LMFDB - Embedded newform 896.2.bh.a.81.4

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			81.4
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87086 + 1.43556i) q^{3} +(-0.351264 + 0.457777i) q^{5} +(-2.57326 + 0.615072i) q^{7} +(0.662818 - 2.47367i) q^{9} +O(q^{10})$	\(q+(-1.87086 + 1.43556i) q^{3} +(-0.351264 + 0.457777i) q^{5} +(-2.57326 + 0.615072i) q^{7} +(0.662818 - 2.47367i) q^{9} +(0.490370 - 3.72473i) q^{11} +(2.30188 - 5.55723i) q^{13} -1.36069i q^{15} +(-0.807982 - 0.466489i) q^{17} +(5.49286 - 0.723149i) q^{19} +(3.93123 - 4.84478i) q^{21} +(-1.99298 + 7.43790i) q^{23} +(1.20792 + 4.50803i) q^{25} +(-0.396229 - 0.956581i) q^{27} +(4.94484 + 2.04822i) q^{29} +(0.446070 - 0.772617i) q^{31} +(4.42965 + 7.67239i) q^{33} +(0.622330 - 1.39403i) q^{35} +(-4.68468 + 6.10519i) q^{37} +(3.67124 + 13.7013i) q^{39} +(-4.15205 - 4.15205i) q^{41} +(3.17276 - 1.31420i) q^{43} +(0.899564 + 1.17233i) q^{45} +(5.13362 - 2.96390i) q^{47} +(6.24337 - 3.16548i) q^{49} +(2.18129 - 0.287172i) q^{51} +(-0.661564 + 5.02508i) q^{53} +(1.53284 + 1.53284i) q^{55} +(-9.23823 + 9.23823i) q^{57} +(7.94898 + 1.04650i) q^{59} +(-0.0407619 - 0.309617i) q^{61} +(-0.184120 + 6.77308i) q^{63} +(1.73540 + 3.00580i) q^{65} +(5.30670 - 4.07197i) q^{67} +(-6.94896 - 16.7763i) q^{69} +(6.57616 - 6.57616i) q^{71} +(4.70019 - 1.25941i) q^{73} +(-8.73139 - 6.69983i) q^{75} +(1.02913 + 9.88632i) q^{77} +(1.64201 - 0.948015i) q^{79} +(8.76801 + 5.06221i) q^{81} +(2.91509 - 7.03765i) q^{83} +(0.497363 - 0.206014i) q^{85} +(-12.1914 + 3.26669i) q^{87} +(2.99914 + 0.803618i) q^{89} +(-2.50525 + 15.7160i) q^{91} +(0.274603 + 2.08581i) q^{93} +(-1.59841 + 2.76852i) q^{95} +11.9825 q^{97} +(-8.88872 - 3.68183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.87086	+	1.43556i	−1.08014	+	0.828820i	−0.986001	−	0.166739i	$-0.946676\pi$
$3$	−1.87086	+	1.43556i	−1.08014	+	0.828820i	−0.0941383	+	0.995559i	$0.530010\pi$
$4$		0			0
$5$	−0.351264	+	0.457777i	−0.157090	+	0.204724i	−0.865267	−	0.501311i	$-0.832851\pi$
$5$	−0.351264	+	0.457777i	−0.157090	+	0.204724i	0.708177	+	0.706035i	$0.249518\pi$
$6$		0			0
$7$	−2.57326	+	0.615072i	−0.972602	+	0.232475i
$7$	−2.57326	+	0.615072i	−0.972602	+	0.232475i
$8$		0			0
$9$	0.662818	−	2.47367i	0.220939	−	0.824556i
$10$		0			0
$11$	0.490370	−	3.72473i	0.147852	−	1.12305i	−0.743175	−	0.669097i	$-0.766681\pi$
$11$	0.490370	−	3.72473i	0.147852	−	1.12305i	0.891027	−	0.453951i	$-0.149986\pi$
$12$		0			0
$13$	2.30188	−	5.55723i	0.638426	−	1.54130i	−0.190349	−	0.981716i	$-0.560962\pi$
$13$	2.30188	−	5.55723i	0.638426	−	1.54130i	0.828776	−	0.559581i	$-0.189038\pi$
$14$		0			0
$15$		−	1.36069i		−	0.351330i
$16$		0			0
$17$	−0.807982	−	0.466489i	−0.195964	−	0.113140i	0.398807	−	0.917035i	$-0.369424\pi$
$17$	−0.807982	−	0.466489i	−0.195964	−	0.113140i	−0.594772	+	0.803895i	$0.702758\pi$
$18$		0			0
$19$	5.49286	−	0.723149i	1.26015	−	0.165902i	0.529296	−	0.848437i	$-0.322456\pi$
$19$	5.49286	−	0.723149i	1.26015	−	0.165902i	0.730853	+	0.682535i	$0.239123\pi$
$20$		0			0
$21$	3.93123	−	4.84478i	0.857866	−	1.05722i
$22$		0			0
$23$	−1.99298	+	7.43790i	−0.415565	+	1.55091i	0.368136	+	0.929772i	$0.379996\pi$
$23$	−1.99298	+	7.43790i	−0.415565	+	1.55091i	−0.783701	+	0.621138i	$0.786671\pi$
$24$		0			0
$25$	1.20792	+	4.50803i	0.241584	+	0.901606i
$26$		0			0
$27$	−0.396229	−	0.956581i	−0.0762543	−	0.184094i
$28$		0			0
$29$	4.94484	+	2.04822i	0.918235	+	0.380345i	0.791203	−	0.611553i	$-0.209455\pi$
$29$	4.94484	+	2.04822i	0.918235	+	0.380345i	0.127032	+	0.991899i	$0.459455\pi$
$30$		0			0
$31$	0.446070	−	0.772617i	0.0801166	−	0.138766i	−0.823183	−	0.567776i	$-0.807804\pi$
$31$	0.446070	−	0.772617i	0.0801166	−	0.138766i	0.903300	+	0.429010i	$0.141137\pi$
$32$		0			0
$33$	4.42965	+	7.67239i	0.771104	+	1.33559i
$34$		0			0
$35$	0.622330	−	1.39403i	0.105193	−	0.235635i
$36$		0			0
$37$	−4.68468	+	6.10519i	−0.770156	+	1.00369i	0.229383	+	0.973336i	$0.426329\pi$
$37$	−4.68468	+	6.10519i	−0.770156	+	1.00369i	−0.999539	+	0.0303506i	$0.990338\pi$
$38$		0			0
$39$	3.67124	+	13.7013i	0.587869	+	2.19396i
$40$		0			0
$41$	−4.15205	−	4.15205i	−0.648441	−	0.648441i	0.304175	−	0.952616i	$-0.401619\pi$
$41$	−4.15205	−	4.15205i	−0.648441	−	0.648441i	−0.952616	+	0.304175i	$0.901619\pi$
$42$		0			0
$43$	3.17276	−	1.31420i	0.483842	−	0.200414i	−0.127410	−	0.991850i	$-0.540666\pi$
$43$	3.17276	−	1.31420i	0.483842	−	0.200414i	0.611252	+	0.791436i	$0.290666\pi$
$44$		0			0
$45$	0.899564	+	1.17233i	0.134099	+	0.174761i
$46$		0			0
$47$	5.13362	−	2.96390i	0.748815	−	0.432329i	−0.0764505	−	0.997073i	$-0.524359\pi$
$47$	5.13362	−	2.96390i	0.748815	−	0.432329i	0.825266	+	0.564745i	$0.191025\pi$
$48$		0			0
$49$	6.24337	−	3.16548i	0.891910	−	0.452212i
$50$		0			0
$51$	2.18129	−	0.287172i	0.305442	−	0.0402122i
$52$		0			0
$53$	−0.661564	+	5.02508i	−0.0908728	+	0.690248i	0.884000	+	0.467486i	$0.154840\pi$
$53$	−0.661564	+	5.02508i	−0.0908728	+	0.690248i	−0.974873	+	0.222761i	$0.928493\pi$
$54$		0			0
$55$	1.53284	+	1.53284i	0.206689	+	0.206689i
$56$		0			0
$57$	−9.23823	+	9.23823i	−1.22363	+	1.22363i
$58$		0			0
$59$	7.94898	+	1.04650i	1.03487	+	0.136243i	0.628774	−	0.777588i	$-0.283557\pi$
$59$	7.94898	+	1.04650i	1.03487	+	0.136243i	0.406095	+	0.913831i	$0.366890\pi$
$60$		0			0
$61$	−0.0407619	−	0.309617i	−0.00521903	−	0.0396424i	0.988637	−	0.150321i	$-0.0480308\pi$
$61$	−0.0407619	−	0.309617i	−0.00521903	−	0.0396424i	−0.993856	+	0.110679i	$0.964697\pi$
$62$		0			0
$63$	−0.184120	+	6.77308i	−0.0231970	+	0.853328i
$64$		0			0
$65$	1.73540	+	3.00580i	0.215250	+	0.372824i
$66$		0			0
$67$	5.30670	−	4.07197i	0.648316	−	0.497471i	−0.231469	−	0.972842i	$-0.574353\pi$
$67$	5.30670	−	4.07197i	0.648316	−	0.497471i	0.879785	+	0.475372i	$0.157686\pi$
$68$		0			0
$69$	−6.94896	−	16.7763i	−0.836557	−	2.01963i
$70$		0			0
$71$	6.57616	−	6.57616i	0.780446	−	0.780446i	−0.199460	−	0.979906i	$-0.563919\pi$
$71$	6.57616	−	6.57616i	0.780446	−	0.780446i	0.979906	+	0.199460i	$0.0639188\pi$
$72$		0			0
$73$	4.70019	−	1.25941i	0.550116	−	0.147403i	0.0269543	−	0.999637i	$-0.491419\pi$
$73$	4.70019	−	1.25941i	0.550116	−	0.147403i	0.523161	+	0.852234i	$0.324752\pi$
$74$		0			0
$75$	−8.73139	−	6.69983i	−1.00821	−	0.773630i
$76$		0			0
$77$	1.02913	+	9.88632i	0.117280	+	1.12665i
$78$		0			0
$79$	1.64201	−	0.948015i	0.184741	−	0.106660i	−0.404777	−	0.914415i	$-0.632651\pi$
$79$	1.64201	−	0.948015i	0.184741	−	0.106660i	0.589518	+	0.807755i	$0.299318\pi$
$80$		0			0
$81$	8.76801	+	5.06221i	0.974223	+	0.562468i
$82$		0			0
$83$	2.91509	−	7.03765i	0.319973	−	0.772483i	−0.679282	−	0.733878i	$-0.737709\pi$
$83$	2.91509	−	7.03765i	0.319973	−	0.772483i	0.999255	−	0.0386051i	$-0.0122915\pi$
$84$		0			0
$85$	0.497363	−	0.206014i	0.0539466	−	0.0223454i
$86$		0			0
$87$	−12.1914	+	3.26669i	−1.30706	+	0.350225i
$88$		0			0
$89$	2.99914	+	0.803618i	0.317909	+	0.0851833i	0.414245	−	0.910166i	$-0.364046\pi$
$89$	2.99914	+	0.803618i	0.317909	+	0.0851833i	−0.0963362	+	0.995349i	$0.530712\pi$
$90$		0			0
$91$	−2.50525	+	15.7160i	−0.262621	+	1.64749i
$92$		0			0
$93$	0.274603	+	2.08581i	0.0284750	+	0.216289i
$94$		0			0
$95$	−1.59841	+	2.76852i	−0.163993	+	0.284044i
$96$		0			0
$97$	11.9825			1.21664			0.608318	−	0.793693i	$-0.291845\pi$
$97$	11.9825			1.21664			0.608318	+	0.793693i	$0.291845\pi$
$98$		0			0
$99$	−8.88872	−	3.68183i	−0.893350	−	0.370038i
$100$		0			0
$101$	1.92668	+	0.253652i	0.191711	+	0.0252393i	0.225770	−	0.974181i	$-0.427510\pi$
$101$	1.92668	+	0.253652i	0.191711	+	0.0252393i	−0.0340590	+	0.999420i	$0.510843\pi$
$102$		0			0
$103$	−12.5620	−	3.36598i	−1.23777	−	0.331659i	−0.420170	−	0.907446i	$-0.638029\pi$
$103$	−12.5620	−	3.36598i	−1.23777	−	0.331659i	−0.817600	+	0.575786i	$0.804696\pi$
$104$		0			0
$105$	0.836925	+	3.50143i	0.0816755	+	0.341704i
$106$		0			0
$107$	8.43558	+	6.47285i	0.815498	+	0.625754i	0.929954	−	0.367675i	$-0.119846\pi$
$107$	8.43558	+	6.47285i	0.815498	+	0.625754i	−0.114457	+	0.993428i	$0.536513\pi$
$108$		0			0
$109$	−4.82436	−	6.28722i	−0.462090	−	0.602207i	0.502949	−	0.864316i	$-0.332248\pi$
$109$	−4.82436	−	6.28722i	−0.462090	−	0.602207i	−0.965038	+	0.262110i	$0.915582\pi$
$110$		0			0
$111$		−	18.1471i		−	1.72244i
$112$		0			0
$113$		−	0.280392i		−	0.0263770i	−0.999913	−	0.0131885i	$-0.995802\pi$
$113$		−	0.280392i		−	0.0263770i	0.999913	−	0.0131885i	$-0.00419815\pi$
$114$		0			0
$115$	−2.70483	−	3.52501i	−0.252227	−	0.328709i
$116$		0			0
$117$	−12.2210	−	9.37752i	−1.12983	−	0.866952i
$118$		0			0
$119$	2.36608	+	0.703431i	0.216898	+	0.0644835i
$120$		0			0
$121$	−3.00796	−	0.805981i	−0.273451	−	0.0732710i
$122$		0			0
$123$	13.7284	+	1.80738i	1.23785	+	0.162966i
$124$		0			0
$125$	−5.15343	−	2.13462i	−0.460937	−	0.190926i
$126$		0			0
$127$	4.15998			0.369139			0.184569	−	0.982819i	$-0.440911\pi$
$127$	4.15998			0.369139			0.184569	+	0.982819i	$0.440911\pi$
$128$		0			0
$129$	−4.04917	+	7.01336i	−0.356509	+	0.617492i
$130$		0			0
$131$	1.43833	+	10.9252i	0.125667	+	0.954538i	0.931843	+	0.362862i	$0.118200\pi$
$131$	1.43833	+	10.9252i	0.125667	+	0.954538i	−0.806176	+	0.591676i	$0.798466\pi$
$132$		0			0
$133$	−13.6898	+	5.23936i	−1.18706	+	0.454310i
$134$		0			0
$135$	0.577082	+	0.154629i	0.0496673	+	0.0133083i
$136$		0			0
$137$	11.5293	−	3.08927i	0.985017	−	0.263934i	0.269861	−	0.962899i	$-0.413022\pi$
$137$	11.5293	−	3.08927i	0.985017	−	0.263934i	0.715156	+	0.698965i	$0.246356\pi$
$138$		0			0
$139$	11.4890	−	4.75888i	0.974480	−	0.403643i	0.162102	−	0.986774i	$-0.448173\pi$
$139$	11.4890	−	4.75888i	0.974480	−	0.403643i	0.812378	+	0.583131i	$0.198173\pi$
$140$		0			0
$141$	−5.34942	+	12.9146i	−0.450502	+	1.08761i
$142$		0			0
$143$	−19.5704	−	11.2990i	−1.63656	−	0.944868i
$144$		0			0
$145$	−2.67458	+	1.54417i	−0.222111	+	0.128236i
$146$		0			0
$147$	−7.13622	+	14.8849i	−0.588585	+	1.22769i
$148$		0			0
$149$	−8.31462	−	6.38003i	−0.681160	−	0.522673i	0.209232	−	0.977866i	$-0.432904\pi$
$149$	−8.31462	−	6.38003i	−0.681160	−	0.522673i	−0.890393	+	0.455193i	$0.849570\pi$
$150$		0			0
$151$	9.09944	−	2.43819i	0.740502	−	0.198417i	0.131201	−	0.991356i	$-0.458117\pi$
$151$	9.09944	−	2.43819i	0.740502	−	0.198417i	0.609301	+	0.792939i	$0.291450\pi$
$152$		0			0
$153$	−1.68948	+	1.68948i	−0.136587	+	0.136587i
$154$		0			0
$155$	0.196997	+	0.475593i	0.0158232	+	0.0382006i
$156$		0			0
$157$	8.94160	−	6.86113i	0.713617	−	0.547578i	−0.186910	−	0.982377i	$-0.559847\pi$
$157$	8.94160	−	6.86113i	0.713617	−	0.547578i	0.900527	+	0.434799i	$0.143181\pi$
$158$		0			0
$159$	−5.97610	−	10.3509i	−0.473936	−	0.820881i
$160$		0			0
$161$	0.553618	−	20.3655i	0.0436312	−	1.60503i
$162$		0			0
$163$	−3.20469	−	24.3420i	−0.251010	−	1.90661i	−0.397846	−	0.917452i	$-0.630242\pi$
$163$	−3.20469	−	24.3420i	−0.251010	−	1.90661i	0.146836	−	0.989161i	$-0.453091\pi$
$164$		0			0
$165$	−5.06822	−	0.667244i	−0.394560	−	0.0519448i
$166$		0			0
$167$	−16.0366	+	16.0366i	−1.24095	+	1.24095i	−0.281340	+	0.959608i	$0.590779\pi$
$167$	−16.0366	+	16.0366i	−1.24095	+	1.24095i	−0.959608	+	0.281340i	$0.909221\pi$
$168$		0			0
$169$	−16.3917	−	16.3917i	−1.26090	−	1.26090i
$170$		0			0
$171$	1.85193	−	14.0668i	0.141621	−	1.07572i
$172$		0			0
$173$	−16.6680	+	2.19438i	−1.26724	+	0.166836i	−0.734014	−	0.679135i	$-0.762355\pi$
$173$	−16.6680	+	2.19438i	−1.26724	+	0.166836i	−0.533230	+	0.845970i	$0.679022\pi$
$174$		0			0
$175$	−5.88106	−	10.8574i	−0.444567	−	0.820741i
$176$		0			0
$177$	−16.3737	+	9.45337i	−1.23072	+	0.710558i
$178$		0			0
$179$	−4.89689	−	6.38176i	−0.366011	−	0.476995i	0.573651	−	0.819100i	$-0.305527\pi$
$179$	−4.89689	−	6.38176i	−0.366011	−	0.476995i	−0.939662	+	0.342105i	$0.888860\pi$
$180$		0			0
$181$	14.9173	−	6.17896i	1.10880	−	0.459279i	0.248274	−	0.968690i	$-0.420137\pi$
$181$	14.9173	−	6.17896i	1.10880	−	0.459279i	0.860523	+	0.509411i	$0.170137\pi$
$182$		0			0
$183$	0.520734	+	0.520734i	0.0384937	+	0.0384937i
$184$		0			0
$185$	−1.14925	−	4.28907i	−0.0844947	−	0.315339i
$186$		0			0
$187$	−2.13375	+	2.78076i	−0.156036	+	0.203350i
$188$		0			0
$189$	1.60797	+	2.21783i	0.116962	+	0.161323i
$190$		0			0
$191$	3.29574	+	5.70838i	0.238471	+	0.413044i	0.960276	−	0.279053i	$-0.0900204\pi$
$191$	3.29574	+	5.70838i	0.238471	+	0.413044i	−0.721805	+	0.692097i	$0.756687\pi$
$192$		0			0
$193$	6.59896	−	11.4297i	0.475004	−	0.822731i	−0.524586	−	0.851357i	$-0.675780\pi$
$193$	6.59896	−	11.4297i	0.475004	−	0.822731i	0.999590	+	0.0286266i	$0.00911338\pi$
$194$		0			0
$195$	−7.56169	−	3.13215i	−0.541504	−	0.224298i
$196$		0			0
$197$	−7.11028	−	17.1657i	−0.506586	−	1.22301i	−0.945837	−	0.324643i	$-0.894756\pi$
$197$	−7.11028	−	17.1657i	−0.506586	−	1.22301i	0.439250	−	0.898365i	$-0.355244\pi$
$198$		0			0
$199$	1.36570	+	5.09688i	0.0968123	+	0.361308i	0.997288	−	0.0735980i	$-0.0234482\pi$
$199$	1.36570	+	5.09688i	0.0968123	+	0.361308i	−0.900476	+	0.434906i	$0.856782\pi$
$200$		0			0
$201$	−4.08251	+	15.2362i	−0.287958	+	1.07468i
$202$		0			0
$203$	−13.9842	−	2.22918i	−0.981498	−	0.156458i
$204$		0			0
$205$	3.35918	−	0.442244i	0.234615	−	0.0308877i
$206$		0			0
$207$	17.0779	+	9.85995i	1.18700	+	0.685314i
$208$		0			0
$209$		−	20.8140i		−	1.43974i
$210$		0			0
$211$	−5.53277	+	13.3573i	−0.380892	+	0.919554i	0.610902	+	0.791706i	$0.290807\pi$
$211$	−5.53277	+	13.3573i	−0.380892	+	0.919554i	−0.991794	+	0.127848i	$0.959193\pi$
$212$		0			0
$213$	−2.86259	+	21.7435i	−0.196141	+	1.48984i
$214$		0			0
$215$	−0.512867	+	1.91405i	−0.0349773	+	0.130537i
$216$		0			0
$217$	−0.672642	+	2.26251i	−0.0456619	+	0.153589i
$218$		0			0
$219$	−6.98542	+	9.10358i	−0.472031	+	0.615163i
$220$		0			0
$221$	−4.45226	+	3.41634i	−0.299492	+	0.229808i
$222$		0			0
$223$	7.69604			0.515365			0.257682	−	0.966230i	$-0.417041\pi$
$223$	7.69604			0.515365			0.257682	+	0.966230i	$0.417041\pi$
$224$		0			0
$225$	11.9520			0.796800
$226$		0			0
$227$	−14.8321	+	11.3811i	−0.984441	+	0.755388i	−0.969649	−	0.244503i	$-0.921375\pi$
$227$	−14.8321	+	11.3811i	−0.984441	+	0.755388i	−0.0147920	+	0.999891i	$0.504709\pi$
$228$		0			0
$229$	16.7756	−	21.8623i	1.10856	−	1.44470i	0.226230	−	0.974074i	$-0.427360\pi$
$229$	16.7756	−	21.8623i	1.10856	−	1.44470i	0.882330	−	0.470631i	$-0.155974\pi$
$230$		0			0
$231$	−16.1177	−	17.0185i	−1.06047	−	1.11974i
$232$		0			0
$233$	−3.54777	+	13.2405i	−0.232422	+	0.867411i	0.746872	+	0.664968i	$0.231555\pi$
$233$	−3.54777	+	13.2405i	−0.232422	+	0.867411i	−0.979294	+	0.202443i	$0.935112\pi$
$234$		0			0
$235$	−0.446455	+	3.39116i	−0.0291235	+	0.221215i
$236$		0			0
$237$	−1.71103	+	4.13080i	−0.111144	+	0.268324i
$238$		0			0
$239$			27.8812i			1.80349i	0.432271	+	0.901744i	$0.357712\pi$
$239$			27.8812i			1.80349i	−0.432271	+	0.901744i	$0.642288\pi$
$240$		0			0
$241$	12.5355	+	7.23739i	0.807484	+	0.466201i	0.846081	−	0.533054i	$-0.178956\pi$
$241$	12.5355	+	7.23739i	0.807484	+	0.466201i	−0.0385975	+	0.999255i	$0.512289\pi$
$242$		0			0
$243$	−20.5912	+	2.71088i	−1.32092	+	0.173903i
$244$		0			0
$245$	−0.743989	+	3.96999i	−0.0475317	+	0.253633i
$246$		0			0
$247$	8.62520	−	32.1897i	0.548808	−	2.04818i
$248$		0			0
$249$	4.64925	+	17.3512i	0.294634	+	1.09959i
$250$		0			0
$251$	−6.85898	−	16.5590i	−0.432935	−	1.04520i	−0.978336	−	0.207023i	$-0.933623\pi$
$251$	−6.85898	−	16.5590i	−0.432935	−	1.04520i	0.545401	−	0.838175i	$-0.316377\pi$
$252$		0			0
$253$	26.7269	+	11.0706i	1.68030	+	0.696005i
$254$		0			0
$255$	−0.634749	+	1.09942i	−0.0397495	+	0.0688482i
$256$		0			0
$257$	1.48954	+	2.57995i	0.0929147	+	0.160933i	0.908736	−	0.417371i	$-0.137048\pi$
$257$	1.48954	+	2.57995i	0.0929147	+	0.160933i	−0.815822	+	0.578304i	$0.803715\pi$
$258$		0			0
$259$	8.29978	−	18.5917i	0.515723	−	1.15523i
$260$		0			0
$261$	8.34415	−	10.8743i	0.516490	−	0.673103i
$262$		0			0
$263$	5.57618	+	20.8106i	0.343842	+	1.28324i	0.893959	+	0.448148i	$0.147916\pi$
$263$	5.57618	+	20.8106i	0.343842	+	1.28324i	−0.550117	+	0.835087i	$0.685417\pi$
$264$		0			0
$265$	−2.06798	−	2.06798i	−0.127035	−	0.127035i
$266$		0			0
$267$	−6.76461	+	2.80199i	−0.413987	+	0.171479i
$268$		0			0
$269$	−2.47716	−	3.22829i	−0.151035	−	0.196833i	0.711708	−	0.702476i	$-0.247922\pi$
$269$	−2.47716	−	3.22829i	−0.151035	−	0.196833i	−0.862743	+	0.505643i	$0.831255\pi$
$270$		0			0
$271$	−15.5524	+	8.97921i	−0.944743	+	0.545448i	−0.891444	−	0.453131i	$-0.850307\pi$
$271$	−15.5524	+	8.97921i	−0.944743	+	0.545448i	−0.0532993	+	0.998579i	$0.516974\pi$
$272$		0			0
$273$	−17.8743	−	32.9989i	−1.08180	−	1.99718i
$274$		0			0
$275$	17.3835	−	2.28858i	1.04827	−	0.138007i
$276$		0			0
$277$	−0.274365	+	2.08401i	−0.0164850	+	0.125216i	−0.997709	−	0.0676578i	$-0.978447\pi$
$277$	−0.274365	+	2.08401i	−0.0164850	+	0.125216i	0.981224	+	0.192874i	$0.0617807\pi$
$278$		0			0
$279$	−1.61553	−	1.61553i	−0.0967195	−	0.0967195i
$280$		0			0
$281$	−15.6188	+	15.6188i	−0.931742	+	0.931742i	−0.997815	−	0.0660724i	$-0.978953\pi$
$281$	−15.6188	+	15.6188i	−0.931742	+	0.931742i	0.0660724	+	0.997815i	$0.478953\pi$
$282$		0			0
$283$	22.5899	+	2.97401i	1.34283	+	0.176787i	0.767455	−	0.641103i	$-0.221523\pi$
$283$	22.5899	+	2.97401i	1.34283	+	0.176787i	0.575374	+	0.817890i	$0.304856\pi$
$284$		0			0
$285$	−0.983985	−	7.47411i	−0.0582862	−	0.442728i
$286$		0			0
$287$	13.2381	+	8.13051i	0.781422	+	0.479929i
$288$		0			0
$289$	−8.06478	−	13.9686i	−0.474399	−	0.821683i
$290$		0			0
$291$	−22.4175	+	17.2015i	−1.31414	+	1.00837i
$292$		0			0
$293$	6.04172	+	14.5860i	0.352961	+	0.852123i	0.996252	+	0.0865013i	$0.0275687\pi$
$293$	6.04172	+	14.5860i	0.352961	+	0.852123i	−0.643291	+	0.765622i	$0.722431\pi$
$294$		0			0
$295$	−3.27126	+	3.27126i	−0.190460	+	0.190460i
$296$		0			0
$297$	−3.75730	+	1.00677i	−0.218021	+	0.0584185i
$298$		0			0
$299$	36.7465	+	28.1966i	2.12511	+	1.63065i
$300$		0			0
$301$	−7.35602	+	5.33326i	−0.423994	+	0.307404i
$302$		0			0
$303$	−3.96866	+	2.29131i	−0.227994	+	0.131632i
$304$		0			0
$305$	0.156054	+	0.0900977i	0.00893561	+	0.00515898i
$306$		0			0
$307$	1.29084	−	3.11637i	0.0736723	−	0.177861i	−0.882753	−	0.469837i	$-0.844313\pi$
$307$	1.29084	−	3.11637i	0.0736723	−	0.177861i	0.956426	+	0.291976i	$0.0943128\pi$
$308$		0			0
$309$	28.3337	−	11.7362i	1.61185	−	0.667650i
$310$		0			0
$311$	12.2693	−	3.28754i	0.695726	−	0.186419i	0.106411	−	0.994322i	$-0.466064\pi$
$311$	12.2693	−	3.28754i	0.695726	−	0.186419i	0.589315	+	0.807903i	$0.299398\pi$
$312$		0			0
$313$	−11.6451	−	3.12028i	−0.658218	−	0.176369i	−0.0857762	−	0.996314i	$-0.527337\pi$
$313$	−11.6451	−	3.12028i	−0.658218	−	0.176369i	−0.572442	+	0.819945i	$0.694004\pi$
$314$		0			0
$315$	−3.03588	−	2.46343i	−0.171053	−	0.138798i
$316$		0			0
$317$	0.873625	+	6.63584i	0.0490677	+	0.372706i	0.998308	+	0.0581532i	$0.0185212\pi$
$317$	0.873625	+	6.63584i	0.0490677	+	0.372706i	−0.949240	+	0.314553i	$0.898145\pi$
$318$		0			0
$319$	10.0539	−	17.4138i	0.562909	−	0.974987i
$320$		0			0
$321$	−25.0739			−1.39949
$322$		0			0
$323$	−4.77548	−	1.97807i	−0.265715	−	0.110063i
$324$		0			0
$325$	27.8326	+	3.66424i	1.54388	+	0.203255i
$326$		0			0
$327$	18.0514	+	4.83685i	0.998242	+	0.267478i
$328$		0			0
$329$	−11.3871	+	10.7844i	−0.627794	+	0.594565i
$330$		0			0
$331$	11.5193	+	8.83910i	0.633160	+	0.485841i	0.874774	−	0.484532i	$-0.161010\pi$
$331$	11.5193	+	8.83910i	0.633160	+	0.485841i	−0.241614	+	0.970373i	$0.577677\pi$
$332$		0			0
$333$	11.9971	+	15.6350i	0.657439	+	0.856791i
$334$		0			0
$335$			3.85962i			0.210874i
$336$		0			0
$337$			29.7522i			1.62071i	0.585941	+	0.810354i	$0.300725\pi$
$337$			29.7522i			1.62071i	−0.585941	+	0.810354i	$0.699275\pi$
$338$		0			0
$339$	0.402518	+	0.524572i	0.0218618	+	0.0284909i
$340$		0			0
$341$	−2.65905	−	2.04036i	−0.143996	−	0.110492i
$342$		0			0
$343$	−14.1188	+	11.9858i	−0.762346	+	0.647170i
$344$		0			0
$345$	10.1207	+	2.71184i	0.544881	+	0.146000i
$346$		0			0
$347$	−21.1564	−	2.78530i	−1.13574	−	0.149522i	−0.460873	−	0.887466i	$-0.652464\pi$
$347$	−21.1564	−	2.78530i	−1.13574	−	0.149522i	−0.674863	+	0.737943i	$0.735797\pi$
$348$		0			0
$349$	1.15285	+	0.477524i	0.0617104	+	0.0255613i	0.413325	−	0.910584i	$-0.364367\pi$
$349$	1.15285	+	0.477524i	0.0617104	+	0.0255613i	−0.351615	+	0.936145i	$0.614367\pi$
$350$		0			0
$351$	−6.22801			−0.332427
$352$		0			0
$353$	7.90214	−	13.6869i	0.420588	−	0.728480i	−0.575409	−	0.817866i	$-0.695157\pi$
$353$	7.90214	−	13.6869i	0.420588	−	0.728480i	0.995997	+	0.0893857i	$0.0284904\pi$
$354$		0			0
$355$	0.700441	+	5.32038i	0.0371756	+	0.282376i
$356$		0			0
$357$	−5.43640	+	2.08062i	−0.287725	+	0.110118i
$358$		0			0
$359$	−5.17792	−	1.38742i	−0.273280	−	0.0732253i	0.119576	−	0.992825i	$-0.461846\pi$
$359$	−5.17792	−	1.38742i	−0.273280	−	0.0732253i	−0.392857	+	0.919600i	$0.628513\pi$
$360$		0			0
$361$	11.2960	−	3.02675i	0.594526	−	0.159303i
$362$		0			0
$363$	6.78449	−	2.81023i	0.356094	−	0.147499i
$364$		0			0
$365$	−1.07448	+	2.59402i	−0.0562408	+	0.135777i
$366$		0			0
$367$	5.59035	+	3.22759i	0.291814	+	0.168479i	0.638760	−	0.769406i	$-0.279448\pi$
$367$	5.59035	+	3.22759i	0.291814	+	0.168479i	−0.346946	+	0.937885i	$0.612781\pi$
$368$		0			0
$369$	−13.0228	+	7.51874i	−0.677942	+	0.391410i
$370$		0			0
$371$	−1.38841	−	13.3378i	−0.0720824	−	0.692462i
$372$		0			0
$373$	10.1633	+	7.79855i	0.526234	+	0.403793i	0.837424	−	0.546554i	$-0.184061\pi$
$373$	10.1633	+	7.79855i	0.526234	+	0.403793i	−0.311190	+	0.950348i	$0.600728\pi$
$374$		0			0
$375$	12.7057	−	3.40448i	0.656119	−	0.175807i
$376$		0			0
$377$	22.7649	−	22.7649i	1.17245	−	1.17245i
$378$		0			0
$379$	−13.0353	−	31.4700i	−0.669579	−	1.61651i	−0.782316	−	0.622882i	$-0.785962\pi$
$379$	−13.0353	−	31.4700i	−0.669579	−	1.61651i	0.112737	−	0.993625i	$-0.464038\pi$
$380$		0			0
$381$	−7.78273	+	5.97190i	−0.398721	+	0.305950i
$382$		0			0
$383$	−5.96508	−	10.3318i	−0.304801	−	0.527931i	0.672416	−	0.740174i	$-0.265257\pi$
$383$	−5.96508	−	10.3318i	−0.304801	−	0.527931i	−0.977217	+	0.212242i	$0.931923\pi$
$384$		0			0
$385$	−4.88722	−	3.00160i	−0.249076	−	0.152976i
$386$		0			0
$387$	−1.14794	−	8.71944i	−0.0583529	−	0.443234i
$388$		0			0
$389$	5.03302	+	0.662610i	0.255184	+	0.0335957i	0.257033	−	0.966403i	$-0.417255\pi$
$389$	5.03302	+	0.662610i	0.255184	+	0.0335957i	−0.00184861	+	0.999998i	$0.500588\pi$
$390$		0			0
$391$	5.07999	−	5.07999i	0.256906	−	0.256906i
$392$		0			0
$393$	−18.3746	−	18.3746i	−0.926878	−	0.926878i
$394$		0			0
$395$	−0.142801	+	1.08468i	−0.00718507	+	0.0545761i
$396$		0			0
$397$	−29.4107	+	3.87199i	−1.47608	+	0.194330i	−0.825196	−	0.564846i	$-0.808935\pi$
$397$	−29.4107	+	3.87199i	−1.47608	+	0.194330i	−0.650885	+	0.759176i	$0.725602\pi$
$398$		0			0
$399$	18.0902	−	29.4546i	0.905644	−	1.47457i
$400$		0			0
$401$	29.3305	−	16.9340i	1.46469	−	0.845642i	0.465472	−	0.885063i	$-0.345885\pi$
$401$	29.3305	−	16.9340i	1.46469	−	0.845642i	0.999223	+	0.0394208i	$0.0125513\pi$
$402$		0			0
$403$	−3.26681	−	4.25738i	−0.162731	−	0.212075i
$404$		0			0
$405$	−5.39725	+	2.23561i	−0.268192	+	0.111089i
$406$		0			0
$407$	20.4429	+	20.4429i	1.01332	+	1.01332i
$408$		0			0
$409$	−7.65126	−	28.5549i	−0.378330	−	1.41195i	−0.848417	−	0.529328i	$-0.822444\pi$
$409$	−7.65126	−	28.5549i	−0.378330	−	1.41195i	0.470087	−	0.882620i	$-0.344222\pi$
$410$		0			0
$411$	−17.1349	+	22.3306i	−0.845201	+	1.10149i
$412$		0			0
$413$	−21.0985	+	2.19627i	−1.03819	+	0.108071i
$414$		0			0
$415$	2.19770	+	3.80654i	0.107881	+	0.186856i
$416$		0			0
$417$	−14.6625	+	25.3962i	−0.718027	+	1.24366i
$418$		0			0
$419$	0.305430	+	0.126513i	0.0149212	+	0.00618058i	0.390132	−	0.920759i	$-0.372430\pi$
$419$	0.305430	+	0.126513i	0.0149212	+	0.00618058i	−0.375210	+	0.926940i	$0.622430\pi$
$420$		0			0
$421$	3.21719	+	7.76698i	0.156796	+	0.378539i	0.982683	−	0.185297i	$-0.0593248\pi$
$421$	3.21719	+	7.76698i	0.156796	+	0.378539i	−0.825886	+	0.563837i	$0.809325\pi$
$422$		0			0
$423$	−3.92905	−	14.6634i	−0.191037	−	0.712959i
$424$		0			0
$425$	1.12696	−	4.20589i	0.0546658	−	0.204016i
$426$		0			0
$427$	0.295328	+	0.771656i	0.0142919	+	0.0373430i
$428$		0			0
$429$	52.8337	−	6.95569i	2.55084	−	0.335824i
$430$		0			0
$431$	−1.19677	−	0.690958i	−0.0576466	−	0.0332823i	0.470900	−	0.882187i	$-0.343929\pi$
$431$	−1.19677	−	0.690958i	−0.0576466	−	0.0332823i	−0.528546	+	0.848904i	$0.677263\pi$
$432$		0			0
$433$		−	1.35753i		−	0.0652385i	−0.999468	−	0.0326193i	$-0.989615\pi$
$433$		−	1.35753i		−	0.0652385i	0.999468	−	0.0326193i	$-0.0103849\pi$
$434$		0			0
$435$	2.78700	−	6.72842i	0.133627	−	0.322603i
$436$		0			0
$437$	−5.56845	+	42.2966i	−0.266375	+	2.02332i
$438$		0			0
$439$	7.51378	−	28.0418i	0.358613	−	1.33836i	−0.517264	−	0.855826i	$-0.673049\pi$
$439$	7.51378	−	28.0418i	0.358613	−	1.33836i	0.875876	−	0.482535i	$-0.160284\pi$
$440$		0			0
$441$	−3.69214	−	17.5422i	−0.175816	−	0.835342i
$442$		0			0
$443$	0.000901585	−	0.00117497i	4.28356e−5	−	5.58244e-5i	−0.793332	−	0.608789i	$-0.791655\pi$
$443$	0.000901585	−	0.00117497i	4.28356e−5	−	5.58244e-5i	0.793375	+	0.608734i	$0.208322\pi$
$444$		0			0
$445$	−1.42137	+	1.09066i	−0.0673794	+	0.0517020i
$446$		0			0
$447$	24.7144			1.16895
$448$		0			0
$449$	3.52807			0.166500			0.0832501	−	0.996529i	$-0.473470\pi$
$449$	3.52807			0.166500			0.0832501	+	0.996529i	$0.473470\pi$
$450$		0			0
$451$	−17.5013	+	13.4292i	−0.824104	+	0.632357i
$452$		0			0
$453$	−13.5236	+	17.6243i	−0.635394	+	0.828061i
$454$		0			0
$455$	−6.31443	−	6.66732i	−0.296025	−	0.312569i
$456$		0			0
$457$	4.95685	−	18.4992i	0.231872	−	0.865358i	−0.747662	−	0.664079i	$-0.768824\pi$
$457$	4.95685	−	18.4992i	0.231872	−	0.865358i	0.979534	−	0.201278i	$-0.0645096\pi$
$458$		0			0
$459$	−0.126088	+	0.957737i	−0.00588531	+	0.0447033i
$460$		0			0
$461$	7.51964	−	18.1540i	0.350225	−	0.845517i	−0.646367	−	0.763027i	$-0.723713\pi$
$461$	7.51964	−	18.1540i	0.350225	−	0.845517i	0.996592	−	0.0824907i	$-0.0262875\pi$
$462$		0			0
$463$		−	6.20731i		−	0.288478i	−0.989543	−	0.144239i	$-0.953927\pi$
$463$		−	6.20731i		−	0.288478i	0.989543	−	0.144239i	$-0.0460734\pi$
$464$		0			0
$465$	−1.05130	−	0.606965i	−0.0487526	−	0.0281474i
$466$		0			0
$467$	−14.6713	+	1.93152i	−0.678908	+	0.0893799i	−0.462091	−	0.886832i	$-0.652901\pi$
$467$	−14.6713	+	1.93152i	−0.678908	+	0.0893799i	−0.216817	+	0.976212i	$0.569567\pi$
$468$		0			0
$469$	−11.1510	+	13.7423i	−0.514904	+	0.634559i
$470$		0			0
$471$	−6.87889	+	25.6724i	−0.316963	+	1.18292i
$472$		0			0
$473$	−3.33922	−	12.4621i	−0.153537	−	0.573009i
$474$		0			0
$475$	9.89493	+	23.8885i	0.454010	+	1.09608i
$476$		0			0
$477$	11.9919	+	4.96720i	0.549071	+	0.227433i
$478$		0			0
$479$	14.7109	−	25.4801i	0.672160	−	1.16422i	−0.305130	−	0.952311i	$-0.598700\pi$
$479$	14.7109	−	25.4801i	0.672160	−	1.16422i	0.977290	−	0.211905i	$-0.0679668\pi$
$480$		0			0
$481$	23.1444	+	40.0872i	1.05529	+	1.82782i
$482$		0			0
$483$	28.2001	+	38.8957i	1.28315	+	1.76982i
$484$		0			0
$485$	−4.20902	+	5.48530i	−0.191122	+	0.249074i
$486$		0			0
$487$	−5.37932	−	20.0759i	−0.243760	−	0.909725i	−0.974003	−	0.226537i	$-0.927260\pi$
$487$	−5.37932	−	20.0759i	−0.243760	−	0.909725i	0.730242	−	0.683188i	$-0.239407\pi$
$488$		0			0
$489$	40.9399	+	40.9399i	1.85137	+	1.85137i
$490$		0			0
$491$	−21.8177	+	9.03718i	−0.984618	+	0.407842i	−0.816134	−	0.577862i	$-0.803887\pi$
$491$	−21.8177	+	9.03718i	−0.984618	+	0.407842i	−0.168484	+	0.985704i	$0.553887\pi$
$492$		0			0
$493$	−3.03987	−	3.96164i	−0.136909	−	0.178423i
$494$		0			0
$495$	4.80775	−	2.77575i	0.216092	−	0.124761i
$496$		0			0
$497$	−12.8774	+	20.9670i	−0.577629	+	0.940498i
$498$		0			0
$499$	33.4008	−	4.39729i	1.49522	−	0.196850i	0.661882	−	0.749608i	$-0.269758\pi$
$499$	33.4008	−	4.39729i	1.49522	−	0.196850i	0.833342	+	0.552758i	$0.186425\pi$
$500$		0			0
$501$	6.98069	−	53.0236i	0.311874	−	2.36892i
$502$		0			0
$503$	4.18188	+	4.18188i	0.186461	+	0.186461i	0.794164	−	0.607703i	$-0.207909\pi$
$503$	4.18188	+	4.18188i	0.186461	+	0.186461i	−0.607703	+	0.794164i	$0.707909\pi$
$504$		0			0
$505$	−0.792888	+	0.792888i	−0.0352831	+	0.0352831i
$506$		0			0
$507$	54.1979	+	7.13529i	2.40701	+	0.316889i
$508$		0			0
$509$	−2.58369	−	19.6251i	−0.114520	−	0.869867i	−0.948212	−	0.317637i	$-0.897111\pi$
$509$	−2.58369	−	19.6251i	−0.114520	−	0.869867i	0.833692	−	0.552229i	$-0.186223\pi$
$510$		0			0
$511$	−11.3202	+	6.13176i	−0.500776	+	0.271253i
$512$		0			0
$513$	−2.86818	−	4.96784i	−0.126633	−	0.219335i
$514$		0			0
$515$	5.95344	−	4.56824i	0.262340	−	0.201301i
$516$		0			0
$517$	−8.52234	−	20.5747i	−0.374812	−	0.904876i
$518$		0			0
$519$	28.0332	−	28.0332i	1.23052	−	1.23052i
$520$		0			0
$521$	−24.5343	+	6.57395i	−1.07487	+	0.288010i	−0.752491	−	0.658602i	$-0.771148\pi$
$521$	−24.5343	+	6.57395i	−1.07487	+	0.288010i	−0.322376	+	0.946612i	$0.604481\pi$
$522$		0			0
$523$	−30.7519	−	23.5967i	−1.34469	−	1.03181i	−0.995500	−	0.0947596i	$-0.969792\pi$
$523$	−30.7519	−	23.5967i	−1.34469	−	1.03181i	−0.349185	−	0.937054i	$-0.613542\pi$
$524$		0			0
$525$	26.5890	+	11.8700i	1.16044	+	0.518049i
$526$		0			0
$527$	−0.720834	+	0.416174i	−0.0314000	+	0.0181288i
$528$		0			0
$529$	−31.4318	−	18.1472i	−1.36660	−	0.789008i
$530$		0			0
$531$	7.85742	−	18.9695i	0.340983	−	0.823206i
$532$		0			0
$533$	−32.6314	+	13.5164i	−1.41342	+	0.585459i
$534$		0			0
$535$	−5.92623	+	1.58793i	−0.256213	+	0.0686522i
$536$		0			0
$537$	18.3228	+	4.90957i	0.790686	+	0.211864i
$538$		0			0
$539$	−8.72901	−	24.8071i	−0.375985	−	1.06852i
$540$		0			0
$541$	0.581574	+	4.41749i	0.0250038	+	0.189923i	0.999389	−	0.0349647i	$-0.0111319\pi$
$541$	0.581574	+	4.41749i	0.0250038	+	0.189923i	−0.974385	+	0.224888i	$0.927799\pi$
$542$		0			0
$543$	−19.0379	+	32.9747i	−0.816996	+	1.41508i
$544$		0			0
$545$	4.57277			0.195876
$546$		0			0
$547$	31.1091	+	12.8858i	1.33013	+	0.550958i	0.930693	−	0.365802i	$-0.119205\pi$
$547$	31.1091	+	12.8858i	1.33013	+	0.550958i	0.399438	+	0.916760i	$0.369205\pi$
$548$		0			0
$549$	−0.792909	−	0.104388i	−0.0338405	−	0.00445519i
$550$		0			0
$551$	28.6425	+	7.67474i	1.22021	+	0.326955i
$552$		0			0
$553$	−3.64223	+	3.44945i	−0.154883	+	0.146685i
$554$		0			0
$555$	8.30730	+	6.37441i	0.352625	+	0.270579i
$556$		0			0
$557$	11.2012	+	14.5977i	0.474612	+	0.618526i	0.967899	−	0.251341i	$-0.0808715\pi$
$557$	11.2012	+	14.5977i	0.474612	+	0.618526i	−0.493287	+	0.869867i	$0.664205\pi$
$558$		0			0
$559$		−	20.6569i		−	0.873693i
$560$		0			0
$561$		−	8.26554i		−	0.348971i
$562$		0			0
$563$	16.0639	+	20.9349i	0.677012	+	0.882299i	0.997897	−	0.0648191i	$-0.0206470\pi$
$563$	16.0639	+	20.9349i	0.677012	+	0.882299i	−0.320885	+	0.947118i	$0.603980\pi$
$564$		0			0
$565$	0.128357	+	0.0984915i	0.00540001	+	0.00414357i
$566$		0			0
$567$	−25.6760	−	7.63345i	−1.07829	−	0.320575i
$568$		0			0
$569$	26.7202	+	7.15966i	1.12017	+	0.300149i	0.770952	−	0.636893i	$-0.219781\pi$
$569$	26.7202	+	7.15966i	1.12017	+	0.300149i	0.349218	+	0.937042i	$0.386447\pi$
$570$		0			0
$571$	−25.0356	−	3.29600i	−1.04771	−	0.137933i	−0.413035	−	0.910715i	$-0.635531\pi$
$571$	−25.0356	−	3.29600i	−1.04771	−	0.137933i	−0.634672	+	0.772782i	$0.718865\pi$
$572$		0			0
$573$	−14.3606	−	5.94834i	−0.599921	−	0.248495i
$574$		0			0
$575$	−35.9376			−1.49870
$576$		0			0
$577$	−1.97485	+	3.42054i	−0.0822142	+	0.142399i	−0.904201	−	0.427108i	$-0.859532\pi$
$577$	−1.97485	+	3.42054i	−0.0822142	+	0.142399i	0.821987	+	0.569507i	$0.192866\pi$
$578$		0			0
$579$	4.06235	+	30.8566i	0.168825	+	1.28236i
$580$		0			0
$581$	−3.17264	+	19.9027i	−0.131623	+	0.825704i
$582$		0			0
$583$	18.3926	+	4.92829i	0.761745	+	0.204109i
$584$		0			0
$585$	8.58561	−	2.30051i	0.354971	−	0.0951143i
$586$		0			0
$587$	−39.2818	+	16.2711i	−1.62133	+	0.671578i	−0.994221	−	0.107350i	$-0.965763\pi$
$587$	−39.2818	+	16.2711i	−1.62133	+	0.671578i	−0.627112	+	0.778929i	$0.715763\pi$
$588$		0			0
$589$	1.89149	−	4.56645i	0.0779373	−	0.188157i
$590$		0			0
$591$	37.9447	+	21.9074i	1.56084	+	0.901150i
$592$		0			0
$593$	3.79969	−	2.19375i	0.156034	−	0.0900865i	−0.419950	−	0.907547i	$-0.637952\pi$
$593$	3.79969	−	2.19375i	0.156034	−	0.0900865i	0.575984	+	0.817461i	$0.304619\pi$
$594$		0			0
$595$	−1.15313	+	0.836043i	−0.0472738	+	0.0342744i
$596$		0			0
$597$	−9.87191	−	7.57498i	−0.404030	−	0.310023i
$598$		0			0
$599$	−5.62925	+	1.50835i	−0.230005	+	0.0616297i	−0.371981	−	0.928240i	$-0.621321\pi$
$599$	−5.62925	+	1.50835i	−0.230005	+	0.0616297i	0.141976	+	0.989870i	$0.454655\pi$
$600$		0			0
$601$	−25.8043	+	25.8043i	−1.05258	+	1.05258i	−0.0540386	+	0.998539i	$0.517209\pi$
$601$	−25.8043	+	25.8043i	−1.05258	+	1.05258i	−0.998539	+	0.0540386i	$0.982791\pi$
$602$		0			0
$603$	−6.55534	−	15.8260i	−0.266954	−	0.644484i
$604$		0			0
$605$	1.42555	−	1.09386i	0.0579568	−	0.0444718i
$606$		0			0
$607$	−4.80696	−	8.32590i	−0.195108	−	0.337938i	0.751828	−	0.659360i	$-0.229173\pi$
$607$	−4.80696	−	8.32590i	−0.195108	−	0.337938i	−0.946936	+	0.321422i	$0.895839\pi$
$608$		0			0
$609$	29.3625	−	15.9047i	1.18983	−	0.644489i
$610$		0			0
$611$	−4.65408	−	35.3512i	−0.188284	−	1.43016i
$612$		0			0
$613$	20.1836	+	2.65723i	0.815209	+	0.107324i	0.526590	−	0.850120i	$-0.323470\pi$
$613$	20.1836	+	2.65723i	0.815209	+	0.107324i	0.288619	+	0.957444i	$0.406804\pi$
$614$		0			0
$615$	−5.64967	+	5.64967i	−0.227817	+	0.227817i
$616$		0			0
$617$	10.2970	+	10.2970i	0.414540	+	0.414540i	0.883317	−	0.468777i	$-0.155305\pi$
$617$	10.2970	+	10.2970i	0.414540	+	0.414540i	−0.468777	+	0.883317i	$0.655305\pi$
$618$		0			0
$619$	−1.21352	+	9.21763i	−0.0487756	+	0.370488i	0.949598	+	0.313471i	$0.101492\pi$
$619$	−1.21352	+	9.21763i	−0.0487756	+	0.370488i	−0.998373	+	0.0570162i	$0.981841\pi$
$620$		0			0
$621$	7.90463	−	1.04066i	0.317202	−	0.0417604i
$622$		0			0
$623$	−8.21187	−	0.223232i	−0.329002	−	0.00894362i
$624$		0			0
$625$	−17.4215	+	10.0583i	−0.696862	+	0.402333i
$626$		0			0
$627$	29.8798	+	38.9401i	1.19328	+	1.55512i
$628$		0			0
$629$	6.63314	−	2.74753i	0.264480	−	0.109551i
$630$		0			0
$631$	6.64184	+	6.64184i	0.264408	+	0.264408i	0.826842	−	0.562434i	$-0.190135\pi$
$631$	6.64184	+	6.64184i	0.264408	+	0.264408i	−0.562434	+	0.826842i	$0.690135\pi$
$632$		0			0
$633$	−8.82416	−	32.9322i	−0.350729	−	1.30894i
$634$		0			0
$635$	−1.46125	+	1.90434i	−0.0579881	+	0.0755716i
$636$		0			0
$637$	−3.21983	−	41.9824i	−0.127574	−	1.66340i
$638$		0			0
$639$	−11.9084	−	20.6260i	−0.471091	−	0.815953i
$640$		0			0
$641$	−18.7666	+	32.5047i	−0.741236	+	1.28386i	0.210697	+	0.977551i	$0.432427\pi$
$641$	−18.7666	+	32.5047i	−0.741236	+	1.28386i	−0.951933	+	0.306307i	$0.900907\pi$
$642$		0			0
$643$	18.7447	+	7.76429i	0.739217	+	0.306194i	0.720334	−	0.693628i	$-0.243989\pi$
$643$	18.7447	+	7.76429i	0.739217	+	0.306194i	0.0188838	+	0.999822i	$0.493989\pi$
$644$		0			0
$645$	−1.78823	−	4.31716i	−0.0704113	−	0.169988i
$646$		0			0
$647$	0.978974	+	3.65358i	0.0384875	+	0.143637i	0.982496	−	0.186284i	$-0.0596445\pi$
$647$	0.978974	+	3.65358i	0.0384875	+	0.143637i	−0.944008	+	0.329921i	$0.892978\pi$
$648$		0			0
$649$	7.79588	−	29.0946i	0.306015	−	1.14206i
$650$		0			0
$651$	−1.98955	−	5.19845i	−0.0779767	−	0.203743i
$652$		0			0
$653$	38.7444	−	5.10079i	1.51618	−	0.199609i	0.673973	−	0.738756i	$-0.264587\pi$
$653$	38.7444	−	5.10079i	1.51618	−	0.199609i	0.842212	+	0.539147i	$0.181253\pi$
$654$		0			0
$655$	−5.50653	−	3.17919i	−0.215158	−	0.124221i
$656$		0			0
$657$		−	12.4615i		−	0.486169i
$658$		0			0
$659$	1.94642	−	4.69907i	0.0758217	−	0.183050i	−0.881424	−	0.472326i	$-0.843415\pi$
$659$	1.94642	−	4.69907i	0.0758217	−	0.183050i	0.957246	+	0.289276i	$0.0934145\pi$
$660$		0			0
$661$	−2.33639	+	17.7467i	−0.0908752	+	0.690266i	0.883996	+	0.467495i	$0.154843\pi$
$661$	−2.33639	+	17.7467i	−0.0908752	+	0.690266i	−0.974871	+	0.222771i	$0.928490\pi$
$662$		0			0
$663$	3.42518	−	12.7830i	0.133023	−	0.496449i
$664$		0			0
$665$	2.41028	−	8.10727i	0.0934667	−	0.314386i
$666$		0			0
$667$	−25.0895	+	32.6972i	−0.971467	+	1.26604i
$668$		0			0
$669$	−14.3982	+	11.0481i	−0.556666	+	0.427145i
$670$		0			0
$671$	−1.17323			−0.0452920
$672$		0			0
$673$	20.4014			0.786415			0.393208	−	0.919450i	$-0.371365\pi$
$673$	20.4014			0.786415			0.393208	+	0.919450i	$0.371365\pi$
$674$		0			0
$675$	3.83368	−	2.94169i	0.147558	−	0.113226i
$676$		0			0
$677$	−16.5047	+	21.5094i	−0.634329	+	0.826673i	−0.994337	−	0.106276i	$-0.966107\pi$
$677$	−16.5047	+	21.5094i	−0.634329	+	0.826673i	0.360008	+	0.932949i	$0.382774\pi$
$678$		0			0
$679$	−30.8341	+	7.37008i	−1.18330	+	0.282838i
$680$		0			0
$681$	11.4105	−	42.5847i	0.437252	−	1.63185i
$682$		0			0
$683$	−0.568841	+	4.32078i	−0.0217661	+	0.165330i	−0.998876	−	0.0474067i	$-0.984904\pi$
$683$	−0.568841	+	4.32078i	−0.0217661	+	0.165330i	0.977110	+	0.212737i	$0.0682377\pi$
$684$		0			0
$685$	−2.63564	+	6.36301i	−0.100703	+	0.243118i
$686$		0			0
$687$			64.9836i			2.47928i
$688$		0			0
$689$	26.4027	+	15.2436i	1.00586	+	0.580734i
$690$		0			0
$691$	−23.2798	+	3.06484i	−0.885606	+	0.116592i	−0.559587	−	0.828771i	$-0.689040\pi$
$691$	−23.2798	+	3.06484i	−0.885606	+	0.116592i	−0.326018	+	0.945364i	$0.605707\pi$
$692$		0			0
$693$	25.1376	+	4.00711i	0.954899	+	0.152218i
$694$		0			0
$695$	−1.85716	+	6.93100i	−0.0704459	+	0.262908i
$696$		0			0
$697$	1.41790	+	5.29166i	0.0537067	+	0.200436i
$698$		0			0
$699$	−12.3701	−	29.8640i	−0.467879	−	1.12956i
$700$		0			0
$701$	−10.1016	−	4.18423i	−0.381533	−	0.158036i	0.183670	−	0.982988i	$-0.441202\pi$
$701$	−10.1016	−	4.18423i	−0.381533	−	0.158036i	−0.565203	+	0.824952i	$0.691202\pi$
$702$		0			0
$703$	−21.3173	+	36.9227i	−0.803998	+	1.39257i
$704$		0			0
$705$	−4.03296	−	6.98529i	−0.151890	−	0.263081i
$706$		0			0
$707$	−5.11386	+	0.532331i	−0.192326	+	0.0200204i
$708$		0			0
$709$	−1.93074	+	2.51619i	−0.0725105	+	0.0944975i	−0.828200	−	0.560432i	$-0.810635\pi$
$709$	−1.93074	+	2.51619i	−0.0725105	+	0.0944975i	0.755690	+	0.654930i	$0.227302\pi$
$710$		0			0
$711$	−1.25672	−	4.69015i	−0.0471308	−	0.175894i
$712$		0			0
$713$	4.85764	+	4.85764i	0.181920	+	0.181920i
$714$		0			0
$715$	12.0468	−	4.98994i	0.450524	−	0.186613i
$716$		0			0
$717$	−40.0251	−	52.1618i	−1.49477	−	1.94802i
$718$		0			0
$719$	−3.60159	+	2.07938i	−0.134317	+	0.0775477i	−0.565653	−	0.824644i	$-0.691376\pi$
$719$	−3.60159	+	2.07938i	−0.134317	+	0.0775477i	0.431336	+	0.902191i	$0.358042\pi$
$720$		0			0
$721$	34.3956	+	0.935015i	1.28096	+	0.0348218i
$722$		0			0
$723$	−33.8418	+	4.45536i	−1.25859	+	0.165697i
$724$		0			0
$725$	−3.26045	+	24.7656i	−0.121090	+	0.919771i
$726$		0			0
$727$	0.314165	+	0.314165i	0.0116517	+	0.0116517i	0.712909	−	0.701257i	$-0.247377\pi$
$727$	0.314165	+	0.314165i	0.0116517	+	0.0116517i	−0.701257	+	0.712909i	$0.747377\pi$
$728$		0			0
$729$	13.1543	−	13.1543i	0.487198	−	0.487198i
$730$		0			0
$731$	−3.17659	−	0.418207i	−0.117491	−	0.0154679i
$732$		0			0
$733$	1.29256	+	9.81797i	0.0477418	+	0.362635i	0.998595	+	0.0529926i	$0.0168760\pi$
$733$	1.29256	+	9.81797i	0.0477418	+	0.362635i	−0.950853	+	0.309642i	$0.899791\pi$
$734$		0			0
$735$	−4.30726	−	8.49532i	−0.158876	−	0.313355i
$736$		0			0
$737$	−12.5648	−	21.7628i	−0.462829	−	0.801643i
$738$		0			0
$739$	19.6390	−	15.0696i	0.722434	−	0.554343i	−0.180785	−	0.983523i	$-0.557864\pi$
$739$	19.6390	−	15.0696i	0.722434	−	0.554343i	0.903219	+	0.429180i	$0.141197\pi$
$740$		0			0
$741$	30.0737	+	72.6043i	1.10478	+	2.66718i
$742$		0			0
$743$	5.31724	−	5.31724i	0.195071	−	0.195071i	−0.602812	−	0.797883i	$-0.705953\pi$
$743$	5.31724	−	5.31724i	0.195071	−	0.195071i	0.797883	+	0.602812i	$0.205953\pi$
$744$		0			0
$745$	5.84126	−	1.56516i	0.214007	−	0.0573431i
$746$		0			0
$747$	−15.4767	−	11.8757i	−0.566261	−	0.434507i
$748$		0			0
$749$	−25.6882	−	11.4679i	−0.938627	−	0.419026i
$750$		0			0
$751$	−13.2369	+	7.64236i	−0.483023	+	0.278874i	−0.721675	−	0.692232i	$-0.756628\pi$
$751$	−13.2369	+	7.64236i	−0.483023	+	0.278874i	0.238652	+	0.971105i	$0.423294\pi$
$752$		0			0
$753$	36.6037	+	21.1331i	1.33391	+	0.770134i
$754$		0			0
$755$	−2.08016	+	5.02196i	−0.0757049	+	0.182768i
$756$		0			0
$757$	37.3581	−	15.4742i	1.35780	−	0.562420i	0.419349	−	0.907825i	$-0.362258\pi$
$757$	37.3581	−	15.4742i	1.35780	−	0.562420i	0.938454	+	0.345405i	$0.112258\pi$
$758$		0			0
$759$	−65.8947	+	17.6564i	−2.39183	+	0.640888i
$760$		0			0
$761$	30.5125	+	8.17579i	1.10608	+	0.296372i	0.765236	−	0.643750i	$-0.222622\pi$
$761$	30.5125	+	8.17579i	1.10608	+	0.296372i	0.340839	+	0.940122i	$0.389289\pi$
$762$		0			0
$763$	16.2814	+	13.2114i	0.589428	+	0.478283i
$764$		0			0
$765$	−0.179951	−	1.36686i	−0.00650613	−	0.0494190i
$766$		0			0
$767$	24.1132	−	41.7654i	0.870679	−	1.50806i
$768$		0			0
$769$	−50.3733			−1.81651			−0.908254	−	0.418419i	$-0.862584\pi$
$769$	−50.3733			−1.81651			−0.908254	+	0.418419i	$0.862584\pi$
$770$		0			0
$771$	−6.49038	−	2.68840i	−0.233745	−	0.0968205i
$772$		0			0
$773$	−25.8948	−	3.40911i	−0.931370	−	0.122617i	−0.350453	−	0.936580i	$-0.613972\pi$
$773$	−25.8948	−	3.40911i	−0.931370	−	0.122617i	−0.580917	+	0.813963i	$0.697306\pi$
$774$		0			0
$775$	4.02180	+	1.07764i	0.144467	+	0.0387099i
$776$		0			0
$777$	11.1617	+	46.6972i	0.400425	+	1.67525i
$778$		0			0
$779$	−25.8092	−	19.8041i	−0.924710	−	0.709555i
$780$		0			0
$781$	−21.2696	−	27.7191i	−0.761088	−	0.991869i
$782$		0			0
$783$		−	5.54171i		−	0.198045i
$784$		0			0
$785$			6.50332i			0.232114i
$786$		0			0
$787$	12.8966	+	16.8071i	0.459712	+	0.599109i	0.964483	−	0.264145i	$-0.0850896\pi$
$787$	12.8966	+	16.8071i	0.459712	+	0.599109i	−0.504771	+	0.863253i	$0.668423\pi$
$788$		0			0
$789$	−40.3070	−	30.9287i	−1.43497	−	1.10109i
$790$		0			0
$791$	0.172461	+	0.721521i	0.00613201	+	0.0256544i
$792$		0			0
$793$	−1.81444	−	0.486179i	−0.0644328	−	0.0172647i
$794$		0			0
$795$	6.83760	+	0.900187i	0.242505	+	0.0319263i
$796$		0			0
$797$	2.30371	+	0.954227i	0.0816015	+	0.0338005i	0.423111	−	0.906078i	$-0.360938\pi$
$797$	2.30371	+	0.954227i	0.0816015	+	0.0338005i	−0.341509	+	0.939878i	$0.610938\pi$
$798$		0			0
$799$	−5.53050			−0.195655
$800$		0			0
$801$	3.97577	−	6.88624i	0.140477	−	0.243313i
$802$		0			0
$803$	−2.38614	−	18.1245i	−0.0842050	−	0.639600i
$804$		0			0
$805$	9.12839	+	7.40711i	0.321733	+	0.261066i
$806$		0			0
$807$	9.26881	+	2.48357i	0.326278	+	0.0874258i
$808$		0			0
$809$	−43.4428	+	11.6405i	−1.52737	+	0.409257i	−0.922159	−	0.386811i	$-0.873577\pi$
$809$	−43.4428	+	11.6405i	−1.52737	+	0.409257i	−0.605208	+	0.796068i	$0.706910\pi$
$810$		0			0
$811$	−22.0565	+	9.13609i	−0.774507	+	0.320811i	−0.734697	−	0.678396i	$-0.762676\pi$
$811$	−22.0565	+	9.13609i	−0.774507	+	0.320811i	−0.0398108	+	0.999207i	$0.512676\pi$
$812$		0			0
$813$	16.2062	−	39.1252i	0.568376	−	1.37218i
$814$		0			0
$815$	12.2689	+	7.08345i	0.429760	+	0.248122i
$816$		0			0
$817$	16.4772	−	9.51310i	0.576463	−	0.332821i
$818$		0			0
$819$	37.2157	+	16.6140i	1.30042	+	0.580541i
$820$		0			0
$821$	−38.1892	−	29.3036i	−1.33281	−	1.02270i	−0.996724	−	0.0808730i	$-0.974229\pi$
$821$	−38.1892	−	29.3036i	−1.33281	−	1.02270i	−0.336089	−	0.941830i	$-0.609104\pi$
$822$		0			0
$823$	8.59075	−	2.30188i	0.299455	−	0.0802386i	−0.105963	−	0.994370i	$-0.533793\pi$
$823$	8.59075	−	2.30188i	0.299455	−	0.0802386i	0.405418	+	0.914131i	$0.367126\pi$
$824$		0			0
$825$	−29.2367	+	29.2367i	−1.01789	+	1.01789i
$826$		0			0
$827$	−4.43394	−	10.7045i	−0.154183	−	0.372231i	0.827847	−	0.560953i	$-0.189565\pi$
$827$	−4.43394	−	10.7045i	−0.154183	−	0.372231i	−0.982030	+	0.188723i	$0.939565\pi$
$828$		0			0
$829$	−8.99630	+	6.90310i	−0.312454	+	0.239755i	−0.753069	−	0.657942i	$-0.771427\pi$
$829$	−8.99630	+	6.90310i	−0.312454	+	0.239755i	0.440614	+	0.897696i	$0.354761\pi$
$830$		0			0
$831$	−2.47842	−	4.29274i	−0.0859753	−	0.148914i
$832$		0			0
$833$	−6.52120	−	0.354808i	−0.225946	−	0.0122934i
$834$		0			0
$835$	−1.70809	−	12.9743i	−0.0591110	−	0.448993i
$836$		0			0
$837$	−0.915817	−	0.120570i	−0.0316552	−	0.00416749i
$838$		0			0
$839$	−0.421565	+	0.421565i	−0.0145540	+	0.0145540i	−0.714346	−	0.699792i	$-0.753276\pi$
$839$	−0.421565	+	0.421565i	−0.0145540	+	0.0145540i	0.699792	+	0.714346i	$0.253276\pi$
$840$		0			0
$841$	−0.249818	−	0.249818i	−0.00861440	−	0.00861440i
$842$		0			0
$843$	6.79885	−	51.6424i	0.234165	−	1.77866i
$844$		0			0
$845$	13.2616	−	1.74592i	0.456213	−	0.0600615i
$846$		0			0
$847$	8.23601	+	0.223889i	0.282993	+	0.00769290i
$848$		0			0
$849$	−46.5318	+	26.8651i	−1.59697	+	0.922009i
$850$		0			0
$851$	−36.0733	−	47.0117i	−1.23658	−	1.61154i
$852$		0			0
$853$	27.8632	−	11.5413i	0.954016	−	0.395167i	0.149277	−	0.988795i	$-0.452305\pi$
$853$	27.8632	−	11.5413i	0.954016	−	0.395167i	0.804739	+	0.593629i	$0.202305\pi$
$854$		0			0
$855$	5.78895	+	5.78895i	0.197978	+	0.197978i
$856$		0			0
$857$	−8.96740	−	33.4668i	−0.306321	−	1.14320i	−0.931802	−	0.362966i	$-0.881764\pi$
$857$	−8.96740	−	33.4668i	−0.306321	−	1.14320i	0.625482	−	0.780239i	$-0.284902\pi$
$858$		0			0
$859$	0.136053	−	0.177307i	0.00464205	−	0.00604964i	−0.791027	−	0.611782i	$-0.790453\pi$
$859$	0.136053	−	0.177307i	0.00464205	−	0.00604964i	0.795669	+	0.605732i	$0.207120\pi$
$860$		0			0
$861$	−36.4384	+	3.79309i	−1.24182	+	0.129268i
$862$		0			0
$863$	8.33543	+	14.4374i	0.283741	+	0.491454i	0.972303	−	0.233723i	$-0.0750910\pi$
$863$	8.33543	+	14.4374i	0.283741	+	0.491454i	−0.688562	+	0.725178i	$0.741758\pi$
$864$		0			0
$865$	4.85033	−	8.40102i	0.164916	−	0.285643i
$866$		0			0
$867$	35.1408	+	14.5558i	1.19344	+	0.494341i
$868$		0			0
$869$	−2.72591	−	6.58092i	−0.0924701	−	0.223243i
$870$		0			0
$871$	−10.4135	−	38.8637i	−0.352848	−	1.31685i
$872$		0			0
$873$	7.94220	−	29.6407i	0.268803	−	1.00319i
$874$		0			0
$875$	14.5741	+	2.32321i	0.492694	+	0.0785389i
$876$		0			0
$877$	−36.3668	+	4.78778i	−1.22802	+	0.161672i	−0.716492	−	0.697596i	$-0.754253\pi$
$877$	−36.3668	+	4.78778i	−1.22802	+	0.161672i	−0.511527	+	0.859267i	$0.670920\pi$
$878$		0			0
$879$	−32.2422	−	18.6151i	−1.08750	−	0.627871i
$880$		0			0
$881$			10.2928i			0.346775i	0.984854	+	0.173387i	$0.0554713\pi$
$881$			10.2928i			0.346775i	−0.984854	+	0.173387i	$0.944529\pi$
$882$		0			0
$883$	13.4928	−	32.5745i	0.454069	−	1.09622i	−0.516691	−	0.856172i	$-0.672837\pi$
$883$	13.4928	−	32.5745i	0.454069	−	1.09622i	0.970761	−	0.240049i	$-0.0771635\pi$
$884$		0			0
$885$	1.42397	−	10.8161i	0.0478662	−	0.363580i
$886$		0			0
$887$	1.11340	−	4.15526i	0.0373842	−	0.139520i	−0.944711	−	0.327903i	$-0.893658\pi$
$887$	1.11340	−	4.15526i	0.0373842	−	0.139520i	0.982096	+	0.188383i	$0.0603247\pi$
$888$		0			0
$889$	−10.7047	+	2.55869i	−0.359025	+	0.0858157i
$890$		0			0
$891$	23.1549	−	30.1761i	0.775720	−	1.01094i
$892$		0			0
$893$	26.0549	−	19.9926i	0.871895	−	0.669028i
$894$		0			0
$895$	4.64152			0.155149
$896$		0			0
$897$	−109.225			−3.64693
$898$		0			0
$899$	3.78824	−	2.90682i	0.126345	−	0.0969478i
$900$		0			0
$901$	2.87867	−	3.75156i	0.0959025	−	0.124983i
$902$		0			0
$903$	6.10585	−	20.5378i	0.203190	−	0.683454i
$904$		0			0
$905$	−2.41134	+	8.99926i	−0.0801558	+	0.299145i
$906$		0			0
$907$	−2.21108	+	16.7948i	−0.0734177	+	0.557663i	0.914719	+	0.404089i	$0.132412\pi$
$907$	−2.21108	+	16.7948i	−0.0734177	+	0.557663i	−0.988137	+	0.153574i	$0.950922\pi$
$908$		0			0
$909$	1.90448	−	4.59783i	0.0631678	−	0.152501i
$910$		0			0
$911$			40.4940i			1.34162i	0.741627	+	0.670812i	$0.234054\pi$
$911$			40.4940i			1.34162i	−0.741627	+	0.670812i	$0.765946\pi$
$912$		0			0
$913$	−24.7839	−	14.3090i	−0.820227	−	0.473558i
$914$		0			0
$915$	−0.421295	+	0.0554645i	−0.0139276	+	0.00183360i
$916$		0			0
$917$	−10.4210	−	27.2287i	−0.344131	−	0.899171i
$918$		0			0
$919$	−3.20230	+	11.9512i	−0.105634	+	0.394232i	−0.998416	−	0.0562565i	$-0.982084\pi$
$919$	−3.20230	+	11.9512i	−0.105634	+	0.394232i	0.892782	+	0.450489i	$0.148750\pi$
$920$		0			0
$921$	2.05875	+	7.68336i	0.0678381	+	0.253175i
$922$		0			0
$923$	−21.4077	−	51.6827i	−0.704642	−	1.70116i
$924$		0			0
$925$	−33.1811	−	13.7441i	−1.09099	−	0.451902i
$926$		0			0
$927$	−16.6526	+	28.8432i	−0.546944	+	0.947335i
$928$		0			0
$929$	6.10079	+	10.5669i	0.200160	+	0.346688i	0.948580	−	0.316538i	$-0.102520\pi$
$929$	6.10079	+	10.5669i	0.200160	+	0.346688i	−0.748420	+	0.663225i	$0.769187\pi$
$930$		0			0
$931$	32.0049	−	21.9025i	1.04892	−	0.717824i
$932$		0			0
$933$	−18.2346	+	23.7638i	−0.596973	+	0.777990i
$934$		0			0
$935$	−0.523456	−	1.95357i	−0.0171188	−	0.0638884i
$936$		0			0
$937$	−18.9839	−	18.9839i	−0.620178	−	0.620178i	0.325399	−	0.945577i	$-0.394501\pi$
$937$	−18.9839	−	18.9839i	−0.620178	−	0.620178i	−0.945577	+	0.325399i	$0.894501\pi$
$938$		0			0
$939$	26.2656	−	10.8796i	0.857145	−	0.355041i
$940$		0			0
$941$	−2.52504	−	3.29070i	−0.0823140	−	0.107274i	0.750381	−	0.661005i	$-0.229870\pi$
$941$	−2.52504	−	3.29070i	−0.0823140	−	0.107274i	−0.832695	+	0.553732i	$0.813203\pi$
$942$		0			0
$943$	39.1575	−	22.6076i	1.27514	−	0.736204i
$944$		0			0
$945$	−1.58009	−	0.0429534i	−0.0514004	−	0.00139727i
$946$		0			0
$947$	−55.5724	+	7.31624i	−1.80586	+	0.237746i	−0.956840	−	0.290616i	$-0.906140\pi$
$947$	−55.5724	+	7.31624i	−1.80586	+	0.237746i	−0.849019	+	0.528362i	$0.822806\pi$
$948$		0			0
$949$	3.82043	−	29.0190i	0.124016	−	0.941998i
$950$		0			0
$951$	−11.1606	−	11.1606i	−0.361906	−	0.361906i
$952$		0			0
$953$	−10.9988	+	10.9988i	−0.356284	+	0.356284i	−0.862441	−	0.506157i	$-0.831066\pi$
$953$	−10.9988	+	10.9988i	−0.356284	+	0.356284i	0.506157	+	0.862441i	$0.331066\pi$
$954$		0			0
$955$	−3.77084	−	0.496440i	−0.122021	−	0.0160644i
$956$		0			0
$957$	6.18921	+	47.0117i	0.200069	+	1.51967i
$958$		0			0
$959$	−27.7679	+	15.0409i	−0.896671	+	0.485695i
$960$		0			0
$961$	15.1020	+	26.1575i	0.487163	+	0.843790i
$962$		0			0
$963$	21.6029	−	16.5765i	0.696145	−	0.534171i
$964$		0			0
$965$	2.91429	+	7.03571i	0.0938142	+	0.226487i
$966$		0			0
$967$	−36.1298	+	36.1298i	−1.16186	+	1.16186i	−0.177787	+	0.984069i	$0.556894\pi$
$967$	−36.1298	+	36.1298i	−1.16186	+	1.16186i	−0.984069	+	0.177787i	$0.943106\pi$
$968$		0			0
$969$	11.7739	−	3.15480i	0.378231	−	0.101347i
$970$		0			0
$971$	12.4338	+	9.54081i	0.399021	+	0.306179i	0.788708	−	0.614768i	$-0.210750\pi$
$971$	12.4338	+	9.54081i	0.399021	+	0.306179i	−0.389687	+	0.920947i	$0.627417\pi$
$972$		0			0
$973$	−26.6371	+	19.3124i	−0.853945	+	0.619127i
$974$		0			0
$975$	−57.3311	+	33.1001i	−1.83606	+	1.06005i
$976$		0			0
$977$	−7.65159	−	4.41765i	−0.244796	−	0.141333i	0.372583	−	0.927999i	$-0.378472\pi$
$977$	−7.65159	−	4.41765i	−0.244796	−	0.141333i	−0.617379	+	0.786666i	$0.711806\pi$
$978$		0			0
$979$	4.46395	−	10.7769i	0.142668	−	0.344432i
$980$		0			0
$981$	−18.7502	+	7.76658i	−0.598647	+	0.247968i
$982$		0			0
$983$	17.9737	−	4.81605i	0.573273	−	0.153608i	0.0394759	−	0.999221i	$-0.487431\pi$
$983$	17.9737	−	4.81605i	0.573273	−	0.153608i	0.533797	+	0.845612i	$0.320764\pi$
$984$		0			0
$985$	10.3557	+	2.77479i	0.329959	+	0.0884121i
$986$		0			0
$987$	5.82203	−	36.5230i	0.185317	−	1.16254i
$988$		0			0
$989$	3.45165	+	26.2179i	0.109756	+	0.833680i
$990$		0			0
$991$	3.04877	−	5.28062i	0.0968473	−	0.167744i	−0.813531	−	0.581522i	$-0.802457\pi$
$991$	3.04877	−	5.28062i	0.0968473	−	0.167744i	0.910378	+	0.413777i	$0.135791\pi$
$992$		0			0
$993$	−34.2401			−1.08658
$994$		0			0
$995$	−2.81296	−	1.16516i	−0.0891767	−	0.0369382i
$996$		0			0
$997$	28.8862	+	3.80293i	0.914834	+	0.120440i	0.573221	−	0.819401i	$-0.305694\pi$
$997$	28.8862	+	3.80293i	0.914834	+	0.120440i	0.341613	+	0.939841i	$0.389027\pi$
$998$		0			0
$999$	7.69631	+	2.06222i	0.243501	+	0.0652458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.4		240
4.3	odd	2		224.2.bd.a.221.5	yes	240
7.2	even	3	inner	896.2.bh.a.849.4		240
28.23	odd	6		224.2.bd.a.93.25	yes	240
32.11	odd	8		224.2.bd.a.53.25	✓	240
32.21	even	8	inner	896.2.bh.a.305.4		240
224.107	odd	24		224.2.bd.a.149.5	yes	240
224.149	even	24	inner	896.2.bh.a.177.4		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.25	✓	240	32.11	odd	8
224.2.bd.a.93.25	yes	240	28.23	odd	6
224.2.bd.a.149.5	yes	240	224.107	odd	24
224.2.bd.a.221.5	yes	240	4.3	odd	2
896.2.bh.a.81.4		240	1.1	even	1	trivial
896.2.bh.a.177.4		240	224.149	even	24	inner
896.2.bh.a.305.4		240	32.21	even	8	inner
896.2.bh.a.849.4		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)

\(f(q)\)	\(=\)	\(q+(-1.87086 + 1.43556i) q^{3} +(-0.351264 + 0.457777i) q^{5} +(-2.57326 + 0.615072i) q^{7} +(0.662818 - 2.47367i) q^{9} +O(q^{10})\)	\(q+(-1.87086 + 1.43556i) q^{3} +(-0.351264 + 0.457777i) q^{5} +(-2.57326 + 0.615072i) q^{7} +(0.662818 - 2.47367i) q^{9} +(0.490370 - 3.72473i) q^{11} +(2.30188 - 5.55723i) q^{13} -1.36069i q^{15} +(-0.807982 - 0.466489i) q^{17} +(5.49286 - 0.723149i) q^{19} +(3.93123 - 4.84478i) q^{21} +(-1.99298 + 7.43790i) q^{23} +(1.20792 + 4.50803i) q^{25} +(-0.396229 - 0.956581i) q^{27} +(4.94484 + 2.04822i) q^{29} +(0.446070 - 0.772617i) q^{31} +(4.42965 + 7.67239i) q^{33} +(0.622330 - 1.39403i) q^{35} +(-4.68468 + 6.10519i) q^{37} +(3.67124 + 13.7013i) q^{39} +(-4.15205 - 4.15205i) q^{41} +(3.17276 - 1.31420i) q^{43} +(0.899564 + 1.17233i) q^{45} +(5.13362 - 2.96390i) q^{47} +(6.24337 - 3.16548i) q^{49} +(2.18129 - 0.287172i) q^{51} +(-0.661564 + 5.02508i) q^{53} +(1.53284 + 1.53284i) q^{55} +(-9.23823 + 9.23823i) q^{57} +(7.94898 + 1.04650i) q^{59} +(-0.0407619 - 0.309617i) q^{61} +(-0.184120 + 6.77308i) q^{63} +(1.73540 + 3.00580i) q^{65} +(5.30670 - 4.07197i) q^{67} +(-6.94896 - 16.7763i) q^{69} +(6.57616 - 6.57616i) q^{71} +(4.70019 - 1.25941i) q^{73} +(-8.73139 - 6.69983i) q^{75} +(1.02913 + 9.88632i) q^{77} +(1.64201 - 0.948015i) q^{79} +(8.76801 + 5.06221i) q^{81} +(2.91509 - 7.03765i) q^{83} +(0.497363 - 0.206014i) q^{85} +(-12.1914 + 3.26669i) q^{87} +(2.99914 + 0.803618i) q^{89} +(-2.50525 + 15.7160i) q^{91} +(0.274603 + 2.08581i) q^{93} +(-1.59841 + 2.76852i) q^{95} +11.9825 q^{97} +(-8.88872 - 3.68183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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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