6.25100	+	0.307092i	−0.356764	+	0.0175267i	−0.130103	+	0.991500i	$0.541531\pi$
$308$	−16.2771	+	27.3515i	−0.927475	+	1.55850i
$309$	−0.268091	−	0.0671534i	−0.0152512	−	0.00382022i
$310$	10.0777	−	11.1543i	0.572376	−	0.633519i
$311$	9.10741	+	17.0388i	0.516434	+	0.966180i	0.996058	+	0.0887057i	$0.0282731\pi$
$311$	9.10741	+	17.0388i	0.516434	+	0.966180i	−0.479624	+	0.877474i	$0.659227\pi$
$312$	−4.65650	−	0.903415i	−0.263622	−	0.0511458i
$313$	4.58795	−	1.39174i	0.259326	−	0.0786657i	−0.157944	−	0.987448i	$-0.550487\pi$
$313$	4.58795	−	1.39174i	0.259326	−	0.0786657i	0.417271	+	0.908782i	$0.362987\pi$
$314$	−14.6662	−	0.697384i	−0.827664	−	0.0393556i
$315$	8.70639	+	9.60603i	0.490550	+	0.541238i
$316$	−31.4469	+	0.0989269i	−1.76903	+	0.00556507i
$317$	−3.30085	−	4.45067i	−0.185394	−	0.249975i	0.700726	−	0.713430i	$-0.252859\pi$
$317$	−3.30085	−	4.45067i	−0.185394	−	0.249975i	−0.886120	+	0.463455i	$0.846609\pi$
$318$	−4.23867	−	3.46744i	−0.237693	−	0.194444i
$319$	−32.2683	−	32.2683i	−1.80668	−	1.80668i
$320$	2.43442	−	10.1231i	0.136088	−	0.565901i
$321$	2.78313	−	2.78313i	0.155339	−	0.155339i
$322$	−7.45539	+	0.746134i	−0.415473	+	0.0415804i
$323$	2.87075	−	2.12909i	0.159733	−	0.118466i
$324$	−5.70670	−	13.6555i	−0.317039	−	0.758641i
$325$	9.64481	−	8.74154i	0.534998	−	0.484894i
$326$	−4.48369	−	4.93138i	−0.248328	−	0.273124i
$327$	0.753285	+	2.48325i	0.0416568	+	0.137324i
$328$	9.78227	−	9.87503i	0.540135	−	0.545257i
$329$	12.2344	−	6.53940i	0.674502	−	0.360529i
$330$	0.178766	+	3.52569i	0.00984072	+	0.194083i
$331$	0.00580505	−	0.0231750i	0.000319074	−	0.00127382i	−0.969872	−	0.243617i	$-0.921666\pi$
$331$	0.00580505	−	0.0231750i	0.000319074	−	0.00127382i	0.970191	+	0.242343i	$0.0779160\pi$
$332$	2.32964	−	1.73917i	0.127856	−	0.0954492i
$333$	−0.651829	−	13.2683i	−0.0357200	−	0.727097i
$334$	8.99571	+	21.6213i	0.492223	+	1.18307i
$335$	−8.50580	+	5.68339i	−0.464722	+	0.310517i
$336$	−5.85025	−	1.42635i	−0.319157	−	0.0778140i
$337$	26.1806	+	17.4933i	1.42615	+	0.952920i	0.998807	+	0.0488288i	$0.0155489\pi$
$337$	26.1806	+	17.4933i	1.42615	+	0.952920i	0.427339	+	0.904092i	$0.359451\pi$
$338$	3.46983	+	0.684521i	0.188734	+	0.0372330i
$339$	0.498880	−	1.39428i	0.0270955	−	0.0757267i
$340$	6.68977	−	14.2602i	0.362804	−	0.773369i
$341$	5.39631	+	36.3790i	0.292227	+	1.97003i
$342$	2.32932	+	0.341779i	0.125955	+	0.0184813i
$343$	−0.522860	−	5.30869i	−0.0282318	−	0.286642i
$344$	3.36906	−	3.75262i	0.181648	−	0.202328i
$345$	−0.642402	+	0.527205i	−0.0345857	+	0.0283838i
$346$	11.1876	+	8.27006i	0.601450	+	0.444601i
$347$	−15.3991	+	5.50989i	−0.826668	+	0.295786i	−0.716026	−	0.698074i	$-0.754041\pi$
$347$	−15.3991	+	5.50989i	−0.826668	+	0.295786i	−0.110642	+	0.993860i	$0.535291\pi$
$348$	4.04585	−	7.62687i	0.216880	−	0.408843i
$349$	−7.50733	+	12.5252i	−0.401858	+	0.670460i	−0.990435	−	0.137981i	$-0.955939\pi$
$349$	−7.50733	+	12.5252i	−0.401858	+	0.670460i	0.588576	+	0.808442i	$0.299689\pi$
$350$	12.7573	−	10.5032i	0.681905	−	0.561422i
$351$	−3.73417	−	9.01508i	−0.199315	−	0.481189i
$352$	15.3342	+	20.3396i	0.817318	+	1.08410i
$353$	−9.25250	+	22.3375i	−0.492461	+	1.18891i	0.461003	+	0.887399i	$0.347490\pi$
$353$	−9.25250	+	22.3375i	−0.492461	+	1.18891i	−0.953464	+	0.301507i	$0.902510\pi$
$354$	2.08044	+	6.81966i	0.110574	+	0.362461i
$355$	−1.01254	−	4.04227i	−0.0537398	−	0.214541i
$356$	15.9955	−	1.62624i	0.847761	−	0.0861908i
$357$	−8.23516	−	3.89494i	−0.435851	−	0.206142i
$358$	−29.3722	−	7.30827i	−1.55237	−	0.386254i
$359$	−0.108622	+	1.10285i	−0.00573283	+	0.0582064i	−0.997626	−	0.0688720i	$-0.978060\pi$
$359$	−0.108622	+	1.10285i	−0.00573283	+	0.0582064i	0.991893	+	0.127078i	$0.0405600\pi$
$360$	9.75234	−	3.54144i	0.513993	−	0.186650i
$361$	11.8322	−	14.4175i	0.622746	−	0.758818i
$362$	0.160282	+	0.0957270i	0.00842423	+	0.00503130i
$363$	−3.17363	−	2.35372i	−0.166572	−	0.123538i
$364$	27.0163	+	6.67698i	1.41604	+	0.349969i
$365$	−16.9792	+	8.03056i	−0.888732	+	0.420339i
$366$	1.29650	+	6.46480i	0.0677693	+	0.337920i
$367$	11.4006	−	2.26772i	0.595107	−	0.118374i	0.111658	−	0.993747i	$-0.464384\pi$
$367$	11.4006	−	2.26772i	0.595107	−	0.118374i	0.483449	+	0.875373i	$0.339384\pi$
$368$	−1.70451	+	5.74899i	−0.0888538	+	0.299687i
$369$	13.5853	+	2.70229i	0.707225	+	0.140676i
$370$	8.67477	−	0.0136447i	0.450980	−	0.000709353i
$371$	23.8062	+	21.5767i	1.23596	+	1.12021i
$372$	−6.28043	+	2.99463i	−0.325625	+	0.155265i
$373$	−3.11292	+	1.86581i	−0.161181	+	0.0966082i	−0.592419	−	0.805630i	$-0.701827\pi$
$373$	−3.11292	+	1.86581i	−0.161181	+	0.0966082i	0.431238	+	0.902238i	$0.358077\pi$
$374$	16.5309	+	34.8099i	0.854793	+	1.79998i
$375$	1.33666	−	4.40637i	0.0690246	−	0.227544i
$376$	−1.14032	−	11.0434i	−0.0588073	−	0.569517i
$377$	−18.8089	+	35.1889i	−0.968705	+	1.81232i
$378$	−4.19157	−	11.6568i	−0.215591	−	0.599561i
$379$	−1.33879	+	27.2517i	−0.0687691	+	1.39983i	0.678156	+	0.734918i	$0.262780\pi$
$379$	−1.33879	+	27.2517i	−0.0687691	+	1.39983i	−0.746925	+	0.664909i	$0.768470\pi$
$380$	−0.295180	+	1.50876i	−0.0151424	+	0.0773976i
$381$	3.35908	+	0.498272i	0.172091	+	0.0255272i
$382$	14.1823	+	26.4331i	0.725629	+	1.35244i
$383$			7.51517i			0.384007i	0.981394	+	0.192004i	$0.0614986\pi$
$383$			7.51517i			0.384007i	−0.981394	+	0.192004i	$0.938501\pi$
$384$	−2.82794	+	3.90211i	−0.144313	+	0.199129i
$385$		−	20.7118i		−	1.05557i
$386$	14.2224	−	7.63084i	0.723903	−	0.388400i
$387$	4.97111	+	0.737394i	0.252696	+	0.0374839i
$388$	−20.0681	+	13.5006i	−1.01880	+	0.685388i
$389$	−0.708233	+	14.4164i	−0.0359088	+	0.730941i	0.911574	+	0.411135i	$0.134868\pi$
$389$	−0.708233	+	14.4164i	−0.0359088	+	0.730941i	−0.947483	+	0.319806i	$0.896382\pi$
$390$	2.90457	−	1.04443i	0.147079	−	0.0528867i
$391$	−4.27631	+	8.00041i	−0.216262	+	0.404598i
$392$	14.8823	+	4.43791i	0.751669	+	0.224149i
$393$	−0.309552	+	1.02046i	−0.0156148	+	0.0514752i
$394$	10.2186	−	4.85273i	0.514806	−	0.244477i
$395$	17.5523	−	10.5204i	0.883152	−	0.529341i
$396$	−8.47620	+	23.9264i	−0.425945	+	1.20235i
$397$	1.39007	+	1.25989i	0.0697659	+	0.0632321i	0.705697	−	0.708514i	$-0.250634\pi$
$397$	1.39007	+	1.25989i	0.0697659	+	0.0632321i	−0.635931	+	0.771746i	$0.719384\pi$
$398$	−0.0197703	−	12.5692i	−0.000990995	−	0.630037i
$399$	0.872046	+	0.173461i	0.0436569	+	0.00868390i
$400$	−3.91848	−	12.6309i	−0.195924	−	0.631543i
$401$	10.1428	−	2.01752i	0.506505	−	0.100750i	0.0647784	−	0.997900i	$-0.479366\pi$
$401$	10.1428	−	2.01752i	0.506505	−	0.100750i	0.441727	+	0.897149i	$0.354366\pi$
$402$	4.64246	−	0.931037i	0.231545	−	0.0464359i
$403$	29.0687	−	13.7484i	1.44801	−	0.684859i
$404$	3.39733	+	5.62788i	0.169024	+	0.279998i
$405$	7.73559	+	5.73710i	0.384384	+	0.285079i
$406$	−25.9725	+	43.4875i	−1.28899	+	2.15825i
$407$	−13.4636	+	16.4054i	−0.667366	+	0.813187i
$408$	−5.37879	+	4.92148i	−0.266290	+	0.243650i
$409$	2.15321	−	21.8619i	0.106470	−	1.08100i	−0.782379	−	0.622802i	$-0.785994\pi$
$409$	2.15321	−	21.8619i	0.106470	−	1.08100i	0.888849	−	0.458201i	$-0.151506\pi$
$410$	−2.18400	+	8.77755i	−0.107860	+	0.433492i
$411$	2.07534	+	0.981564i	0.102369	+	0.0484170i
$412$	0.820077	−	1.00570i	0.0404023	−	0.0495474i
$413$	−10.1642	−	40.5778i	−0.500148	−	1.99670i
$414$	−5.71541	+	1.74357i	−0.280897	+	0.0856919i
$415$	−0.723972	+	1.74782i	−0.0355384	+	0.0857972i
$416$	13.1261	−	17.9925i	0.643561	−	0.882157i
$417$	−2.11670	−	5.11017i	−0.103655	−	0.250246i
$418$	−2.39061	−	2.90365i	−0.116929	−	0.142022i
$419$	0.302031	−	0.503909i	0.0147552	−	0.0246176i	−0.850263	−	0.526359i	$-0.823557\pi$
$419$	0.302031	−	0.503909i	0.0147552	−	0.0246176i	0.865018	+	0.501741i	$0.167307\pi$
$420$	3.74615	−	1.14926i	0.182793	−	0.0560783i
$421$	−4.53606	+	1.62303i	−0.221074	+	0.0791015i	−0.445097	−	0.895482i	$-0.646831\pi$
$421$	−4.53606	+	1.62303i	−0.221074	+	0.0791015i	0.224023	+	0.974584i	$0.428081\pi$
$422$	−21.1596	+	28.6244i	−1.03003	+	1.39341i
$423$	8.55209	−	7.01852i	0.415817	−	0.341252i
$424$	23.1922	−	11.1033i	1.12631	−	0.539224i
$425$	−1.96103	−	19.9107i	−0.0951239	−	0.965809i
$426$	−0.280009	+	1.90834i	−0.0135665	+	0.0924594i
$427$	−5.67616	−	38.2656i	−0.274689	−	1.85180i
$428$	6.28066	+	17.3807i	0.303587	+	0.840127i
$429$	−2.54401	+	7.11003i	−0.122826	+	0.343275i
$430$	−0.635166	+	3.21965i	−0.0306304	+	0.155266i
$431$	−11.2699	−	7.53028i	−0.542850	−	0.362721i	0.253710	−	0.967280i	$-0.418349\pi$
$431$	−11.2699	−	7.53028i	−0.542850	−	0.362721i	−0.796560	+	0.604559i	$0.793349\pi$
$432$	−9.90464	−	0.424135i	−0.476537	−	0.0204062i
$433$	−25.7067	+	17.1767i	−1.23539	+	0.825459i	−0.989597	−	0.143865i	$-0.954047\pi$
$433$	−25.7067	+	17.1767i	−1.23539	+	0.825459i	−0.245789	+	0.969323i	$0.579047\pi$
$434$	37.6898	−	15.6811i	1.80917	−	0.752717i
$435$	0.275669	+	5.61137i	0.0132173	+	0.269045i
$436$	−12.0581	−	1.74990i	−0.577478	−	0.0838050i
$437$	0.215135	−	0.858865i	0.0102913	−	0.0410851i
$438$	8.68237	−	0.440228i	0.414860	−	0.0210349i
$439$	−14.2370	+	7.60984i	−0.679496	+	0.363198i	−0.774761	−	0.632254i	$-0.782130\pi$
$439$	−14.2370	+	7.60984i	−0.679496	+	0.363198i	0.0952656	+	0.995452i	$0.469630\pi$
$440$	−15.3437	−	6.27090i	−0.731482	−	0.298954i
$441$	4.49237	+	14.8094i	0.213922	+	0.705208i
$442$	24.9297	−	22.6665i	1.18579	−	1.07814i
$443$	−20.2906	+	18.3903i	−0.964035	+	0.873750i	−0.992048	−	0.125857i	$-0.959832\pi$
$443$	−20.2906	+	18.3903i	−0.964035	+	0.873750i	0.0280134	+	0.999608i	$0.491082\pi$
$444$	−3.71432	−	1.52485i	−0.176274	−	0.0723662i
$445$	−8.40355	+	6.23250i	−0.398367	+	0.295449i
$446$	0.0607904	+	0.607419i	0.00287851	+	0.0287621i
$447$	2.68046	−	2.68046i	0.126781	−	0.126781i
$448$	17.7296	−	22.0242i	0.837644	−	1.04054i
$449$	−21.4227	−	21.4227i	−1.01100	−	1.01100i	−0.999939	−	0.0110596i	$-0.996480\pi$
$449$	−21.4227	−	21.4227i	−1.01100	−	1.01100i	−0.0110596	−	0.999939i	$-0.503520\pi$
$450$	8.34439	−	10.2003i	0.393358	−	0.480849i
$451$	−13.1822	−	17.7742i	−0.620726	−	0.836952i
$452$	4.93202	+	4.90108i	0.231983	+	0.230528i
$453$	−4.66421	−	5.14616i	−0.219144	−	0.241788i
$454$	−0.540868	+	11.3747i	−0.0253842	+	0.533839i
$455$	−17.3296	+	5.25688i	−0.812424	+	0.246446i
$456$	0.392531	−	0.593508i	0.0183820	−	0.0277936i
$457$	1.40935	+	2.63670i	0.0659265	+	0.123340i	0.912726	−	0.408573i	$-0.133973\pi$
$457$	1.40935	+	2.63670i	0.0659265	+	0.123340i	−0.846799	+	0.531913i	$0.821473\pi$
$458$	−13.2784	−	11.9969i	−0.620461	−	0.560578i
$459$	−14.5485	−	3.64421i	−0.679065	−	0.170097i
$460$	−0.960019	−	3.78209i	−0.0447611	−	0.176341i
$461$	4.46892	−	0.219544i	0.208138	−	0.0102252i	0.0552685	−	0.998472i	$-0.482399\pi$
$461$	4.46892	−	0.219544i	0.208138	−	0.0102252i	0.152870	+	0.988246i	$0.451149\pi$
$462$	−3.65467	+	8.86254i	−0.170030	+	0.412323i
$463$	12.9195	+	19.3354i	0.600421	+	0.898593i	0.999835	−	0.0181773i	$-0.00578635\pi$
$463$	12.9195	+	19.3354i	0.600421	+	0.898593i	−0.399414	+	0.916771i	$0.630786\pi$
$464$	24.3526	+	32.4075i	1.13054	+	1.50448i
$465$	2.51546	−	3.76465i	0.116652	−	0.174582i
$466$	16.6571	−	11.1679i	0.771626	−	0.517341i
$467$	−29.7082	−	10.6298i	−1.37473	−	0.491888i	−0.457136	−	0.889397i	$-0.651125\pi$
$467$	−29.7082	−	10.6298i	−1.37473	−	0.491888i	−0.917598	+	0.397509i	$0.869875\pi$
$468$	22.1706	+	1.01927i	1.02484	+	0.0471157i
$469$	−27.4790	+	4.07613i	−1.26886	+	0.188218i
$470$	4.31275	+	5.79599i	0.198932	+	0.267349i
$471$	−4.40107	+	0.433468i	−0.202791	+	0.0199731i
$472$	−33.1381	−	4.75588i	−1.52531	−	0.218907i
$473$	−5.09334	−	6.20625i	−0.234192	−	0.285364i
$474$	−9.36694	+	1.40452i	−0.430238	+	0.0645116i
$475$	0.657850	+	1.83857i	0.0301842	+	0.0843592i
$476$	32.9791	−	27.2393i	1.51159	−	1.24851i
$477$	21.9779	+	13.1731i	1.00630	+	0.603153i
$478$	−39.7836	−	3.85517i	−1.81966	−	0.176331i
$479$	−13.3726	+	5.53911i	−0.611009	+	0.253088i	−0.666660	−	0.745362i	$-0.732277\pi$
$479$	−13.3726	+	5.53911i	−0.611009	+	0.253088i	0.0556508	+	0.998450i	$0.482277\pi$
$480$	0.282824	−	3.12317i	0.0129091	−	0.142553i
$481$	17.1436	+	7.10112i	0.781682	+	0.323783i
$482$	−6.07317	−	3.23391i	−0.276625	−	0.147300i
$483$	−2.18910	+	0.548341i	−0.0996076	+	0.0249504i
$484$	16.3341	−	8.79691i	0.742457	−	0.399860i
$485$	6.72933	−	14.2280i	0.305563	−	0.646059i
$486$	−7.71772	−	12.8304i	−0.350083	−	0.582000i
$487$	−19.9377	−	1.96369i	−0.903461	−	0.0889832i	−0.364393	−	0.931245i	$-0.618723\pi$
$487$	−19.9377	−	1.96369i	−0.903461	−	0.0889832i	−0.539068	+	0.842262i	$0.681223\pi$
$488$	−30.0664	−	7.38063i	−1.36104	−	0.334105i
$489$	−1.55178	−	1.27351i	−0.0701738	−	0.0575902i
$490$	−9.79910	+	2.47093i	−0.442678	+	0.111625i
$491$	18.4602	−	24.8907i	0.833098	−	1.12330i	−0.157638	−	0.987497i	$-0.550388\pi$
$491$	18.4602	−	24.8907i	0.833098	−	1.12330i	0.990736	−	0.135805i	$-0.0433622\pi$
$492$	2.48335	−	3.37052i	0.111958	−	0.151955i
$493$	26.2208	+	55.4392i	1.18093	+	2.49686i
$494$	−1.82272	+	2.73720i	−0.0820080	+	0.123153i
$495$	−3.22248	−	16.2005i	−0.144840	−	0.728158i
$496$	−0.205545	−	32.6690i	−0.00922923	−	1.46688i
$497$	2.20767	−	11.0987i	0.0990274	−	0.497845i
$498$	0.618194	−	0.620142i	0.0277019	−	0.0277892i
$499$	12.3004	−	13.5714i	0.550643	−	0.607541i	−0.400498	−	0.916298i	$-0.631163\pi$
$499$	12.3004	−	13.5714i	0.550643	−	0.607541i	0.951141	+	0.308757i	$0.0999129\pi$
$500$	16.0653	+	14.4689i	0.718462	+	0.647071i
$501$	3.62615	+	6.04987i	0.162004	+	0.270288i
$502$	4.28463	−	12.0344i	0.191232	−	0.537121i
$503$	6.62016	+	2.00820i	0.295178	+	0.0895414i	0.434401	−	0.900720i	$-0.356960\pi$
$503$	6.62016	+	2.00820i	0.295178	+	0.0895414i	−0.139222	+	0.990261i	$0.544460\pi$
$504$	28.0521	+	2.62930i	1.24954	+	0.117118i
$505$	−3.77268	−	2.01654i	−0.167882	−	0.0897349i
$506$	8.63615	+	4.06799i	0.383924	+	0.180844i
$507$	1.06395	+	0.0522685i	0.0472517	+	0.00232133i
$508$	−8.81663	+	13.2853i	−0.391175	+	0.589440i
$509$	−3.35886	+	22.6436i	−0.148879	+	1.00366i	0.777990	+	0.628277i	$0.216239\pi$
$509$	−3.35886	+	22.6436i	−0.148879	+	1.00366i	−0.926869	+	0.375385i	$0.877511\pi$
$510$	1.37003	−	4.54210i	0.0606660	−	0.201127i
$511$	−51.0050			−2.25633
$512$	−10.9479	−	19.8026i	−0.483834	−	0.875160i
$513$	1.46382			0.0646294
$514$	−9.93825	+	32.9485i	−0.438357	+	1.45330i
$515$	−0.123905	+	0.835302i	−0.00545992	+	0.0368078i
$516$	0.839903	−	1.26561i	0.0369747	−	0.0557152i
$517$	−17.6534	−	0.867255i	−0.776395	−	0.0381418i
$518$	21.3110	+	10.0383i	0.936350	+	0.441060i
$519$	3.69556	+	1.97532i	0.162217	+	0.0867067i
$520$	−1.35248	+	14.4297i	−0.0593102	+	0.632783i
$521$	−32.0951	−	9.73593i	−1.40611	−	0.426539i	−0.506126	−	0.862460i	$-0.668923\pi$
$521$	−32.0951	−	9.73593i	−1.40611	−	0.426539i	−0.899985	+	0.435921i	$0.856423\pi$
$522$	−13.5493	+	38.0562i	−0.593035	+	1.66568i
$523$	20.6186	+	34.4000i	0.901587	+	1.50421i	0.863151	+	0.504946i	$0.168487\pi$
$523$	20.6186	+	34.4000i	0.901587	+	1.50421i	0.0384357	+	0.999261i	$0.487763\pi$
$524$	−3.72051	−	3.35081i	−0.162531	−	0.146381i
$525$	3.34244	−	3.68781i	0.145876	−	0.160949i
$526$	−5.46130	+	5.47851i	−0.238124	+	0.238874i
$527$	9.64219	−	48.4745i	0.420020	−	2.11158i
$528$	5.45901	+	5.39074i	0.237573	+	0.234602i
$529$	−4.04866	−	20.3540i	−0.176029	−	0.884956i
$530$	−9.27410	+	13.9271i	−0.402841	+	0.604952i
$531$	−14.2636	−	30.1579i	−0.618989	−	1.30874i
$532$	−2.47636	+	3.36103i	−0.107364	+	0.145719i
$533$	−11.5259	+	15.5408i	−0.499240	+	0.673147i
$534$	4.69560	−	1.18404i	0.203199	−	0.0512384i
$535$	−9.29623	−	7.62922i	−0.401911	−	0.329840i
$536$	−5.30013	+	21.5911i	−0.228931	+	0.932592i
$537$	−9.07255	−	0.893568i	−0.391509	−	0.0385603i
$538$	8.07505	+	13.4245i	0.348140	+	0.578770i
$539$	10.5708	−	22.3501i	0.455317	−	0.962687i
$540$	5.67985	−	3.05896i	0.244422	−	0.131636i
$541$	1.36811	−	0.342694i	0.0588196	−	0.0147335i	−0.213459	−	0.976952i	$-0.568473\pi$
$541$	1.36811	−	0.342694i	0.0588196	−	0.0147335i	0.272278	+	0.962219i	$0.412223\pi$
$542$	−6.60775	−	3.51856i	−0.283827	−	0.151135i
$543$	0.0519502	+	0.0215185i	0.00222940	+	0.000923446i
$544$	−10.1943	−	32.6787i	−0.437077	−	1.40109i
$545$	7.32527	−	3.03423i	0.313780	−	0.129972i
$546$	8.34288	+	0.808454i	0.357042	+	0.0345986i
$547$	−0.466924	−	0.279864i	−0.0199642	−	0.0119661i	0.504086	−	0.863654i	$-0.331830\pi$
$547$	−0.466924	−	0.279864i	−0.0199642	−	0.0119661i	−0.524050	+	0.851687i	$0.675580\pi$
$548$	−8.31106	+	6.86458i	−0.355031	+	0.293240i
$549$	−10.3934	−	29.0476i	−0.443580	−	1.23972i
$550$	−20.8212	+	3.12201i	−0.887819	+	0.133123i
$551$	−3.79725	−	4.62696i	−0.161768	−	0.197115i
$552$	−0.256571	+	1.78774i	−0.0109204	+	0.0760915i
$553$	55.3027	−	5.44684i	2.35171	−	0.231623i
$554$	−7.12506	−	9.57551i	−0.302715	−	0.406825i
$555$	2.58451	−	0.383376i	0.109706	−	0.0162734i
$556$	25.9437	+	1.19273i	1.10026	+	0.0505831i
$557$	32.3880	+	11.5886i	1.37232	+	0.491025i	0.916853	−	0.399225i	$-0.130721\pi$
$557$	32.3880	+	11.5886i	1.37232	+	0.491025i	0.455471	+	0.890251i	$0.349471\pi$
$558$	27.0406	−	18.1295i	1.14472	−	0.767485i
$559$	−3.90003	+	5.83681i	−0.164954	+	0.246871i
$560$	−2.58509	+	18.2161i	−0.109240	+	0.769773i
$561$	6.44834	+	9.65062i	0.272249	+	0.407450i
$562$	3.91703	−	9.49879i	0.165230	−	0.400682i
$563$	−10.9432	+	0.537604i	−0.461200	+	0.0226573i	−0.278342	−	0.960482i	$-0.589785\pi$
$563$	−10.9432	+	0.537604i	−0.461200	+	0.0226573i	−0.182858	+	0.983139i	$0.558535\pi$
$564$	−0.822694	−	3.24109i	−0.0346417	−	0.136474i
$565$	−4.38902	−	1.09939i	−0.184647	−	0.0462517i
$566$	−6.79025	−	6.13490i	−0.285416	−	0.257869i
$567$	12.3285	+	23.0650i	0.517749	+	0.968641i
$568$	−7.55369	−	4.99582i	−0.316946	−	0.209620i
$569$	22.7308	−	6.89532i	0.952925	−	0.289067i	0.224718	−	0.974424i	$-0.427854\pi$
$569$	22.7308	−	6.89532i	0.952925	−	0.289067i	0.728207	+	0.685357i	$0.240354\pi$
$570$	−0.0219930	+	0.462521i	−0.000921185	+	0.0193729i
$571$	−9.81247	−	10.8264i	−0.410639	−	0.453071i	0.500152	−	0.865938i	$-0.333277\pi$
$571$	−9.81247	−	10.8264i	−0.410639	−	0.453071i	−0.910791	+	0.412867i	$0.864527\pi$
$572$	−25.1505	−	24.9928i	−1.05160	−	1.04500i
$573$	5.38216	+	7.25701i	0.224843	+	0.303166i
$574$	−15.5525	+	19.0117i	−0.649150	+	0.793533i
$575$	−3.50460	−	3.50460i	−0.146152	−	0.146152i
$576$	10.4412	−	19.9854i	0.435048	−	0.832727i
$577$	18.2684	−	18.2684i	0.760523	−	0.760523i	−0.215894	−	0.976417i	$-0.569267\pi$
$577$	18.2684	−	18.2684i	0.760523	−	0.760523i	0.976417	+	0.215894i	$0.0692666\pi$
$578$	−2.76301	−	27.6081i	−0.114926	−	1.14835i
$579$	3.90466	−	2.89590i	0.162272	−	0.120349i
$580$	−24.4029	−	10.0182i	−1.01327	−	0.415982i
$581$	−3.80654	+	3.45005i	−0.157922	+	0.143132i
$582$	−5.39003	+	4.90070i	−0.223424	+	0.203141i
$583$	−11.8830	−	39.1729i	−0.492143	−	1.62238i
$584$	−15.4427	+	37.7854i	−0.639025	+	1.56357i
$585$	−12.7371	+	6.80810i	−0.526612	+	0.281480i
$586$	0.534927	−	0.0271228i	0.0220976	−	0.00112043i
$587$	−1.81221	+	7.23475i	−0.0747980	+	0.298610i	−0.995871	−	0.0907797i	$-0.971064\pi$
$587$	−1.81221	+	7.23475i	−0.0747980	+	0.298610i	0.921073	+	0.389390i	$0.127314\pi$
$588$	4.62901	+	0.671774i	0.190897	+	0.0277035i
$589$	0.236697	+	4.81807i	0.00975291	+	0.198525i
$590$	20.1136	−	8.36843i	0.828066	−	0.344523i
$591$	2.83299	−	1.89294i	0.116533	−	0.0778652i
$592$	13.8889	−	12.7482i	0.570829	−	0.523949i
$593$	25.0118	+	16.7124i	1.02711	+	0.686295i	0.950487	−	0.310765i	$-0.100585\pi$
$593$	25.0118	+	16.7124i	1.02711	+	0.686295i	0.0766259	+	0.997060i	$0.475585\pi$
$594$	−3.05472	+	15.4844i	−0.125337	+	0.635331i
$595$	−9.37712	+	26.2073i	−0.384425	+	1.07439i
$596$	6.04897	+	16.7395i	0.247775	+	0.685678i
$597$	−0.555488	−	3.74479i	−0.0227346	−	0.153264i
$598$	1.21174	−	8.25837i	0.0495517	−	0.337710i
$599$	−2.40721	−	24.4408i	−0.0983561	−	0.998626i	−0.910038	−	0.414526i	$-0.863947\pi$
$599$	−2.40721	−	24.4408i	−0.0983561	−	0.998626i	0.811682	−	0.584100i	$-0.198553\pi$
$600$	−1.72001	−	3.59269i	−0.0702191	−	0.146671i
$601$	27.1837	−	22.3091i	1.10885	−	0.910007i	0.112353	−	0.993668i	$-0.464161\pi$
$601$	27.1837	−	22.3091i	1.10885	−	0.910007i	0.996494	+	0.0836609i	$0.0266613\pi$
$602$	−5.29741	+	7.16626i	−0.215906	+	0.292075i
$603$	−20.8595	+	7.46365i	−0.849464	+	0.303943i
$604$	31.1768	−	9.56457i	1.26856	−	0.389177i
$605$	−6.20656	+	10.3550i	−0.252333	+	0.420991i
$606$	1.25850	+	1.52857i	0.0511230	+	0.0620941i
$607$	1.94454	+	4.69453i	0.0789263	+	0.190545i	0.958417	−	0.285371i	$-0.0921167\pi$
$607$	1.94454	+	4.69453i	0.0789263	+	0.190545i	−0.879491	+	0.475916i	$0.842117\pi$
$608$	1.74014	+	2.85215i	0.0705722	+	0.115670i
$609$	−5.83836	+	14.0951i	−0.236582	+	0.571160i
$610$	19.2694	−	5.87841i	0.780194	−	0.238010i
$611$	3.75498	+	14.9907i	0.151910	+	0.606459i
$612$	21.5577	−	26.4373i	0.871418	−	1.06866i
$613$	−3.40861	−	1.61215i	−0.137673	−	0.0651143i	0.357477	−	0.933922i	$-0.383637\pi$
$613$	−3.40861	−	1.61215i	−0.137673	−	0.0651143i	−0.495150	+	0.868807i	$0.664887\pi$
$614$	2.13709	−	8.58904i	0.0862459	−	0.346625i
$615$	−0.267033	+	2.71123i	−0.0107678	+	0.109327i
$616$	−30.3854	−	33.2088i	−1.22426	−	1.33802i
$617$	−1.67859	+	2.04537i	−0.0675774	+	0.0823433i	−0.805702	−	0.592321i	$-0.798212\pi$
$617$	−1.67859	+	2.04537i	−0.0675774	+	0.0823433i	0.738125	+	0.674664i	$0.235712\pi$
$618$	0.200410	−	0.335560i	0.00806169	−	0.0134982i
$619$	26.6493	+	19.7644i	1.07112	+	0.794400i	0.979510	−	0.201394i	$-0.0645473\pi$
$619$	26.6493	+	19.7644i	1.07112	+	0.794400i	0.0916144	+	0.995795i	$0.470797\pi$
$620$	10.9867	+	18.2002i	0.441238	+	0.730937i
$621$	−3.35867	+	1.58853i	−0.134779	+	0.0637455i
$622$	−26.7893	+	5.37253i	−1.07415	+	0.215419i
$623$	−27.8656	+	5.54281i	−1.11641	+	0.222068i
$624$	3.12488	−	5.93577i	0.125095	−	0.237621i
$625$	2.41442	+	0.480258i	0.0965768	+	0.0192103i
$626$	0.0106648	+	6.78029i	0.000426252	+	0.270995i
$627$	−0.839373	−	0.760764i	−0.0335213	−	0.0303820i
$628$	6.93386	−	19.5727i	0.276691	−	0.781037i
$629$	24.4633	−	14.6627i	0.975416	−	0.584642i
$630$	−16.5618	+	7.86507i	−0.659840	+	0.313352i
$631$	5.42742	−	17.8918i	0.216062	−	0.712261i	−0.780173	−	0.625564i	$-0.784869\pi$
$631$	5.42742	−	17.8918i	0.216062	−	0.712261i	0.996235	−	0.0866971i	$-0.0276312\pi$
$632$	12.7088	−	42.6183i	0.505530	−	1.69527i
$633$	−5.05399	+	9.45535i	−0.200878	+	0.375816i
$634$	7.37409	−	2.65158i	0.292863	−	0.105308i
$635$	0.509113	−	10.3632i	0.0202036	−	0.411253i
$636$	6.42583	−	4.32291i	0.254801	−	0.171414i
$637$	−21.3833	−	3.17191i	−0.847237	−	0.125676i
$638$	56.8682	−	30.5118i	2.25144	−	1.20797i
$639$		−	9.02472i		−	0.357012i
$640$	12.7121	+	7.43036i	0.502492	+	0.293711i
$641$		−	47.7060i		−	1.88427i	−0.335227	−	0.942137i	$-0.608813\pi$
$641$		−	47.7060i		−	1.88427i	0.335227	−	0.942137i	$-0.391187\pi$
$642$	2.63163	+	4.90487i	0.103862	+	0.193580i
$643$	−43.1582	−	6.40192i	−1.70199	−	0.252467i	−0.776198	−	0.630489i	$-0.782854\pi$
$643$	−43.1582	−	6.40192i	−1.70199	−	0.252467i	−0.925797	+	0.378022i	$0.876604\pi$
$644$	2.03451	−	10.3990i	0.0801709	−	0.409779i
$645$	−0.0484999	+	0.987239i	−0.00190968	+	0.0388725i
$646$	1.71031	+	4.75640i	0.0672913	+	0.187138i
$647$	−1.42446	+	2.66497i	−0.0560011	+	0.104771i	−0.908365	−	0.418179i	$-0.862668\pi$
$647$	−1.42446	+	2.66497i	−0.0560011	+	0.104771i	0.852363	+	0.522950i	$0.175168\pi$
$648$	20.8197	−	2.14980i	0.817874	−	0.0844522i
$649$	−15.4713	+	51.0021i	−0.607302	+	2.00201i
$650$	7.89682	+	16.6287i	0.309739	+	0.652232i
$651$	10.5460	−	6.32102i	0.413330	−	0.247740i
$652$	8.50801	−	4.05679i	0.333199	−	0.158876i
$653$	12.7568	+	11.5621i	0.499211	+	0.452459i	0.881912	−	0.471414i	$-0.156256\pi$
$653$	12.7568	+	11.5621i	0.499211	+	0.452459i	−0.382701	+	0.923872i	$0.625006\pi$
$654$	−3.66986	+	0.00577238i	−0.143503	+	0.000225718i
$655$	3.19563	+	0.635650i	0.124863	+	0.0248369i
$656$	9.37538	+	17.2777i	0.366047	+	0.674582i
$657$	−39.8953	+	7.93568i	−1.55647	+	0.309600i
$658$	3.85764	+	19.2355i	0.150387	+	0.749878i
$659$	4.54909	−	2.15156i	0.177207	−	0.0838128i	−0.336893	−	0.941543i	$-0.609376\pi$
$659$	4.54909	−	2.15156i	0.177207	−	0.0838128i	0.514100	+	0.857730i	$0.328126\pi$
$660$	−4.84666	−	1.19783i	−0.188656	−	0.0466257i
$661$	37.5308	+	27.8347i	1.45978	+	1.08264i	0.978541	+	0.206054i	$0.0660624\pi$
$661$	37.5308	+	27.8347i	1.45978	+	1.08264i	0.481237	+	0.876590i	$0.340188\pi$
$662$	0.0290074	+	0.0173244i	0.00112740	+	0.000673332i
$663$	6.43802	−	7.84475i	0.250032	−	0.304665i
$664$	1.40335	+	3.86452i	0.0544606	+	0.149972i
$665$	0.266281	−	2.70360i	0.0103259	−	0.104841i
$666$	18.2309	+	4.53615i	0.706435	+	0.175772i
$667$	13.7337	+	6.49557i	0.531772	+	0.251510i
$668$	−32.9482	+	3.34981i	−1.27481	+	0.129608i
$669$	0.0446754	+	0.178354i	0.00172725	+	0.00689558i
$670$	−4.22137	−	13.8376i	−0.163086	−	0.534593i
$671$	−18.8614	+	45.5355i	−0.728137	+	1.75788i
$672$	4.32044	−	7.33849i	0.166665	−	0.283089i
$673$	−11.6743	−	28.1844i	−0.450013	−	1.08643i	−0.972317	−	0.233668i	$-0.924927\pi$
$673$	−11.6743	−	28.1844i	−0.450013	−	1.08643i	0.522304	−	0.852760i	$-0.325073\pi$
$674$	−34.3773	+	28.3033i	−1.32416	+	1.09020i
$675$	4.21263	−	7.02834i	0.162144	−	0.270521i
$676$	−2.34388	+	4.41847i	−0.0901492	+	0.169941i
$677$	32.6581	−	11.6853i	1.25515	−	0.449101i	0.376436	−	0.926443i	$-0.377149\pi$
$677$	32.6581	−	11.6853i	1.25515	−	0.449101i	0.878718	+	0.477341i	$0.158399\pi$
$678$	1.68406	+	1.24488i	0.0646758	+	0.0478094i
$679$	33.0387	−	27.1142i	1.26791	−	1.04055i
$680$	16.5757	+	14.8815i	0.635650	+	0.570679i
$681$	0.336183	+	3.41333i	0.0128826	+	0.130799i
$682$	−51.4596	−	7.55061i	−1.97049	−	0.289128i
$683$	6.39831	+	43.1339i	0.244824	+	1.65047i	0.667807	+	0.744334i	$0.267233\pi$
$683$	6.39831	+	43.1339i	0.244824	+	1.65047i	−0.422983	+	0.906138i	$0.639017\pi$
$684$	−1.41404	+	3.01424i	−0.0540672	+	0.115252i
$685$	2.36313	−	6.60450i	0.0902905	−	0.252345i
$686$	7.40130	+	1.46011i	0.282583	+	0.0557473i
$687$	−4.48158	−	2.99450i	−0.170983	−	0.114247i
$688$	3.70500	+	6.09413i	0.141252	+	0.232337i
$689$	−29.7600	+	19.8850i	−1.13376	+	0.757557i
$690$	−0.451462	−	1.08510i	−0.0171869	−	0.0413089i
$691$	0.0296884	+	0.604321i	0.00112940	+	0.0229894i	0.999294	−	0.0375697i	$-0.0119616\pi$
$691$	0.0296884	+	0.604321i	0.00112940	+	0.0229894i	−0.998165	+	0.0605591i	$0.980712\pi$
$692$	−15.7663	+	11.7702i	−0.599346	+	0.447434i
$693$	10.8989	−	43.5110i	0.414016	−	1.65285i
$694$	−1.17126	−	23.1000i	−0.0444603	−	0.876865i
$695$	−14.9047	+	7.96673i	−0.565367	+	0.302195i
$696$	8.67418	+	8.59270i	0.328794	+	0.325706i
$697$	8.63273	+	28.4583i	0.326988	+	1.07794i
$698$	−13.8927	−	15.2799i	−0.525847	−	0.578352i
$699$	4.47554	−	4.05639i	0.169281	−	0.153427i
$700$	9.01099	+	21.5623i	0.340583	+	0.814980i
$701$	−8.87189	+	6.57984i	−0.335087	+	0.248517i	−0.750139	−	0.661280i	$-0.770013\pi$
$701$	−8.87189	+	6.57984i	−0.335087	+	0.248517i	0.415052	+	0.909798i	$0.363763\pi$
$702$	13.7311	−	1.37420i	0.518246	−	0.0518660i
$703$	−1.96837	+	1.96837i	−0.0742386	+	0.0742386i
$704$	−33.8014	+	12.4554i	−1.27394	+	0.469431i
$705$	1.53864	+	1.53864i	0.0579487	+	0.0579487i
$706$	−26.4655	−	21.6501i	−0.996041	−	0.814811i
$707$	−6.92001	−	9.33055i	−0.260254	−	0.350911i
$708$	−10.0832	+	0.0317201i	−0.378950	+	0.00119212i
$709$	3.53444	+	3.89965i	0.132738	+	0.146454i	0.803693	−	0.595044i	$-0.202865\pi$
$709$	3.53444	+	3.89965i	0.132738	+	0.146454i	−0.670955	+	0.741498i	$0.734115\pi$
$710$	5.88659	+	0.279909i	0.220920	+	0.0105048i
$711$	42.4095	−	12.8648i	1.59048	−	0.482467i
$712$	−4.33062	+	22.3215i	−0.162297	+	0.836533i
$713$	−5.77162	−	10.7979i	−0.216149	−	0.404386i
$714$	8.63680	−	9.55942i	0.323224	−	0.357752i
$715$	22.3815	+	5.60628i	0.837021	+	0.209663i
$716$	21.8906	−	36.7842i	0.818090	−	1.37469i
$717$	−12.0242	+	0.590711i	−0.449052	+	0.0220605i
$718$	−1.44886	−	0.597470i	−0.0540710	−	0.0222974i
$719$	17.7943	+	26.6311i	0.663617	+	0.993172i	0.998699	+	0.0509837i	$0.0162357\pi$
$719$	17.7943	+	26.6311i	0.663617	+	0.993172i	−0.335083	+	0.942189i	$0.608764\pi$
$720$	0.812167	+	14.6506i	0.0302677	+	0.545996i
$721$	−1.27399	+	1.90667i	−0.0474461	+	0.0710080i
$722$	14.6886	+	21.9084i	0.546653	+	0.815345i
$723$	−1.95123	−	0.698160i	−0.0725669	−	0.0259648i
$724$	−0.195069	+	0.177921i	−0.00724969	+	0.00661239i
$725$	−33.1435	+	4.91637i	−1.23092	+	0.182590i
$726$	4.48294	−	3.33572i	0.166378	−	0.123800i
$727$	−17.2229	+	1.69631i	−0.638761	+	0.0629125i	−0.412213	−	0.911087i	$-0.635244\pi$
$727$	−17.2229	+	1.69631i	−0.638761	+	0.0629125i	−0.226548	+	0.974000i	$0.572744\pi$
$728$	−20.0737	+	33.8522i	−0.743981	+	1.25465i
$729$	11.2226	+	13.6748i	0.415652	+	0.506474i
$730$	−3.93885	−	26.2688i	−0.145783	−	0.972253i
$731$	3.63492	+	10.1589i	0.134442	+	0.375741i
$732$	−9.28258	−	0.884778i	−0.343094	−	0.0327024i
$733$	2.07878	+	1.24597i	0.0767815	+	0.0460210i	0.551978	−	0.833858i	$-0.313873\pi$
$733$	2.07878	+	1.24597i	0.0767815	+	0.0460210i	−0.475197	+	0.879880i	$0.657623\pi$
$734$	−1.58555	+	16.3621i	−0.0585236	+	0.603937i
$735$	−2.81212	+	1.16482i	−0.103726	+	0.0429649i
$736$	−7.08780	−	4.65570i	−0.261260	−	0.171612i
$737$	32.6997	+	13.5446i	1.20451	+	0.498923i
$738$	−9.20699	+	17.2904i	−0.338914	+	0.636470i
$739$	26.4736	−	6.63128i	0.973845	−	0.243936i	0.276772	−	0.960936i	$-0.410735\pi$
$739$	26.4736	−	6.63128i	0.973845	−	0.243936i	0.697073	+	0.717000i	$0.254485\pi$
$740$	−3.52426	+	11.7509i	−0.129554	+	0.431971i
$741$	−0.423489	+	0.895393i	−0.0155573	+	0.0328931i
$742$	−38.9364	+	23.4209i	−1.42940	+	0.859808i
$743$	6.89728	+	0.679322i	0.253037	+	0.0249219i	0.223740	−	0.974649i	$-0.428173\pi$
$743$	6.89728	+	0.679322i	0.253037	+	0.0249219i	0.0292964	+	0.999571i	$0.490673\pi$
$744$	−1.48972	−	9.72646i	−0.0546159	−	0.356589i
$745$	−8.95329	−	7.34778i	−0.328023	−	0.269202i
$746$	−1.25494	−	4.97677i	−0.0459465	−	0.182212i
$747$	−2.44064	+	3.29082i	−0.0892983	+	0.120405i
$748$	−53.8824	+	8.16602i	−1.97014	+	0.298579i
$749$	−13.9628	−	29.5218i	−0.510189	−	1.07870i
$750$	5.42017	+	3.60932i	0.197917	+	0.131794i
$751$	3.09328	+	15.5510i	0.112875	+	0.567463i	0.995286	+	0.0969832i	$0.0309193\pi$
$751$	3.09328	+	15.5510i	0.112875	+	0.567463i	−0.882411	+	0.470480i	$0.844081\pi$
$752$	15.4180	+	2.96611i	0.562236	+	0.108163i
$753$	0.750621	−	3.77363i	0.0273541	−	0.137519i
$754$	−39.9630	−	39.8374i	−1.45537	−	1.45079i
$755$	−14.2512	+	15.7238i	−0.518653	+	0.572246i
$756$	17.4947	−	0.914636i	0.636276	−	0.0332650i
$757$	1.11447	+	1.85938i	0.0405062	+	0.0675805i	0.877316	−	0.479913i	$-0.159332\pi$
$757$	1.11447	+	1.85938i	0.0405062	+	0.0675805i	−0.836810	+	0.547494i	$0.815582\pi$
$758$	−36.3510	−	12.9422i	−1.32033	−	0.470080i
$759$	2.75147	+	0.834650i	0.0998721	+	0.0302959i
$760$	−1.92225	−	1.01583i	−0.0697274	−	0.0368481i
$761$	9.84644	+	5.26303i	0.356933	+	0.190785i	0.640111	−	0.768283i	$-0.278889\pi$
$761$	9.84644	+	5.26303i	0.356933	+	0.190785i	−0.283177	+	0.959068i	$0.591389\pi$
$762$	−2.04647	+	4.34457i	−0.0741359	+	0.157387i
$763$	21.5052	+	1.05648i	0.778541	+	0.0382473i
$764$	−41.5814	+	8.40712i	−1.50436	+	0.304159i
$765$	−3.25715	+	21.9579i	−0.117762	+	0.793890i
$766$	−10.1753	−	3.06916i	−0.367647	−	0.110893i
$767$	46.6002			1.68264
$768$	−4.12839	−	5.42253i	−0.148970	−	0.195669i
$769$	−50.9207			−1.83625			−0.918123	−	0.396295i	$-0.870296\pi$
$769$	−50.9207			−1.83625			−0.918123	+	0.396295i	$0.870296\pi$
$770$	28.0431	+	8.45862i	1.01060	+	0.304828i
$771$	−1.52093	+	10.2533i	−0.0547751	+	0.369263i
$772$	4.52349	+	22.3731i	0.162804	+	0.805224i
$773$	25.2602	+	1.24095i	0.908545	+	0.0446340i	0.497972	−	0.867193i	$-0.334078\pi$
$773$	25.2602	+	1.24095i	0.908545	+	0.0446340i	0.410574	+	0.911827i	$0.365328\pi$
$774$	−3.02858	+	6.42954i	−0.108860	+	0.231105i
$775$	23.8144	+	12.7291i	0.855440	+	0.457242i
$776$	−10.0836	−	32.6850i	−0.361979	−	1.17332i
$777$	6.78966	+	2.05962i	0.243578	+	0.0738885i
$778$	−19.2300	−	6.84652i	−0.689430	−	0.245460i
$779$	−1.49221	−	2.48961i	−0.0534641	−	0.0891994i
$780$	0.227904	+	4.35922i	0.00816026	+	0.156085i
$781$	−9.68238	+	10.6829i	−0.346463	+	0.382263i
$782$	−9.08583	−	9.05729i	−0.324909	−	0.323888i
$783$	−4.90016	+	24.6348i	−0.175118	+	0.880375i
$784$	−12.0866	+	18.3376i	−0.431665	+	0.654915i
$785$	2.63611	+	13.2526i	0.0940868	+	0.473006i
$786$	−1.25524	−	0.835870i	−0.0447729	−	0.0298145i
$787$	−21.7947	−	46.0809i	−0.776896	−	1.64261i	−0.766147	−	0.642665i	$-0.777829\pi$
$787$	−21.7947	−	46.0809i	−0.776896	−	1.64261i	−0.0107486	−	0.999942i	$-0.503421\pi$
$788$	2.39717	+	15.8174i	0.0853958	+	0.563473i
$789$	−1.38793	+	1.87141i	−0.0494117	+	0.0666239i
$790$	7.07600	+	28.0616i	0.251753	+	0.998388i
$791$	−9.49786	−	7.79469i	−0.337705	−	0.277147i
$792$	−28.9338	−	21.2479i	−1.02812	−	0.755011i
$793$	42.8867	+	4.22398i	1.52295	+	0.149998i
$794$	−2.27354	+	1.36758i	−0.0806851	+	0.0485334i
$795$	−2.15474	+	4.55581i	−0.0764207	+	0.161578i
$796$	17.0263	+	5.10644i	0.603481	+	0.180993i
$797$	39.5102	−	9.89679i	1.39952	−	0.350562i	0.531488	−	0.847066i	$-0.321633\pi$
$797$	39.5102	−	9.89679i	1.39952	−	0.350562i	0.868035	+	0.496503i	$0.165383\pi$
$798$	−0.590999	+	1.10988i	−0.0209211	+	0.0392892i
$799$	21.9447	+	9.08980i	0.776348	+	0.321574i
$800$	18.7020	−	0.147086i	0.661215	−	0.00520028i
$801$	−20.9336	+	8.67100i	−0.739654	+	0.306375i
$802$	−1.41061	+	14.5569i	−0.0498104	+	0.514021i
$803$	55.7394	+	33.4089i	1.96700	+	1.17898i
$804$	−0.635372	+	6.66595i	−0.0224078	+	0.235090i
$805$	2.32296	+	6.49223i	0.0818735	+	0.228821i
$806$	6.74337	+	44.9727i	0.237525	+	1.58409i
$807$	2.99338	+	3.64744i	0.105372	+	0.128396i
$808$	−9.00740	+	2.30146i	−0.316879	+	0.0809651i
$809$	−16.6861	+	1.64344i	−0.586653	+	0.0577803i	−0.386989	−	0.922084i	$-0.626485\pi$
$809$	−16.6861	+	1.64344i	−0.586653	+	0.0577803i	−0.199664	+	0.979864i	$0.563985\pi$
$810$	−10.9270	+	8.13069i	−0.383936	+	0.285683i
$811$	1.23877	−	0.183754i	0.0434991	−	0.00645248i	−0.124945	−	0.992164i	$-0.539876\pi$
$811$	1.23877	−	0.183754i	0.0434991	−	0.00645248i	0.168445	+	0.985711i	$0.446126\pi$
$812$	−48.2734	−	52.9259i	−1.69406	−	1.85733i
$813$	−2.12298	−	0.759614i	−0.0744561	−	0.0266408i
$814$	−16.7139	−	24.9291i	−0.585821	−	0.873765i
$815$	−3.40766	+	5.09992i	−0.119365	+	0.178643i
$816$	−4.46683	−	9.29259i	−0.156370	−	0.325306i
$817$	−0.585063	−	0.875609i	−0.0204688	−	0.0306337i
$818$	28.7209	+	11.8437i	1.00420	+	0.414105i
$819$	−39.1719	+	1.92439i	−1.36878	+	0.0672437i
$820$	−10.9925	−	6.54176i	−0.383876	−	0.228448i
$821$	2.13887	+	0.535760i	0.0746472	+	0.0186982i	0.280124	−	0.959964i	$-0.409624\pi$
$821$	2.13887	+	0.535760i	0.0746472	+	0.0186982i	−0.205477	+	0.978662i	$0.565874\pi$
$822$	−2.17656	+	2.40907i	−0.0759163	+	0.0840259i
$823$	22.9183	+	42.8772i	0.798882	+	1.49460i	0.867763	+	0.496979i	$0.165557\pi$
$823$	22.9183	+	42.8772i	0.798882	+	1.49460i	−0.0688804	+	0.997625i	$0.521943\pi$
$824$	1.02677	+	1.52108i	0.0357691	+	0.0529892i
$825$	−6.06827	+	1.84079i	−0.211270	+	0.0640880i
$826$	59.0918	+	2.80983i	2.05607	+	0.0977665i
$827$	−2.91071	−	3.21147i	−0.101215	−	0.111674i	0.688237	−	0.725486i	$-0.258385\pi$
$827$	−2.91071	−	3.21147i	−0.101215	−	0.111674i	−0.789452	+	0.613813i	$0.789635\pi$
$828$	−0.0265839	−	8.45051i	−0.000923855	−	0.293676i
$829$	−14.6818	−	19.7961i	−0.509920	−	0.687548i	0.470961	−	0.882154i	$-0.343907\pi$
$829$	−14.6818	−	19.7961i	−0.509920	−	0.687548i	−0.980881	+	0.194606i	$0.937657\pi$
$830$	−2.07082	−	1.69403i	−0.0718792	−	0.0588007i
$831$	−2.54198	−	2.54198i	−0.0881804	−	0.0881804i
$832$	19.0006	+	25.1203i	0.658727	+	0.870891i
$833$	−23.4944	+	23.4944i	−0.814032	+	0.814032i
$834$	7.78343	−	0.778965i	0.269518	−	0.0269733i
$835$	17.3100	−	12.8380i	0.599037	−	0.444276i
$836$	4.90774	−	2.05097i	0.169738	−	0.0709341i
$837$	14.9986	−	13.5939i	0.518427	−	0.469875i
$838$	0.558925	+	0.614733i	0.0193078	+	0.0212356i
$839$	11.7098	+	38.6022i	0.404269	+	1.33270i	0.888950	+	0.458005i	$0.151436\pi$
$839$	11.7098	+	38.6022i	0.404269	+	1.33270i	−0.484681	+	0.874691i	$0.661064\pi$
$840$	0.0261491	+	5.54149i	0.000902229	+	0.191200i
$841$	65.0030	−	34.7448i	2.24148	−	1.19810i
$842$	−0.345012	−	6.80448i	−0.0118899	−	0.234498i
$843$	0.751947	−	3.00194i	0.0258984	−	0.103392i
$844$	−30.1148	−	40.3393i	−1.03660	−	1.38854i
$845$	−0.159703	−	3.25083i	−0.00549395	−	0.111832i
$846$	6.01017	+	14.4455i	0.206634	+	0.496648i
$847$	−27.2588	+	18.2137i	−0.936622	+	0.625831i
$848$	5.56187	+	35.9359i	0.190995	+	1.23404i
$849$	−2.29177	−	1.53131i	−0.0786532	−	0.0525544i
$850$	27.7592	+	5.47626i	0.952131	+	0.187834i
$851$	2.38026	−	6.65239i	0.0815943	−	0.228041i
$852$	−2.46947	−	1.15848i	−0.0846025	−	0.0396888i
$853$	−7.42155	−	50.0320i	−0.254109	−	1.71306i	−0.621851	−	0.783136i	$-0.713619\pi$
$853$	−7.42155	−	50.0320i	−0.254109	−	1.71306i	0.367742	−	0.929928i	$-0.380131\pi$
$854$	54.1282	+	7.94217i	1.85223	+	0.271776i
$855$	−0.212362	−	2.15614i	−0.00726261	−	0.0737386i
$856$	−26.0978	+	1.40558i	−0.892004	+	0.0480416i
$857$	−44.1278	+	36.2148i	−1.50738	+	1.23707i	−0.612736	+	0.790288i	$0.709931\pi$
$857$	−44.1278	+	36.2148i	−1.50738	+	1.23707i	−0.894642	+	0.446784i	$0.852569\pi$
$858$	−8.58775	−	6.34820i	−0.293181	−	0.216724i
$859$	−38.3483	+	13.7212i	−1.30843	+	0.468162i	−0.896495	−	0.443053i	$-0.853895\pi$
$859$	−38.3483	+	13.7212i	−1.30843	+	0.468162i	−0.411930	+	0.911215i	$0.635145\pi$
$860$	−4.09989	−	2.17488i	−0.139805	−	0.0741629i
$861$	−3.80340	+	6.34558i	−0.129619	+	0.216257i
$862$	14.7983	−	12.1836i	0.504031	−	0.414976i
$863$	−13.4306	−	32.4243i	−0.457183	−	1.10374i	−0.969533	−	0.244960i	$-0.921225\pi$
$863$	−13.4306	−	32.4243i	−0.457183	−	1.10374i	0.512351	−	0.858776i	$-0.328775\pi$
$864$	4.61927	−	13.2373i	0.157151	−	0.450342i
$865$	4.89962	−	11.8287i	0.166592	−	0.402189i
$866$	−12.7581	−	41.8208i	−0.433537	−	1.42113i
$867$	−2.03057	−	8.10648i	−0.0689617	−	0.275310i
$868$	5.83930	+	57.4346i	0.198199	+	1.94946i
$869$	−64.0039	−	30.2716i	−2.17118	−	1.02689i
$870$	−7.71017	−	1.91841i	−0.261399	−	0.0650403i
$871$	3.03330	−	30.7976i	0.102779	−	1.04354i
$872$	7.29377	−	15.6116i	0.246998	−	0.528674i
$873$	21.6238	−	26.3487i	0.731855	−	0.891768i
$874$	1.07501	+	0.642041i	0.0363628	+	0.0217173i
$875$	−30.6871	−	22.7591i	−1.03741	−	0.769397i
$876$	−2.94979	+	11.9354i	−0.0996641	+	0.403259i
$877$	−33.6662	+	15.9229i	−1.13683	+	0.537679i	−0.900872	−	0.434085i	$-0.857072\pi$
$877$	−33.6662	+	15.9229i	−1.13683	+	0.537679i	−0.235955	+	0.971764i	$0.575822\pi$
$878$	−4.48911	−	22.3842i	−0.151500	−	0.755430i
$879$	0.158224	−	0.0314727i	0.00533676	−	0.00106155i
$880$	14.7569	−	18.2138i	0.497454	−	0.613986i
$881$	7.59023	+	1.50979i	0.255721	+	0.0508662i	0.321286	−	0.946982i	$-0.395885\pi$
$881$	7.59023	+	1.50979i	0.255721	+	0.0508662i	−0.0655647	+	0.997848i	$0.520885\pi$
$882$	−21.8860	+	0.0344248i	−0.736939	+	0.00115914i
$883$	39.9706	+	36.2273i	1.34512	+	1.21915i	0.954362	+	0.298651i	$0.0965367\pi$
$883$	39.9706	+	36.2273i	1.34512	+	1.21915i	0.390757	+	0.920494i	$0.372213\pi$
$884$	20.5084	+	43.0108i	0.689773	+	1.44661i
$885$	5.62801	−	3.37330i	0.189183	−	0.113392i
$886$	−16.6132	−	34.9832i	−0.558132	−	1.17528i
$887$	4.36363	−	14.3850i	0.146516	−	0.482999i	−0.852708	−	0.522388i	$-0.825041\pi$
$887$	4.36363	−	14.3850i	0.146516	−	0.482999i	0.999224	+	0.0393889i	$0.0125411\pi$
$888$	3.58150	−	4.40631i	0.120187	−	0.147866i
$889$	13.2820	−	24.8489i	0.445465	−	0.833406i
$890$	−5.00660	−	13.9234i	−0.167821	−	0.466714i
$891$	1.63501	−	33.2814i	0.0547748	−	1.11497i
$892$	−0.847249	−	0.165759i	−0.0283680	−	0.00555003i
$893$	−2.29322	−	0.340166i	−0.0767395	−	0.0113832i
$894$	2.53455	+	4.72393i	0.0847682	+	0.157992i
$895$			27.8547i			0.931080i
$896$	22.5792	+	32.9997i	0.754318	+	1.10244i
$897$		−	2.51400i		−	0.0839400i
$898$	37.7544	−	20.2566i	1.25988	−	0.675970i
$899$	−81.8759	−	12.1451i	−2.73071	−	0.405063i
$900$	10.4031	+	15.4638i	0.346769	+	0.515458i
$901$	−2.69935	+	54.9466i	−0.0899285	+	1.83054i
$902$	29.4491	−	10.5893i	0.980547	−	0.352586i
$903$	−1.26529	+	2.36720i	−0.0421063	+	0.0787754i
$904$	−8.65010	+	4.67618i	−0.287698	+	0.155528i
$905$	0.0498734	−	0.164411i	0.00165785	−	0.00546519i
$906$	8.87254	−	4.21349i	0.294770	−	0.139984i
$907$	−40.7017	+	24.3956i	−1.35148	+	0.810044i	−0.992375	−	0.123254i	$-0.960667\pi$
$907$	−40.7017	+	24.3956i	−1.35148	+	0.810044i	−0.359102	+	0.933298i	$0.616917\pi$
$908$	−15.1800	−	5.37767i	−0.503765	−	0.178464i
$909$	−6.86443	−	6.22156i	−0.227679	−	0.206356i
$910$	−0.0402831	−	25.6105i	−0.00133537	−	0.848980i
$911$	33.4326	+	6.65016i	1.10767	+	0.220330i	0.714845	−	0.699283i	$-0.246497\pi$
$911$	33.4326	+	6.65016i	1.10767	+	0.220330i	0.392827	+	0.919613i	$0.371497\pi$
$912$	0.643280	+	0.773858i	0.0213011	+	0.0256250i
$913$	6.41970	−	1.27696i	0.212461	−	0.0422611i
$914$	−4.14557	+	0.831385i	−0.137123	+	0.0274998i
$915$	5.48529	−	2.59435i	0.181338	−	0.0857665i
$916$	21.6662	−	13.0790i	0.715871	−	0.432143i
$917$	7.10671	+	5.27070i	0.234684	+	0.174054i
$918$	10.8757	−	18.2098i	0.358950	−	0.601014i
$919$	24.4275	−	29.7649i	0.805787	−	0.981855i	−0.194212	−	0.980960i	$-0.562215\pi$
$919$	24.4275	−	29.7649i	0.805787	−	0.981855i	1.00000		0.000895319i	$-0.000284989\pi$
$920$	5.51287	+	0.244759i	0.181754	+	0.00806948i
$921$	0.261298	−	2.65300i	0.00861006	−	0.0874194i
$922$	−1.52783	+	6.14040i	−0.0503164	+	0.202223i
$923$	11.3958	+	5.38983i	0.375099	+	0.177408i
$924$	−10.5070	−	8.56770i	−0.345655	−	0.281857i
$925$	3.78623	+	15.1155i	0.124491	+	0.496994i
$926$	−31.4557	+	9.59604i	−1.03370	+	0.315345i
$927$	−0.699848	+	1.68958i	−0.0229860	+	0.0554932i
$928$	−53.8241	+	19.7374i	−1.76686	+	0.647912i
$929$	5.91609	+	14.2827i	0.194101	+	0.468600i	0.990726	−	0.135873i	$-0.0433838\pi$
$929$	5.91609	+	14.2827i	0.194101	+	0.468600i	−0.796626	+	0.604473i	$0.793384\pi$
$930$	4.06989	+	4.94330i	0.133457	+	0.162097i
$931$	1.66719	−	2.78154i	0.0546400	−	0.0911614i
$932$	8.31817	+	27.1140i	0.272471	+	0.888148i
$933$	−7.74836	+	2.77241i	−0.253670	+	0.0907645i
$934$	26.5250	−	35.8827i	0.867926	−	1.17412i
$935$	27.4137	−	22.4978i	0.896523	−	0.735758i
$936$	−10.4344	+	29.6019i	−0.341059	+	0.967567i
$937$	−0.956842	−	9.71498i	−0.0312587	−	0.317375i	−0.998081	−	0.0619242i	$-0.980276\pi$
$937$	−0.956842	−	9.71498i	−0.0312587	−	0.317375i	0.966822	−	0.255450i	$-0.0822237\pi$
$938$	5.70338	−	38.8702i	0.186222	−	1.26916i
$939$	0.299650	+	2.02008i	0.00977872	+	0.0659228i
$940$	−9.60886	+	3.47224i	−0.313407	+	0.113252i
$941$	7.50607	−	20.9781i	0.244691	−	0.683865i	−0.754916	−	0.655822i	$-0.772322\pi$
$941$	7.50607	−	20.9781i	0.244691	−	0.683865i	0.999607	−	0.0280435i	$-0.00892771\pi$
$942$	1.21048	−	6.13591i	0.0394395	−	0.199919i
$943$	6.12551	+	4.09293i	0.199474	+	0.133284i
$944$	19.9727	−	42.9255i	0.650057	−	1.39711i
$945$	−9.47871	+	6.33347i	−0.308342	+	0.206028i
$946$	10.4831	−	4.36158i	0.340836	−	0.141807i
$947$	−0.359635	−	7.32054i	−0.0116866	−	0.237885i	−0.997531	−	0.0702242i	$-0.977629\pi$
$947$	−0.359635	−	7.32054i	−0.0116866	−	0.237885i	0.985845	−	0.167661i	$-0.0536215\pi$
$948$	1.92376	−	13.2561i	0.0624807	−	0.430538i
$949$	13.8060	−	55.1167i	0.448162	−	1.78916i
$950$	−2.75801	+	0.139841i	−0.0894817	+	0.00453705i
$951$	2.08156	−	1.11262i	0.0674991	−	0.0360790i
$952$	23.4125	+	55.7768i	0.758803	+	1.80774i
$953$	−7.42208	−	24.4673i	−0.240425	−	0.792575i	−0.991241	−	0.132064i	$-0.957840\pi$
$953$	−7.42208	−	24.4673i	−0.240425	−	0.792575i	0.750816	−	0.660511i	$-0.229660\pi$
$954$	−26.8115	+	24.3774i	−0.868054	+	0.789249i
$955$	20.4547	−	18.5390i	0.661897	−	0.599909i
$956$	21.4672	−	52.2911i	0.694299	−	1.69121i
$957$	15.6127	−	11.5792i	0.504688	−	0.374302i
$958$	−2.03844	−	20.3681i	−0.0658589	−	0.658064i
$959$	13.4692	−	13.4692i	0.434945	−	0.434945i
$960$	4.11315	+	1.65842i	0.132751	+	0.0535253i
$961$	25.2483	+	25.2483i	0.814462	+	0.814462i
$962$	−16.6160	+	20.3118i	−0.535722	+	0.654877i
$963$	−15.5147	−	20.9191i	−0.499953	−	0.674109i
$964$	6.85884	−	6.90213i	0.220908	−	0.222303i
$965$	−9.97500	−	11.0057i	−0.321107	−	0.354287i
$966$	0.151585	−	3.18790i	0.00487718	−	0.102569i
$967$	−37.4513	+	11.3607i	−1.20435	+	0.365336i	−0.827781	−	0.561052i	$-0.810397\pi$
$967$	−37.4513	+	11.3607i	−1.20435	+	0.365336i	−0.376571	+	0.926388i	$0.622897\pi$
$968$	5.23993	+	25.7083i	0.168418	+	0.826297i
$969$	0.717654	+	1.34264i	0.0230544	+	0.0431317i
$970$	16.5159	+	14.9219i	0.530293	+	0.479113i
$971$	9.07649	+	2.27354i	0.291279	+	0.0729615i	0.385865	−	0.922555i	$-0.373903\pi$
$971$	9.07649	+	2.27354i	0.291279	+	0.0729615i	−0.0945867	+	0.995517i	$0.530153\pi$
$972$	20.5238	−	5.20961i	0.658301	−	0.167098i
$973$	−45.8383	+	2.25189i	−1.46951	+	0.0721924i
$974$	10.8012	−	26.1929i	0.346093	−	0.839273i
$975$	3.08037	+	4.61011i	0.0986509	+	0.147642i
$976$	22.2721	−	37.6945i	0.712911	−	1.20657i
$977$	−7.25099	+	10.8519i	−0.231980	+	0.347182i	−0.929137	−	0.369736i	$-0.879448\pi$
$977$	−7.25099	+	10.8519i	−0.231980	+	0.347182i	0.697157	+	0.716918i	$0.254448\pi$
$978$	2.35803	−	1.58095i	0.0754013	−	0.0505533i
$979$	34.0828	+	12.1950i	1.08929	+	0.389754i
$980$	0.656357	−	14.2767i	0.0209666	−	0.456053i
$981$	16.9854	−	2.51955i	0.542303	−	0.0804430i
$982$	26.1620	+	35.1597i	0.834864	+	1.12199i
$983$	49.6165	−	4.88679i	1.58252	−	0.155865i	0.731813	−	0.681506i	$-0.238675\pi$
$983$	49.6165	−	4.88679i	1.58252	−	0.155865i	0.850706	+	0.525641i	$0.176175\pi$
$984$	3.54937	+	4.73887i	0.113150	+	0.151070i
$985$	−6.60434	−	8.04742i	−0.210432	−	0.256412i
$986$	−85.7711	+	12.8608i	−2.73151	+	0.409573i
$987$	1.99067	+	5.56356i	0.0633638	+	0.177090i
$988$	−2.96168	−	3.58575i	−0.0942235	−	0.114078i
$989$	2.29260	+	1.37413i	0.0729004	+	0.0436948i
$990$	23.2509	+	2.25309i	0.738962	+	0.0716080i
$991$	−34.8076	+	14.4178i	−1.10570	+	0.457996i	−0.859455	−	0.511211i	$-0.829197\pi$
$991$	−34.8076	+	14.4178i	−1.10570	+	0.457996i	−0.246245	+	0.969208i	$0.579197\pi$
$992$	44.3165	+	13.0636i	1.40705	+	0.414768i
$993$	0.00940180	+	0.00389435i	0.000298357	+	0.000123584i
$994$	14.1256	+	7.52175i	0.448037	+	0.238576i
$995$	−11.2205	+	2.81059i	−0.355714	+	0.0891018i
$996$	0.587181	+	1.09027i	0.0186055	+	0.0345467i
$997$	−3.12590	+	6.60915i	−0.0989982	+	0.209314i	−0.947410	−	0.320023i	$-0.896309\pi$
$997$	−3.12590	+	6.60915i	−0.0989982	+	0.209314i	0.848412	+	0.529337i	$0.177559\pi$
$998$	13.3518	+	22.1968i	0.422643	+	0.702628i
$999$	11.6249	+	1.14496i	0.367796	+	0.0362248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.14	✓	992
256.205	even	64	inner	256.2.m.a.205.14	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.14	✓	992	1.1	even	1	trivial
256.2.m.a.205.14	yes	992	256.205	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)

\(f(q)\)	\(=\)	\(q+(-0.408395 + 1.35396i) q^{2} +(-0.0625001 + 0.421342i) q^{3} +(-1.66643 - 1.10590i) q^{4} +(1.29990 + 0.0638600i) q^{5} +(-0.544956 - 0.256697i) q^{6} +(3.11690 + 1.66602i) q^{7} +(2.17791 - 1.80463i) q^{8} +(2.69720 + 0.818186i) q^{9} +O(q^{10})\)	\(q+(-0.408395 + 1.35396i) q^{2} +(-0.0625001 + 0.421342i) q^{3} +(-1.66643 - 1.10590i) q^{4} +(1.29990 + 0.0638600i) q^{5} +(-0.544956 - 0.256697i) q^{6} +(3.11690 + 1.66602i) q^{7} +(2.17791 - 1.80463i) q^{8} +(2.69720 + 0.818186i) q^{9} +(-0.617338 + 1.73394i) q^{10} +(-2.31496 - 3.86227i) q^{11} +(0.570115 - 0.633016i) q^{12} +(-2.64400 + 2.91721i) q^{13} +(-3.52865 + 3.53977i) q^{14} +(-0.108151 + 0.543711i) q^{15} +(1.55395 + 3.68581i) q^{16} +(1.18057 + 5.93512i) q^{17} +(-2.20932 + 3.31776i) q^{18} +(-0.252525 - 0.533919i) q^{19} +(-2.09557 - 1.54398i) q^{20} +(-0.896768 + 1.20915i) q^{21} +(6.17478 - 1.55703i) q^{22} +(1.15881 + 0.951011i) q^{23} +(0.624247 + 1.03044i) q^{24} +(-3.29026 - 0.324062i) q^{25} +(-2.86999 - 4.77125i) q^{26} +(-1.05967 + 2.24047i) q^{27} +(-3.35162 - 6.22328i) q^{28} +(9.83069 - 2.46246i) q^{29} +(-0.691996 - 0.368481i) q^{30} +(-7.54570 - 3.12553i) q^{31} +(-5.62508 + 0.598726i) q^{32} +(1.77202 - 0.733995i) q^{33} +(-8.51807 - 0.825430i) q^{34} +(3.94526 + 2.36470i) q^{35} +(-3.58985 - 4.34629i) q^{36} +(-1.58781 - 4.43762i) q^{37} +(0.826036 - 0.123859i) q^{38} +(-1.06389 - 1.29635i) q^{39} +(2.94631 - 2.20676i) q^{40} +(4.89071 - 0.481693i) q^{41} +(-1.27091 - 1.70800i) q^{42} +(1.76370 - 0.261620i) q^{43} +(-0.413595 + 8.99630i) q^{44} +(3.45384 + 1.23580i) q^{45} +(-1.76089 + 1.18060i) q^{46} +(2.18071 - 3.26366i) q^{47} +(-1.65011 + 0.424382i) q^{48} +(3.05044 + 4.56531i) q^{49} +(1.78249 - 4.32254i) q^{50} +(-2.57450 + 0.126477i) q^{51} +(7.63218 - 1.93730i) q^{52} +(8.81849 + 2.20892i) q^{53} +(-2.60075 - 2.34975i) q^{54} +(-2.76257 - 5.16840i) q^{55} +(9.79487 - 1.99641i) q^{56} +(0.240745 - 0.0730293i) q^{57} +(-0.680731 + 14.3160i) q^{58} +(-7.94867 - 8.77000i) q^{59} +(0.781518 - 0.786450i) q^{60} +(-6.52032 - 8.79163i) q^{61} +(7.31348 - 8.94014i) q^{62} +(7.04378 + 7.04378i) q^{63} +(1.48661 - 7.86066i) q^{64} +(-3.62323 + 3.62323i) q^{65} +(0.270116 + 2.69901i) q^{66} +(-6.31339 + 4.68233i) q^{67} +(4.59634 - 11.1960i) q^{68} +(-0.473126 + 0.428817i) q^{69} +(-4.81294 + 4.37600i) q^{70} +(-0.929458 - 3.06401i) q^{71} +(7.35079 - 3.08551i) q^{72} +(-12.7277 + 6.80310i) q^{73} +(6.65683 - 0.337526i) q^{74} +(0.342183 - 1.36607i) q^{75} +(-0.169649 + 1.16901i) q^{76} +(-0.780873 - 15.8950i) q^{77} +(2.18970 - 0.911042i) q^{78} +(13.0736 - 8.73553i) q^{79} +(1.78461 + 4.89043i) q^{80} +(6.15288 + 4.11122i) q^{81} +(-1.34515 + 6.81856i) q^{82} +(-0.489707 + 1.36864i) q^{83} +(2.83160 - 1.02322i) q^{84} +(1.15561 + 7.79046i) q^{85} +(-0.366064 + 2.49483i) q^{86} +(0.423117 + 4.29598i) q^{87} +(-12.0117 - 4.23404i) q^{88} +(-6.21422 + 5.09988i) q^{89} +(-3.08376 + 4.17167i) q^{90} +(-13.1012 + 4.68768i) q^{91} +(-0.879346 - 2.86632i) q^{92} +(1.78852 - 2.98397i) q^{93} +(3.52828 + 4.28546i) q^{94} +(-0.294161 - 0.710168i) q^{95} +(0.0993002 - 2.40750i) q^{96} +(4.62792 - 11.1728i) q^{97} +(-7.42704 + 2.26573i) q^{98} +(-3.08384 - 12.3114i) 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

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Database

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