LMFDB - Embedded newform 896.2.bh.a.753.7

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			753.7
Character	$\chi$	$=$	896.753
Dual form			896.2.bh.a.401.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70169 - 0.224032i) q^{3} +(0.296167 + 2.24961i) q^{5} +(-1.30976 - 2.29881i) q^{7} +(-0.0522197 - 0.0139922i) q^{9} +O(q^{10})$	\(q+(-1.70169 - 0.224032i) q^{3} +(0.296167 + 2.24961i) q^{5} +(-1.30976 - 2.29881i) q^{7} +(-0.0522197 - 0.0139922i) q^{9} +(-0.577665 - 0.752827i) q^{11} +(2.44244 - 1.01169i) q^{13} -3.89449i q^{15} +(-0.0434878 - 0.0251077i) q^{17} +(4.68988 + 3.59867i) q^{19} +(1.71379 + 4.20529i) q^{21} +(-0.220924 - 0.0591965i) q^{23} +(-0.143408 + 0.0384260i) q^{25} +(4.84289 + 2.00599i) q^{27} +(-0.876670 - 2.11647i) q^{29} +(-4.67044 + 8.08944i) q^{31} +(0.814349 + 1.41049i) q^{33} +(4.78353 - 3.62728i) q^{35} +(0.776202 + 5.89584i) q^{37} +(-4.38292 + 1.17440i) q^{39} +(1.81397 - 1.81397i) q^{41} +(-3.88053 + 9.36842i) q^{43} +(0.0160113 - 0.121618i) q^{45} +(5.15262 - 2.97487i) q^{47} +(-3.56907 + 6.02177i) q^{49} +(0.0683779 + 0.0524682i) q^{51} +(7.63303 + 9.94755i) q^{53} +(1.52248 - 1.52248i) q^{55} +(-7.17450 - 7.17450i) q^{57} +(6.92726 - 5.31547i) q^{59} +(1.09772 - 1.43058i) q^{61} +(0.0362297 + 0.138370i) q^{63} +(2.99928 + 5.19490i) q^{65} +(7.73959 + 1.01894i) q^{67} +(0.362683 + 0.150228i) q^{69} +(7.65167 + 7.65167i) q^{71} +(-0.206301 - 0.769926i) q^{73} +(0.252644 - 0.0332612i) q^{75} +(-0.974008 + 2.31396i) q^{77} +(-10.5808 + 6.10885i) q^{79} +(-7.65124 - 4.41745i) q^{81} +(13.0219 - 5.39387i) q^{83} +(0.0436030 - 0.105267i) q^{85} +(1.01766 + 3.79797i) q^{87} +(0.558378 - 2.08390i) q^{89} +(-5.52469 - 4.28963i) q^{91} +(9.75994 - 12.7194i) q^{93} +(-6.70662 + 11.6162i) q^{95} +18.1541 q^{97} +(0.0196318 + 0.0473953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

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

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
$3$	−1.70169	−	0.224032i	−0.982471	−	0.129345i	−0.377858	−	0.925864i	$-0.623339\pi$
$3$	−1.70169	−	0.224032i	−0.982471	−	0.129345i	−0.604614	+	0.796519i	$0.706672\pi$
$4$		0			0
$5$	0.296167	+	2.24961i	0.132450	+	1.00606i	0.920582	+	0.390550i	$0.127715\pi$
$5$	0.296167	+	2.24961i	0.132450	+	1.00606i	−0.788132	+	0.615507i	$0.788951\pi$
$6$		0			0
$7$	−1.30976	−	2.29881i	−0.495042	−	0.868869i
$7$	−1.30976	−	2.29881i	−0.495042	−	0.868869i
$8$		0			0
$9$	−0.0522197	−	0.0139922i	−0.0174066	−	0.00466408i
$10$		0			0
$11$	−0.577665	−	0.752827i	−0.174172	−	0.226986i	0.698107	−	0.715993i	$-0.254026\pi$
$11$	−0.577665	−	0.752827i	−0.174172	−	0.226986i	−0.872280	+	0.489007i	$0.837359\pi$
$12$		0			0
$13$	2.44244	−	1.01169i	0.677410	−	0.280592i	−0.0173337	−	0.999850i	$-0.505518\pi$
$13$	2.44244	−	1.01169i	0.677410	−	0.280592i	0.694744	+	0.719257i	$0.255518\pi$
$14$		0			0
$15$		−	3.89449i		−	1.00555i
$16$		0			0
$17$	−0.0434878	−	0.0251077i	−0.0105474	−	0.00608952i	0.494717	−	0.869054i	$-0.335272\pi$
$17$	−0.0434878	−	0.0251077i	−0.0105474	−	0.00608952i	−0.505264	+	0.862965i	$0.668605\pi$
$18$		0			0
$19$	4.68988	+	3.59867i	1.07593	+	0.825591i	0.985392	−	0.170302i	$-0.0544743\pi$
$19$	4.68988	+	3.59867i	1.07593	+	0.825591i	0.0905393	+	0.995893i	$0.471141\pi$
$20$		0			0
$21$	1.71379	+	4.20529i	0.373981	+	0.917670i
$22$		0			0
$23$	−0.220924	−	0.0591965i	−0.0460659	−	0.0123433i	0.235712	−	0.971823i	$-0.424258\pi$
$23$	−0.220924	−	0.0591965i	−0.0460659	−	0.0123433i	−0.281778	+	0.959480i	$0.590924\pi$
$24$		0			0
$25$	−0.143408	+	0.0384260i	−0.0286816	+	0.00768520i
$26$		0			0
$27$	4.84289	+	2.00599i	0.932015	+	0.386053i
$28$		0			0
$29$	−0.876670	−	2.11647i	−0.162793	−	0.393018i	0.821342	−	0.570436i	$-0.193226\pi$
$29$	−0.876670	−	2.11647i	−0.162793	−	0.393018i	−0.984136	+	0.177418i	$0.943226\pi$
$30$		0			0
$31$	−4.67044	+	8.08944i	−0.838836	+	1.45291i	0.0520321	+	0.998645i	$0.483430\pi$
$31$	−4.67044	+	8.08944i	−0.838836	+	1.45291i	−0.890868	+	0.454262i	$0.849903\pi$
$32$		0			0
$33$	0.814349	+	1.41049i	0.141760	+	0.245535i
$34$		0			0
$35$	4.78353	−	3.62728i	0.808563	−	0.613122i
$36$		0			0
$37$	0.776202	+	5.89584i	0.127607	+	0.969271i	0.928726	+	0.370766i	$0.120905\pi$
$37$	0.776202	+	5.89584i	0.127607	+	0.969271i	−0.801119	+	0.598505i	$0.795762\pi$
$38$		0			0
$39$	−4.38292	+	1.17440i	−0.701829	+	0.188054i
$40$		0			0
$41$	1.81397	−	1.81397i	0.283295	−	0.283295i	−0.551127	−	0.834422i	$-0.685802\pi$
$41$	1.81397	−	1.81397i	0.283295	−	0.283295i	0.834422	+	0.551127i	$0.185802\pi$
$42$		0			0
$43$	−3.88053	+	9.36842i	−0.591775	+	1.42867i	0.290012	+	0.957023i	$0.406341\pi$
$43$	−3.88053	+	9.36842i	−0.591775	+	1.42867i	−0.881787	+	0.471648i	$0.843659\pi$
$44$		0			0
$45$	0.0160113	−	0.121618i	0.00238683	−	0.0181298i
$46$		0			0
$47$	5.15262	−	2.97487i	0.751587	−	0.433929i	−0.0746801	−	0.997208i	$-0.523794\pi$
$47$	5.15262	−	2.97487i	0.751587	−	0.433929i	0.826267	+	0.563279i	$0.190460\pi$
$48$		0			0
$49$	−3.56907	+	6.02177i	−0.509867	+	0.860253i
$50$		0			0
$51$	0.0683779	+	0.0524682i	0.00957482	+	0.00734702i
$52$		0			0
$53$	7.63303	+	9.94755i	1.04848	+	1.36640i	0.927533	+	0.373742i	$0.121926\pi$
$53$	7.63303	+	9.94755i	1.04848	+	1.36640i	0.120944	+	0.992659i	$0.461408\pi$
$54$		0			0
$55$	1.52248	−	1.52248i	0.205292	−	0.205292i
$56$		0			0
$57$	−7.17450	−	7.17450i	−0.950285	−	0.950285i
$58$		0			0
$59$	6.92726	−	5.31547i	0.901852	−	0.692016i	−0.0499421	−	0.998752i	$-0.515904\pi$
$59$	6.92726	−	5.31547i	0.901852	−	0.692016i	0.951795	+	0.306736i	$0.0992370\pi$
$60$		0			0
$61$	1.09772	−	1.43058i	0.140549	−	0.183167i	−0.717775	−	0.696275i	$-0.754839\pi$
$61$	1.09772	−	1.43058i	0.140549	−	0.183167i	0.858324	+	0.513108i	$0.171506\pi$
$62$		0			0
$63$	0.0362297	+	0.138370i	0.00456451	+	0.0174330i
$64$		0			0
$65$	2.99928	+	5.19490i	0.372015	+	0.644349i
$66$		0			0
$67$	7.73959	+	1.01894i	0.945541	+	0.124483i	0.587501	−	0.809223i	$-0.300112\pi$
$67$	7.73959	+	1.01894i	0.945541	+	0.124483i	0.358040	+	0.933706i	$0.383445\pi$
$68$		0			0
$69$	0.362683	+	0.150228i	0.0436619	+	0.0180853i
$70$		0			0
$71$	7.65167	+	7.65167i	0.908086	+	0.908086i	0.996118	−	0.0880320i	$-0.0280578\pi$
$71$	7.65167	+	7.65167i	0.908086	+	0.908086i	−0.0880320	+	0.996118i	$0.528058\pi$
$72$		0			0
$73$	−0.206301	−	0.769926i	−0.0241457	−	0.0901130i	0.952802	−	0.303594i	$-0.0981866\pi$
$73$	−0.206301	−	0.769926i	−0.0241457	−	0.0901130i	−0.976947	+	0.213481i	$0.931520\pi$
$74$		0			0
$75$	0.252644	−	0.0332612i	0.0291728	−	0.00384068i
$76$		0			0
$77$	−0.974008	+	2.31396i	−0.110998	+	0.263701i
$78$		0			0
$79$	−10.5808	+	6.10885i	−1.19044	+	0.687299i	−0.958406	−	0.285409i	$-0.907871\pi$
$79$	−10.5808	+	6.10885i	−1.19044	+	0.687299i	−0.232032	+	0.972708i	$0.574537\pi$
$80$		0			0
$81$	−7.65124	−	4.41745i	−0.850138	−	0.490827i
$82$		0			0
$83$	13.0219	−	5.39387i	1.42934	−	0.592054i	0.472154	−	0.881516i	$-0.343476\pi$
$83$	13.0219	−	5.39387i	1.42934	−	0.592054i	0.957189	+	0.289462i	$0.0934765\pi$
$84$		0			0
$85$	0.0436030	−	0.105267i	0.00472940	−	0.0114178i
$86$		0			0
$87$	1.01766	+	3.79797i	0.109105	+	0.407185i
$88$		0			0
$89$	0.558378	−	2.08390i	0.0591880	−	0.220892i	−0.929997	−	0.367568i	$-0.880191\pi$
$89$	0.558378	−	2.08390i	0.0591880	−	0.220892i	0.989185	+	0.146675i	$0.0468573\pi$
$90$		0			0
$91$	−5.52469	−	4.28963i	−0.579144	−	0.449676i
$92$		0			0
$93$	9.75994	−	12.7194i	1.01206	−	1.31894i
$94$		0			0
$95$	−6.70662	+	11.6162i	−0.688085	+	1.19180i
$96$		0			0
$97$	18.1541			1.84327			0.921633	−	0.388063i	$-0.126856\pi$
$97$	18.1541			1.84327			0.921633	+	0.388063i	$0.126856\pi$
$98$		0			0
$99$	0.0196318	+	0.0473953i	0.00197307	+	0.00476341i
$100$		0			0
$101$	−4.96954	+	3.81326i	−0.494487	+	0.379433i	−0.825688	−	0.564127i	$-0.809213\pi$
$101$	−4.96954	+	3.81326i	−0.494487	+	0.379433i	0.331201	+	0.943560i	$0.392546\pi$
$102$		0			0
$103$	−0.109222	+	0.407621i	−0.0107619	+	0.0401641i	−0.971098	−	0.238681i	$-0.923285\pi$
$103$	−0.109222	+	0.407621i	−0.0107619	+	0.0401641i	0.960336	+	0.278845i	$0.0899516\pi$
$104$		0			0
$105$	−8.95270	+	5.10084i	−0.873694	+	0.497791i
$106$		0			0
$107$	−8.46800	+	1.11483i	−0.818632	+	0.107775i	−0.528199	−	0.849120i	$-0.677133\pi$
$107$	−8.46800	+	1.11483i	−0.818632	+	0.107775i	−0.290433	+	0.956895i	$0.593799\pi$
$108$		0			0
$109$	−0.897255	+	6.81533i	−0.0859414	+	0.652790i	0.893207	+	0.449645i	$0.148450\pi$
$109$	−0.897255	+	6.81533i	−0.0859414	+	0.652790i	−0.979149	+	0.203145i	$0.934884\pi$
$110$		0			0
$111$		−	10.2068i		−	0.968786i
$112$		0			0
$113$		−	17.1078i		−	1.60937i	−0.593705	−	0.804683i	$-0.702335\pi$
$113$		−	17.1078i		−	1.60937i	0.593705	−	0.804683i	$-0.297665\pi$
$114$		0			0
$115$	0.0677386	−	0.514526i	0.00631666	−	0.0479798i
$116$		0			0
$117$	−0.141699	+	0.0186551i	−0.0131001	+	0.00172466i
$118$		0			0
$119$	−0.000759378		0.132855i	−6.96120e−5		0.0121788i
$120$		0			0
$121$	2.61396	−	9.75542i	0.237632	−	0.886856i
$122$		0			0
$123$	−3.49321	+	2.68043i	−0.314972	+	0.241686i
$124$		0			0
$125$	4.21267	+	10.1703i	0.376793	+	0.909658i
$126$		0			0
$127$	3.31241			0.293928			0.146964	−	0.989142i	$-0.453050\pi$
$127$	3.31241			0.293928			0.146964	+	0.989142i	$0.453050\pi$
$128$		0			0
$129$	8.70228	−	15.0728i	0.766193	−	1.32708i
$130$		0			0
$131$	2.41360	−	3.14546i	0.210877	−	0.274820i	−0.675924	−	0.736971i	$-0.736255\pi$
$131$	2.41360	−	3.14546i	0.210877	−	0.274820i	0.886801	+	0.462151i	$0.152922\pi$
$132$		0			0
$133$	2.13006	−	15.4945i	0.184700	−	1.34355i
$134$		0			0
$135$	−3.07840	+	11.4887i	−0.264946	+	0.988793i
$136$		0			0
$137$	−2.68870	−	10.0344i	−0.229711	−	0.857294i	−0.980462	−	0.196708i	$-0.936975\pi$
$137$	−2.68870	−	10.0344i	−0.229711	−	0.857294i	0.750751	−	0.660585i	$-0.229692\pi$
$138$		0			0
$139$	−0.721994	+	1.74305i	−0.0612387	+	0.147843i	−0.951537	−	0.307535i	$-0.900496\pi$
$139$	−0.721994	+	1.74305i	−0.0612387	+	0.147843i	0.890298	+	0.455378i	$0.150496\pi$
$140$		0			0
$141$	−9.43463	+	3.90795i	−0.794539	+	0.329109i
$142$		0			0
$143$	−2.17254	−	1.25432i	−0.181677	−	0.104891i
$144$		0			0
$145$	4.50159	−	2.59899i	0.373837	−	0.215835i
$146$		0			0
$147$	7.42252	−	9.44760i	0.612199	−	0.779225i
$148$		0			0
$149$	−17.2594	+	2.27224i	−1.41394	+	0.186149i	−0.798481	−	0.602019i	$-0.794363\pi$
$149$	−17.2594	+	2.27224i	−1.41394	+	0.186149i	−0.615460	+	0.788168i	$0.711030\pi$
$150$		0			0
$151$	0.153216	+	0.571811i	0.0124686	+	0.0465333i	0.971880	−	0.235477i	$-0.0756653\pi$
$151$	0.153216	+	0.571811i	0.0124686	+	0.0465333i	−0.959411	+	0.282011i	$0.908999\pi$
$152$		0			0
$153$	0.00191961	+	0.00191961i	0.000155191	+	0.000155191i
$154$		0			0
$155$	−19.5813	−	8.11086i	−1.57281	−	0.651480i
$156$		0			0
$157$	−20.2829	−	2.67029i	−1.61875	−	0.213112i	−0.733989	−	0.679161i	$-0.762344\pi$
$157$	−20.2829	−	2.67029i	−1.61875	−	0.213112i	−0.884759	+	0.466049i	$0.845677\pi$
$158$		0			0
$159$	−10.7605	−	18.6377i	−0.853361	−	1.47806i
$160$		0			0
$161$	0.153276	+	0.585396i	0.0120798	+	0.0461357i
$162$		0			0
$163$	−6.33032	+	8.24984i	−0.495829	+	0.646177i	−0.972500	−	0.232905i	$-0.925177\pi$
$163$	−6.33032	+	8.24984i	−0.495829	+	0.646177i	0.476670	+	0.879082i	$0.341844\pi$
$164$		0			0
$165$	−2.93188	+	2.24971i	−0.228247	+	0.175140i
$166$		0			0
$167$	6.21642	+	6.21642i	0.481041	+	0.481041i	0.905464	−	0.424423i	$-0.139523\pi$
$167$	6.21642	+	6.21642i	0.481041	+	0.481041i	−0.424423	+	0.905464i	$0.639523\pi$
$168$		0			0
$169$	−4.25041	+	4.25041i	−0.326955	+	0.326955i
$170$		0			0
$171$	−0.194551	−	0.253543i	−0.0148777	−	0.0193889i
$172$		0			0
$173$	−4.73212	−	3.63108i	−0.359776	−	0.276066i	0.413018	−	0.910723i	$-0.364475\pi$
$173$	−4.73212	−	3.63108i	−0.359776	−	0.276066i	−0.772794	+	0.634657i	$0.781141\pi$
$174$		0			0
$175$	0.276164	+	0.279339i	0.0208760	+	0.0211160i
$176$		0			0
$177$	−12.9789	+	7.49336i	−0.975553	+	0.563236i
$178$		0			0
$179$	1.71689	−	13.0411i	0.128326	−	0.974736i	−0.799223	−	0.601035i	$-0.794755\pi$
$179$	1.71689	−	13.0411i	0.128326	−	0.974736i	0.927549	−	0.373701i	$-0.121911\pi$
$180$		0			0
$181$	−9.30204	+	22.4571i	−0.691415	+	1.66922i	0.0504948	+	0.998724i	$0.483920\pi$
$181$	−9.30204	+	22.4571i	−0.691415	+	1.66922i	−0.741910	+	0.670500i	$0.766080\pi$
$182$		0			0
$183$	−2.18848	+	2.18848i	−0.161777	+	0.161777i
$184$		0			0
$185$	−13.0335	+	3.49231i	−0.958240	+	0.256760i
$186$		0			0
$187$	0.00621962	+	0.0472427i	0.000454824	+	0.00345473i
$188$		0			0
$189$	−1.73162	−	13.7603i	−0.125957	−	1.00091i
$190$		0			0
$191$	−12.2545	−	21.2254i	−0.886705	−	1.53582i	−0.843747	−	0.536742i	$-0.819655\pi$
$191$	−12.2545	−	21.2254i	−0.886705	−	1.53582i	−0.0429586	−	0.999077i	$-0.513678\pi$
$192$		0			0
$193$	−7.24339	+	12.5459i	−0.521391	+	0.903075i	0.478300	+	0.878197i	$0.341253\pi$
$193$	−7.24339	+	12.5459i	−0.521391	+	0.903075i	−0.999690	+	0.0248786i	$0.992080\pi$
$194$		0			0
$195$	−3.94002	−	9.51205i	−0.282151	−	0.681172i
$196$		0			0
$197$	24.0632	+	9.96730i	1.71443	+	0.710141i	0.999945	+	0.0104922i	$0.00333983\pi$
$197$	24.0632	+	9.96730i	1.71443	+	0.710141i	0.714487	+	0.699649i	$0.246660\pi$
$198$		0			0
$199$	11.6896	−	3.13222i	0.828655	−	0.222038i	0.180528	−	0.983570i	$-0.442219\pi$
$199$	11.6896	−	3.13222i	0.828655	−	0.222038i	0.648127	+	0.761532i	$0.275553\pi$
$200$		0			0
$201$	−12.9421	−	3.46783i	−0.912865	−	0.244602i
$202$		0			0
$203$	−3.71714	+	4.78736i	−0.260892	+	0.336007i
$204$		0			0
$205$	4.61797	+	3.54349i	0.322533	+	0.247488i
$206$		0			0
$207$	0.0107083	+	0.00618245i	0.000744280	+	0.000429710i
$208$		0			0
$209$		−	5.60949i		−	0.388017i
$210$		0			0
$211$	−9.72932	+	4.03002i	−0.669794	+	0.277438i	−0.691553	−	0.722325i	$-0.743073\pi$
$211$	−9.72932	+	4.03002i	−0.669794	+	0.277438i	0.0217592	+	0.999763i	$0.493073\pi$
$212$		0			0
$213$	−11.3065	−	14.7350i	−0.774712	−	1.00962i
$214$		0			0
$215$	−22.2246	−	5.95506i	−1.51570	−	0.406132i
$216$		0			0
$217$	24.7133	+	0.141257i	1.67765	+	0.00958912i
$218$		0			0
$219$	0.178573	+	1.35639i	0.0120668	+	0.0916565i
$220$		0			0
$221$	−0.131618	−	0.0173278i	−0.00885355	−	0.00116559i
$222$		0			0
$223$	5.83435			0.390697			0.195349	−	0.980734i	$-0.437416\pi$
$223$	5.83435			0.390697			0.195349	+	0.980734i	$0.437416\pi$
$224$		0			0
$225$	0.00802638			0.000535092
$226$		0			0
$227$	−0.509870	−	0.0671256i	−0.0338413	−	0.00445529i	0.113587	−	0.993528i	$-0.463766\pi$
$227$	−0.509870	−	0.0671256i	−0.0338413	−	0.00445529i	−0.147428	+	0.989073i	$0.547099\pi$
$228$		0			0
$229$	−2.01402	−	15.2980i	−0.133090	−	1.01092i	−0.919465	−	0.393172i	$-0.871378\pi$
$229$	−2.01402	−	15.2980i	−0.133090	−	1.01092i	0.786375	−	0.617750i	$-0.211956\pi$
$230$		0			0
$231$	2.17586	−	3.71944i	0.143161	−	0.244721i
$232$		0			0
$233$	21.2320	+	5.68909i	1.39095	+	0.372705i	0.875087	−	0.483965i	$-0.160804\pi$
$233$	21.2320	+	5.68909i	1.39095	+	0.372705i	0.515865	+	0.856670i	$0.327470\pi$
$234$		0			0
$235$	8.21833	+	10.7103i	0.536105	+	0.698665i
$236$		0			0
$237$	19.3739	−	8.02492i	1.25847	−	0.521275i
$238$		0			0
$239$		−	27.2393i		−	1.76196i	−0.473149	−	0.880982i	$-0.656883\pi$
$239$		−	27.2393i		−	1.76196i	0.473149	−	0.880982i	$-0.343117\pi$
$240$		0			0
$241$	23.4339	+	13.5295i	1.50951	+	0.871515i	0.999939	+	0.0110847i	$0.00352845\pi$
$241$	23.4339	+	13.5295i	1.50951	+	0.871515i	0.509569	+	0.860430i	$0.329805\pi$
$242$		0			0
$243$	−0.445673	−	0.341977i	−0.0285899	−	0.0219378i
$244$		0			0
$245$	−14.6037	−	6.24557i	−0.932995	−	0.399015i
$246$		0			0
$247$	15.0955	+	4.04482i	0.960501	+	0.257366i
$248$		0			0
$249$	−23.3677	+	6.26136i	−1.48087	+	0.396797i
$250$		0			0
$251$	15.4531	+	6.40088i	0.975390	+	0.404020i	0.812716	−	0.582660i	$-0.197988\pi$
$251$	15.4531	+	6.40088i	0.975390	+	0.404020i	0.162674	+	0.986680i	$0.447988\pi$
$252$		0			0
$253$	0.0830555	+	0.200514i	0.00522165	+	0.0126062i
$254$		0			0
$255$	−0.0977818	+	0.169363i	−0.00612333	+	0.0106059i
$256$		0			0
$257$	−1.68247	−	2.91413i	−0.104950	−	0.181778i	0.808768	−	0.588128i	$-0.200135\pi$
$257$	−1.68247	−	2.91413i	−0.104950	−	0.181778i	−0.913718	+	0.406350i	$0.866802\pi$
$258$		0			0
$259$	12.5368	−	9.50647i	0.778999	−	0.590703i
$260$		0			0
$261$	0.0161653	+	0.122788i	0.00100061	+	0.00760038i
$262$		0			0
$263$	−17.6325	+	4.72463i	−1.08727	+	0.291333i	−0.757571	−	0.652753i	$-0.773614\pi$
$263$	−17.6325	+	4.72463i	−1.08727	+	0.291333i	−0.329699	+	0.944086i	$0.606947\pi$
$264$		0			0
$265$	−20.1175	+	20.1175i	−1.23581	+	1.23581i
$266$		0			0
$267$	−1.41704	+	3.42105i	−0.0867217	+	0.209365i
$268$		0			0
$269$	0.880381	−	6.68716i	0.0536778	−	0.407723i	−0.943421	−	0.331599i	$-0.892412\pi$
$269$	0.880381	−	6.68716i	0.0536778	−	0.407723i	0.997098	−	0.0761245i	$-0.0242547\pi$
$270$		0			0
$271$	8.29501	−	4.78912i	0.503886	−	0.290919i	−0.226431	−	0.974027i	$-0.572706\pi$
$271$	8.29501	−	4.78912i	0.503886	−	0.290919i	0.730317	+	0.683109i	$0.239372\pi$
$272$		0			0
$273$	8.44029	+	8.53733i	0.510829	+	0.516703i
$274$		0			0
$275$	0.111770	+	0.0857640i	0.00673997	+	0.00517176i
$276$		0			0
$277$	7.95345	+	10.3651i	0.477877	+	0.622781i	0.968627	−	0.248519i	$-0.0799439\pi$
$277$	7.95345	+	10.3651i	0.477877	+	0.622781i	−0.490750	+	0.871300i	$0.663277\pi$
$278$		0			0
$279$	0.357079	−	0.357079i	0.0213777	−	0.0213777i
$280$		0			0
$281$	6.54883	+	6.54883i	0.390670	+	0.390670i	0.874926	−	0.484256i	$-0.160910\pi$
$281$	6.54883	+	6.54883i	0.390670	+	0.390670i	−0.484256	+	0.874926i	$0.660910\pi$
$282$		0			0
$283$	11.4944	−	8.81998i	0.683272	−	0.524293i	−0.207790	−	0.978173i	$-0.566627\pi$
$283$	11.4944	−	8.81998i	0.683272	−	0.524293i	0.891063	+	0.453880i	$0.149961\pi$
$284$		0			0
$285$	14.0150	−	18.2647i	0.830176	−	1.08191i
$286$		0			0
$287$	−6.54585	−	1.79412i	−0.386389	−	0.105903i
$288$		0			0
$289$	−8.49874	−	14.7202i	−0.499926	−	0.865897i
$290$		0			0
$291$	−30.8926	−	4.06708i	−1.81095	−	0.238417i
$292$		0			0
$293$	2.86102	+	1.18507i	0.167143	+	0.0692328i	0.464686	−	0.885476i	$-0.346167\pi$
$293$	2.86102	+	1.18507i	0.167143	+	0.0692328i	−0.297543	+	0.954708i	$0.596167\pi$
$294$		0			0
$295$	14.0094	+	14.0094i	0.815657	+	0.815657i
$296$		0			0
$297$	−1.28740	−	4.80465i	−0.0747027	−	0.278794i
$298$		0			0
$299$	−0.599482	+	0.0789233i	−0.0346690	+	0.00456425i
$300$		0			0
$301$	26.6188	−	3.34976i	1.53428	−	0.193077i
$302$		0			0
$303$	9.31090	−	5.37565i	0.534897	−	0.308823i
$304$		0			0
$305$	3.54336	+	2.04576i	0.202892	+	0.117140i
$306$		0			0
$307$	−5.22184	+	2.16296i	−0.298026	+	0.123447i	−0.526686	−	0.850060i	$-0.676566\pi$
$307$	−5.22184	+	2.16296i	−0.298026	+	0.123447i	0.228660	+	0.973506i	$0.426566\pi$
$308$		0			0
$309$	0.277181	−	0.669175i	0.0157683	−	0.0380680i
$310$		0			0
$311$	1.87916	+	7.01313i	0.106558	+	0.397678i	0.998517	−	0.0544368i	$-0.0173363\pi$
$311$	1.87916	+	7.01313i	0.106558	+	0.397678i	−0.891960	+	0.452115i	$0.850670\pi$
$312$		0			0
$313$	0.759576	−	2.83478i	0.0429338	−	0.160231i	−0.941131	−	0.338043i	$-0.890235\pi$
$313$	0.759576	−	2.83478i	0.0429338	−	0.160231i	0.984065	+	0.177812i	$0.0569018\pi$
$314$		0			0
$315$	−0.300548	+	0.122483i	−0.0169340	+	0.00690115i
$316$		0			0
$317$	−8.73096	+	11.3784i	−0.490380	+	0.639075i	−0.971348	−	0.237663i	$-0.923619\pi$
$317$	−8.73096	+	11.3784i	−0.490380	+	0.639075i	0.480968	+	0.876738i	$0.340285\pi$
$318$		0			0
$319$	−1.08691	+	1.88259i	−0.0608555	+	0.105405i
$320$		0			0
$321$	14.6597			0.818222
$322$		0			0
$323$	−0.113598	−	0.274250i	−0.00632078	−	0.0152597i
$324$		0			0
$325$	−0.311389	+	0.238937i	−0.0172728	+	0.0132539i
$326$		0			0
$327$	3.05370	−	11.3966i	0.168870	−	0.630231i
$328$		0			0
$329$	−13.5873	−	7.94855i	−0.749094	−	0.438218i
$330$		0			0
$331$	15.7301	−	2.07090i	0.864603	−	0.113827i	0.314837	−	0.949146i	$-0.398050\pi$
$331$	15.7301	−	2.07090i	0.864603	−	0.113827i	0.549766	+	0.835319i	$0.314717\pi$
$332$		0			0
$333$	0.0419629	−	0.318740i	0.00229956	−	0.0174669i
$334$		0			0
$335$			17.7128i			0.967756i
$336$		0			0
$337$			8.12319i			0.442499i	0.975217	+	0.221249i	$0.0710134\pi$
$337$			8.12319i			0.442499i	−0.975217	+	0.221249i	$0.928987\pi$
$338$		0			0
$339$	−3.83269	+	29.1122i	−0.208163	+	1.58116i
$340$		0			0
$341$	8.78791	−	1.15695i	0.475892	−	0.0626523i
$342$		0			0
$343$	18.5175	+	0.317556i	0.999853	+	0.0171464i
$344$		0			0
$345$	−0.230540	+	0.860388i	−0.0124119	+	0.0463217i
$346$		0			0
$347$	−13.6865	+	10.5020i	−0.734731	+	0.563779i	−0.906929	−	0.421284i	$-0.861580\pi$
$347$	−13.6865	+	10.5020i	−0.734731	+	0.563779i	0.172198	+	0.985062i	$0.444913\pi$
$348$		0			0
$349$	0.275206	+	0.664405i	0.0147314	+	0.0355648i	0.931074	−	0.364830i	$-0.118873\pi$
$349$	0.275206	+	0.664405i	0.0147314	+	0.0355648i	−0.916343	+	0.400395i	$0.868873\pi$
$350$		0			0
$351$	13.8579			0.739680
$352$		0			0
$353$	−10.2028	+	17.6718i	−0.543041	+	0.940574i	0.455687	+	0.890140i	$0.349394\pi$
$353$	−10.2028	+	17.6718i	−0.543041	+	0.940574i	−0.998727	+	0.0504339i	$0.983940\pi$
$354$		0			0
$355$	−14.9471	+	19.4794i	−0.793310	+	1.03386i
$356$		0			0
$357$	0.0310560	−	0.225909i	0.00164366	−	0.0119563i
$358$		0			0
$359$	−3.11891	+	11.6399i	−0.164610	+	0.614333i	0.833480	+	0.552550i	$0.186345\pi$
$359$	−3.11891	+	11.6399i	−0.164610	+	0.614333i	−0.998090	+	0.0617827i	$0.980321\pi$
$360$		0			0
$361$	4.12696	+	15.4020i	0.217208	+	0.810633i
$362$		0			0
$363$	−6.63367	+	16.0151i	−0.348177	+	0.840574i
$364$		0			0
$365$	1.67093	−	0.692124i	0.0874607	−	0.0362274i
$366$		0			0
$367$	20.3624	+	11.7562i	1.06291	+	0.613671i	0.926236	−	0.376945i	$-0.123025\pi$
$367$	20.3624	+	11.7562i	1.06291	+	0.613671i	0.136674	+	0.990616i	$0.456359\pi$
$368$		0			0
$369$	−0.120107	+	0.0693437i	−0.00625251	+	0.00360989i
$370$		0			0
$371$	12.8701	−	30.5758i	0.668184	−	1.58741i
$372$		0			0
$373$	12.1456	−	1.59900i	0.628877	−	0.0827932i	0.190651	−	0.981658i	$-0.438940\pi$
$373$	12.1456	−	1.59900i	0.628877	−	0.0827932i	0.438226	+	0.898865i	$0.355607\pi$
$374$		0			0
$375$	−4.89019	−	18.2504i	−0.252528	−	0.942449i
$376$		0			0
$377$	−4.28242	−	4.28242i	−0.220556	−	0.220556i
$378$		0			0
$379$	−23.3198	−	9.65936i	−1.19786	−	0.496168i	−0.307550	−	0.951532i	$-0.599509\pi$
$379$	−23.3198	−	9.65936i	−1.19786	−	0.496168i	−0.890306	+	0.455364i	$0.849509\pi$
$380$		0			0
$381$	−5.63669	−	0.742084i	−0.288776	−	0.0380181i
$382$		0			0
$383$	−13.1708	−	22.8125i	−0.672998	−	1.16567i	−0.977050	−	0.213011i	$-0.931673\pi$
$383$	−13.1708	−	22.8125i	−0.672998	−	1.16567i	0.304052	−	0.952655i	$-0.401660\pi$
$384$		0			0
$385$	−5.49399	−	1.50582i	−0.280000	−	0.0767436i
$386$		0			0
$387$	0.333725	−	0.434919i	0.0169642	−	0.0221082i
$388$		0			0
$389$	−5.37119	+	4.12146i	−0.272330	+	0.208966i	−0.735893	−	0.677098i	$-0.763237\pi$
$389$	−5.37119	+	4.12146i	−0.272330	+	0.208966i	0.463563	+	0.886064i	$0.346571\pi$
$390$		0			0
$391$	0.00812123	+	0.00812123i	0.000410709	+	0.000410709i
$392$		0			0
$393$	−4.81188	+	4.81188i	−0.242727	+	0.242727i
$394$		0			0
$395$	−16.8762	−	21.9935i	−0.849136	−	1.10662i
$396$		0			0
$397$	−12.2950	−	9.43432i	−0.617070	−	0.473495i	0.252305	−	0.967648i	$-0.418812\pi$
$397$	−12.2950	−	9.43432i	−0.617070	−	0.473495i	−0.869375	+	0.494153i	$0.835478\pi$
$398$		0			0
$399$	−7.09596	+	25.8897i	−0.355243	+	1.29610i
$400$		0			0
$401$	1.80550	−	1.04241i	0.0901625	−	0.0520553i	−0.454241	−	0.890879i	$-0.650089\pi$
$401$	1.80550	−	1.04241i	0.0901625	−	0.0520553i	0.544403	+	0.838824i	$0.316756\pi$
$402$		0			0
$403$	−3.22325	+	24.4830i	−0.160561	+	1.21958i
$404$		0			0
$405$	7.67149	−	18.5206i	0.381200	−	0.920297i
$406$		0			0
$407$	3.99017	−	3.99017i	0.197785	−	0.197785i
$408$		0			0
$409$	−16.8550	+	4.51629i	−0.833427	+	0.223316i	−0.650208	−	0.759756i	$-0.725318\pi$
$409$	−16.8550	+	4.51629i	−0.833427	+	0.223316i	−0.183219	+	0.983072i	$0.558652\pi$
$410$		0			0
$411$	2.32732	+	17.6777i	0.114798	+	0.871978i
$412$		0			0
$413$	−21.2923	−	8.96248i	−1.04773	−	0.441015i
$414$		0			0
$415$	15.9908	+	27.6968i	0.784956	+	1.35958i
$416$		0			0
$417$	1.61911	−	2.80438i	0.0792880	−	0.137331i
$418$		0			0
$419$	1.85032	+	4.46707i	0.0903942	+	0.218231i	0.962610	−	0.270890i	$-0.0873178\pi$
$419$	1.85032	+	4.46707i	0.0903942	+	0.218231i	−0.872216	+	0.489120i	$0.837318\pi$
$420$		0			0
$421$	−19.5246	−	8.08736i	−0.951572	−	0.394154i	−0.147750	−	0.989025i	$-0.547203\pi$
$421$	−19.5246	−	8.08736i	−0.951572	−	0.394154i	−0.803821	+	0.594871i	$0.797203\pi$
$422$		0			0
$423$	−0.310694	+	0.0832501i	−0.0151064	+	0.00404776i
$424$		0			0
$425$	0.00720129	+	0.00192958i	0.000349314	+	9.35983e-5i
$426$		0			0
$427$	−4.72638	−	0.649744i	−0.228726	−	0.0314433i
$428$		0			0
$429$	3.41598	+	2.62117i	0.164925	+	0.126551i
$430$		0			0
$431$	5.91156	+	3.41304i	0.284750	+	0.164400i	0.635572	−	0.772042i	$-0.280764\pi$
$431$	5.91156	+	3.41304i	0.284750	+	0.164400i	−0.350822	+	0.936442i	$0.614098\pi$
$432$		0			0
$433$		−	5.72011i		−	0.274891i	−0.990509	−	0.137446i	$-0.956111\pi$
$433$		−	5.72011i		−	0.274891i	0.990509	−	0.137446i	$-0.0438892\pi$
$434$		0			0
$435$	−8.24257	+	3.41418i	−0.395201	+	0.163698i
$436$		0			0
$437$	−0.823079	−	1.07266i	−0.0393732	−	0.0513122i
$438$		0			0
$439$	−30.4743	−	8.16557i	−1.45446	−	0.389721i	−0.556887	−	0.830588i	$-0.688005\pi$
$439$	−30.4743	−	8.16557i	−1.45446	−	0.389721i	−0.897573	+	0.440867i	$0.854671\pi$
$440$		0			0
$441$	0.270634	−	0.264516i	0.0128873	−	0.0125960i
$442$		0			0
$443$	1.72509	+	13.1034i	0.0819616	+	0.622560i	0.982292	+	0.187354i	$0.0599912\pi$
$443$	1.72509	+	13.1034i	0.0819616	+	0.622560i	−0.900331	+	0.435206i	$0.856675\pi$
$444$		0			0
$445$	4.85333	+	0.638953i	0.230070	+	0.0302893i
$446$		0			0
$447$	29.8791			1.41323
$448$		0			0
$449$	−12.5172			−0.590722			−0.295361	−	0.955386i	$-0.595440\pi$
$449$	−12.5172			−0.590722			−0.295361	+	0.955386i	$0.595440\pi$
$450$		0			0
$451$	−2.41348	−	0.317740i	−0.113646	−	0.0149618i
$452$		0			0
$453$	−0.132623	−	1.00737i	−0.00623116	−	0.0473304i
$454$		0			0
$455$	8.01378	−	13.6988i	0.375692	−	0.642212i
$456$		0			0
$457$	31.7422	+	8.50530i	1.48484	+	0.397861i	0.907991	−	0.418991i	$-0.137616\pi$
$457$	31.7422	+	8.50530i	1.48484	+	0.397861i	0.576848	+	0.816852i	$0.304283\pi$
$458$		0			0
$459$	−0.160241	−	0.208830i	−0.00747942	−	0.00974737i
$460$		0			0
$461$	−2.08517	+	0.863705i	−0.0971160	+	0.0402268i	−0.430712	−	0.902489i	$-0.641738\pi$
$461$	−2.08517	+	0.863705i	−0.0971160	+	0.0402268i	0.333597	+	0.942716i	$0.391738\pi$
$462$		0			0
$463$		−	4.71931i		−	0.219325i	−0.993969	−	0.109663i	$-0.965023\pi$
$463$		−	4.71931i		−	0.219325i	0.993969	−	0.109663i	$-0.0349770\pi$
$464$		0			0
$465$	31.5043	+	18.1890i	1.46098	+	0.843495i
$466$		0			0
$467$	26.0046	+	19.9540i	1.20335	+	0.923362i	0.998463	−	0.0554244i	$-0.0176512\pi$
$467$	26.0046	+	19.9540i	1.20335	+	0.923362i	0.204885	+	0.978786i	$0.434318\pi$
$468$		0			0
$469$	−7.79464	−	19.1264i	−0.359923	−	0.883176i
$470$		0			0
$471$	33.9169	+	9.08801i	1.56281	+	0.418753i
$472$		0			0
$473$	9.29445	−	2.49044i	0.427359	−	0.114511i
$474$		0			0
$475$	−0.810847	−	0.335864i	−0.0372042	−	0.0154105i
$476$		0			0
$477$	−0.259406	−	0.626262i	−0.0118774	−	0.0286746i
$478$		0			0
$479$	−14.5613	+	25.2209i	−0.665322	+	1.15237i	0.313876	+	0.949464i	$0.398372\pi$
$479$	−14.5613	+	25.2209i	−0.665322	+	1.15237i	−0.979198	+	0.202907i	$0.934961\pi$
$480$		0			0
$481$	7.86059	+	13.6149i	0.358412	+	0.620788i
$482$		0			0
$483$	−0.129680	−	1.03050i	−0.00590066	−	0.0468895i
$484$		0			0
$485$	5.37663	+	40.8396i	0.244140	+	1.85443i
$486$		0			0
$487$	9.16682	−	2.45624i	0.415388	−	0.111303i	−0.0450711	−	0.998984i	$-0.514351\pi$
$487$	9.16682	−	2.45624i	0.415388	−	0.111303i	0.460459	+	0.887681i	$0.347685\pi$
$488$		0			0
$489$	12.6205	−	12.6205i	0.570718	−	0.570718i
$490$		0			0
$491$	11.6185	−	28.0495i	0.524334	−	1.26586i	−0.410853	−	0.911702i	$-0.634769\pi$
$491$	11.6185	−	28.0495i	0.524334	−	1.26586i	0.935187	−	0.354153i	$-0.115231\pi$
$492$		0			0
$493$	−0.0150152	+	0.114052i	−0.000676251	+	0.00513663i
$494$		0			0
$495$	−0.100807	+	0.0582008i	−0.00453092	+	0.00261593i
$496$		0			0
$497$	7.56791	−	27.6116i	0.339467	−	1.23855i
$498$		0			0
$499$	−18.2706	−	14.0195i	−0.817902	−	0.627598i	0.112701	−	0.993629i	$-0.464050\pi$
$499$	−18.2706	−	14.0195i	−0.817902	−	0.627598i	−0.930603	+	0.366031i	$0.880717\pi$
$500$		0			0
$501$	−9.18575	−	11.9711i	−0.410389	−	0.534829i
$502$		0			0
$503$	3.99460	−	3.99460i	0.178110	−	0.178110i	−0.612421	−	0.790532i	$-0.709804\pi$
$503$	3.99460	−	3.99460i	0.178110	−	0.178110i	0.790532	+	0.612421i	$0.209804\pi$
$504$		0			0
$505$	−10.0502	−	10.0502i	−0.447226	−	0.447226i
$506$		0			0
$507$	8.18510	−	6.28065i	0.363513	−	0.278934i
$508$		0			0
$509$	0.229036	−	0.298486i	0.0101518	−	0.0132301i	−0.788250	−	0.615355i	$-0.789013\pi$
$509$	0.229036	−	0.298486i	0.0101518	−	0.0132301i	0.798402	+	0.602125i	$0.205679\pi$
$510$		0			0
$511$	−1.49971	+	1.48266i	−0.0663433	+	0.0655892i
$512$		0			0
$513$	15.4937	+	26.8358i	0.684062	+	1.18483i
$514$		0			0
$515$	−0.949336	−	0.124982i	−0.0418327	−	0.00550738i
$516$		0			0
$517$	−5.21605	−	2.16056i	−0.229402	−	0.0950212i
$518$		0			0
$519$	7.23912	+	7.23912i	0.317762	+	0.317762i
$520$		0			0
$521$	3.11751	+	11.6347i	0.136581	+	0.509725i	0.999986	+	0.00521550i	$0.00166015\pi$
$521$	3.11751	+	11.6347i	0.136581	+	0.509725i	−0.863406	+	0.504510i	$0.831673\pi$
$522$		0			0
$523$	35.2138	−	4.63598i	1.53979	−	0.202717i	0.687655	−	0.726038i	$-0.258640\pi$
$523$	35.2138	−	4.63598i	1.53979	−	0.202717i	0.852136	+	0.523320i	$0.175307\pi$
$524$		0			0
$525$	−0.407364	−	0.537217i	−0.0177788	−	0.0234461i
$526$		0			0
$527$	0.406215	−	0.234528i	0.0176950	−	0.0102162i
$528$		0			0
$529$	−19.8733	−	11.4738i	−0.864056	−	0.498863i
$530$		0			0
$531$	−0.436115	+	0.180645i	−0.0189258	+	0.00783932i
$532$		0			0
$533$	2.59533	−	6.26569i	0.112416	−	0.271397i
$534$		0			0
$535$	−5.01588	−	18.7195i	−0.216855	−	0.809316i
$536$		0			0
$537$	−5.84323	+	21.8072i	−0.252154	+	0.941051i
$538$		0			0
$539$	6.59508	−	0.791672i	0.284070	−	0.0340997i
$540$		0			0
$541$	−8.55443	+	11.1484i	−0.367784	+	0.479305i	−0.940183	−	0.340670i	$-0.889346\pi$
$541$	−8.55443	+	11.1484i	−0.367784	+	0.479305i	0.572399	+	0.819975i	$0.306013\pi$
$542$		0			0
$543$	20.8603	−	36.1311i	0.895201	−	1.55053i
$544$		0			0
$545$	−15.5976			−0.668127
$546$		0			0
$547$	4.13041	+	9.97168i	0.176603	+	0.426358i	0.987250	−	0.159177i	$-0.0508842\pi$
$547$	4.13041	+	9.97168i	0.176603	+	0.426358i	−0.810647	+	0.585536i	$0.800884\pi$
$548$		0			0
$549$	−0.0773398	+	0.0593449i	−0.00330078	+	0.00253278i
$550$		0			0
$551$	3.50499	−	13.0808i	0.149318	−	0.557261i
$552$		0			0
$553$	27.9014	+	16.3222i	1.18649	+	0.694092i
$554$		0			0
$555$	22.9613	−	3.02291i	0.974653	−	0.128316i
$556$		0			0
$557$	2.55667	−	19.4198i	0.108330	−	0.822844i	−0.847886	−	0.530179i	$-0.822125\pi$
$557$	2.55667	−	19.4198i	0.108330	−	0.822844i	0.956215	−	0.292665i	$-0.0945421\pi$
$558$		0			0
$559$			26.8077i			1.13384i
$560$		0			0
$561$		−	0.0817858i		−	0.00345300i
$562$		0			0
$563$	−4.09080	+	31.0727i	−0.172407	+	1.30956i	0.658261	+	0.752790i	$0.271292\pi$
$563$	−4.09080	+	31.0727i	−0.172407	+	1.30956i	−0.830667	+	0.556769i	$0.812041\pi$
$564$		0			0
$565$	38.4859	−	5.06676i	1.61911	−	0.213160i
$566$		0			0
$567$	−0.133605	+	23.3745i	−0.00561087	+	0.981639i
$568$		0			0
$569$	9.88389	−	36.8872i	0.414354	−	1.54639i	−0.371771	−	0.928324i	$-0.621249\pi$
$569$	9.88389	−	36.8872i	0.414354	−	1.54639i	0.786125	−	0.618067i	$-0.212084\pi$
$570$		0			0
$571$	−17.4748	+	13.4089i	−0.731297	+	0.561144i	−0.905898	−	0.423495i	$-0.860803\pi$
$571$	−17.4748	+	13.4089i	−0.731297	+	0.561144i	0.174601	+	0.984639i	$0.444136\pi$
$572$		0			0
$573$	16.0982	+	38.8645i	0.672512	+	1.62359i
$574$		0			0
$575$	0.0339570			0.00141610
$576$		0			0
$577$	2.30610	−	3.99428i	0.0960042	−	0.166284i	−0.814023	−	0.580833i	$-0.802727\pi$
$577$	2.30610	−	3.99428i	0.0960042	−	0.166284i	0.910027	+	0.414548i	$0.136060\pi$
$578$		0			0
$579$	15.1367	−	19.7265i	0.629059	−	0.819806i
$580$		0			0
$581$	−29.4551	−	22.8703i	−1.22200	−	0.948821i
$582$		0			0
$583$	3.07946	−	11.4927i	0.127538	−	0.475979i
$584$		0			0
$585$	−0.0839333	−	0.313243i	−0.00347021	−	0.0129510i
$586$		0			0
$587$	−8.83831	+	21.3376i	−0.364796	+	0.880695i	0.629789	+	0.776766i	$0.283141\pi$
$587$	−8.83831	+	21.3376i	−0.364796	+	0.880695i	−0.994585	+	0.103929i	$0.966859\pi$
$588$		0			0
$589$	−51.0150	+	21.1311i	−2.10204	+	0.870692i
$590$		0			0
$591$	−38.7151	−	22.3522i	−1.59253	−	0.919446i
$592$		0			0
$593$	−31.6538	+	18.2753i	−1.29986	+	0.750477i	−0.980380	−	0.197115i	$-0.936843\pi$
$593$	−31.6538	+	18.2753i	−1.29986	+	0.750477i	−0.319484	+	0.947592i	$0.603509\pi$
$594$		0			0
$595$	−0.299098	+	0.0376391i	−0.0122618	+	0.00154305i
$596$		0			0
$597$	−20.5938	+	2.71123i	−0.842849	+	0.110963i
$598$		0			0
$599$	1.77346	+	6.61863i	0.0724614	+	0.270430i	0.992646	−	0.121056i	$-0.0386280\pi$
$599$	1.77346	+	6.61863i	0.0724614	+	0.270430i	−0.920184	+	0.391485i	$0.871961\pi$
$600$		0			0
$601$	27.8002	+	27.8002i	1.13400	+	1.13400i	0.989506	+	0.144489i	$0.0461538\pi$
$601$	27.8002	+	27.8002i	1.13400	+	1.13400i	0.144489	+	0.989506i	$0.453846\pi$
$602$		0			0
$603$	−0.389902	−	0.161503i	−0.0158780	−	0.00657690i
$604$		0			0
$605$	22.7201	+	2.99115i	0.923702	+	0.121608i
$606$		0			0
$607$	17.2445	+	29.8684i	0.699933	+	1.21232i	0.968489	+	0.249056i	$0.0801202\pi$
$607$	17.2445	+	29.8684i	0.699933	+	1.21232i	−0.268556	+	0.963264i	$0.586546\pi$
$608$		0			0
$609$	7.39793	−	7.31384i	0.299779	−	0.296372i
$610$		0			0
$611$	9.57531	−	12.4788i	0.387375	−	0.504837i
$612$		0			0
$613$	13.4973	−	10.3568i	0.545149	−	0.418307i	−0.299129	−	0.954213i	$-0.596696\pi$
$613$	13.4973	−	10.3568i	0.545149	−	0.418307i	0.844278	+	0.535905i	$0.180030\pi$
$614$		0			0
$615$	−7.06450	−	7.06450i	−0.284868	−	0.284868i
$616$		0			0
$617$	21.9050	−	21.9050i	0.881864	−	0.881864i	−0.111860	−	0.993724i	$-0.535681\pi$
$617$	21.9050	−	21.9050i	0.881864	−	0.881864i	0.993724	+	0.111860i	$0.0356808\pi$
$618$		0			0
$619$	−17.6139	−	22.9549i	−0.707963	−	0.922635i	0.291461	−	0.956583i	$-0.405859\pi$
$619$	−17.6139	−	22.9549i	−0.707963	−	0.922635i	−0.999424	+	0.0339476i	$0.989192\pi$
$620$		0			0
$621$	−0.951165	−	0.729855i	−0.0381690	−	0.0292881i
$622$		0			0
$623$	−5.52182	+	1.44579i	−0.221227	+	0.0579244i
$624$		0			0
$625$	−22.2744	+	12.8601i	−0.890977	+	0.514406i
$626$		0			0
$627$	−1.25670	+	9.54561i	−0.0501879	+	0.381215i
$628$		0			0
$629$	0.114276	−	0.275886i	0.00455647	−	0.0110003i
$630$		0			0
$631$	−11.4925	+	11.4925i	−0.457510	+	0.457510i	−0.897837	−	0.440327i	$-0.854863\pi$
$631$	−11.4925	+	11.4925i	−0.457510	+	0.457510i	0.440327	+	0.897837i	$0.354863\pi$
$632$		0			0
$633$	17.4591	−	4.67816i	0.693938	−	0.185940i
$634$		0			0
$635$	0.981025	+	7.45162i	0.0389308	+	0.295709i
$636$		0			0
$637$	−2.62506	+	18.3186i	−0.104009	+	0.725809i
$638$		0			0
$639$	−0.292504	−	0.506632i	−0.0115713	−	0.0200421i
$640$		0			0
$641$	−0.491952	+	0.852086i	−0.0194309	+	0.0336554i	−0.875577	−	0.483078i	$-0.839519\pi$
$641$	−0.491952	+	0.852086i	−0.0194309	+	0.0336554i	0.856146	+	0.516733i	$0.172852\pi$
$642$		0			0
$643$	−5.00573	−	12.0849i	−0.197407	−	0.476582i	0.793917	−	0.608026i	$-0.208039\pi$
$643$	−5.00573	−	12.0849i	−0.197407	−	0.476582i	−0.991324	+	0.131444i	$0.958039\pi$
$644$		0			0
$645$	36.4852	+	15.1127i	1.43660	+	0.595061i
$646$		0			0
$647$	−1.94029	+	0.519900i	−0.0762808	+	0.0204394i	−0.296758	−	0.954953i	$-0.595905\pi$
$647$	−1.94029	+	0.519900i	−0.0762808	+	0.0204394i	0.220477	+	0.975392i	$0.429239\pi$
$648$		0			0
$649$	−8.00327	−	2.14447i	−0.314156	−	0.0841778i
$650$		0			0
$651$	−42.0226	−	5.77693i	−1.64700	−	0.226416i
$652$		0			0
$653$	−29.6365	−	22.7409i	−1.15977	−	0.889921i	−0.164431	−	0.986389i	$-0.552579\pi$
$653$	−29.6365	−	22.7409i	−1.15977	−	0.889921i	−0.995336	+	0.0964676i	$0.969246\pi$
$654$		0			0
$655$	7.79090	+	4.49808i	0.304416	+	0.175754i
$656$		0			0
$657$			0.0430919i			0.00168118i
$658$		0			0
$659$	1.18124	−	0.489288i	0.0460148	−	0.0190599i	−0.359557	−	0.933123i	$-0.617072\pi$
$659$	1.18124	−	0.489288i	0.0460148	−	0.0190599i	0.405572	+	0.914063i	$0.367072\pi$
$660$		0			0
$661$	16.3004	+	21.2431i	0.634013	+	0.826262i	0.994304	−	0.106578i	$-0.0339894\pi$
$661$	16.3004	+	21.2431i	0.634013	+	0.826262i	−0.360291	+	0.932840i	$0.617323\pi$
$662$		0			0
$663$	0.220090	+	0.0589730i	0.00854760	+	0.00229032i
$664$		0			0
$665$	35.4875	+	0.202840i	1.37615	+	0.00786581i
$666$		0			0
$667$	0.0683902	+	0.519475i	0.00264808	+	0.0201142i
$668$		0			0
$669$	−9.92826	−	1.30708i	−0.383849	−	0.0505346i
$670$		0			0
$671$	−1.71110			−0.0660561
$672$		0			0
$673$	−32.0683			−1.23614			−0.618072	−	0.786122i	$-0.712086\pi$
$673$	−32.0683			−1.23614			−0.618072	+	0.786122i	$0.712086\pi$
$674$		0			0
$675$	−0.771591	−	0.101582i	−0.0296986	−	0.00390989i
$676$		0			0
$677$	−0.187527	−	1.42441i	−0.00720725	−	0.0547445i	0.987463	−	0.157849i	$-0.0504558\pi$
$677$	−0.187527	−	1.42441i	−0.00720725	−	0.0547445i	−0.994671	+	0.103104i	$0.967122\pi$
$678$		0			0
$679$	−23.7774	−	41.7328i	−0.912494	−	1.60156i
$680$		0			0
$681$	0.852602	+	0.228454i	0.0326718	+	0.00875438i
$682$		0			0
$683$	−0.190979	−	0.248889i	−0.00730761	−	0.00952346i	0.789685	−	0.613512i	$-0.210244\pi$
$683$	−0.190979	−	0.248889i	−0.00730761	−	0.00952346i	−0.796993	+	0.603989i	$0.793577\pi$
$684$		0			0
$685$	21.7771	−	9.02038i	0.832061	−	0.344651i
$686$		0			0
$687$			26.4837i			1.01042i
$688$		0			0
$689$	28.7070	+	16.5740i	1.09365	+	0.631419i
$690$		0			0
$691$	−12.6748	−	9.72574i	−0.482173	−	0.369984i	0.338886	−	0.940827i	$-0.389950\pi$
$691$	−12.6748	−	9.72574i	−0.482173	−	0.369984i	−0.821059	+	0.570843i	$0.806617\pi$
$692$		0			0
$693$	0.0832400	−	0.107206i	0.00316202	−	0.00407242i
$694$		0			0
$695$	−4.13501	−	1.10797i	−0.156850	−	0.0420278i
$696$		0			0
$697$	−0.124430	+	0.0333410i	−0.00471314	+	0.00126288i
$698$		0			0
$699$	−34.8557	−	14.4377i	−1.31836	−	0.546084i
$700$		0			0
$701$	15.4207	+	37.2289i	0.582433	+	1.40612i	0.890601	+	0.454785i	$0.150284\pi$
$701$	15.4207	+	37.2289i	0.582433	+	1.40612i	−0.308168	+	0.951332i	$0.599716\pi$
$702$		0			0
$703$	−17.5769	+	30.4441i	−0.662925	+	1.14822i
$704$		0			0
$705$	−11.5856	−	20.0668i	−0.436339	−	0.755761i
$706$		0			0
$707$	15.2749	+	6.42958i	0.574470	+	0.241809i
$708$		0			0
$709$	0.412906	+	3.13633i	0.0155070	+	0.117787i	0.997448	−	0.0714020i	$-0.0227473\pi$
$709$	0.412906	+	3.13633i	0.0155070	+	0.117787i	−0.981941	+	0.189189i	$0.939414\pi$
$710$		0			0
$711$	0.638005	−	0.170953i	0.0239271	−	0.00641124i
$712$		0			0
$713$	1.51068	−	1.51068i	0.0565755	−	0.0565755i
$714$		0			0
$715$	2.17829	−	5.25885i	0.0814634	−	0.196670i
$716$		0			0
$717$	−6.10247	+	46.3529i	−0.227901	+	1.73108i
$718$		0			0
$719$	−18.2626	+	10.5439i	−0.681082	+	0.393223i	−0.800262	−	0.599650i	$-0.795307\pi$
$719$	−18.2626	+	10.5439i	−0.681082	+	0.393223i	0.119181	+	0.992873i	$0.461973\pi$
$720$		0			0
$721$	1.08010	−	0.282804i	0.0402249	−	0.0105322i
$722$		0			0
$723$	−36.8461	−	28.2730i	−1.37032	−	1.05148i
$724$		0			0
$725$	0.207049	+	0.269831i	0.00768959	+	0.0100213i
$726$		0			0
$727$	−1.49231	+	1.49231i	−0.0553467	+	0.0553467i	−0.734238	−	0.678892i	$-0.762461\pi$
$727$	−1.49231	+	1.49231i	−0.0553467	+	0.0553467i	0.678892	+	0.734238i	$0.262461\pi$
$728$		0			0
$729$	19.4234	+	19.4234i	0.719386	+	0.719386i
$730$		0			0
$731$	0.403976	−	0.309981i	0.0149416	−	0.0114651i
$732$		0			0
$733$	9.92943	−	12.9403i	0.366752	−	0.477960i	−0.573128	−	0.819466i	$-0.694270\pi$
$733$	9.92943	−	12.9403i	0.366752	−	0.477960i	0.939880	+	0.341506i	$0.110937\pi$
$734$		0			0
$735$	23.4517	+	13.8997i	0.865031	+	0.512699i
$736$		0			0
$737$	−3.70380	−	6.41518i	−0.136431	−	0.236306i
$738$		0			0
$739$	29.0602	+	3.82585i	1.06900	+	0.140736i	0.644433	−	0.764661i	$-0.277093\pi$
$739$	29.0602	+	3.82585i	1.06900	+	0.140736i	0.424566	+	0.905397i	$0.360427\pi$
$740$		0			0
$741$	−24.7816	−	10.2649i	−0.910376	−	0.377090i
$742$		0			0
$743$	−22.4851	−	22.4851i	−0.824899	−	0.824899i	0.161907	−	0.986806i	$-0.448236\pi$
$743$	−22.4851	−	22.4851i	−0.824899	−	0.824899i	−0.986806	+	0.161907i	$0.948236\pi$
$744$		0			0
$745$	−10.2233	−	38.1539i	−0.374553	−	1.39785i
$746$		0			0
$747$	−0.755475	+	0.0994601i	−0.0276414	+	0.00363906i
$748$		0			0
$749$	13.6538	+	18.0062i	0.498899	+	0.657931i
$750$		0			0
$751$	26.9574	−	15.5639i	0.983690	−	0.567934i	0.0803077	−	0.996770i	$-0.474410\pi$
$751$	26.9574	−	15.5639i	0.983690	−	0.567934i	0.903382	+	0.428837i	$0.141076\pi$
$752$		0			0
$753$	−24.8624	−	14.3543i	−0.906034	−	0.523099i
$754$		0			0
$755$	−1.24097	+	0.514028i	−0.0451637	+	0.0187074i
$756$		0			0
$757$	1.79118	−	4.32429i	0.0651016	−	0.157169i	−0.887980	−	0.459881i	$-0.847892\pi$
$757$	1.79118	−	4.32429i	0.0651016	−	0.157169i	0.953082	+	0.302712i	$0.0978920\pi$
$758$		0			0
$759$	−0.0964132	−	0.359819i	−0.00349958	−	0.0130606i
$760$		0			0
$761$	−5.62750	+	21.0021i	−0.203997	+	0.761326i	0.785756	+	0.618536i	$0.212274\pi$
$761$	−5.62750	+	21.0021i	−0.203997	+	0.761326i	−0.989753	+	0.142790i	$0.954393\pi$
$762$		0			0
$763$	16.8423	−	6.86381i	0.609734	−	0.248487i
$764$		0			0
$765$	−0.00374985	+	0.00488690i	−0.000135576	+	0.000176686i
$766$		0			0
$767$	11.5418	−	19.9909i	0.416750	−	0.721831i
$768$		0			0
$769$	−36.3367			−1.31033			−0.655167	−	0.755484i	$-0.727402\pi$
$769$	−36.3367			−1.31033			−0.655167	+	0.755484i	$0.727402\pi$
$770$		0			0
$771$	2.21019	+	5.33587i	0.0795981	+	0.192167i
$772$		0			0
$773$	28.0530	−	21.5258i	1.00900	−	0.774230i	0.0346760	−	0.999399i	$-0.488960\pi$
$773$	28.0530	−	21.5258i	1.00900	−	0.774230i	0.974320	+	0.225169i	$0.0722934\pi$
$774$		0			0
$775$	0.358933	−	1.33956i	0.0128932	−	0.0481183i
$776$		0			0
$777$	−23.4635	+	13.3684i	−0.841748	+	0.479589i
$778$		0			0
$779$	15.0352	−	1.97942i	0.538692	−	0.0709201i
$780$		0			0
$781$	1.34029	−	10.1805i	0.0479592	−	0.364286i
$782$		0			0
$783$		−	12.0084i		−	0.429146i
$784$		0			0
$785$		−	46.4194i		−	1.65678i
$786$		0			0
$787$	5.66525	−	43.0318i	0.201944	−	1.53392i	−0.527308	−	0.849674i	$-0.676799\pi$
$787$	5.66525	−	43.0318i	0.201944	−	1.53392i	0.729252	−	0.684245i	$-0.239868\pi$
$788$		0			0
$789$	31.0636	−	4.08960i	1.10589	−	0.145594i
$790$		0			0
$791$	−39.3276	+	22.4071i	−1.39833	+	0.796703i
$792$		0			0
$793$	1.23381	−	4.60466i	0.0438140	−	0.163516i
$794$		0			0
$795$	38.7407	−	29.7268i	1.37399	−	1.05430i
$796$		0			0
$797$	−9.23619	−	22.2981i	−0.327163	−	0.789841i	−0.998801	−	0.0489611i	$-0.984409\pi$
$797$	−9.23619	−	22.2981i	−0.327163	−	0.789841i	0.671638	−	0.740879i	$-0.265591\pi$
$798$		0			0
$799$	−0.298769			−0.0105697
$800$		0			0
$801$	−0.0583167	+	0.101008i	−0.00206052	+	0.00356893i
$802$		0			0
$803$	−0.460448	+	0.600068i	−0.0162489	+	0.0211759i
$804$		0			0
$805$	−1.27152	+	0.518186i	−0.0448152	+	0.0182637i
$806$		0			0
$807$	−2.99627	+	11.1822i	−0.105474	+	0.393633i
$808$		0			0
$809$	−7.82034	−	29.1859i	−0.274949	−	1.02612i	−0.955876	−	0.293771i	$-0.905090\pi$
$809$	−7.82034	−	29.1859i	−0.274949	−	1.02612i	0.680927	−	0.732351i	$-0.261577\pi$
$810$		0			0
$811$	3.30832	−	7.98700i	0.116171	−	0.280461i	−0.855090	−	0.518480i	$-0.826498\pi$
$811$	3.30832	−	7.98700i	0.116171	−	0.280461i	0.971261	+	0.238019i	$0.0764980\pi$
$812$		0			0
$813$	−15.1884	+	6.29126i	−0.532682	+	0.220644i
$814$		0			0
$815$	−20.4338	−	11.7974i	−0.715764	−	0.413246i
$816$		0			0
$817$	−51.9130	+	29.9720i	−1.81621	+	1.04859i
$818$		0			0
$819$	0.228476	+	0.301306i	0.00798360	+	0.0105285i
$820$		0			0
$821$	29.3021	−	3.85769i	1.02265	−	0.134634i	0.399496	−	0.916735i	$-0.369185\pi$
$821$	29.3021	−	3.85769i	1.02265	−	0.134634i	0.623152	+	0.782100i	$0.285852\pi$
$822$		0			0
$823$	−2.63947	−	9.85062i	−0.0920060	−	0.343371i	0.904543	−	0.426383i	$-0.140213\pi$
$823$	−2.63947	−	9.85062i	−0.0920060	−	0.343371i	−0.996549	+	0.0830124i	$0.973546\pi$
$824$		0			0
$825$	−0.170984	−	0.170984i	−0.00595289	−	0.00595289i
$826$		0			0
$827$	36.1787	+	14.9857i	1.25806	+	0.521105i	0.909313	−	0.416113i	$-0.136608\pi$
$827$	36.1787	+	14.9857i	1.25806	+	0.521105i	0.348745	+	0.937218i	$0.386608\pi$
$828$		0			0
$829$	−26.9221	−	3.54436i	−0.935042	−	0.123101i	−0.352418	−	0.935843i	$-0.614640\pi$
$829$	−26.9221	−	3.54436i	−0.935042	−	0.123101i	−0.582624	+	0.812742i	$0.697974\pi$
$830$		0			0
$831$	−11.2122	−	19.4201i	−0.388946	−	0.673675i
$832$		0			0
$833$	0.306404	−	0.172263i	0.0106163	−	0.00596855i
$834$		0			0
$835$	−12.1434	+	15.8256i	−0.420241	+	0.547669i
$836$		0			0
$837$	−38.8458	+	29.8074i	−1.34271	+	1.03030i
$838$		0			0
$839$	−28.0292	−	28.0292i	−0.967677	−	0.967677i	0.0318170	−	0.999494i	$-0.489871\pi$
$839$	−28.0292	−	28.0292i	−0.967677	−	0.967677i	−0.999494	+	0.0318170i	$0.989871\pi$
$840$		0			0
$841$	16.7952	−	16.7952i	0.579145	−	0.579145i
$842$		0			0
$843$	−9.67693	−	12.6112i	−0.333291	−	0.434354i
$844$		0			0
$845$	−10.8206	−	8.30294i	−0.372240	−	0.285630i
$846$		0			0
$847$	−25.8495	+	6.76824i	−0.888200	+	0.232560i
$848$		0			0
$849$	−21.5359	+	12.4338i	−0.739110	+	0.426725i
$850$		0			0
$851$	0.177531	−	1.34848i	0.00608569	−	0.0462254i
$852$		0			0
$853$	−1.68705	+	4.07290i	−0.0577635	+	0.139453i	−0.950126	−	0.311865i	$-0.899046\pi$
$853$	−1.68705	+	4.07290i	−0.0577635	+	0.139453i	0.892363	+	0.451319i	$0.149046\pi$
$854$		0			0
$855$	0.512755	−	0.512755i	0.0175358	−	0.0175358i
$856$		0			0
$857$	−21.3876	+	5.73079i	−0.730586	+	0.195760i	−0.604890	−	0.796309i	$-0.706783\pi$
$857$	−21.3876	+	5.73079i	−0.730586	+	0.195760i	−0.125696	+	0.992069i	$0.540116\pi$
$858$		0			0
$859$	−0.338525	−	2.57135i	−0.0115503	−	0.0877334i	0.984699	−	0.174265i	$-0.0557550\pi$
$859$	−0.338525	−	2.57135i	−0.0115503	−	0.0877334i	−0.996249	+	0.0865317i	$0.972422\pi$
$860$		0			0
$861$	10.7371	+	4.51951i	0.365918	+	0.154024i
$862$		0			0
$863$	0.598235	+	1.03617i	0.0203642	+	0.0352718i	0.876028	−	0.482260i	$-0.160184\pi$
$863$	0.598235	+	1.03617i	0.0203642	+	0.0352718i	−0.855664	+	0.517532i	$0.826851\pi$
$864$		0			0
$865$	6.76703	−	11.7208i	0.230086	−	0.398520i
$866$		0			0
$867$	11.1644	+	26.9533i	0.379163	+	0.915381i
$868$		0			0
$869$	10.7111	+	4.43668i	0.363349	+	0.150504i
$870$		0			0
$871$	19.9343	−	5.34138i	0.675448	−	0.180986i
$872$		0			0
$873$	−0.948000	−	0.254016i	−0.0320850	−	0.00859714i
$874$		0			0
$875$	17.8620	−	23.0048i	0.603846	−	0.777703i
$876$		0			0
$877$	−6.60440	−	5.06773i	−0.223015	−	0.171125i	0.491211	−	0.871041i	$-0.336554\pi$
$877$	−6.60440	−	5.06773i	−0.223015	−	0.171125i	−0.714226	+	0.699915i	$0.753221\pi$
$878$		0			0
$879$	−4.60308	−	2.65759i	−0.155258	−	0.0896382i
$880$		0			0
$881$		−	44.7478i		−	1.50759i	−0.657108	−	0.753797i	$-0.728220\pi$
$881$		−	44.7478i		−	1.50759i	0.657108	−	0.753797i	$-0.271780\pi$
$882$		0			0
$883$	−42.5710	+	17.6335i	−1.43263	+	0.593414i	−0.957999	−	0.286772i	$-0.907418\pi$
$883$	−42.5710	+	17.6335i	−1.43263	+	0.593414i	−0.474629	+	0.880186i	$0.657418\pi$
$884$		0			0
$885$	−20.7011	−	26.9782i	−0.695859	−	0.906861i
$886$		0			0
$887$	43.7152	+	11.7135i	1.46781	+	0.393299i	0.902181	−	0.431358i	$-0.141965\pi$
$887$	43.7152	+	11.7135i	1.46781	+	0.393299i	0.565633	+	0.824657i	$0.308632\pi$
$888$		0			0
$889$	−4.33845	−	7.61460i	−0.145507	−	0.255385i
$890$		0			0
$891$	1.09428	+	8.31187i	0.0366597	+	0.278458i
$892$		0			0
$893$	34.8707	+	4.59082i	1.16690	+	0.153626i
$894$		0			0
$895$	29.8458			0.997636
$896$		0			0
$897$	1.03781			0.0346516
$898$		0			0
$899$	21.2155	+	2.79307i	0.707576	+	0.0931541i
$900$		0			0
$901$	−0.0821835	−	0.624246i	−0.00273793	−	0.0207966i
$902$		0			0
$903$	−46.0474	−	0.263198i	−1.53236	−	0.00875870i
$904$		0			0
$905$	−53.2747	−	14.2749i	−1.77091	−	0.474514i
$906$		0			0
$907$	13.1731	+	17.1676i	0.437407	+	0.570040i	0.959091	−	0.283099i	$-0.0913626\pi$
$907$	13.1731	+	17.1676i	0.437407	+	0.570040i	−0.521684	+	0.853139i	$0.674696\pi$
$908$		0			0
$909$	0.312864	−	0.129592i	0.0103770	−	0.00429831i
$910$		0			0
$911$		−	36.0398i		−	1.19405i	−0.802222	−	0.597026i	$-0.796349\pi$
$911$		−	36.0398i		−	1.19405i	0.802222	−	0.597026i	$-0.203651\pi$
$912$		0			0
$913$	−11.5830	−	6.68743i	−0.383340	−	0.221322i
$914$		0			0
$915$	−5.57138	−	4.27507i	−0.184184	−	0.141329i
$916$		0			0
$917$	−10.3921	−	1.42861i	−0.343176	−	0.0471770i
$918$		0			0
$919$	−39.1843	−	10.4994i	−1.29257	−	0.346344i	−0.453935	−	0.891035i	$-0.649980\pi$
$919$	−39.1843	−	10.4994i	−1.29257	−	0.346344i	−0.838637	+	0.544691i	$0.816647\pi$
$920$		0			0
$921$	9.37053	−	2.51083i	0.308769	−	0.0827345i
$922$		0			0
$923$	26.4298	+	10.9476i	0.869948	+	0.360344i
$924$		0			0
$925$	−0.337867	−	0.815683i	−0.0111090	−	0.0268195i
$926$		0			0
$927$	0.0114071	−	0.0197576i	0.000374657	−	0.000648924i
$928$		0			0
$929$	−13.6580	−	23.6564i	−0.448106	−	0.776142i	0.550157	−	0.835061i	$-0.314568\pi$
$929$	−13.6580	−	23.6564i	−0.448106	−	0.776142i	−0.998263	+	0.0589191i	$0.981235\pi$
$930$		0			0
$931$	−38.4089	+	15.3975i	−1.25880	+	0.504632i
$932$		0			0
$933$	−1.62659	−	12.3552i	−0.0532521	−	0.404490i
$934$		0			0
$935$	−0.104436	+	0.0279835i	−0.00341541	+	0.000915157i
$936$		0			0
$937$	39.8612	−	39.8612i	1.30221	−	1.30221i	0.375311	−	0.926899i	$-0.377536\pi$
$937$	39.8612	−	39.8612i	1.30221	−	1.30221i	0.926899	−	0.375311i	$-0.122464\pi$
$938$		0			0
$939$	−1.92764	+	4.65374i	−0.0629062	+	0.151869i
$940$		0			0
$941$	−1.46095	+	11.0970i	−0.0476256	+	0.361752i	0.950993	+	0.309212i	$0.100065\pi$
$941$	−1.46095	+	11.0970i	−0.0476256	+	0.361752i	−0.998619	+	0.0525405i	$0.983268\pi$
$942$		0			0
$943$	−0.508132	+	0.293370i	−0.0165470	+	0.00955344i
$944$		0			0
$945$	30.4424	−	7.97081i	0.990291	−	0.259290i
$946$		0			0
$947$	−12.2675	−	9.41317i	−0.398640	−	0.305887i	0.389916	−	0.920850i	$-0.372504\pi$
$947$	−12.2675	−	9.41317i	−0.398640	−	0.305887i	−0.788556	+	0.614964i	$0.789171\pi$
$948$		0			0
$949$	−1.28280	−	1.67178i	−0.0416416	−	0.0542683i
$950$		0			0
$951$	17.4065	−	17.4065i	0.564445	−	0.564445i
$952$		0			0
$953$	−36.3082	−	36.3082i	−1.17614	−	1.17614i	−0.980720	−	0.195417i	$-0.937394\pi$
$953$	−36.3082	−	36.3082i	−1.17614	−	1.17614i	−0.195417	−	0.980720i	$-0.562606\pi$
$954$		0			0
$955$	44.1196	−	33.8542i	1.42768	−	1.09549i
$956$		0			0
$957$	2.27135	−	2.96008i	0.0734223	−	0.0956858i
$958$		0			0
$959$	−19.5456	+	19.3234i	−0.631159	+	0.623985i
$960$		0			0
$961$	−28.1261	−	48.7158i	−0.907293	−	1.57148i
$962$		0			0
$963$	0.457796	+	0.0602699i	0.0147523	+	0.00194217i
$964$		0			0
$965$	−30.3687	−	12.5791i	−0.977603	−	0.404936i
$966$		0			0
$967$	−1.50632	−	1.50632i	−0.0484399	−	0.0484399i	0.682472	−	0.730912i	$-0.260905\pi$
$967$	−1.50632	−	1.50632i	−0.0484399	−	0.0484399i	−0.730912	+	0.682472i	$0.760905\pi$
$968$		0			0
$969$	0.131868	+	0.492139i	0.00423622	+	0.0158098i
$970$		0			0
$971$	0.0390120	−	0.00513603i	0.00125195	−	0.000164823i	−0.129900	−	0.991527i	$-0.541466\pi$
$971$	0.0390120	−	0.00513603i	0.00125195	−	0.000164823i	0.131152	+	0.991362i	$0.458132\pi$
$972$		0			0
$973$	4.95257	−	0.623242i	0.158772	−	0.0199802i
$974$		0			0
$975$	0.583417	−	0.336836i	0.0186843	−	0.0107874i
$976$		0			0
$977$	29.9664	+	17.3011i	0.958710	+	0.553511i	0.895776	−	0.444506i	$-0.146621\pi$
$977$	29.9664	+	17.3011i	0.958710	+	0.553511i	0.0629341	+	0.998018i	$0.479954\pi$
$978$		0			0
$979$	−1.89137	+	0.783431i	−0.0604484	+	0.0250386i
$980$		0			0
$981$	0.142216	−	0.343340i	0.00454061	−	0.0109620i
$982$		0			0
$983$	−1.24979	−	4.66428i	−0.0398621	−	0.148767i	0.943126	−	0.332434i	$-0.107870\pi$
$983$	−1.24979	−	4.66428i	−0.0398621	−	0.148767i	−0.982989	+	0.183667i	$0.941203\pi$
$984$		0			0
$985$	−15.2958	+	57.0848i	−0.487366	+	1.81887i
$986$		0			0
$987$	21.3407	+	16.5700i	0.679282	+	0.527428i
$988$		0			0
$989$	1.41188	−	1.84000i	0.0448952	−	0.0585086i
$990$		0			0
$991$	−5.73345	+	9.93063i	−0.182129	+	0.315457i	−0.942605	−	0.333909i	$-0.891632\pi$
$991$	−5.73345	+	9.93063i	−0.182129	+	0.315457i	0.760476	+	0.649366i	$0.224966\pi$
$992$		0			0
$993$	−27.2316			−0.864170
$994$		0			0
$995$	10.5084	+	25.3694i	0.333138	+	0.804265i
$996$		0			0
$997$	31.7634	−	24.3729i	1.00596	−	0.771899i	0.0321991	−	0.999481i	$-0.489749\pi$
$997$	31.7634	−	24.3729i	1.00596	−	0.771899i	0.973759	+	0.227583i	$0.0730823\pi$
$998$		0			0
$999$	−8.06795	+	30.1100i	−0.255259	+	0.952638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.753.7		240
4.3	odd	2		224.2.bd.a.165.12	yes	240
7.2	even	3	inner	896.2.bh.a.625.24		240
28.23	odd	6		224.2.bd.a.37.8	✓	240
32.13	even	8	inner	896.2.bh.a.529.24		240
32.19	odd	8		224.2.bd.a.109.8	yes	240
224.51	odd	24		224.2.bd.a.205.12	yes	240
224.205	even	24	inner	896.2.bh.a.401.7		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.8	✓	240	28.23	odd	6
224.2.bd.a.109.8	yes	240	32.19	odd	8
224.2.bd.a.165.12	yes	240	4.3	odd	2
224.2.bd.a.205.12	yes	240	224.51	odd	24
896.2.bh.a.401.7		240	224.205	even	24	inner
896.2.bh.a.529.24		240	32.13	even	8	inner
896.2.bh.a.625.24		240	7.2	even	3	inner
896.2.bh.a.753.7		240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.70169 - 0.224032i) q^{3} +(0.296167 + 2.24961i) q^{5} +(-1.30976 - 2.29881i) q^{7} +(-0.0522197 - 0.0139922i) q^{9} +O(q^{10})\)	\(q+(-1.70169 - 0.224032i) q^{3} +(0.296167 + 2.24961i) q^{5} +(-1.30976 - 2.29881i) q^{7} +(-0.0522197 - 0.0139922i) q^{9} +(-0.577665 - 0.752827i) q^{11} +(2.44244 - 1.01169i) q^{13} -3.89449i q^{15} +(-0.0434878 - 0.0251077i) q^{17} +(4.68988 + 3.59867i) q^{19} +(1.71379 + 4.20529i) q^{21} +(-0.220924 - 0.0591965i) q^{23} +(-0.143408 + 0.0384260i) q^{25} +(4.84289 + 2.00599i) q^{27} +(-0.876670 - 2.11647i) q^{29} +(-4.67044 + 8.08944i) q^{31} +(0.814349 + 1.41049i) q^{33} +(4.78353 - 3.62728i) q^{35} +(0.776202 + 5.89584i) q^{37} +(-4.38292 + 1.17440i) q^{39} +(1.81397 - 1.81397i) q^{41} +(-3.88053 + 9.36842i) q^{43} +(0.0160113 - 0.121618i) q^{45} +(5.15262 - 2.97487i) q^{47} +(-3.56907 + 6.02177i) q^{49} +(0.0683779 + 0.0524682i) q^{51} +(7.63303 + 9.94755i) q^{53} +(1.52248 - 1.52248i) q^{55} +(-7.17450 - 7.17450i) q^{57} +(6.92726 - 5.31547i) q^{59} +(1.09772 - 1.43058i) q^{61} +(0.0362297 + 0.138370i) q^{63} +(2.99928 + 5.19490i) q^{65} +(7.73959 + 1.01894i) q^{67} +(0.362683 + 0.150228i) q^{69} +(7.65167 + 7.65167i) q^{71} +(-0.206301 - 0.769926i) q^{73} +(0.252644 - 0.0332612i) q^{75} +(-0.974008 + 2.31396i) q^{77} +(-10.5808 + 6.10885i) q^{79} +(-7.65124 - 4.41745i) q^{81} +(13.0219 - 5.39387i) q^{83} +(0.0436030 - 0.105267i) q^{85} +(1.01766 + 3.79797i) q^{87} +(0.558378 - 2.08390i) q^{89} +(-5.52469 - 4.28963i) q^{91} +(9.75994 - 12.7194i) q^{93} +(-6.70662 + 11.6162i) q^{95} +18.1541 q^{97} +(0.0196318 + 0.0473953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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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Modular forms

Varieties

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Database

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