LMFDB - Embedded newform 896.2.bh.a.81.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, degree $8$, not 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.5
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80239 + 1.38302i) q^{3} +(-0.194347 + 0.253278i) q^{5} +(1.82678 + 1.91386i) q^{7} +(0.559406 - 2.08773i) q^{9} +O(q^{10})$	\(q+(-1.80239 + 1.38302i) q^{3} +(-0.194347 + 0.253278i) q^{5} +(1.82678 + 1.91386i) q^{7} +(0.559406 - 2.08773i) q^{9} +(-0.320355 + 2.43334i) q^{11} +(0.658558 - 1.58990i) q^{13} -0.725295i q^{15} +(4.96716 + 2.86779i) q^{17} +(-1.74633 + 0.229909i) q^{19} +(-5.93950 - 0.923053i) q^{21} +(-0.172532 + 0.643898i) q^{23} +(1.26772 + 4.73118i) q^{25} +(-0.729102 - 1.76021i) q^{27} +(1.87266 + 0.775679i) q^{29} +(1.04241 - 1.80550i) q^{31} +(-2.78796 - 4.82889i) q^{33} +(-0.839770 + 0.0907296i) q^{35} +(-5.15588 + 6.71927i) q^{37} +(1.01189 + 3.77642i) q^{39} +(-8.43246 - 8.43246i) q^{41} +(-10.1899 + 4.22079i) q^{43} +(0.420058 + 0.547431i) q^{45} +(2.84457 - 1.64231i) q^{47} +(-0.325749 + 6.99242i) q^{49} +(-12.9190 + 1.70082i) q^{51} +(0.276691 - 2.10168i) q^{53} +(-0.554051 - 0.554051i) q^{55} +(2.82960 - 2.82960i) q^{57} +(-2.60380 - 0.342796i) q^{59} +(1.11745 + 8.48784i) q^{61} +(5.01755 - 2.74320i) q^{63} +(0.274698 + 0.475791i) q^{65} +(4.33912 - 3.32952i) q^{67} +(-0.579556 - 1.39917i) q^{69} +(-11.4382 + 11.4382i) q^{71} +(-8.47361 + 2.27050i) q^{73} +(-8.82826 - 6.77417i) q^{75} +(-5.24229 + 3.83205i) q^{77} +(1.67439 - 0.966709i) q^{79} +(9.36397 + 5.40629i) q^{81} +(2.14419 - 5.17654i) q^{83} +(-1.69170 + 0.700727i) q^{85} +(-4.44805 + 1.19185i) q^{87} +(-11.3160 - 3.03211i) q^{89} +(4.24589 - 1.64401i) q^{91} +(0.618227 + 4.69590i) q^{93} +(0.281164 - 0.486990i) q^{95} -2.69611 q^{97} +(4.90094 + 2.03004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.80239	+	1.38302i	−1.04061	+	0.798490i	−0.979865	−	0.199663i	$-0.936015\pi$
$3$	−1.80239	+	1.38302i	−1.04061	+	0.798490i	−0.0607476	+	0.998153i	$0.519348\pi$
$4$		0			0
$5$	−0.194347	+	0.253278i	−0.0869148	+	0.113270i	−0.834787	−	0.550574i	$-0.814409\pi$
$5$	−0.194347	+	0.253278i	−0.0869148	+	0.113270i	0.747872	+	0.663843i	$0.231076\pi$
$6$		0			0
$7$	1.82678	+	1.91386i	0.690458	+	0.723373i
$7$	1.82678	+	1.91386i	0.690458	+	0.723373i
$8$		0			0
$9$	0.559406	−	2.08773i	0.186469	−	0.695911i
$10$		0			0
$11$	−0.320355	+	2.43334i	−0.0965906	+	0.733678i	0.872787	+	0.488102i	$0.162311\pi$
$11$	−0.320355	+	2.43334i	−0.0965906	+	0.733678i	−0.969377	+	0.245576i	$0.921023\pi$
$12$		0			0
$13$	0.658558	−	1.58990i	0.182651	−	0.440959i	−0.805860	−	0.592106i	$-0.798297\pi$
$13$	0.658558	−	1.58990i	0.182651	−	0.440959i	0.988511	+	0.151147i	$0.0482968\pi$
$14$		0			0
$15$		−	0.725295i		−	0.187270i
$16$		0			0
$17$	4.96716	+	2.86779i	1.20471	+	0.695541i	0.961600	−	0.274457i	$-0.0884979\pi$
$17$	4.96716	+	2.86779i	1.20471	+	0.695541i	0.243113	+	0.969998i	$0.421831\pi$
$18$		0			0
$19$	−1.74633	+	0.229909i	−0.400635	+	0.0527447i	−0.328152	−	0.944625i	$-0.606426\pi$
$19$	−1.74633	+	0.229909i	−0.400635	+	0.0527447i	−0.0724835	+	0.997370i	$0.523092\pi$
$20$		0			0
$21$	−5.93950	−	0.923053i	−1.29610	−	0.201427i
$22$		0			0
$23$	−0.172532	+	0.643898i	−0.0359754	+	0.134262i	−0.981578	−	0.191062i	$-0.938807\pi$
$23$	−0.172532	+	0.643898i	−0.0359754	+	0.134262i	0.945603	+	0.325324i	$0.105473\pi$
$24$		0			0
$25$	1.26772	+	4.73118i	0.253543	+	0.946236i
$26$		0			0
$27$	−0.729102	−	1.76021i	−0.140316	−	0.338752i
$28$		0			0
$29$	1.87266	+	0.775679i	0.347743	+	0.144040i	0.549717	−	0.835351i	$-0.314736\pi$
$29$	1.87266	+	0.775679i	0.347743	+	0.144040i	−0.201974	+	0.979391i	$0.564736\pi$
$30$		0			0
$31$	1.04241	−	1.80550i	0.187222	−	0.324278i	−0.757101	−	0.653298i	$-0.773385\pi$
$31$	1.04241	−	1.80550i	0.187222	−	0.324278i	0.944323	+	0.329020i	$0.106718\pi$
$32$		0			0
$33$	−2.78796	−	4.82889i	−0.485321	−	0.840601i
$34$		0			0
$35$	−0.839770	+	0.0907296i	−0.141947	+	0.0153361i
$36$		0			0
$37$	−5.15588	+	6.71927i	−0.847621	+	1.10464i	0.145708	+	0.989328i	$0.453454\pi$
$37$	−5.15588	+	6.71927i	−0.847621	+	1.10464i	−0.993329	+	0.115313i	$0.963213\pi$
$38$		0			0
$39$	1.01189	+	3.77642i	0.162032	+	0.604712i
$40$		0			0
$41$	−8.43246	−	8.43246i	−1.31693	−	1.31693i	−0.916194	−	0.400735i	$-0.868755\pi$
$41$	−8.43246	−	8.43246i	−1.31693	−	1.31693i	−0.400735	−	0.916194i	$-0.631245\pi$
$42$		0			0
$43$	−10.1899	+	4.22079i	−1.55394	+	0.643665i	−0.984024	−	0.178036i	$-0.943026\pi$
$43$	−10.1899	+	4.22079i	−1.55394	+	0.643665i	−0.569920	+	0.821700i	$0.693026\pi$
$44$		0			0
$45$	0.420058	+	0.547431i	0.0626186	+	0.0816062i
$46$		0			0
$47$	2.84457	−	1.64231i	0.414923	−	0.239556i	−0.277980	−	0.960587i	$-0.589665\pi$
$47$	2.84457	−	1.64231i	0.414923	−	0.239556i	0.692903	+	0.721031i	$0.256332\pi$
$48$		0			0
$49$	−0.325749	+	6.99242i	−0.0465356	+	0.998917i
$50$		0			0
$51$	−12.9190	+	1.70082i	−1.80902	+	0.238162i
$52$		0			0
$53$	0.276691	−	2.10168i	0.0380065	−	0.288688i	−0.961878	−	0.273479i	$-0.911825\pi$
$53$	0.276691	−	2.10168i	0.0380065	−	0.288688i	0.999884	−	0.0152084i	$-0.00484118\pi$
$54$		0			0
$55$	−0.554051	−	0.554051i	−0.0747083	−	0.0747083i
$56$		0			0
$57$	2.82960	−	2.82960i	0.374790	−	0.374790i
$58$		0			0
$59$	−2.60380	−	0.342796i	−0.338986	−	0.0446283i	−0.0408881	−	0.999164i	$-0.513019\pi$
$59$	−2.60380	−	0.342796i	−0.338986	−	0.0446283i	−0.298097	+	0.954535i	$0.596352\pi$
$60$		0			0
$61$	1.11745	+	8.48784i	0.143074	+	1.08676i	0.900816	+	0.434202i	$0.142969\pi$
$61$	1.11745	+	8.48784i	0.143074	+	1.08676i	−0.757742	+	0.652555i	$0.773697\pi$
$62$		0			0
$63$	5.01755	−	2.74320i	0.632151	−	0.345611i
$64$		0			0
$65$	0.274698	+	0.475791i	0.0340721	+	0.0590146i
$66$		0			0
$67$	4.33912	−	3.32952i	0.530107	−	0.406766i	−0.308728	−	0.951150i	$-0.599903\pi$
$67$	4.33912	−	3.32952i	0.530107	−	0.406766i	0.838836	+	0.544385i	$0.183237\pi$
$68$		0			0
$69$	−0.579556	−	1.39917i	−0.0697704	−	0.168441i
$70$		0			0
$71$	−11.4382	+	11.4382i	−1.35746	+	1.35746i	−0.480423	+	0.877037i	$0.659517\pi$
$71$	−11.4382	+	11.4382i	−1.35746	+	1.35746i	−0.877037	+	0.480423i	$0.840483\pi$
$72$		0			0
$73$	−8.47361	+	2.27050i	−0.991761	+	0.265742i	−0.717990	−	0.696053i	$-0.754938\pi$
$73$	−8.47361	+	2.27050i	−0.991761	+	0.265742i	−0.273771	+	0.961795i	$0.588271\pi$
$74$		0			0
$75$	−8.82826	−	6.77417i	−1.01940	−	0.782213i
$76$		0			0
$77$	−5.24229	+	3.83205i	−0.597414	+	0.436703i
$78$		0			0
$79$	1.67439	−	0.966709i	0.188383	−	0.108763i	−0.402842	−	0.915269i	$-0.631978\pi$
$79$	1.67439	−	0.966709i	0.188383	−	0.108763i	0.591226	+	0.806506i	$0.298644\pi$
$80$		0			0
$81$	9.36397	+	5.40629i	1.04044	+	0.600699i
$82$		0			0
$83$	2.14419	−	5.17654i	0.235356	−	0.568199i	−0.761436	−	0.648240i	$-0.775505\pi$
$83$	2.14419	−	5.17654i	0.235356	−	0.568199i	0.996792	+	0.0800414i	$0.0255053\pi$
$84$		0			0
$85$	−1.69170	+	0.700727i	−0.183491	+	0.0760045i
$86$		0			0
$87$	−4.44805	+	1.19185i	−0.476881	+	0.127780i
$88$		0			0
$89$	−11.3160	−	3.03211i	−1.19949	−	0.321403i	−0.396860	−	0.917879i	$-0.629900\pi$
$89$	−11.3160	−	3.03211i	−1.19949	−	0.321403i	−0.802631	+	0.596476i	$0.796567\pi$
$90$		0			0
$91$	4.24589	−	1.64401i	0.445090	−	0.172339i
$92$		0			0
$93$	0.618227	+	4.69590i	0.0641072	+	0.486942i
$94$		0			0
$95$	0.281164	−	0.486990i	0.0288468	−	0.0499641i
$96$		0			0
$97$	−2.69611			−0.273749			−0.136874	−	0.990588i	$-0.543706\pi$
$97$	−2.69611			−0.273749			−0.136874	+	0.990588i	$0.543706\pi$
$98$		0			0
$99$	4.90094	+	2.03004i	0.492563	+	0.204026i
$100$		0			0
$101$	−4.74819	−	0.625111i	−0.472463	−	0.0622009i	−0.109464	−	0.993991i	$-0.534914\pi$
$101$	−4.74819	−	0.625111i	−0.472463	−	0.0622009i	−0.362998	+	0.931790i	$0.618247\pi$
$102$		0			0
$103$	15.1053	+	4.04745i	1.48837	+	0.398807i	0.909186	−	0.416390i	$-0.136705\pi$
$103$	15.1053	+	4.04745i	1.48837	+	0.398807i	0.579183	+	0.815197i	$0.303372\pi$
$104$		0			0
$105$	1.38812	−	1.32495i	0.135466	−	0.129302i
$106$		0			0
$107$	0.262603	+	0.201502i	0.0253867	+	0.0194799i	0.621377	−	0.783512i	$-0.286574\pi$
$107$	0.262603	+	0.201502i	0.0253867	+	0.0194799i	−0.595990	+	0.802992i	$0.703240\pi$
$108$		0			0
$109$	7.61308	+	9.92156i	0.729201	+	0.950313i	0.999924	−	0.0123440i	$-0.00392933\pi$
$109$	7.61308	+	9.92156i	0.729201	+	0.950313i	−0.270723	+	0.962657i	$0.587263\pi$
$110$		0			0
$111$		−	19.2415i		−	1.82632i
$112$		0			0
$113$		−	19.0471i		−	1.79180i	−0.444260	−	0.895898i	$-0.646533\pi$
$113$		−	19.0471i		−	1.79180i	0.444260	−	0.895898i	$-0.353467\pi$
$114$		0			0
$115$	−0.129554	−	0.168838i	−0.0120810	−	0.0157443i
$116$		0			0
$117$	−2.95088	−	2.26429i	−0.272809	−	0.209334i
$118$		0			0
$119$	3.58535	+	14.7453i	0.328668	+	1.35170i
$120$		0			0
$121$	4.80669	+	1.28795i	0.436972	+	0.117086i
$122$		0			0
$123$	26.8609	+	3.53631i	2.42197	+	0.318858i
$124$		0			0
$125$	−2.91943	−	1.20927i	−0.261122	−	0.108160i
$126$		0			0
$127$	12.9079			1.14539			0.572697	−	0.819767i	$-0.305897\pi$
$127$	12.9079			1.14539			0.572697	+	0.819767i	$0.305897\pi$
$128$		0			0
$129$	12.5287	−	21.7004i	1.10309	−	1.91061i
$130$		0			0
$131$	−0.599453	−	4.55330i	−0.0523744	−	0.397823i	−0.997474	−	0.0710394i	$-0.977368\pi$
$131$	−0.599453	−	4.55330i	−0.0523744	−	0.397823i	0.945099	−	0.326784i	$-0.105965\pi$
$132$		0			0
$133$	−3.63017	−	2.92224i	−0.314776	−	0.253391i
$134$		0			0
$135$	0.587522	+	0.157426i	0.0505658	+	0.0135491i
$136$		0			0
$137$	−7.79930	+	2.08982i	−0.666339	+	0.178545i	−0.576105	−	0.817376i	$-0.695428\pi$
$137$	−7.79930	+	2.08982i	−0.666339	+	0.178545i	−0.0902340	+	0.995921i	$0.528761\pi$
$138$		0			0
$139$	12.5809	−	5.21116i	1.06709	−	0.442005i	0.221130	−	0.975244i	$-0.429026\pi$
$139$	12.5809	−	5.21116i	1.06709	−	0.442005i	0.845964	+	0.533240i	$0.179026\pi$
$140$		0			0
$141$	−2.85567	+	6.89420i	−0.240491	+	0.580596i
$142$		0			0
$143$	3.65779	+	2.11182i	0.305879	+	0.176600i
$144$		0			0
$145$	−0.560409	+	0.323552i	−0.0465394	+	0.0268695i
$146$		0			0
$147$	−9.08356	−	13.0536i	−0.749199	−	1.07664i
$148$		0			0
$149$	10.0346	+	7.69980i	0.822064	+	0.630792i	0.931720	−	0.363178i	$-0.118308\pi$
$149$	10.0346	+	7.69980i	0.822064	+	0.630792i	−0.109656	+	0.993970i	$0.534975\pi$
$150$		0			0
$151$	−11.8022	+	3.16239i	−0.960450	+	0.257352i	−0.704791	−	0.709415i	$-0.748959\pi$
$151$	−11.8022	+	3.16239i	−0.960450	+	0.257352i	−0.255659	+	0.966767i	$0.582293\pi$
$152$		0			0
$153$	8.76584	−	8.76584i	0.708676	−	0.708676i
$154$		0			0
$155$	0.254706	+	0.614914i	0.0204585	+	0.0493911i
$156$		0			0
$157$	−11.3497	+	8.70891i	−0.905802	+	0.695046i	−0.952719	−	0.303852i	$-0.901727\pi$
$157$	−11.3497	+	8.70891i	−0.905802	+	0.695046i	0.0469170	+	0.998899i	$0.485060\pi$
$158$		0			0
$159$	2.40797	+	4.17072i	0.190964	+	0.330760i
$160$		0			0
$161$	−1.54751	+	0.846057i	−0.121961	+	0.0666786i
$162$		0			0
$163$	0.354318	+	2.69131i	0.0277523	+	0.210800i	0.999703	−	0.0243866i	$-0.00776325\pi$
$163$	0.354318	+	2.69131i	0.0277523	+	0.210800i	−0.971950	+	0.235186i	$0.924430\pi$
$164$		0			0
$165$	1.76489	+	0.232352i	0.137396	+	0.0180885i
$166$		0			0
$167$	15.6149	−	15.6149i	1.20832	−	1.20832i	0.236751	−	0.971570i	$-0.423918\pi$
$167$	15.6149	−	15.6149i	1.20832	−	1.20832i	0.971570	−	0.236751i	$-0.0760824\pi$
$168$		0			0
$169$	7.09831	+	7.09831i	0.546024	+	0.546024i
$170$		0			0
$171$	−0.496920	+	3.77448i	−0.0380004	+	0.288642i
$172$		0			0
$173$	22.2934	−	2.93498i	1.69493	−	0.223142i	0.779725	−	0.626122i	$-0.215359\pi$
$173$	22.2934	−	2.93498i	1.69493	−	0.223142i	0.915209	+	0.402980i	$0.132026\pi$
$174$		0			0
$175$	−6.73900	+	11.0691i	−0.509420	+	0.836743i
$176$		0			0
$177$	5.16716	−	2.98326i	0.388388	−	0.224236i
$178$		0			0
$179$	4.85975	+	6.33335i	0.363235	+	0.473377i	0.938841	−	0.344350i	$-0.111901\pi$
$179$	4.85975	+	6.33335i	0.363235	+	0.473377i	−0.575607	+	0.817727i	$0.695234\pi$
$180$		0			0
$181$	19.5931	−	8.11571i	1.45634	−	0.603236i	0.492643	−	0.870232i	$-0.336031\pi$
$181$	19.5931	−	8.11571i	1.45634	−	0.603236i	0.963698	+	0.266995i	$0.0860309\pi$
$182$		0			0
$183$	−13.7530	−	13.7530i	−1.01665	−	1.01665i
$184$		0			0
$185$	−0.699815	−	2.61174i	−0.0514514	−	0.192019i
$186$		0			0
$187$	−8.56955	+	11.1681i	−0.626668	+	0.816689i
$188$		0			0
$189$	2.03689	−	4.61091i	0.148162	−	0.335395i
$190$		0			0
$191$	−7.24192	−	12.5434i	−0.524007	−	0.907607i	−0.999609	−	0.0279465i	$-0.991103\pi$
$191$	−7.24192	−	12.5434i	−0.524007	−	0.907607i	0.475602	−	0.879660i	$-0.342230\pi$
$192$		0			0
$193$	−1.75774	+	3.04450i	−0.126525	+	0.219148i	−0.922328	−	0.386408i	$-0.873716\pi$
$193$	−1.75774	+	3.04450i	−0.126525	+	0.219148i	0.795803	+	0.605556i	$0.207049\pi$
$194$		0			0
$195$	−1.15314	−	0.477648i	−0.0825784	−	0.0342051i
$196$		0			0
$197$	4.90109	+	11.8323i	0.349188	+	0.843015i	0.996716	+	0.0809734i	$0.0258029\pi$
$197$	4.90109	+	11.8323i	0.349188	+	0.843015i	−0.647528	+	0.762042i	$0.724197\pi$
$198$		0			0
$199$	3.89536	+	14.5377i	0.276135	+	1.03055i	0.955077	+	0.296357i	$0.0957719\pi$
$199$	3.89536	+	14.5377i	0.276135	+	1.03055i	−0.678943	+	0.734191i	$0.737561\pi$
$200$		0			0
$201$	−3.21598	+	12.0022i	−0.226838	+	0.846571i
$202$		0			0
$203$	1.93639	+	5.00100i	0.135908	+	0.351002i
$204$		0			0
$205$	3.77459	−	0.496934i	0.263629	−	0.0347074i
$206$		0			0
$207$	1.24777	+	0.720401i	0.0867260	+	0.0500713i
$208$		0			0
$209$		−	4.32306i		−	0.299032i
$210$		0			0
$211$	8.89496	−	21.4743i	0.612354	−	1.47835i	−0.248053	−	0.968746i	$-0.579791\pi$
$211$	8.89496	−	21.4743i	0.612354	−	1.47835i	0.860407	−	0.509607i	$-0.170209\pi$
$212$		0			0
$213$	4.79680	−	36.4353i	0.328671	−	2.49651i
$214$		0			0
$215$	0.911343	−	3.40118i	0.0621531	−	0.231958i
$216$		0			0
$217$	5.35973	−	1.30323i	0.363842	−	0.0884690i
$218$		0			0
$219$	12.1326	−	15.8115i	0.819847	−	1.06845i
$220$		0			0
$221$	7.83066	−	6.00867i	0.526747	−	0.404187i
$222$		0			0
$223$	−2.06618			−0.138362			−0.0691809	−	0.997604i	$-0.522039\pi$
$223$	−2.06618			−0.138362			−0.0691809	+	0.997604i	$0.522039\pi$
$224$		0			0
$225$	10.5866			0.705774
$226$		0			0
$227$	−16.9133	+	12.9781i	−1.12258	+	0.861384i	−0.991515	−	0.129990i	$-0.958505\pi$
$227$	−16.9133	+	12.9781i	−1.12258	+	0.861384i	−0.131062	+	0.991374i	$0.541839\pi$
$228$		0			0
$229$	−3.11476	+	4.05923i	−0.205829	+	0.268242i	−0.884849	−	0.465878i	$-0.845738\pi$
$229$	−3.11476	+	4.05923i	−0.205829	+	0.268242i	0.679020	+	0.734120i	$0.262405\pi$
$230$		0			0
$231$	4.14884	−	14.1571i	0.272974	−	0.931468i
$232$		0			0
$233$	−0.980702	+	3.66003i	−0.0642479	+	0.239777i	−0.990581	−	0.136929i	$-0.956277\pi$
$233$	−0.980702	+	3.66003i	−0.0642479	+	0.239777i	0.926333	+	0.376706i	$0.122943\pi$
$234$		0			0
$235$	−0.136872	+	1.03965i	−0.00892855	+	0.0678191i
$236$		0			0
$237$	−1.68092	+	4.05811i	−0.109188	+	0.263603i
$238$		0			0
$239$			24.3136i			1.57272i	0.617771	+	0.786358i	$0.288036\pi$
$239$			24.3136i			1.57272i	−0.617771	+	0.786358i	$0.711964\pi$
$240$		0			0
$241$	9.68344	+	5.59074i	0.623765	+	0.360131i	0.778333	−	0.627851i	$-0.216065\pi$
$241$	9.68344	+	5.59074i	0.623765	+	0.360131i	−0.154568	+	0.987982i	$0.549399\pi$
$242$		0			0
$243$	−18.6878	+	2.46029i	−1.19882	+	0.157828i
$244$		0			0
$245$	−1.70772	−	1.44146i	−0.109102	−	0.0920917i
$246$		0			0
$247$	−0.784527	+	2.92790i	−0.0499183	+	0.186298i
$248$		0			0
$249$	3.29460	+	12.2956i	0.208787	+	0.779204i
$250$		0			0
$251$	5.28669	+	12.7632i	0.333693	+	0.805606i	0.998293	+	0.0584065i	$0.0186020\pi$
$251$	5.28669	+	12.7632i	0.333693	+	0.805606i	−0.664600	+	0.747199i	$0.731398\pi$
$252$		0			0
$253$	−1.51155	−	0.626104i	−0.0950302	−	0.0393628i
$254$		0			0
$255$	2.07999	−	3.60265i	0.130254	−	0.225607i
$256$		0			0
$257$	−6.57191	−	11.3829i	−0.409944	−	0.710044i	0.584939	−	0.811077i	$-0.301119\pi$
$257$	−6.57191	−	11.3829i	−0.409944	−	0.710044i	−0.994883	+	0.101033i	$0.967785\pi$
$258$		0			0
$259$	−22.2784	+	2.40698i	−1.38431	+	0.149563i
$260$		0			0
$261$	2.66699	−	3.47568i	0.165082	−	0.215139i
$262$		0			0
$263$	0.858637	+	3.20448i	0.0529458	+	0.197597i	0.987333	−	0.158663i	$-0.0507184\pi$
$263$	0.858637	+	3.20448i	0.0529458	+	0.197597i	−0.934387	+	0.356260i	$0.884052\pi$
$264$		0			0
$265$	0.478536	+	0.478536i	0.0293962	+	0.0293962i
$266$		0			0
$267$	24.5893	−	10.1852i	1.50484	−	0.623326i
$268$		0			0
$269$	3.09854	+	4.03810i	0.188922	+	0.246207i	0.878205	−	0.478284i	$-0.158741\pi$
$269$	3.09854	+	4.03810i	0.188922	+	0.246207i	−0.689283	+	0.724492i	$0.742075\pi$
$270$		0			0
$271$	−17.3457	+	10.0146i	−1.05368	+	0.608341i	−0.923677	−	0.383172i	$-0.874832\pi$
$271$	−17.3457	+	10.0146i	−1.05368	+	0.608341i	−0.130001	+	0.991514i	$0.541498\pi$
$272$		0			0
$273$	−5.37906	+	8.83532i	−0.325556	+	0.534738i
$274$		0			0
$275$	−11.9187	+	1.56912i	−0.718723	+	0.0946217i
$276$		0			0
$277$	3.11682	−	23.6746i	0.187271	−	1.42247i	−0.597095	−	0.802170i	$-0.703679\pi$
$277$	3.11682	−	23.6746i	0.187271	−	1.42247i	0.784367	−	0.620297i	$-0.212988\pi$
$278$		0			0
$279$	−3.18628	−	3.18628i	−0.190757	−	0.190757i
$280$		0			0
$281$	−9.89183	+	9.89183i	−0.590097	+	0.590097i	−0.937657	−	0.347561i	$-0.887010\pi$
$281$	−9.89183	+	9.89183i	−0.590097	+	0.590097i	0.347561	+	0.937657i	$0.387010\pi$
$282$		0			0
$283$	−17.3268	−	2.28112i	−1.02997	−	0.135598i	−0.403449	−	0.915002i	$-0.632189\pi$
$283$	−17.3268	−	2.28112i	−1.02997	−	0.135598i	−0.626522	+	0.779404i	$0.715522\pi$
$284$		0			0
$285$	0.166751	+	1.26660i	0.00987751	+	0.0750271i
$286$		0			0
$287$	0.734331	−	31.5428i	0.0433462	−	1.86191i
$288$		0			0
$289$	7.94844	+	13.7671i	0.467556	+	0.809830i
$290$		0			0
$291$	4.85946	−	3.72879i	0.284866	−	0.218586i
$292$		0			0
$293$	−8.97963	−	21.6787i	−0.524596	−	1.26649i	−0.935021	−	0.354592i	$-0.884620\pi$
$293$	−8.97963	−	21.6787i	−0.524596	−	1.26649i	0.410426	−	0.911894i	$-0.365380\pi$
$294$		0			0
$295$	0.592864	−	0.592864i	0.0345179	−	0.0345179i
$296$		0			0
$297$	4.51675	−	1.21026i	0.262088	−	0.0702263i
$298$		0			0
$299$	0.910110	+	0.698352i	0.0526330	+	0.0403867i
$300$		0			0
$301$	−26.6927	−	11.7916i	−1.53854	−	0.679657i
$302$		0			0
$303$	9.42265	−	5.44017i	0.541317	−	0.312530i
$304$		0			0
$305$	−2.36696	−	1.36656i	−0.135532	−	0.0782493i
$306$		0			0
$307$	6.27653	−	15.1529i	0.358221	−	0.864821i	−0.637330	−	0.770591i	$-0.719961\pi$
$307$	6.27653	−	15.1529i	0.358221	−	0.864821i	0.995550	−	0.0942298i	$-0.0300389\pi$
$308$		0			0
$309$	−32.8234	+	13.5959i	−1.86726	+	0.773444i
$310$		0			0
$311$	26.0348	−	6.97601i	1.47630	−	0.395573i	0.571213	−	0.820802i	$-0.306473\pi$
$311$	26.0348	−	6.97601i	1.47630	−	0.395573i	0.905086	+	0.425228i	$0.139806\pi$
$312$		0			0
$313$	−19.0423	−	5.10237i	−1.07634	−	0.288403i	−0.323242	−	0.946316i	$-0.604773\pi$
$313$	−19.0423	−	5.10237i	−1.07634	−	0.288403i	−0.753094	+	0.657913i	$0.771439\pi$
$314$		0			0
$315$	−0.280354	+	1.80397i	−0.0157961	+	0.101642i
$316$		0			0
$317$	−3.84277	−	29.1887i	−0.215831	−	1.63940i	−0.665637	−	0.746276i	$-0.731840\pi$
$317$	−3.84277	−	29.1887i	−0.215831	−	1.63940i	0.449806	−	0.893127i	$-0.351493\pi$
$318$		0			0
$319$	−2.48740	+	4.30831i	−0.139268	+	0.241219i
$320$		0			0
$321$	−0.751995			−0.0419723
$322$		0			0
$323$	−9.33363	−	3.86611i	−0.519337	−	0.215116i
$324$		0			0
$325$	8.35696	+	1.10022i	0.463561	+	0.0610289i
$326$		0			0
$327$	−27.4435	−	7.35347i	−1.51763	−	0.406648i
$328$		0			0
$329$	8.33956	+	2.44397i	0.459775	+	0.134741i
$330$		0			0
$331$	26.7748	+	20.5450i	1.47167	+	1.12926i	0.963403	+	0.268059i	$0.0863821\pi$
$331$	26.7748	+	20.5450i	1.47167	+	1.12926i	0.508272	+	0.861197i	$0.330285\pi$
$332$		0			0
$333$	11.1438	+	14.5229i	0.610677	+	0.795849i
$334$		0			0
$335$			1.74609i			0.0953990i
$336$		0			0
$337$		−	4.94619i		−	0.269436i	−0.990884	−	0.134718i	$-0.956987\pi$
$337$		−	4.94619i		−	0.269436i	0.990884	−	0.134718i	$-0.0430129\pi$
$338$		0			0
$339$	26.3425	+	34.3303i	1.43073	+	1.86456i
$340$		0			0
$341$	4.05945	+	3.11493i	0.219832	+	0.168683i
$342$		0			0
$343$	−13.9776	+	12.1502i	−0.754720	+	0.656047i
$344$		0			0
$345$	0.467016	+	0.125136i	0.0251433	+	0.00673712i
$346$		0			0
$347$	−6.86031	−	0.903176i	−0.368281	−	0.0484851i	−0.0558851	−	0.998437i	$-0.517798\pi$
$347$	−6.86031	−	0.903176i	−0.368281	−	0.0484851i	−0.312395	+	0.949952i	$0.601131\pi$
$348$		0			0
$349$	0.0499558	+	0.0206924i	0.00267407	+	0.00110764i	0.384020	−	0.923325i	$-0.374539\pi$
$349$	0.0499558	+	0.0206924i	0.00267407	+	0.00110764i	−0.381346	+	0.924432i	$0.624539\pi$
$350$		0			0
$351$	−3.27871			−0.175004
$352$		0			0
$353$	−2.86427	+	4.96106i	−0.152450	+	0.264051i	−0.932127	−	0.362130i	$-0.882050\pi$
$353$	−2.86427	+	4.96106i	−0.152450	+	0.264051i	0.779678	+	0.626181i	$0.215383\pi$
$354$		0			0
$355$	−0.674063	−	5.12002i	−0.0357755	−	0.271742i
$356$		0			0
$357$	−26.8553	−	21.6182i	−1.42133	−	1.14416i
$358$		0			0
$359$	−7.88209	−	2.11200i	−0.416001	−	0.111467i	0.0447468	−	0.998998i	$-0.485752\pi$
$359$	−7.88209	−	2.11200i	−0.416001	−	0.111467i	−0.460747	+	0.887531i	$0.652419\pi$
$360$		0			0
$361$	−15.3558	+	4.11457i	−0.808199	+	0.216556i
$362$		0			0
$363$	−10.4448	+	4.32638i	−0.548210	+	0.227076i
$364$		0			0
$365$	1.07176	−	2.58745i	0.0560983	−	0.135433i
$366$		0			0
$367$	3.00290	+	1.73373i	0.156750	+	0.0904997i	0.576323	−	0.817222i	$-0.304487\pi$
$367$	3.00290	+	1.73373i	0.156750	+	0.0904997i	−0.419573	+	0.907722i	$0.637820\pi$
$368$		0			0
$369$	−22.3219	+	12.8875i	−1.16203	+	0.670899i
$370$		0			0
$371$	4.52778	−	3.30975i	0.235071	−	0.171834i
$372$		0			0
$373$	15.9787	+	12.2609i	0.827345	+	0.634844i	0.933128	−	0.359545i	$-0.117068\pi$
$373$	15.9787	+	12.2609i	0.827345	+	0.634844i	−0.105783	+	0.994389i	$0.533735\pi$
$374$		0			0
$375$	6.93440	−	1.85807i	0.358091	−	0.0959502i
$376$		0			0
$377$	2.46650	−	2.46650i	0.127031	−	0.127031i
$378$		0			0
$379$	12.3991	+	29.9342i	0.636902	+	1.53762i	0.830786	+	0.556592i	$0.187891\pi$
$379$	12.3991	+	29.9342i	0.636902	+	1.53762i	−0.193884	+	0.981024i	$0.562109\pi$
$380$		0			0
$381$	−23.2652	+	17.8520i	−1.19191	+	0.914585i
$382$		0			0
$383$	4.26715	+	7.39093i	0.218041	+	0.377659i	0.954209	−	0.299140i	$-0.0966999\pi$
$383$	4.26715	+	7.39093i	0.218041	+	0.377659i	−0.736168	+	0.676799i	$0.763367\pi$
$384$		0			0
$385$	0.0482489	−	2.07251i	0.00245899	−	0.105625i
$386$		0			0
$387$	3.11159	+	23.6349i	0.158171	+	1.20143i
$388$		0			0
$389$	17.5902	+	2.31579i	0.891857	+	0.117415i	0.562507	−	0.826793i	$-0.309837\pi$
$389$	17.5902	+	2.31579i	0.891857	+	0.117415i	0.329350	+	0.944208i	$0.393170\pi$
$390$		0			0
$391$	−2.70356	+	2.70356i	−0.136725	+	0.136725i
$392$		0			0
$393$	7.37777	+	7.37777i	0.372159	+	0.372159i
$394$		0			0
$395$	−0.0805666	+	0.611964i	−0.00405375	+	0.0307913i
$396$		0			0
$397$	7.50495	−	0.988045i	0.376663	−	0.0495886i	0.0601816	−	0.998187i	$-0.480832\pi$
$397$	7.50495	−	0.988045i	0.376663	−	0.0495886i	0.316481	+	0.948599i	$0.397499\pi$
$398$		0			0
$399$	10.5845	+	0.246413i	0.529890	+	0.0123361i
$400$		0			0
$401$	16.1760	−	9.33922i	0.807791	−	0.466378i	−0.0383971	−	0.999263i	$-0.512225\pi$
$401$	16.1760	−	9.33922i	0.807791	−	0.466378i	0.846188	+	0.532884i	$0.178892\pi$
$402$		0			0
$403$	−2.18408	−	2.84635i	−0.108797	−	0.141787i
$404$		0			0
$405$	−3.18916	+	1.32099i	−0.158471	+	0.0656407i
$406$		0			0
$407$	−14.6985	−	14.6985i	−0.728579	−	0.728579i
$408$		0			0
$409$	7.23139	+	26.9879i	0.357569	+	1.33447i	0.877220	+	0.480088i	$0.159395\pi$
$409$	7.23139	+	26.9879i	0.357569	+	1.33447i	−0.519651	+	0.854379i	$0.673938\pi$
$410$		0			0
$411$	11.1671	−	14.5533i	0.550834	−	0.717861i
$412$		0			0
$413$	−4.10050	−	5.60953i	−0.201772	−	0.276027i
$414$		0			0
$415$	0.894387	+	1.54912i	0.0439037	+	0.0760435i
$416$		0			0
$417$	−15.4685	+	26.7922i	−0.757495	+	1.31202i
$418$		0			0
$419$	2.82293	+	1.16930i	0.137909	+	0.0571239i	0.450571	−	0.892741i	$-0.351221\pi$
$419$	2.82293	+	1.16930i	0.137909	+	0.0571239i	−0.312661	+	0.949865i	$0.601221\pi$
$420$		0			0
$421$	8.03424	+	19.3964i	0.391565	+	0.945321i	0.989599	+	0.143851i	$0.0459486\pi$
$421$	8.03424	+	19.3964i	0.391565	+	0.945321i	−0.598034	+	0.801470i	$0.704051\pi$
$422$		0			0
$423$	−1.83744	−	6.85741i	−0.0893393	−	0.333419i
$424$		0			0
$425$	−7.27109	+	27.1361i	−0.352700	+	1.31629i
$426$		0			0
$427$	−14.2032	+	17.6441i	−0.687343	+	0.853856i
$428$		0			0
$429$	−9.51347	+	1.25247i	−0.459315	+	0.0604699i
$430$		0			0
$431$	−12.3085	−	7.10632i	−0.592880	−	0.342299i	0.173356	−	0.984859i	$-0.444539\pi$
$431$	−12.3085	−	7.10632i	−0.592880	−	0.342299i	−0.766235	+	0.642560i	$0.777872\pi$
$432$		0			0
$433$			15.0172i			0.721679i	0.932628	+	0.360840i	$0.117510\pi$
$433$			15.0172i			0.721679i	−0.932628	+	0.360840i	$0.882490\pi$
$434$		0			0
$435$	0.562596	−	1.35823i	0.0269744	−	0.0651220i
$436$		0			0
$437$	0.153260	−	1.16412i	0.00733141	−	0.0556876i
$438$		0			0
$439$	−2.91944	+	10.8955i	−0.139337	+	0.520013i	0.860605	+	0.509273i	$0.170086\pi$
$439$	−2.91944	+	10.8955i	−0.139337	+	0.520013i	−0.999942	+	0.0107406i	$0.996581\pi$
$440$		0			0
$441$	14.4161	+	4.59168i	0.686479	+	0.218651i
$442$		0			0
$443$	17.1980	−	22.4128i	0.817101	−	1.06487i	−0.179603	−	0.983739i	$-0.557481\pi$
$443$	17.1980	−	22.4128i	0.817101	−	1.06487i	0.996704	−	0.0811271i	$-0.0258520\pi$
$444$		0			0
$445$	2.96720	−	2.27681i	0.140659	−	0.107931i
$446$		0			0
$447$	−28.7352			−1.35913
$448$		0			0
$449$	−6.75785			−0.318923			−0.159461	−	0.987204i	$-0.550976\pi$
$449$	−6.75785			−0.318923			−0.159461	+	0.987204i	$0.550976\pi$
$450$		0			0
$451$	23.2204	−	17.8176i	1.09341	−	0.838999i
$452$		0			0
$453$	16.8986	−	22.0226i	0.793964	−	1.03471i
$454$		0			0
$455$	−0.408786	+	1.39490i	−0.0191642	+	0.0653939i
$456$		0			0
$457$	4.88648	−	18.2366i	0.228580	−	0.853073i	−0.752358	−	0.658754i	$-0.771084\pi$
$457$	4.88648	−	18.2366i	0.228580	−	0.853073i	0.980938	−	0.194319i	$-0.0622495\pi$
$458$		0			0
$459$	1.42634	−	10.8341i	0.0665759	−	0.505694i
$460$		0			0
$461$	−0.511143	+	1.23401i	−0.0238063	+	0.0574735i	−0.935336	−	0.353762i	$-0.884902\pi$
$461$	−0.511143	+	1.23401i	−0.0238063	+	0.0574735i	0.911529	+	0.411235i	$0.134902\pi$
$462$		0			0
$463$		−	5.28217i		−	0.245483i	−0.992439	−	0.122742i	$-0.960831\pi$
$463$		−	5.28217i		−	0.245483i	0.992439	−	0.122742i	$-0.0391686\pi$
$464$		0			0
$465$	−1.30952	−	0.756052i	−0.0607276	−	0.0350611i
$466$		0			0
$467$	7.22194	−	0.950787i	0.334192	−	0.0439972i	0.0384368	−	0.999261i	$-0.487762\pi$
$467$	7.22194	−	0.950787i	0.334192	−	0.0439972i	0.295755	+	0.955264i	$0.404429\pi$
$468$		0			0
$469$	14.2989	+	2.22218i	0.660260	+	0.102611i
$470$		0			0
$471$	8.41193	−	31.3937i	0.387601	−	1.44655i
$472$		0			0
$473$	−7.00622	−	26.1476i	−0.322146	−	1.20227i
$474$		0			0
$475$	−3.30159	−	7.97074i	−0.151487	−	0.365723i
$476$		0			0
$477$	−4.23296	−	1.75335i	−0.193814	−	0.0802803i
$478$		0			0
$479$	11.3380	−	19.6380i	0.518048	−	0.897285i	−0.481732	−	0.876318i	$-0.659992\pi$
$479$	11.3380	−	19.6380i	0.518048	−	0.897285i	0.999780	−	0.0209667i	$-0.00667439\pi$
$480$		0			0
$481$	7.28751	+	12.6223i	0.332282	+	0.575529i
$482$		0			0
$483$	1.61910	−	3.66517i	0.0736718	−	0.166771i
$484$		0			0
$485$	0.523983	−	0.682867i	0.0237928	−	0.0310074i
$486$		0			0
$487$	−0.879562	−	3.28257i	−0.0398568	−	0.148748i	0.943130	−	0.332424i	$-0.107867\pi$
$487$	−0.879562	−	3.28257i	−0.0398568	−	0.148748i	−0.982987	+	0.183677i	$0.941200\pi$
$488$		0			0
$489$	−4.36077	−	4.36077i	−0.197201	−	0.197201i
$490$		0			0
$491$	−18.5715	+	7.69255i	−0.838118	+	0.347160i	−0.760111	−	0.649793i	$-0.774856\pi$
$491$	−18.5715	+	7.69255i	−0.838118	+	0.347160i	−0.0780069	+	0.996953i	$0.524856\pi$
$492$		0			0
$493$	7.07729	+	9.22331i	0.318745	+	0.415397i
$494$		0			0
$495$	−1.46665	+	0.846771i	−0.0659210	+	0.0380595i
$496$		0			0
$497$	−42.7861	−	0.996078i	−1.91922	−	0.0446802i
$498$		0			0
$499$	17.9564	−	2.36401i	0.803840	−	0.105828i	0.282600	−	0.959238i	$-0.408803\pi$
$499$	17.9564	−	2.36401i	0.803840	−	0.105828i	0.521240	+	0.853410i	$0.325470\pi$
$500$		0			0
$501$	−6.54841	+	49.7401i	−0.292562	+	2.22223i
$502$		0			0
$503$	22.0540	+	22.0540i	0.983337	+	0.983337i	0.999863	−	0.0165262i	$-0.00526069\pi$
$503$	22.0540	+	22.0540i	0.983337	+	0.983337i	−0.0165262	+	0.999863i	$0.505261\pi$
$504$		0			0
$505$	1.08113	−	1.08113i	0.0481095	−	0.0481095i
$506$		0			0
$507$	−22.6111	−	2.97681i	−1.00419	−	0.132205i
$508$		0			0
$509$	−1.15470	−	8.77082i	−0.0511812	−	0.388760i	−0.997794	−	0.0663870i	$-0.978853\pi$
$509$	−1.15470	−	8.77082i	−0.0511812	−	0.388760i	0.946613	−	0.322373i	$-0.104481\pi$
$510$		0			0
$511$	−19.8248	−	12.0696i	−0.877000	−	0.533929i
$512$		0			0
$513$	1.67794	+	2.90628i	0.0740828	+	0.128315i
$514$		0			0
$515$	−3.96081	+	3.03924i	−0.174534	+	0.133925i
$516$		0			0
$517$	3.08503	+	7.44791i	0.135679	+	0.327559i
$518$		0			0
$519$	−36.1223	+	36.1223i	−1.58559	+	1.58559i
$520$		0			0
$521$	−3.98770	+	1.06850i	−0.174704	+	0.0468119i	−0.345111	−	0.938562i	$-0.612159\pi$
$521$	−3.98770	+	1.06850i	−0.174704	+	0.0468119i	0.170406	+	0.985374i	$0.445492\pi$
$522$		0			0
$523$	−28.3677	−	21.7673i	−1.24043	−	0.951819i	−0.240611	−	0.970622i	$-0.577348\pi$
$523$	−28.3677	−	21.7673i	−1.24043	−	0.951819i	−0.999823	+	0.0188025i	$0.994015\pi$
$524$		0			0
$525$	−3.16247	−	29.2710i	−0.138021	−	1.27749i
$526$		0			0
$527$	10.3556	−	5.97881i	0.451097	−	0.260441i
$528$		0			0
$529$	19.5337	+	11.2778i	0.849293	+	0.490340i
$530$		0			0
$531$	−2.17225	+	5.24427i	−0.0942675	+	0.227582i
$532$		0			0
$533$	−18.9600	+	7.85350i	−0.821250	+	0.340173i
$534$		0			0
$535$	−0.102072	+	0.0273502i	−0.00441297	+	0.00118245i
$536$		0			0
$537$	−17.5184	−	4.69403i	−0.755973	−	0.202562i
$538$		0			0
$539$	−16.9105	−	3.03271i	−0.728389	−	0.130628i
$540$		0			0
$541$	−2.70235	−	20.5264i	−0.116183	−	0.882497i	−0.945933	−	0.324362i	$-0.894850\pi$
$541$	−2.70235	−	20.5264i	−0.116183	−	0.882497i	0.829750	−	0.558135i	$-0.188483\pi$
$542$		0			0
$543$	−24.0902	+	41.7254i	−1.03381	+	1.79061i
$544$		0			0
$545$	−3.99250			−0.171020
$546$		0			0
$547$	35.7892	+	14.8244i	1.53023	+	0.633844i	0.979610	−	0.200909i	$-0.0643896\pi$
$547$	35.7892	+	14.8244i	1.53023	+	0.633844i	0.550625	+	0.834753i	$0.314390\pi$
$548$		0			0
$549$	18.3454	+	2.41522i	0.782964	+	0.103079i
$550$		0			0
$551$	−3.44861	−	0.924052i	−0.146916	−	0.0393659i
$552$		0			0
$553$	4.90889	+	1.43859i	0.208747	+	0.0611750i
$554$		0			0
$555$	4.87345	+	3.73953i	0.206866	+	0.158734i
$556$		0			0
$557$	3.20903	+	4.18209i	0.135971	+	0.177201i	0.856376	−	0.516353i	$-0.172711\pi$
$557$	3.20903	+	4.18209i	0.135971	+	0.177201i	−0.720405	+	0.693554i	$0.756044\pi$
$558$		0			0
$559$			18.9805i			0.802791i
$560$		0			0
$561$		−	31.9811i		−	1.35024i
$562$		0			0
$563$	10.7545	+	14.0155i	0.453248	+	0.590684i	0.962954	−	0.269664i	$-0.0869126\pi$
$563$	10.7545	+	14.0155i	0.453248	+	0.590684i	−0.509706	+	0.860348i	$0.670246\pi$
$564$		0			0
$565$	4.82421	+	3.70174i	0.202956	+	0.155734i
$566$		0			0
$567$	6.75901	+	27.7975i	0.283852	+	1.16738i
$568$		0			0
$569$	−22.5592	−	6.04472i	−0.945732	−	0.253408i	−0.247182	−	0.968969i	$-0.579504\pi$
$569$	−22.5592	−	6.04472i	−0.945732	−	0.253408i	−0.698550	+	0.715561i	$0.746171\pi$
$570$		0			0
$571$	−4.51573	−	0.594507i	−0.188977	−	0.0248794i	0.0354433	−	0.999372i	$-0.488716\pi$
$571$	−4.51573	−	0.594507i	−0.188977	−	0.0248794i	−0.224421	+	0.974492i	$0.572049\pi$
$572$		0			0
$573$	30.4006	+	12.5923i	1.27000	+	0.526053i
$574$		0			0
$575$	−3.26512			−0.136165
$576$		0			0
$577$	2.11188	−	3.65787i	0.0879185	−	0.152279i	−0.818713	−	0.574203i	$-0.805312\pi$
$577$	2.11188	−	3.65787i	0.0879185	−	0.152279i	0.906631	+	0.421924i	$0.138645\pi$
$578$		0			0
$579$	−1.04248	−	7.91839i	−0.0433238	−	0.329077i
$580$		0			0
$581$	13.8242	−	5.35270i	0.573523	−	0.222068i
$582$		0			0
$583$	5.02545	+	1.34657i	0.208133	+	0.0557690i
$584$		0			0
$585$	1.14699	−	0.307336i	0.0474223	−	0.0127068i
$586$		0			0
$587$	15.2109	−	6.30058i	0.627823	−	0.260053i	−0.0460049	−	0.998941i	$-0.514649\pi$
$587$	15.2109	−	6.30058i	0.627823	−	0.260053i	0.673828	+	0.738888i	$0.264649\pi$
$588$		0			0
$589$	−1.40529	+	3.39266i	−0.0579038	+	0.139792i
$590$		0			0
$591$	−25.1980	−	14.5481i	−1.03651	−	0.598428i
$592$		0			0
$593$	−9.79845	+	5.65714i	−0.402374	+	0.232311i	−0.687508	−	0.726177i	$-0.741295\pi$
$593$	−9.79845	+	5.65714i	−0.402374	+	0.232311i	0.285134	+	0.958488i	$0.407962\pi$
$594$		0			0
$595$	−4.43147	−	1.95762i	−0.181672	−	0.0802545i
$596$		0			0
$597$	−27.1269	−	20.8152i	−1.11023	−	0.851911i
$598$		0			0
$599$	9.57873	−	2.56661i	0.391376	−	0.104869i	−0.0577638	−	0.998330i	$-0.518397\pi$
$599$	9.57873	−	2.56661i	0.391376	−	0.104869i	0.449140	+	0.893461i	$0.351730\pi$
$600$		0			0
$601$	16.7676	−	16.7676i	0.683965	−	0.683965i	−0.276926	−	0.960891i	$-0.589316\pi$
$601$	16.7676	−	16.7676i	0.683965	−	0.683965i	0.960891	+	0.276926i	$0.0893158\pi$
$602$		0			0
$603$	−4.52382	−	10.9215i	−0.184224	−	0.444756i
$604$		0			0
$605$	−1.26038	+	0.967121i	−0.0512416	+	0.0393191i
$606$		0			0
$607$	20.8181	+	36.0580i	0.844980	+	1.46355i	0.885639	+	0.464374i	$0.153721\pi$
$607$	20.8181	+	36.0580i	0.844980	+	1.46355i	−0.0406594	+	0.999173i	$0.512946\pi$
$608$		0			0
$609$	−10.4066	−	6.33571i	−0.421698	−	0.256736i
$610$		0			0
$611$	−0.737798	−	5.60413i	−0.0298481	−	0.226719i
$612$		0			0
$613$	−21.7628	−	2.86513i	−0.878992	−	0.115721i	−0.322495	−	0.946571i	$-0.604522\pi$
$613$	−21.7628	−	2.86513i	−0.878992	−	0.115721i	−0.556497	+	0.830850i	$0.687855\pi$
$614$		0			0
$615$	−6.11602	+	6.11602i	−0.246622	+	0.246622i
$616$		0			0
$617$	−2.34370	−	2.34370i	−0.0943536	−	0.0943536i	0.658354	−	0.752708i	$-0.271253\pi$
$617$	−2.34370	−	2.34370i	−0.0943536	−	0.0943536i	−0.752708	+	0.658354i	$0.771253\pi$
$618$		0			0
$619$	2.60758	−	19.8065i	0.104807	−	0.796091i	−0.855629	−	0.517590i	$-0.826829\pi$
$619$	2.60758	−	19.8065i	0.104807	−	0.796091i	0.960436	−	0.278501i	$-0.0898375\pi$
$620$		0			0
$621$	1.25919	−	0.165775i	0.0505294	−	0.00665233i
$622$		0			0
$623$	−14.8688	−	27.1962i	−0.595704	−	1.08959i
$624$		0			0
$625$	−20.3356	+	11.7408i	−0.813426	+	0.469631i
$626$		0			0
$627$	5.97890	+	7.79185i	0.238774	+	0.311177i
$628$		0			0
$629$	−44.8795	+	18.5897i	−1.78946	+	0.741220i
$630$		0			0
$631$	−10.1536	−	10.1536i	−0.404209	−	0.404209i	0.475505	−	0.879713i	$-0.342265\pi$
$631$	−10.1536	−	10.1536i	−0.404209	−	0.404209i	−0.879713	+	0.475505i	$0.842265\pi$
$632$		0			0
$633$	13.6673	+	51.0071i	0.543227	+	2.02735i
$634$		0			0
$635$	−2.50862	+	3.26930i	−0.0995517	+	0.129738i
$636$		0			0
$637$	10.9027	+	5.12282i	0.431981	+	0.202973i
$638$		0			0
$639$	17.4812	+	30.2784i	0.691547	+	1.19779i
$640$		0			0
$641$	20.3581	−	35.2612i	0.804096	−	1.39273i	−0.112804	−	0.993617i	$-0.535983\pi$
$641$	20.3581	−	35.2612i	0.804096	−	1.39273i	0.916900	−	0.399117i	$-0.130683\pi$
$642$		0			0
$643$	14.6195	+	6.05560i	0.576538	+	0.238810i	0.651847	−	0.758351i	$-0.273994\pi$
$643$	14.6195	+	6.05560i	0.576538	+	0.238810i	−0.0753093	+	0.997160i	$0.523994\pi$
$644$		0			0
$645$	3.06132	+	7.39067i	0.120539	+	0.291007i
$646$		0			0
$647$	−3.32881	−	12.4233i	−0.130869	−	0.488410i	0.869112	−	0.494616i	$-0.164691\pi$
$647$	−3.32881	−	12.4233i	−0.130869	−	0.488410i	−0.999981	+	0.00620565i	$0.998025\pi$
$648$		0			0
$649$	1.66828	−	6.22610i	0.0654856	−	0.244396i
$650$		0			0
$651$	−7.85795	+	9.76158i	−0.307977	+	0.382586i
$652$		0			0
$653$	9.45343	−	1.24457i	0.369941	−	0.0487037i	0.0567361	−	0.998389i	$-0.481931\pi$
$653$	9.45343	−	1.24457i	0.369941	−	0.0487037i	0.313205	+	0.949686i	$0.398597\pi$
$654$		0			0
$655$	1.26975	+	0.733093i	0.0496134	+	0.0286443i
$656$		0			0
$657$			18.9608i			0.739730i
$658$		0			0
$659$	−8.51868	+	20.5659i	−0.331841	+	0.801134i	0.666606	+	0.745411i	$0.267747\pi$
$659$	−8.51868	+	20.5659i	−0.331841	+	0.801134i	−0.998446	+	0.0557237i	$0.982253\pi$
$660$		0			0
$661$	−0.981033	+	7.45168i	−0.0381578	+	0.289837i	0.961718	+	0.274043i	$0.0883610\pi$
$661$	−0.981033	+	7.45168i	−0.0381578	+	0.289837i	−0.999875	+	0.0157942i	$0.994972\pi$
$662$		0			0
$663$	−5.80378	+	21.6600i	−0.225400	+	0.841204i
$664$		0			0
$665$	1.44566	−	0.351514i	0.0560601	−	0.0136311i
$666$		0			0
$667$	−0.822551	+	1.07197i	−0.0318493	+	0.0415068i
$668$		0			0
$669$	3.72407	−	2.85758i	0.143981	−	0.110481i
$670$		0			0
$671$	−21.0117			−0.811149
$672$		0			0
$673$	−13.8723			−0.534736			−0.267368	−	0.963594i	$-0.586154\pi$
$673$	−13.8723			−0.534736			−0.267368	+	0.963594i	$0.586154\pi$
$674$		0			0
$675$	7.40357	−	5.68096i	0.284963	−	0.218660i
$676$		0			0
$677$	−6.80004	+	8.86198i	−0.261347	+	0.340594i	−0.905534	−	0.424274i	$-0.860529\pi$
$677$	−6.80004	+	8.86198i	−0.261347	+	0.340594i	0.644187	+	0.764868i	$0.277196\pi$
$678$		0			0
$679$	−4.92521	−	5.15999i	−0.189012	−	0.198022i
$680$		0			0
$681$	12.5355	−	46.7831i	0.480361	−	1.79273i
$682$		0			0
$683$	−0.852246	+	6.47345i	−0.0326103	+	0.247700i	−0.999984	−	0.00565391i	$-0.998200\pi$
$683$	−0.852246	+	6.47345i	−0.0326103	+	0.247700i	0.967374	+	0.253354i	$0.0815336\pi$
$684$		0			0
$685$	0.986468	−	2.38154i	0.0376910	−	0.0909942i
$686$		0			0
$687$		−	11.6241i		−	0.443488i
$688$		0			0
$689$	−3.15924	−	1.82399i	−0.120357	−	0.0694884i
$690$		0			0
$691$	7.82194	−	1.02978i	0.297561	−	0.0391746i	0.0197321	−	0.999805i	$-0.493719\pi$
$691$	7.82194	−	1.02978i	0.297561	−	0.0391746i	0.277828	+	0.960631i	$0.410385\pi$
$692$		0			0
$693$	5.06773	+	13.0882i	0.192507	+	0.497179i
$694$		0			0
$695$	−1.12518	+	4.19923i	−0.0426806	+	0.159286i
$696$		0			0
$697$	−17.7028	−	66.0679i	−0.670543	−	2.50250i
$698$		0			0
$699$	−3.29430	−	7.95315i	−0.124602	−	0.300816i
$700$		0			0
$701$	47.2215	+	19.5598i	1.78353	+	0.738764i	0.991785	+	0.127916i	$0.0408289\pi$
$701$	47.2215	+	19.5598i	1.78353	+	0.738764i	0.791748	+	0.610847i	$0.209171\pi$
$702$		0			0
$703$	7.45904	−	12.9194i	0.281323	−	0.487266i
$704$		0			0
$705$	−1.19116	−	2.06315i	−0.0448617	−	0.0777027i
$706$		0			0
$707$	−7.47752	−	10.2293i	−0.281221	−	0.384714i
$708$		0			0
$709$	−13.7737	+	17.9503i	−0.517283	+	0.674136i	−0.976830	−	0.214017i	$-0.931345\pi$
$709$	−13.7737	+	17.9503i	−0.517283	+	0.674136i	0.459547	+	0.888153i	$0.348012\pi$
$710$		0			0
$711$	−1.08157	−	4.03646i	−0.0405619	−	0.151379i
$712$		0			0
$713$	0.982710	+	0.982710i	0.0368028	+	0.0368028i
$714$		0			0
$715$	−1.24576	+	0.516011i	−0.0465888	+	0.0192977i
$716$		0			0
$717$	−33.6263	−	43.8227i	−1.25580	−	1.63659i
$718$		0			0
$719$	15.9413	−	9.20372i	0.594510	−	0.343241i	−0.172369	−	0.985033i	$-0.555142\pi$
$719$	15.9413	−	9.20372i	0.594510	−	0.343241i	0.766879	+	0.641792i	$0.221809\pi$
$720$		0			0
$721$	19.8478	+	36.3033i	0.739170	+	1.35201i
$722$		0			0
$723$	−25.1855	+	3.31573i	−0.936658	+	0.123313i
$724$		0			0
$725$	−1.29588	+	9.84321i	−0.0481279	+	0.365568i
$726$		0			0
$727$	−24.7183	−	24.7183i	−0.916751	−	0.916751i	0.0800404	−	0.996792i	$-0.474495\pi$
$727$	−24.7183	−	24.7183i	−0.916751	−	0.916751i	−0.996792	+	0.0800404i	$0.974495\pi$
$728$		0			0
$729$	7.34313	−	7.34313i	0.271968	−	0.271968i
$730$		0			0
$731$	−62.7191	−	8.25713i	−2.31975	−	0.305401i
$732$		0			0
$733$	−5.51579	−	41.8966i	−0.203730	−	1.54749i	−0.721772	−	0.692131i	$-0.756672\pi$
$733$	−5.51579	−	41.8966i	−0.203730	−	1.54749i	0.518042	−	0.855355i	$-0.326661\pi$
$734$		0			0
$735$	5.07156	+	0.236264i	0.187067	+	0.00871474i
$736$		0			0
$737$	6.71179	+	11.6252i	0.247232	+	0.428218i
$738$		0			0
$739$	−4.39884	+	3.37535i	−0.161814	+	0.124164i	−0.686494	−	0.727135i	$-0.740851\pi$
$739$	−4.39884	+	3.37535i	−0.161814	+	0.124164i	0.524681	+	0.851299i	$0.324185\pi$
$740$		0			0
$741$	−2.63533	−	6.36224i	−0.0968111	−	0.233723i
$742$		0			0
$743$	24.7435	−	24.7435i	0.907752	−	0.907752i	−0.0883382	−	0.996091i	$-0.528156\pi$
$743$	24.7435	−	24.7435i	0.907752	−	0.907752i	0.996091	+	0.0883382i	$0.0281556\pi$
$744$		0			0
$745$	−3.90038	+	1.04510i	−0.142899	+	0.0382897i
$746$		0			0
$747$	−9.60775	−	7.37228i	−0.351529	−	0.269738i
$748$		0			0
$749$	0.0940697	+	0.870685i	0.00343723	+	0.0318141i
$750$		0			0
$751$	−4.86579	+	2.80926i	−0.177555	+	0.102512i	−0.586143	−	0.810207i	$-0.699355\pi$
$751$	−4.86579	+	2.80926i	−0.177555	+	0.102512i	0.408588	+	0.912719i	$0.366021\pi$
$752$		0			0
$753$	−27.1805	−	15.6927i	−0.990513	−	0.571873i
$754$		0			0
$755$	1.49276	−	3.60385i	0.0543272	−	0.131157i
$756$		0			0
$757$	18.0749	−	7.48687i	0.656944	−	0.272115i	−0.0292081	−	0.999573i	$-0.509299\pi$
$757$	18.0749	−	7.48687i	0.656944	−	0.272115i	0.686152	+	0.727458i	$0.259299\pi$
$758$		0			0
$759$	3.59032	−	0.962023i	0.130320	−	0.0349192i
$760$		0			0
$761$	2.72292	+	0.729605i	0.0987059	+	0.0264482i	0.307834	−	0.951440i	$-0.400396\pi$
$761$	2.72292	+	0.729605i	0.0987059	+	0.0264482i	−0.209128	+	0.977888i	$0.567063\pi$
$762$		0			0
$763$	−5.08109	+	32.6949i	−0.183948	+	1.18364i
$764$		0			0
$765$	0.516580	+	3.92381i	0.0186770	+	0.141866i
$766$		0			0
$767$	−2.25976	+	3.91402i	−0.0815953	+	0.141327i
$768$		0			0
$769$	39.8241			1.43609			0.718046	−	0.695995i	$-0.245037\pi$
$769$	39.8241			1.43609			0.718046	+	0.695995i	$0.245037\pi$
$770$		0			0
$771$	27.5880	+	11.4273i	0.993556	+	0.411545i
$772$		0			0
$773$	39.2695	+	5.16993i	1.41243	+	0.185949i	0.797825	−	0.602889i	$-0.205984\pi$
$773$	39.2695	+	5.16993i	1.41243	+	0.185949i	0.614601	+	0.788838i	$0.289317\pi$
$774$		0			0
$775$	9.86363	+	2.64295i	0.354312	+	0.0949377i
$776$		0			0
$777$	36.8256	−	35.1499i	1.32111	−	1.26100i
$778$		0			0
$779$	16.6646	+	12.7872i	0.597070	+	0.458148i
$780$		0			0
$781$	−24.1686	−	31.4972i	−0.864821	−	1.12706i
$782$		0			0
$783$		−	3.86181i		−	0.138010i
$784$		0			0
$785$		−	4.56718i		−	0.163010i
$786$		0			0
$787$	21.5173	+	28.0419i	0.767009	+	0.999585i	0.999635	+	0.0270188i	$0.00860141\pi$
$787$	21.5173	+	28.0419i	0.767009	+	0.999585i	−0.232626	+	0.972566i	$0.574732\pi$
$788$		0			0
$789$	−5.97947	−	4.58821i	−0.212875	−	0.163345i
$790$		0			0
$791$	36.4535	−	34.7948i	1.29614	−	1.23716i
$792$		0			0
$793$	14.2307	+	3.81311i	0.505347	+	0.135407i
$794$		0			0
$795$	−1.52434	−	0.200683i	−0.0540626	−	0.00711748i
$796$		0			0
$797$	25.7639	+	10.6718i	0.912605	+	0.378013i	0.789053	−	0.614325i	$-0.210572\pi$
$797$	25.7639	+	10.6718i	0.912605	+	0.378013i	0.123552	+	0.992338i	$0.460572\pi$
$798$		0			0
$799$	18.8392			0.666484
$800$		0			0
$801$	−12.6605	+	21.9285i	−0.447335	+	0.774807i
$802$		0			0
$803$	−2.81032	−	21.3465i	−0.0991741	−	0.753302i
$804$		0			0
$805$	0.0864666	−	0.556380i	0.00304755	−	0.0196098i
$806$		0			0
$807$	−11.1696	−	2.99288i	−0.393188	−	0.105354i
$808$		0			0
$809$	42.8073	−	11.4702i	1.50502	−	0.403270i	0.590245	−	0.807224i	$-0.299031\pi$
$809$	42.8073	−	11.4702i	1.50502	−	0.403270i	0.914779	+	0.403954i	$0.132364\pi$
$810$		0			0
$811$	−25.7149	+	10.6515i	−0.902974	+	0.374024i	−0.785363	−	0.619036i	$-0.787524\pi$
$811$	−25.7149	+	10.6515i	−0.902974	+	0.374024i	−0.117611	+	0.993060i	$0.537524\pi$
$812$		0			0
$813$	17.4134	−	42.0398i	0.610716	−	1.47440i
$814$		0			0
$815$	−0.750512	−	0.433309i	−0.0262893	−	0.0151781i
$816$		0			0
$817$	16.8245	−	9.71363i	0.588615	−	0.339837i
$818$		0			0
$819$	−1.05707	−	9.78395i	−0.0369369	−	0.341879i
$820$		0			0
$821$	30.5936	+	23.4753i	1.06772	+	0.819293i	0.984173	−	0.177211i	$-0.0567075\pi$
$821$	30.5936	+	23.4753i	1.06772	+	0.819293i	0.0835500	+	0.996504i	$0.473374\pi$
$822$		0			0
$823$	39.5934	−	10.6090i	1.38014	−	0.369808i	0.508968	−	0.860785i	$-0.330027\pi$
$823$	39.5934	−	10.6090i	1.38014	−	0.369808i	0.871172	+	0.490978i	$0.163360\pi$
$824$		0			0
$825$	19.3120	−	19.3120i	0.672357	−	0.672357i
$826$		0			0
$827$	−4.21400	−	10.1735i	−0.146535	−	0.353767i	0.833521	−	0.552488i	$-0.186321\pi$
$827$	−4.21400	−	10.1735i	−0.146535	−	0.353767i	−0.980056	+	0.198721i	$0.936321\pi$
$828$		0			0
$829$	−39.5155	+	30.3213i	−1.37243	+	1.05310i	−0.380709	+	0.924695i	$0.624320\pi$
$829$	−39.5155	+	30.3213i	−1.37243	+	1.05310i	−0.991721	+	0.128407i	$0.959013\pi$
$830$		0			0
$831$	27.1248	+	46.9815i	0.940949	+	1.62977i
$832$		0			0
$833$	−21.6708	+	33.7983i	−0.750850	+	1.17104i
$834$		0			0
$835$	0.920206	+	6.98965i	0.0318450	+	0.241887i
$836$		0			0
$837$	−3.93808	−	0.518458i	−0.136120	−	0.0179205i
$838$		0			0
$839$	19.4736	−	19.4736i	0.672304	−	0.672304i	−0.285942	−	0.958247i	$-0.592307\pi$
$839$	19.4736	−	19.4736i	0.672304	−	0.672304i	0.958247	+	0.285942i	$0.0923066\pi$
$840$		0			0
$841$	−17.6009	−	17.6009i	−0.606929	−	0.606929i
$842$		0			0
$843$	4.14832	−	31.5096i	0.142876	−	1.08525i
$844$		0			0
$845$	−3.17739	+	0.418311i	−0.109305	+	0.0143903i
$846$		0			0
$847$	6.31581	+	11.5521i	0.217014	+	0.396936i
$848$		0			0
$849$	34.3845	−	19.8519i	1.18007	−	0.681316i
$850$		0			0
$851$	−3.43697	−	4.47914i	−0.117818	−	0.153543i
$852$		0			0
$853$	19.5019	−	8.07795i	0.667732	−	0.276584i	−0.0229560	−	0.999736i	$-0.507308\pi$
$853$	19.5019	−	8.07795i	0.667732	−	0.276584i	0.690688	+	0.723153i	$0.257308\pi$
$854$		0			0
$855$	−0.859419	−	0.859419i	−0.0293915	−	0.0293915i
$856$		0			0
$857$	3.94440	+	14.7207i	0.134738	+	0.502850i	0.999999	+	0.00152754i	$0.000486231\pi$
$857$	3.94440	+	14.7207i	0.134738	+	0.502850i	−0.865261	+	0.501322i	$0.832847\pi$
$858$		0			0
$859$	18.8988	−	24.6294i	0.644819	−	0.840345i	−0.350543	−	0.936547i	$-0.614003\pi$
$859$	18.8988	−	24.6294i	0.644819	−	0.840345i	0.995362	+	0.0962021i	$0.0306695\pi$
$860$		0			0
$861$	42.3010	+	57.8682i	1.44161	+	1.97214i
$862$		0			0
$863$	4.26214	+	7.38224i	0.145085	+	0.251294i	0.929405	−	0.369062i	$-0.120321\pi$
$863$	4.26214	+	7.38224i	0.145085	+	0.251294i	−0.784320	+	0.620357i	$0.786988\pi$
$864$		0			0
$865$	−3.58929	+	6.21684i	−0.122040	+	0.211379i
$866$		0			0
$867$	−33.3665	−	13.8208i	−1.13319	−	0.469381i
$868$		0			0
$869$	1.81593	+	4.38404i	0.0616012	+	0.148718i
$870$		0			0
$871$	−2.43604	−	9.09144i	−0.0825422	−	0.308052i
$872$		0			0
$873$	−1.50822	+	5.62876i	−0.0510456	+	0.190505i
$874$		0			0
$875$	−3.01878	−	7.79645i	−0.102053	−	0.263568i
$876$		0			0
$877$	−36.6840	+	4.82955i	−1.23873	+	0.163082i	−0.721288	−	0.692635i	$-0.756450\pi$
$877$	−36.6840	+	4.82955i	−1.23873	+	0.163082i	−0.517444	+	0.855717i	$0.673116\pi$
$878$		0			0
$879$	46.1671	+	26.6546i	1.55718	+	0.899036i
$880$		0			0
$881$		−	40.2583i		−	1.35634i	−0.734907	−	0.678168i	$-0.762774\pi$
$881$		−	40.2583i		−	1.35634i	0.734907	−	0.678168i	$-0.237226\pi$
$882$		0			0
$883$	0.177156	−	0.427692i	0.00596177	−	0.0143930i	−0.920871	−	0.389868i	$-0.872521\pi$
$883$	0.177156	−	0.427692i	0.00596177	−	0.0143930i	0.926832	+	0.375475i	$0.122521\pi$
$884$		0			0
$885$	−0.248628	+	1.88852i	−0.00835755	+	0.0634819i
$886$		0			0
$887$	2.57989	−	9.62826i	0.0866241	−	0.323285i	−0.908993	−	0.416812i	$-0.863147\pi$
$887$	2.57989	−	9.62826i	0.0866241	−	0.323285i	0.995617	+	0.0935266i	$0.0298140\pi$
$888$		0			0
$889$	23.5800	+	24.7040i	0.790846	+	0.828547i
$890$		0			0
$891$	−16.1551	+	21.0537i	−0.541216	+	0.705327i
$892$		0			0
$893$	−4.58997	+	3.52201i	−0.153597	+	0.117860i
$894$		0			0
$895$	−2.54858			−0.0851896
$896$		0			0
$897$	−2.60621			−0.0870190
$898$		0			0
$899$	3.35256	−	2.57251i	0.111814	−	0.0857980i
$900$		0			0
$901$	7.40154	−	9.64588i	0.246581	−	0.321351i
$902$		0			0
$903$	64.4188	−	15.6636i	2.14372	−	0.521251i
$904$		0			0
$905$	−1.75233	+	6.53977i	−0.0582493	+	0.217389i
$906$		0			0
$907$	3.68492	−	27.9898i	0.122356	−	0.929385i	−0.814621	−	0.579993i	$-0.803055\pi$
$907$	3.68492	−	27.9898i	0.122356	−	0.929385i	0.936977	−	0.349391i	$-0.113612\pi$
$908$		0			0
$909$	−3.96123	+	9.56326i	−0.131386	+	0.317193i
$910$		0			0
$911$		−	32.5601i		−	1.07876i	−0.842061	−	0.539382i	$-0.818658\pi$
$911$		−	32.5601i		−	1.07876i	0.842061	−	0.539382i	$-0.181342\pi$
$912$		0			0
$913$	11.9094	+	6.87587i	0.394142	+	0.227558i
$914$		0			0
$915$	6.15618	−	0.810477i	0.203517	−	0.0267935i
$916$		0			0
$917$	7.61932	−	9.46514i	0.251612	−	0.312567i
$918$		0			0
$919$	−1.14848	+	4.28617i	−0.0378848	+	0.141388i	−0.982278	−	0.187431i	$-0.939984\pi$
$919$	−1.14848	+	4.28617i	−0.0378848	+	0.141388i	0.944393	+	0.328819i	$0.106651\pi$
$920$		0			0
$921$	9.64404	+	35.9921i	0.317782	+	1.18598i
$922$		0			0
$923$	10.6528	+	25.7182i	0.350642	+	0.846525i
$924$		0			0
$925$	−38.3263	−	15.8753i	−1.26016	−	0.521975i
$926$		0			0
$927$	16.9000	−	29.2716i	0.555069	−	0.961407i
$928$		0			0
$929$	20.8495	+	36.1123i	0.684048	+	1.18481i	0.973735	+	0.227685i	$0.0731156\pi$
$929$	20.8495	+	36.1123i	0.684048	+	1.18481i	−0.289687	+	0.957122i	$0.593551\pi$
$930$		0			0
$931$	−1.03875	−	12.2860i	−0.0340437	−	0.402656i
$932$		0			0
$933$	−37.2770	+	48.5803i	−1.22039	+	1.59045i
$934$		0			0
$935$	−1.16316	−	4.34096i	−0.0380393	−	0.141965i
$936$		0			0
$937$	4.20711	+	4.20711i	0.137440	+	0.137440i	0.772480	−	0.635039i	$-0.219016\pi$
$937$	4.20711	+	4.20711i	0.137440	+	0.137440i	−0.635039	+	0.772480i	$0.719016\pi$
$938$		0			0
$939$	41.3784	−	17.1395i	1.35033	−	0.559327i
$940$		0			0
$941$	−20.2223	−	26.3542i	−0.659227	−	0.859122i	0.337385	−	0.941367i	$-0.390458\pi$
$941$	−20.2223	−	26.3542i	−0.659227	−	0.859122i	−0.996612	+	0.0822452i	$0.973791\pi$
$942$		0			0
$943$	6.88451	−	3.97477i	0.224191	−	0.129436i
$944$		0			0
$945$	0.771981	+	1.41202i	0.0251125	+	0.0459330i
$946$		0			0
$947$	−2.91230	+	0.383412i	−0.0946372	+	0.0124592i	−0.177696	−	0.984085i	$-0.556864\pi$
$947$	−2.91230	+	0.383412i	−0.0946372	+	0.0124592i	0.0830589	+	0.996545i	$0.473531\pi$
$948$		0			0
$949$	−1.97050	+	14.9674i	−0.0639652	+	0.485864i
$950$		0			0
$951$	47.2949	+	47.2949i	1.53364	+	1.53364i
$952$		0			0
$953$	−17.9785	+	17.9785i	−0.582381	+	0.582381i	−0.935557	−	0.353176i	$-0.885102\pi$
$953$	−17.9785	+	17.9785i	−0.582381	+	0.582381i	0.353176	+	0.935557i	$0.385102\pi$
$954$		0			0
$955$	4.58442	+	0.603550i	0.148348	+	0.0195304i
$956$		0			0
$957$	−1.47522	−	11.2054i	−0.0476871	−	0.362219i
$958$		0			0
$959$	−18.2472	−	11.1092i	−0.589234	−	0.358734i
$960$		0			0
$961$	13.3268	+	23.0827i	0.429896	+	0.744602i
$962$		0			0
$963$	0.567584	−	0.435522i	0.0182901	−	0.0140345i
$964$		0			0
$965$	−0.429494	−	1.03689i	−0.0138259	−	0.0333787i
$966$		0			0
$967$	15.2201	−	15.2201i	0.489444	−	0.489444i	−0.418687	−	0.908131i	$-0.637509\pi$
$967$	15.2201	−	15.2201i	0.489444	−	0.489444i	0.908131	+	0.418687i	$0.137509\pi$
$968$		0			0
$969$	22.1698	−	5.94038i	0.712196	−	0.190832i
$970$		0			0
$971$	18.2469	+	14.0013i	0.585571	+	0.449324i	0.858574	−	0.512689i	$-0.171351\pi$
$971$	18.2469	+	14.0013i	0.585571	+	0.449324i	−0.273004	+	0.962013i	$0.588017\pi$
$972$		0			0
$973$	32.9559	+	14.5584i	1.05652	+	0.466721i
$974$		0			0
$975$	−16.5842	+	9.57487i	−0.531118	+	0.306641i
$976$		0			0
$977$	−27.2242	−	15.7179i	−0.870979	−	0.502860i	−0.00330528	−	0.999995i	$-0.501052\pi$
$977$	−27.2242	−	15.7179i	−0.870979	−	0.502860i	−0.867673	+	0.497135i	$0.834385\pi$
$978$		0			0
$979$	11.0033	−	26.5642i	0.351666	−	0.848996i
$980$		0			0
$981$	24.9724	−	10.3439i	0.797306	−	0.330255i
$982$		0			0
$983$	−7.64190	+	2.04764i	−0.243739	+	0.0653096i	−0.378620	−	0.925552i	$-0.623601\pi$
$983$	−7.64190	+	2.04764i	−0.243739	+	0.0653096i	0.134881	+	0.990862i	$0.456935\pi$
$984$		0			0
$985$	−3.94938	−	1.05823i	−0.125838	−	0.0337181i
$986$		0			0
$987$	−18.4112	+	7.12882i	−0.586036	+	0.226913i
$988$		0			0
$989$	−0.959677	−	7.28947i	−0.0305159	−	0.231792i
$990$		0			0
$991$	−7.38697	+	12.7946i	−0.234655	+	0.406434i	−0.959172	−	0.282822i	$-0.908729\pi$
$991$	−7.38697	+	12.7946i	−0.234655	+	0.406434i	0.724517	+	0.689256i	$0.242063\pi$
$992$		0			0
$993$	−76.6729			−2.43314
$994$		0			0
$995$	−4.43913	−	1.83875i	−0.140730	−	0.0582923i
$996$		0			0
$997$	−52.7135	−	6.93987i	−1.66945	−	0.219788i	−0.764297	−	0.644865i	$-0.776914\pi$
$997$	−52.7135	−	6.93987i	−1.66945	−	0.219788i	−0.905157	+	0.425077i	$0.860247\pi$
$998$		0			0
$999$	15.5865	+	4.17638i	0.493134	+	0.132135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.5		240
4.3	odd	2		224.2.bd.a.221.17	yes	240
7.2	even	3	inner	896.2.bh.a.849.5		240
28.23	odd	6		224.2.bd.a.93.4	yes	240
32.11	odd	8		224.2.bd.a.53.4	✓	240
32.21	even	8	inner	896.2.bh.a.305.5		240
224.107	odd	24		224.2.bd.a.149.17	yes	240
224.149	even	24	inner	896.2.bh.a.177.5		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.4	✓	240	32.11	odd	8
224.2.bd.a.93.4	yes	240	28.23	odd	6
224.2.bd.a.149.17	yes	240	224.107	odd	24
224.2.bd.a.221.17	yes	240	4.3	odd	2
896.2.bh.a.81.5		240	1.1	even	1	trivial
896.2.bh.a.177.5		240	224.149	even	24	inner
896.2.bh.a.305.5		240	32.21	even	8	inner
896.2.bh.a.849.5		240	7.2	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80239 + 1.38302i) q^{3} +(-0.194347 + 0.253278i) q^{5} +(1.82678 + 1.91386i) q^{7} +(0.559406 - 2.08773i) q^{9} +O(q^{10})\)	\(q+(-1.80239 + 1.38302i) q^{3} +(-0.194347 + 0.253278i) q^{5} +(1.82678 + 1.91386i) q^{7} +(0.559406 - 2.08773i) q^{9} +(-0.320355 + 2.43334i) q^{11} +(0.658558 - 1.58990i) q^{13} -0.725295i q^{15} +(4.96716 + 2.86779i) q^{17} +(-1.74633 + 0.229909i) q^{19} +(-5.93950 - 0.923053i) q^{21} +(-0.172532 + 0.643898i) q^{23} +(1.26772 + 4.73118i) q^{25} +(-0.729102 - 1.76021i) q^{27} +(1.87266 + 0.775679i) q^{29} +(1.04241 - 1.80550i) q^{31} +(-2.78796 - 4.82889i) q^{33} +(-0.839770 + 0.0907296i) q^{35} +(-5.15588 + 6.71927i) q^{37} +(1.01189 + 3.77642i) q^{39} +(-8.43246 - 8.43246i) q^{41} +(-10.1899 + 4.22079i) q^{43} +(0.420058 + 0.547431i) q^{45} +(2.84457 - 1.64231i) q^{47} +(-0.325749 + 6.99242i) q^{49} +(-12.9190 + 1.70082i) q^{51} +(0.276691 - 2.10168i) q^{53} +(-0.554051 - 0.554051i) q^{55} +(2.82960 - 2.82960i) q^{57} +(-2.60380 - 0.342796i) q^{59} +(1.11745 + 8.48784i) q^{61} +(5.01755 - 2.74320i) q^{63} +(0.274698 + 0.475791i) q^{65} +(4.33912 - 3.32952i) q^{67} +(-0.579556 - 1.39917i) q^{69} +(-11.4382 + 11.4382i) q^{71} +(-8.47361 + 2.27050i) q^{73} +(-8.82826 - 6.77417i) q^{75} +(-5.24229 + 3.83205i) q^{77} +(1.67439 - 0.966709i) q^{79} +(9.36397 + 5.40629i) q^{81} +(2.14419 - 5.17654i) q^{83} +(-1.69170 + 0.700727i) q^{85} +(-4.44805 + 1.19185i) q^{87} +(-11.3160 - 3.03211i) q^{89} +(4.24589 - 1.64401i) q^{91} +(0.618227 + 4.69590i) q^{93} +(0.281164 - 0.486990i) q^{95} -2.69611 q^{97} +(4.90094 + 2.03004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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Database

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