LMFDB - Embedded newform 896.2.u.c.337.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(113,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("896.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.u (of order $8$, degree $4$, 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:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			337.5
Character	$\chi$	$=$	896.337
Dual form			896.2.u.c.561.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.999166 - 0.413868i) q^{3} +(0.523077 + 1.26282i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-1.29427 - 1.29427i) q^{9} +O(q^{10})$	\(q+(-0.999166 - 0.413868i) q^{3} +(0.523077 + 1.26282i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-1.29427 - 1.29427i) q^{9} +(-0.904574 + 0.374687i) q^{11} +(0.430806 - 1.04006i) q^{13} -1.47825i q^{15} -3.31157i q^{17} +(1.25398 - 3.02738i) q^{19} +(0.999166 - 0.413868i) q^{21} +(-2.85663 - 2.85663i) q^{23} +(2.21443 - 2.21443i) q^{25} +(1.99914 + 4.82635i) q^{27} +(7.03942 + 2.91582i) q^{29} +5.90990 q^{31} +1.05889 q^{33} +(-1.26282 - 0.523077i) q^{35} +(-1.70363 - 4.11292i) q^{37} +(-0.860894 + 0.860894i) q^{39} +(-7.31644 - 7.31644i) q^{41} +(-0.902235 + 0.373718i) q^{43} +(0.957430 - 2.31144i) q^{45} -10.7312i q^{47} -1.00000i q^{49} +(-1.37055 + 3.30881i) q^{51} +(5.29777 - 2.19441i) q^{53} +(-0.946323 - 0.946323i) q^{55} +(-2.50588 + 2.50588i) q^{57} +(0.563137 + 1.35953i) q^{59} +(-0.0893244 - 0.0369994i) q^{61} +1.83038 q^{63} +1.53875 q^{65} +(4.92908 + 2.04169i) q^{67} +(1.67198 + 4.03652i) q^{69} +(-0.553232 + 0.553232i) q^{71} +(-6.76325 - 6.76325i) q^{73} +(-3.12907 + 1.29610i) q^{75} +(0.374687 - 0.904574i) q^{77} -11.8884i q^{79} -0.158568i q^{81} +(2.47245 - 5.96903i) q^{83} +(4.18192 - 1.73221i) q^{85} +(-5.82679 - 5.82679i) q^{87} +(-2.11160 + 2.11160i) q^{89} +(0.430806 + 1.04006i) q^{91} +(-5.90497 - 2.44592i) q^{93} +4.47897 q^{95} -6.12164 q^{97} +(1.65571 + 0.685819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) $ 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.999166	−	0.413868i	−0.576869	−	0.238947i	0.0751212	−	0.997174i	$-0.476066\pi$
$3$	−0.999166	−	0.413868i	−0.576869	−	0.238947i	−0.651990	+	0.758228i	$0.726066\pi$
$4$		0			0
$5$	0.523077	+	1.26282i	0.233927	+	0.564750i	0.996633	−	0.0819958i	$-0.0261294\pi$
$5$	0.523077	+	1.26282i	0.233927	+	0.564750i	−0.762705	+	0.646746i	$0.776129\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$	−1.29427	−	1.29427i	−0.431425	−	0.431425i
$10$		0			0
$11$	−0.904574	+	0.374687i	−0.272739	+	0.112972i	−0.514861	−	0.857274i	$-0.672157\pi$
$11$	−0.904574	+	0.374687i	−0.272739	+	0.112972i	0.242122	+	0.970246i	$0.422157\pi$
$12$		0			0
$13$	0.430806	−	1.04006i	0.119484	−	0.288460i	−0.852810	−	0.522222i	$-0.825103\pi$
$13$	0.430806	−	1.04006i	0.119484	−	0.288460i	0.972294	+	0.233761i	$0.0751034\pi$
$14$		0			0
$15$		−	1.47825i		−	0.381683i
$16$		0			0
$17$		−	3.31157i		−	0.803175i	−0.915821	−	0.401587i	$-0.868459\pi$
$17$		−	3.31157i		−	0.803175i	0.915821	−	0.401587i	$-0.131541\pi$
$18$		0			0
$19$	1.25398	−	3.02738i	0.287684	−	0.694530i	−0.712289	−	0.701886i	$-0.752342\pi$
$19$	1.25398	−	3.02738i	0.287684	−	0.694530i	0.999973	+	0.00735628i	$0.00234160\pi$
$20$		0			0
$21$	0.999166	−	0.413868i	0.218036	−	0.0903134i
$22$		0			0
$23$	−2.85663	−	2.85663i	−0.595649	−	0.595649i	0.343503	−	0.939152i	$-0.388386\pi$
$23$	−2.85663	−	2.85663i	−0.595649	−	0.595649i	−0.939152	+	0.343503i	$0.888386\pi$
$24$		0			0
$25$	2.21443	−	2.21443i	0.442886	−	0.442886i
$26$		0			0
$27$	1.99914	+	4.82635i	0.384735	+	0.928832i
$28$		0			0
$29$	7.03942	+	2.91582i	1.30719	+	0.541455i	0.924063	−	0.382241i	$-0.124848\pi$
$29$	7.03942	+	2.91582i	1.30719	+	0.541455i	0.383126	+	0.923696i	$0.374848\pi$
$30$		0			0
$31$	5.90990			1.06145			0.530725	−	0.847544i	$-0.321920\pi$
$31$	5.90990			1.06145			0.530725	+	0.847544i	$0.321920\pi$
$32$		0			0
$33$	1.05889			0.184329
$34$		0			0
$35$	−1.26282	−	0.523077i	−0.213455	−	0.0884162i
$36$		0			0
$37$	−1.70363	−	4.11292i	−0.280074	−	0.676159i	0.719763	−	0.694220i	$-0.244251\pi$
$37$	−1.70363	−	4.11292i	−0.280074	−	0.676159i	−0.999837	+	0.0180612i	$0.994251\pi$
$38$		0			0
$39$	−0.860894	+	0.860894i	−0.137853	+	0.137853i
$40$		0			0
$41$	−7.31644	−	7.31644i	−1.14264	−	1.14264i	−0.987966	−	0.154670i	$-0.950568\pi$
$41$	−7.31644	−	7.31644i	−1.14264	−	1.14264i	−0.154670	−	0.987966i	$-0.549432\pi$
$42$		0			0
$43$	−0.902235	+	0.373718i	−0.137590	+	0.0569915i	−0.450416	−	0.892819i	$-0.648724\pi$
$43$	−0.902235	+	0.373718i	−0.137590	+	0.0569915i	0.312826	+	0.949810i	$0.398724\pi$
$44$		0			0
$45$	0.957430	−	2.31144i	0.142725	−	0.344569i
$46$		0			0
$47$		−	10.7312i		−	1.56530i	−0.622462	−	0.782650i	$-0.713867\pi$
$47$		−	10.7312i		−	1.56530i	0.622462	−	0.782650i	$-0.286133\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−1.37055	+	3.30881i	−0.191916	+	0.463326i
$52$		0			0
$53$	5.29777	−	2.19441i	0.727704	−	0.301425i	0.0120961	−	0.999927i	$-0.496150\pi$
$53$	5.29777	−	2.19441i	0.727704	−	0.301425i	0.715608	+	0.698502i	$0.246150\pi$
$54$		0			0
$55$	−0.946323	−	0.946323i	−0.127602	−	0.127602i
$56$		0			0
$57$	−2.50588	+	2.50588i	−0.331911	+	0.331911i
$58$		0			0
$59$	0.563137	+	1.35953i	0.0733142	+	0.176996i	0.956288	−	0.292426i	$-0.0944624\pi$
$59$	0.563137	+	1.35953i	0.0733142	+	0.176996i	−0.882974	+	0.469422i	$0.844462\pi$
$60$		0			0
$61$	−0.0893244	−	0.0369994i	−0.0114368	−	0.00473729i	0.376958	−	0.926230i	$-0.376970\pi$
$61$	−0.0893244	−	0.0369994i	−0.0114368	−	0.00473729i	−0.388395	+	0.921493i	$0.626970\pi$
$62$		0			0
$63$	1.83038			0.230606
$64$		0			0
$65$	1.53875			0.190859
$66$		0			0
$67$	4.92908	+	2.04169i	0.602184	+	0.249433i	0.662882	−	0.748724i	$-0.269333\pi$
$67$	4.92908	+	2.04169i	0.602184	+	0.249433i	−0.0606989	+	0.998156i	$0.519333\pi$
$68$		0			0
$69$	1.67198	+	4.03652i	0.201283	+	0.485940i
$70$		0			0
$71$	−0.553232	+	0.553232i	−0.0656565	+	0.0656565i	−0.739173	−	0.673516i	$-0.764783\pi$
$71$	−0.553232	+	0.553232i	−0.0656565	+	0.0656565i	0.673516	+	0.739173i	$0.264783\pi$
$72$		0			0
$73$	−6.76325	−	6.76325i	−0.791579	−	0.791579i	0.190172	−	0.981751i	$-0.439095\pi$
$73$	−6.76325	−	6.76325i	−0.791579	−	0.791579i	−0.981751	+	0.190172i	$0.939095\pi$
$74$		0			0
$75$	−3.12907	+	1.29610i	−0.361313	+	0.149661i
$76$		0			0
$77$	0.374687	−	0.904574i	0.0426995	−	0.103086i
$78$		0			0
$79$		−	11.8884i		−	1.33755i	−0.743466	−	0.668773i	$-0.766820\pi$
$79$		−	11.8884i		−	1.33755i	0.743466	−	0.668773i	$-0.233180\pi$
$80$		0			0
$81$		−	0.158568i		−	0.0176187i
$82$		0			0
$83$	2.47245	−	5.96903i	0.271387	−	0.655187i	−0.728156	−	0.685411i	$-0.759622\pi$
$83$	2.47245	−	5.96903i	0.271387	−	0.655187i	0.999543	+	0.0302249i	$0.00962235\pi$
$84$		0			0
$85$	4.18192	−	1.73221i	0.453593	−	0.187884i
$86$		0			0
$87$	−5.82679	−	5.82679i	−0.624697	−	0.624697i
$88$		0			0
$89$	−2.11160	+	2.11160i	−0.223829	+	0.223829i	−0.810109	−	0.586280i	$-0.800592\pi$
$89$	−2.11160	+	2.11160i	−0.223829	+	0.223829i	0.586280	+	0.810109i	$0.300592\pi$
$90$		0			0
$91$	0.430806	+	1.04006i	0.0451608	+	0.109028i
$92$		0			0
$93$	−5.90497	−	2.44592i	−0.612317	−	0.253630i
$94$		0			0
$95$	4.47897			0.459533
$96$		0			0
$97$	−6.12164			−0.621559			−0.310779	−	0.950482i	$-0.600590\pi$
$97$	−6.12164			−0.621559			−0.310779	+	0.950482i	$0.600590\pi$
$98$		0			0
$99$	1.65571	+	0.685819i	0.166405	+	0.0689274i
$100$		0			0
$101$	−2.52035	−	6.08466i	−0.250784	−	0.605446i	0.747484	−	0.664280i	$-0.231262\pi$
$101$	−2.52035	−	6.08466i	−0.250784	−	0.605446i	−0.998268	+	0.0588340i	$0.981262\pi$
$102$		0			0
$103$	8.52867	−	8.52867i	0.840355	−	0.840355i	−0.148550	−	0.988905i	$-0.547461\pi$
$103$	8.52867	−	8.52867i	0.840355	−	0.840355i	0.988905	+	0.148550i	$0.0474607\pi$
$104$		0			0
$105$	1.04528	+	1.04528i	0.102009	+	0.102009i
$106$		0			0
$107$	−10.9686	+	4.54336i	−1.06038	+	0.439223i	−0.843585	−	0.536995i	$-0.819559\pi$
$107$	−10.9686	+	4.54336i	−1.06038	+	0.439223i	−0.216792	+	0.976218i	$0.569559\pi$
$108$		0			0
$109$	−4.93652	+	11.9178i	−0.472833	+	1.14152i	0.490073	+	0.871681i	$0.336970\pi$
$109$	−4.93652	+	11.9178i	−0.472833	+	1.14152i	−0.962906	+	0.269837i	$0.913030\pi$
$110$		0			0
$111$			4.81456i			0.456978i
$112$		0			0
$113$			15.8912i			1.49492i	0.664305	+	0.747461i	$0.268727\pi$
$113$			15.8912i			1.49492i	−0.664305	+	0.747461i	$0.731273\pi$
$114$		0			0
$115$	2.11317	−	5.10165i	0.197054	−	0.475731i
$116$		0			0
$117$	−1.90370	+	0.788539i	−0.175997	+	0.0729005i
$118$		0			0
$119$	2.34164	+	2.34164i	0.214657	+	0.214657i
$120$		0			0
$121$	−7.10031	+	7.10031i	−0.645483	+	0.645483i
$122$		0			0
$123$	4.28230	+	10.3384i	0.386122	+	0.932181i
$124$		0			0
$125$	10.2688	+	4.25349i	0.918473	+	0.380444i
$126$		0			0
$127$	17.0952			1.51695			0.758476	−	0.651702i	$-0.225945\pi$
$127$	17.0952			1.51695			0.758476	+	0.651702i	$0.225945\pi$
$128$		0			0
$129$	1.05615			0.0929891
$130$		0			0
$131$	−16.1070	−	6.67174i	−1.40728	−	0.582913i	−0.455646	−	0.890161i	$-0.650592\pi$
$131$	−16.1070	−	6.67174i	−1.40728	−	0.582913i	−0.951629	+	0.307248i	$0.900592\pi$
$132$		0			0
$133$	1.25398	+	3.02738i	0.108734	+	0.262508i
$134$		0			0
$135$	−5.04911	+	5.04911i	−0.434558	+	0.434558i
$136$		0			0
$137$	−10.0821	−	10.0821i	−0.861372	−	0.861372i	0.130126	−	0.991497i	$-0.458462\pi$
$137$	−10.0821	−	10.0821i	−0.861372	−	0.861372i	−0.991497	+	0.130126i	$0.958462\pi$
$138$		0			0
$139$	10.0075	−	4.14525i	0.848826	−	0.351595i	0.0844986	−	0.996424i	$-0.473071\pi$
$139$	10.0075	−	4.14525i	0.848826	−	0.351595i	0.764327	+	0.644828i	$0.223071\pi$
$140$		0			0
$141$	−4.44128	+	10.7222i	−0.374024	+	0.902973i
$142$		0			0
$143$			1.10223i			0.0921728i
$144$		0			0
$145$			10.4147i			0.864896i
$146$		0			0
$147$	−0.413868	+	0.999166i	−0.0341353	+	0.0824098i
$148$		0			0
$149$	17.8291	−	7.38504i	1.46061	−	0.605006i	0.495917	−	0.868370i	$-0.334832\pi$
$149$	17.8291	−	7.38504i	1.46061	−	0.605006i	0.964697	+	0.263364i	$0.0848320\pi$
$150$		0			0
$151$	6.37361	+	6.37361i	0.518677	+	0.518677i	0.917171	−	0.398494i	$-0.130467\pi$
$151$	6.37361	+	6.37361i	0.518677	+	0.518677i	−0.398494	+	0.917171i	$0.630467\pi$
$152$		0			0
$153$	−4.28608	+	4.28608i	−0.346509	+	0.346509i
$154$		0			0
$155$	3.09133	+	7.46314i	0.248302	+	0.599454i
$156$		0			0
$157$	−0.751603	−	0.311324i	−0.0599844	−	0.0248464i	0.352490	−	0.935816i	$-0.385335\pi$
$157$	−0.751603	−	0.311324i	−0.0599844	−	0.0248464i	−0.412474	+	0.910969i	$0.635335\pi$
$158$		0			0
$159$	−6.20155			−0.491815
$160$		0			0
$161$	4.03989			0.318388
$162$		0			0
$163$	−1.04167	−	0.431475i	−0.0815901	−	0.0337957i	0.341515	−	0.939876i	$-0.389060\pi$
$163$	−1.04167	−	0.431475i	−0.0815901	−	0.0337957i	−0.423105	+	0.906081i	$0.639060\pi$
$164$		0			0
$165$	0.553881	+	1.33719i	0.0431196	+	0.104100i
$166$		0			0
$167$	−7.60002	+	7.60002i	−0.588107	+	0.588107i	−0.937118	−	0.349011i	$-0.886517\pi$
$167$	−7.60002	+	7.60002i	−0.588107	+	0.588107i	0.349011	+	0.937118i	$0.386517\pi$
$168$		0			0
$169$	8.29626	+	8.29626i	0.638174	+	0.638174i
$170$		0			0
$171$	−5.54126	+	2.29527i	−0.423751	+	0.175523i
$172$		0			0
$173$	−8.40483	+	20.2911i	−0.639008	+	1.54270i	0.188996	+	0.981978i	$0.439477\pi$
$173$	−8.40483	+	20.2911i	−0.639008	+	1.54270i	−0.828003	+	0.560723i	$0.810523\pi$
$174$		0			0
$175$			3.13168i			0.236733i
$176$		0			0
$177$		−	1.59146i		−	0.119622i
$178$		0			0
$179$	−7.93735	+	19.1624i	−0.593265	+	1.43227i	0.287067	+	0.957911i	$0.407320\pi$
$179$	−7.93735	+	19.1624i	−0.593265	+	1.43227i	−0.880332	+	0.474358i	$0.842680\pi$
$180$		0			0
$181$	−0.349364	+	0.144711i	−0.0259680	+	0.0107563i	−0.395630	−	0.918410i	$-0.629474\pi$
$181$	−0.349364	+	0.144711i	−0.0259680	+	0.0107563i	0.369662	+	0.929166i	$0.379474\pi$
$182$		0			0
$183$	0.0739371	+	0.0739371i	0.00546559	+	0.00546559i
$184$		0			0
$185$	4.30274	−	4.30274i	0.316344	−	0.316344i
$186$		0			0
$187$	1.24080	+	2.99556i	0.0907365	+	0.219057i
$188$		0			0
$189$	−4.82635	−	1.99914i	−0.351065	−	0.145416i
$190$		0			0
$191$	7.61375			0.550912			0.275456	−	0.961314i	$-0.411171\pi$
$191$	7.61375			0.550912			0.275456	+	0.961314i	$0.411171\pi$
$192$		0			0
$193$	23.7442			1.70914			0.854571	−	0.519334i	$-0.173820\pi$
$193$	23.7442			1.70914			0.854571	+	0.519334i	$0.173820\pi$
$194$		0			0
$195$	−1.53747	−	0.636840i	−0.110100	−	0.0456051i
$196$		0			0
$197$	−0.495698	−	1.19672i	−0.0353171	−	0.0852629i	0.905237	−	0.424907i	$-0.139693\pi$
$197$	−0.495698	−	1.19672i	−0.0353171	−	0.0852629i	−0.940554	+	0.339644i	$0.889693\pi$
$198$		0			0
$199$	−10.1613	+	10.1613i	−0.720317	+	0.720317i	−0.968670	−	0.248353i	$-0.920111\pi$
$199$	−10.1613	+	10.1613i	−0.720317	+	0.720317i	0.248353	+	0.968670i	$0.420111\pi$
$200$		0			0
$201$	−4.07998	−	4.07998i	−0.287780	−	0.287780i
$202$		0			0
$203$	−7.03942	+	2.91582i	−0.494071	+	0.204651i
$204$		0			0
$205$	5.41229	−	13.0664i	0.378010	−	0.912598i
$206$		0			0
$207$			7.39453i			0.513955i
$208$		0			0
$209$			3.20834i			0.221926i
$210$		0			0
$211$	−2.86259	+	6.91091i	−0.197069	+	0.475766i	−0.991263	−	0.131897i	$-0.957893\pi$
$211$	−2.86259	+	6.91091i	−0.197069	+	0.475766i	0.794195	+	0.607664i	$0.207893\pi$
$212$		0			0
$213$	0.781735	−	0.323805i	0.0535636	−	0.0221868i
$214$		0			0
$215$	−0.943877	−	0.943877i	−0.0643719	−	0.0643719i
$216$		0			0
$217$	−4.17893	+	4.17893i	−0.283684	+	0.283684i
$218$		0			0
$219$	3.95852	+	9.55671i	0.267492	+	0.645782i
$220$		0			0
$221$	−3.44423	−	1.42665i	−0.231684	−	0.0959666i
$222$		0			0
$223$	−9.85085			−0.659662			−0.329831	−	0.944040i	$-0.606992\pi$
$223$	−9.85085			−0.659662			−0.329831	+	0.944040i	$0.606992\pi$
$224$		0			0
$225$	−5.73216			−0.382144
$226$		0			0
$227$	−15.7326	−	6.51665i	−1.04421	−	0.432525i	−0.206388	−	0.978470i	$-0.566171\pi$
$227$	−15.7326	−	6.51665i	−1.04421	−	0.432525i	−0.837821	+	0.545945i	$0.816171\pi$
$228$		0			0
$229$	−7.45055	−	17.9872i	−0.492346	−	1.18863i	−0.953523	−	0.301321i	$-0.902573\pi$
$229$	−7.45055	−	17.9872i	−0.492346	−	1.18863i	0.461177	−	0.887308i	$-0.347427\pi$
$230$		0			0
$231$	−0.748748	+	0.748748i	−0.0492640	+	0.0492640i
$232$		0			0
$233$	−3.26240	−	3.26240i	−0.213727	−	0.213727i	0.592122	−	0.805848i	$-0.298290\pi$
$233$	−3.26240	−	3.26240i	−0.213727	−	0.213727i	−0.805848	+	0.592122i	$0.798290\pi$
$234$		0			0
$235$	13.5515	−	5.61322i	0.884003	−	0.366166i
$236$		0			0
$237$	−4.92022	+	11.8785i	−0.319603	+	0.771589i
$238$		0			0
$239$			2.83372i			0.183298i	0.995791	+	0.0916491i	$0.0292138\pi$
$239$			2.83372i			0.183298i	−0.995791	+	0.0916491i	$0.970786\pi$
$240$		0			0
$241$		−	22.5209i		−	1.45070i	−0.688380	−	0.725350i	$-0.741678\pi$
$241$		−	22.5209i		−	1.45070i	0.688380	−	0.725350i	$-0.258322\pi$
$242$		0			0
$243$	5.93180	−	14.3206i	0.380525	−	0.918668i
$244$		0			0
$245$	1.26282	−	0.523077i	0.0806786	−	0.0334182i
$246$		0			0
$247$	−2.60843	−	2.60843i	−0.165971	−	0.165971i
$248$		0			0
$249$	−4.94079	+	4.94079i	−0.313110	+	0.313110i
$250$		0			0
$251$	8.58026	+	20.7146i	0.541581	+	1.30749i	0.923607	+	0.383341i	$0.125227\pi$
$251$	8.58026	+	20.7146i	0.541581	+	1.30749i	−0.382025	+	0.924152i	$0.624773\pi$
$252$		0			0
$253$	3.65437	+	1.51369i	0.229749	+	0.0951650i
$254$		0			0
$255$	−4.89534			−0.306558
$256$		0			0
$257$	8.00130			0.499108			0.249554	−	0.968361i	$-0.419716\pi$
$257$	8.00130			0.499108			0.249554	+	0.968361i	$0.419716\pi$
$258$		0			0
$259$	4.11292	+	1.70363i	0.255564	+	0.105858i
$260$		0			0
$261$	−5.33707	−	12.8848i	−0.330356	−	0.797550i
$262$		0			0
$263$	−15.2011	+	15.2011i	−0.937342	+	0.937342i	−0.998150	−	0.0608073i	$-0.980633\pi$
$263$	−15.2011	+	15.2011i	−0.937342	+	0.937342i	0.0608073	+	0.998150i	$0.480633\pi$
$264$		0			0
$265$	5.54228	+	5.54228i	0.340460	+	0.340460i
$266$		0			0
$267$	2.98376	−	1.23591i	0.182603	−	0.0756367i
$268$		0			0
$269$	−3.43306	+	8.28813i	−0.209317	+	0.505337i	−0.993316	−	0.115426i	$-0.963177\pi$
$269$	−3.43306	+	8.28813i	−0.209317	+	0.505337i	0.783999	+	0.620762i	$0.213177\pi$
$270$		0			0
$271$			16.2410i			0.986571i	0.869867	+	0.493285i	$0.164204\pi$
$271$			16.2410i			0.986571i	−0.869867	+	0.493285i	$0.835796\pi$
$272$		0			0
$273$		−	1.21749i		−	0.0736857i
$274$		0			0
$275$	−1.17340	+	2.83283i	−0.0707585	+	0.170826i
$276$		0			0
$277$	8.18398	−	3.38992i	0.491728	−	0.203680i	−0.123020	−	0.992404i	$-0.539258\pi$
$277$	8.18398	−	3.38992i	0.491728	−	0.203680i	0.614748	+	0.788724i	$0.289258\pi$
$278$		0			0
$279$	−7.64903	−	7.64903i	−0.457935	−	0.457935i
$280$		0			0
$281$	9.52799	−	9.52799i	0.568392	−	0.568392i	−0.363286	−	0.931678i	$-0.618345\pi$
$281$	9.52799	−	9.52799i	0.568392	−	0.568392i	0.931678	+	0.363286i	$0.118345\pi$
$282$		0			0
$283$	−9.29050	−	22.4293i	−0.552263	−	1.33328i	−0.915775	−	0.401691i	$-0.868422\pi$
$283$	−9.29050	−	22.4293i	−0.552263	−	1.33328i	0.363512	−	0.931589i	$-0.381578\pi$
$284$		0			0
$285$	−4.47524	−	1.85370i	−0.265090	−	0.109804i
$286$		0			0
$287$	10.3470			0.610765
$288$		0			0
$289$	6.03348			0.354911
$290$		0			0
$291$	6.11654	+	2.53355i	0.358558	+	0.148519i
$292$		0			0
$293$	8.54419	+	20.6275i	0.499157	+	1.20507i	0.949939	+	0.312437i	$0.101145\pi$
$293$	8.54419	+	20.6275i	0.499157	+	1.20507i	−0.450782	+	0.892634i	$0.648855\pi$
$294$		0			0
$295$	−1.42228	+	1.42228i	−0.0828085	+	0.0828085i
$296$		0			0
$297$	−3.61674	−	3.61674i	−0.209864	−	0.209864i
$298$		0			0
$299$	−4.20172	+	1.74041i	−0.242992	+	0.100650i
$300$		0			0
$301$	0.373718	−	0.902235i	0.0215408	−	0.0520040i
$302$		0			0
$303$			7.12267i			0.409187i
$304$		0			0
$305$		−	0.132154i		−	0.00756713i
$306$		0			0
$307$	12.5759	−	30.3608i	0.717743	−	1.73278i	0.0380638	−	0.999275i	$-0.487881\pi$
$307$	12.5759	−	30.3608i	0.717743	−	1.73278i	0.679679	−	0.733510i	$-0.262119\pi$
$308$		0			0
$309$	−12.0513	+	4.99181i	−0.685574	+	0.283974i
$310$		0			0
$311$	−9.58114	−	9.58114i	−0.543297	−	0.543297i	0.381197	−	0.924494i	$-0.375512\pi$
$311$	−9.58114	−	9.58114i	−0.543297	−	0.543297i	−0.924494	+	0.381197i	$0.875512\pi$
$312$		0			0
$313$	9.48170	−	9.48170i	0.535937	−	0.535937i	−0.386396	−	0.922333i	$-0.626280\pi$
$313$	9.48170	−	9.48170i	0.535937	−	0.535937i	0.922333	+	0.386396i	$0.126280\pi$
$314$		0			0
$315$	0.957430	+	2.31144i	0.0539451	+	0.130235i
$316$		0			0
$317$	−25.8056	−	10.6890i	−1.44939	−	0.600356i	−0.487333	−	0.873216i	$-0.662030\pi$
$317$	−25.8056	−	10.6890i	−1.44939	−	0.600356i	−0.962054	+	0.272860i	$0.912030\pi$
$318$		0			0
$319$	−7.46020			−0.417691
$320$		0			0
$321$	12.8398			0.716650
$322$		0			0
$323$	−10.0254	−	4.15266i	−0.557829	−	0.231060i
$324$		0			0
$325$	−1.34915	−	3.25713i	−0.0748371	−	0.180673i
$326$		0			0
$327$	9.86480	−	9.86480i	0.545525	−	0.545525i
$328$		0			0
$329$	7.58807	+	7.58807i	0.418344	+	0.418344i
$330$		0			0
$331$	11.5634	−	4.78970i	0.635580	−	0.263266i	−0.0415418	−	0.999137i	$-0.513227\pi$
$331$	11.5634	−	4.78970i	0.635580	−	0.263266i	0.677122	+	0.735871i	$0.263227\pi$
$332$		0			0
$333$	−3.11828	+	7.52820i	−0.170881	+	0.412543i
$334$		0			0
$335$			7.29251i			0.398432i
$336$		0			0
$337$			19.5928i			1.06729i	0.845709	+	0.533645i	$0.179178\pi$
$337$			19.5928i			1.06729i	−0.845709	+	0.533645i	$0.820822\pi$
$338$		0			0
$339$	6.57688	−	15.8780i	0.357207	−	0.862374i
$340$		0			0
$341$	−5.34594	+	2.21436i	−0.289499	+	0.119914i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	−4.22282	+	4.22282i	−0.227349	+	0.227349i
$346$		0			0
$347$	−12.3502	−	29.8160i	−0.662993	−	1.60061i	−0.793090	−	0.609105i	$-0.791529\pi$
$347$	−12.3502	−	29.8160i	−0.662993	−	1.60061i	0.130097	−	0.991501i	$-0.458471\pi$
$348$		0			0
$349$	23.5509	+	9.75512i	1.26065	+	0.522179i	0.910110	−	0.414367i	$-0.135997\pi$
$349$	23.5509	+	9.75512i	1.26065	+	0.522179i	0.350543	+	0.936547i	$0.385997\pi$
$350$		0			0
$351$	5.88093			0.313901
$352$		0			0
$353$	−24.8851			−1.32450			−0.662251	−	0.749282i	$-0.730399\pi$
$353$	−24.8851			−1.32450			−0.662251	+	0.749282i	$0.730399\pi$
$354$		0			0
$355$	−0.988014	−	0.409249i	−0.0524384	−	0.0217207i
$356$		0			0
$357$	−1.37055	−	3.30881i	−0.0725375	−	0.175121i
$358$		0			0
$359$	14.2492	−	14.2492i	0.752046	−	0.752046i	−0.222815	−	0.974861i	$-0.571524\pi$
$359$	14.2492	−	14.2492i	0.752046	−	0.752046i	0.974861	+	0.222815i	$0.0715245\pi$
$360$		0			0
$361$	5.84245	+	5.84245i	0.307497	+	0.307497i
$362$		0			0
$363$	10.0330	−	4.15580i	0.526595	−	0.218123i
$364$		0			0
$365$	5.00307	−	12.0785i	0.261872	−	0.632216i
$366$		0			0
$367$		−	20.3633i		−	1.06296i	−0.847072	−	0.531478i	$-0.821637\pi$
$367$		−	20.3633i		−	1.06296i	0.847072	−	0.531478i	$-0.178363\pi$
$368$		0			0
$369$			18.9390i			0.985923i
$370$		0			0
$371$	−2.19441	+	5.29777i	−0.113928	+	0.275046i
$372$		0			0
$373$	−9.97623	+	4.13229i	−0.516550	+	0.213962i	−0.625701	−	0.780063i	$-0.715187\pi$
$373$	−9.97623	+	4.13229i	−0.516550	+	0.213962i	0.109151	+	0.994025i	$0.465187\pi$
$374$		0			0
$375$	−8.49989	−	8.49989i	−0.438933	−	0.438933i
$376$		0			0
$377$	6.06526	−	6.06526i	0.312377	−	0.312377i
$378$		0			0
$379$	8.32592	+	20.1006i	0.427674	+	1.03250i	0.980023	+	0.198883i	$0.0637315\pi$
$379$	8.32592	+	20.1006i	0.427674	+	1.03250i	−0.552349	+	0.833613i	$0.686269\pi$
$380$		0			0
$381$	−17.0809	−	7.07515i	−0.875082	−	0.362471i
$382$		0			0
$383$	−5.23566			−0.267529			−0.133765	−	0.991013i	$-0.542707\pi$
$383$	−5.23566			−0.267529			−0.133765	+	0.991013i	$0.542707\pi$
$384$		0			0
$385$	1.33830			0.0682063
$386$		0			0
$387$	1.65143	+	0.684046i	0.0839471	+	0.0347720i
$388$		0			0
$389$	10.2543	+	24.7560i	0.519912	+	1.25518i	0.937957	+	0.346751i	$0.112715\pi$
$389$	10.2543	+	24.7560i	0.519912	+	1.25518i	−0.418045	+	0.908426i	$0.637285\pi$
$390$		0			0
$391$	−9.45994	+	9.45994i	−0.478410	+	0.478410i
$392$		0			0
$393$	13.3324	+	13.3324i	0.672528	+	0.672528i
$394$		0			0
$395$	15.0129	−	6.21854i	0.755380	−	0.312889i
$396$		0			0
$397$	11.1704	−	26.9677i	0.560627	−	1.35347i	−0.348639	−	0.937257i	$-0.613356\pi$
$397$	11.1704	−	26.9677i	0.560627	−	1.35347i	0.909266	−	0.416215i	$-0.136644\pi$
$398$		0			0
$399$		−	3.54384i		−	0.177414i
$400$		0			0
$401$		−	0.336321i		−	0.0167951i	−0.999965	−	0.00839753i	$-0.997327\pi$
$401$		−	0.336321i		−	0.0167951i	0.999965	−	0.00839753i	$-0.00267305\pi$
$402$		0			0
$403$	2.54602	−	6.14664i	0.126826	−	0.306186i
$404$		0			0
$405$	0.200243	−	0.0829433i	0.00995015	−	0.00412149i
$406$		0			0
$407$	3.08211	+	3.08211i	0.152774	+	0.152774i
$408$		0			0
$409$	−3.23576	+	3.23576i	−0.159998	+	0.159998i	−0.782566	−	0.622568i	$-0.786089\pi$
$409$	−3.23576	+	3.23576i	−0.159998	+	0.159998i	0.622568	+	0.782566i	$0.286089\pi$
$410$		0			0
$411$	5.90103	+	14.2463i	0.291076	+	0.702721i
$412$		0			0
$413$	−1.35953	−	0.563137i	−0.0668983	−	0.0277102i
$414$		0			0
$415$	8.83110			0.433502
$416$		0			0
$417$	−11.7148			−0.573674
$418$		0			0
$419$	16.9870	+	7.03624i	0.829869	+	0.343743i	0.756851	−	0.653588i	$-0.226737\pi$
$419$	16.9870	+	7.03624i	0.829869	+	0.343743i	0.0730182	+	0.997331i	$0.476737\pi$
$420$		0			0
$421$	−15.0999	−	36.4544i	−0.735924	−	1.77668i	−0.621750	−	0.783216i	$-0.713578\pi$
$421$	−15.0999	−	36.4544i	−0.735924	−	1.77668i	−0.114173	−	0.993461i	$-0.536422\pi$
$422$		0			0
$423$	−13.8891	+	13.8891i	−0.675309	+	0.675309i
$424$		0			0
$425$	−7.33325	−	7.33325i	−0.355715	−	0.355715i
$426$		0			0
$427$	0.0893244	−	0.0369994i	0.00432271	−	0.00179053i
$428$		0			0
$429$	0.456176	−	1.10131i	0.0220244	−	0.0531716i
$430$		0			0
$431$			13.1488i			0.633354i	0.948533	+	0.316677i	$0.102567\pi$
$431$			13.1488i			0.633354i	−0.948533	+	0.316677i	$0.897433\pi$
$432$		0			0
$433$		−	40.2052i		−	1.93214i	−0.258282	−	0.966069i	$-0.583156\pi$
$433$		−	40.2052i		−	1.93214i	0.258282	−	0.966069i	$-0.416844\pi$
$434$		0			0
$435$	4.31032	−	10.4060i	0.206664	−	0.498931i
$436$		0			0
$437$	−12.2303	+	5.06595i	−0.585054	+	0.242337i
$438$		0			0
$439$	27.3803	+	27.3803i	1.30679	+	1.30679i	0.923720	+	0.383068i	$0.125133\pi$
$439$	27.3803	+	27.3803i	1.30679	+	1.30679i	0.383068	+	0.923720i	$0.374867\pi$
$440$		0			0
$441$	−1.29427	+	1.29427i	−0.0616321	+	0.0616321i
$442$		0			0
$443$	−13.6912	−	33.0535i	−0.650489	−	1.57042i	−0.812070	−	0.583560i	$-0.801659\pi$
$443$	−13.6912	−	33.0535i	−0.650489	−	1.57042i	0.161581	−	0.986859i	$-0.448341\pi$
$444$		0			0
$445$	−3.77110	−	1.56204i	−0.178767	−	0.0740478i
$446$		0			0
$447$	−20.8706			−0.987147
$448$		0			0
$449$	12.5452			0.592044			0.296022	−	0.955181i	$-0.404340\pi$
$449$	12.5452			0.592044			0.296022	+	0.955181i	$0.404340\pi$
$450$		0			0
$451$	9.35963	+	3.87689i	0.440728	+	0.182556i
$452$		0			0
$453$	−3.73046	−	9.00613i	−0.175272	−	0.423145i
$454$		0			0
$455$	−1.08806	+	1.08806i	−0.0510091	+	0.0510091i
$456$		0			0
$457$	14.2550	+	14.2550i	0.666819	+	0.666819i	0.956978	−	0.290159i	$-0.0937082\pi$
$457$	14.2550	+	14.2550i	0.666819	+	0.666819i	−0.290159	+	0.956978i	$0.593708\pi$
$458$		0			0
$459$	15.9828	−	6.62030i	0.746014	−	0.309009i
$460$		0			0
$461$	−5.52269	+	13.3330i	−0.257217	+	0.620978i	−0.998752	−	0.0499365i	$-0.984098\pi$
$461$	−5.52269	+	13.3330i	−0.257217	+	0.620978i	0.741535	+	0.670914i	$0.234098\pi$
$462$		0			0
$463$			2.24545i			0.104355i	0.998638	+	0.0521775i	$0.0166162\pi$
$463$			2.24545i			0.104355i	−0.998638	+	0.0521775i	$0.983384\pi$
$464$		0			0
$465$		−	8.73632i		−	0.405137i
$466$		0			0
$467$	5.32133	−	12.8468i	0.246242	−	0.594480i	−0.751637	−	0.659577i	$-0.770736\pi$
$467$	5.32133	−	12.8468i	0.246242	−	0.594480i	0.997879	+	0.0650968i	$0.0207356\pi$
$468$		0			0
$469$	−4.92908	+	2.04169i	−0.227604	+	0.0942767i
$470$		0			0
$471$	0.622129	+	0.622129i	0.0286662	+	0.0286662i
$472$		0			0
$473$	0.676111	−	0.676111i	0.0310876	−	0.0310876i
$474$		0			0
$475$	−3.92707	−	9.48079i	−0.180186	−	0.435008i
$476$		0			0
$477$	−9.69693	−	4.01660i	−0.443992	−	0.183907i
$478$		0			0
$479$	15.6342			0.714346			0.357173	−	0.934038i	$-0.383741\pi$
$479$	15.6342			0.714346			0.357173	+	0.934038i	$0.383741\pi$
$480$		0			0
$481$	−5.01160			−0.228509
$482$		0			0
$483$	−4.03652	−	1.67198i	−0.183668	−	0.0760777i
$484$		0			0
$485$	−3.20209	−	7.73053i	−0.145399	−	0.351025i
$486$		0			0
$487$	2.51318	−	2.51318i	0.113883	−	0.113883i	−0.647869	−	0.761752i	$-0.724340\pi$
$487$	2.51318	−	2.51318i	0.113883	−	0.113883i	0.761752	+	0.647869i	$0.224340\pi$
$488$		0			0
$489$	0.862231	+	0.862231i	0.0389914	+	0.0389914i
$490$		0			0
$491$	−26.9210	+	11.1510i	−1.21493	+	0.503239i	−0.895794	−	0.444470i	$-0.853392\pi$
$491$	−26.9210	+	11.1510i	−1.21493	+	0.503239i	−0.319134	+	0.947710i	$0.603392\pi$
$492$		0			0
$493$	9.65597	−	23.3116i	0.434883	−	1.04990i
$494$		0			0
$495$			2.44960i			0.110102i
$496$		0			0
$497$		−	0.782388i		−	0.0350949i
$498$		0			0
$499$	−6.22672	+	15.0326i	−0.278746	+	0.672953i	−0.999801	−	0.0199245i	$-0.993657\pi$
$499$	−6.22672	+	15.0326i	−0.278746	+	0.672953i	0.721055	+	0.692878i	$0.243657\pi$
$500$		0			0
$501$	10.7391	−	4.44828i	0.479787	−	0.198734i
$502$		0			0
$503$	8.16412	+	8.16412i	0.364020	+	0.364020i	0.865291	−	0.501271i	$-0.167134\pi$
$503$	8.16412	+	8.16412i	0.364020	+	0.364020i	−0.501271	+	0.865291i	$0.667134\pi$
$504$		0			0
$505$	6.36549	−	6.36549i	0.283261	−	0.283261i
$506$		0			0
$507$	−4.85578	−	11.7229i	−0.215653	−	0.520632i
$508$		0			0
$509$	13.9521	+	5.77913i	0.618414	+	0.256155i	0.669821	−	0.742522i	$-0.266371\pi$
$509$	13.9521	+	5.77913i	0.618414	+	0.256155i	−0.0514074	+	0.998678i	$0.516371\pi$
$510$		0			0
$511$	9.56468			0.423117
$512$		0			0
$513$	17.1181			0.755783
$514$		0			0
$515$	15.2313	+	6.30902i	0.671172	+	0.278009i
$516$		0			0
$517$	4.02082	+	9.70712i	0.176835	+	0.426919i
$518$		0			0
$519$	16.7957	−	16.7957i	0.737247	−	0.737247i
$520$		0			0
$521$	−0.382095	−	0.382095i	−0.0167399	−	0.0167399i	0.698687	−	0.715427i	$-0.253768\pi$
$521$	−0.382095	−	0.382095i	−0.0167399	−	0.0167399i	−0.715427	+	0.698687i	$0.753768\pi$
$522$		0			0
$523$	−0.581817	+	0.240997i	−0.0254411	+	0.0105380i	−0.395368	−	0.918523i	$-0.629383\pi$
$523$	−0.581817	+	0.240997i	−0.0254411	+	0.0105380i	0.369927	+	0.929061i	$0.379383\pi$
$524$		0			0
$525$	1.29610	−	3.12907i	0.0565665	−	0.136564i
$526$		0			0
$527$		−	19.5711i		−	0.852529i
$528$		0			0
$529$		−	6.67932i		−	0.290405i
$530$		0			0
$531$	1.03076	−	2.48846i	0.0447310	−	0.107990i
$532$		0			0
$533$	−10.7615	+	4.45756i	−0.466132	+	0.193078i
$534$		0			0
$535$	−11.4749	−	11.4749i	−0.496102	−	0.496102i
$536$		0			0
$537$	15.8615	−	15.8615i	0.684472	−	0.684472i
$538$		0			0
$539$	0.374687	+	0.904574i	0.0161389	+	0.0389627i
$540$		0			0
$541$	−9.51992	−	3.94328i	−0.409293	−	0.169535i	0.168530	−	0.985696i	$-0.446098\pi$
$541$	−9.51992	−	3.94328i	−0.409293	−	0.169535i	−0.577824	+	0.816162i	$0.696098\pi$
$542$		0			0
$543$	0.408965			0.0175503
$544$		0			0
$545$	−17.6322			−0.755281
$546$		0			0
$547$	−6.94719	−	2.87762i	−0.297040	−	0.123038i	0.229186	−	0.973383i	$-0.426394\pi$
$547$	−6.94719	−	2.87762i	−0.297040	−	0.123038i	−0.526226	+	0.850344i	$0.676394\pi$
$548$		0			0
$549$	0.0677230	+	0.163498i	0.00289035	+	0.00697791i
$550$		0			0
$551$	17.6546	−	17.6546i	0.752113	−	0.752113i
$552$		0			0
$553$	8.40635	+	8.40635i	0.357474	+	0.357474i
$554$		0			0
$555$	−6.07992	+	2.51839i	−0.258078	+	0.106900i
$556$		0			0
$557$	−4.56082	+	11.0108i	−0.193248	+	0.466542i	−0.990569	−	0.137013i	$-0.956250\pi$
$557$	−4.56082	+	11.0108i	−0.193248	+	0.466542i	0.797321	+	0.603555i	$0.206250\pi$
$558$		0			0
$559$			1.09938i			0.0464987i
$560$		0			0
$561$		−	3.50659i		−	0.148048i
$562$		0			0
$563$	−1.77792	+	4.29228i	−0.0749304	+	0.180898i	−0.956907	−	0.290396i	$-0.906213\pi$
$563$	−1.77792	+	4.29228i	−0.0749304	+	0.180898i	0.881976	+	0.471294i	$0.156213\pi$
$564$		0			0
$565$	−20.0678	+	8.31235i	−0.844258	+	0.349703i
$566$		0			0
$567$	0.112125	+	0.112125i	0.00470879	+	0.00470879i
$568$		0			0
$569$	−16.5347	+	16.5347i	−0.693170	+	0.693170i	−0.962928	−	0.269758i	$-0.913056\pi$
$569$	−16.5347	+	16.5347i	−0.693170	+	0.693170i	0.269758	+	0.962928i	$0.413056\pi$
$570$		0			0
$571$	−14.8785	−	35.9199i	−0.622646	−	1.50320i	−0.848585	−	0.529059i	$-0.822545\pi$
$571$	−14.8785	−	35.9199i	−0.622646	−	1.50320i	0.225939	−	0.974141i	$-0.427455\pi$
$572$		0			0
$573$	−7.60740	−	3.15109i	−0.317804	−	0.131639i
$574$		0			0
$575$	−12.6516			−0.527609
$576$		0			0
$577$	23.0638			0.960160			0.480080	−	0.877225i	$-0.340608\pi$
$577$	23.0638			0.960160			0.480080	+	0.877225i	$0.340608\pi$
$578$		0			0
$579$	−23.7244	−	9.82696i	−0.985951	−	0.408394i
$580$		0			0
$581$	2.47245	+	5.96903i	0.102575	+	0.247637i
$582$		0			0
$583$	−3.97001	+	3.97001i	−0.164421	+	0.164421i
$584$		0			0
$585$	−1.99157	−	1.99157i	−0.0823411	−	0.0823411i
$586$		0			0
$587$	−10.8440	+	4.49173i	−0.447579	+	0.185393i	−0.595077	−	0.803669i	$-0.702878\pi$
$587$	−10.8440	+	4.49173i	−0.447579	+	0.185393i	0.147497	+	0.989062i	$0.452878\pi$
$588$		0			0
$589$	7.41092	−	17.8915i	0.305362	−	0.737208i
$590$		0			0
$591$			1.40088i			0.0576244i
$592$		0			0
$593$			24.5197i			1.00690i	0.864024	+	0.503451i	$0.167937\pi$
$593$			24.5197i			1.00690i	−0.864024	+	0.503451i	$0.832063\pi$
$594$		0			0
$595$	−1.73221	+	4.18192i	−0.0710136	+	0.171442i
$596$		0			0
$597$	14.3583	−	5.94740i	0.587646	−	0.243411i
$598$		0			0
$599$	9.50408	+	9.50408i	0.388326	+	0.388326i	0.874090	−	0.485764i	$-0.161459\pi$
$599$	9.50408	+	9.50408i	0.388326	+	0.388326i	−0.485764	+	0.874090i	$0.661459\pi$
$600$		0			0
$601$	22.7018	−	22.7018i	0.926024	−	0.926024i	−0.0714221	−	0.997446i	$-0.522754\pi$
$601$	22.7018	−	22.7018i	0.926024	−	0.926024i	0.997446	+	0.0714221i	$0.0227537\pi$
$602$		0			0
$603$	−3.73708	−	9.02210i	−0.152185	−	0.367408i
$604$		0			0
$605$	−12.6804	−	5.25240i	−0.515533	−	0.213541i
$606$		0			0
$607$	−46.3175			−1.87997			−0.939985	−	0.341216i	$-0.889161\pi$
$607$	−46.3175			−1.87997			−0.939985	+	0.341216i	$0.889161\pi$
$608$		0			0
$609$	8.24032			0.333915
$610$		0			0
$611$	−11.1610	−	4.62305i	−0.451527	−	0.187029i
$612$		0			0
$613$	5.70272	+	13.7676i	0.230331	+	0.556068i	0.996216	−	0.0869094i	$-0.0276991\pi$
$613$	5.70272	+	13.7676i	0.230331	+	0.556068i	−0.765885	+	0.642977i	$0.777699\pi$
$614$		0			0
$615$	−10.8155	+	10.8155i	−0.436125	+	0.436125i
$616$		0			0
$617$	−16.3375	−	16.3375i	−0.657723	−	0.657723i	0.297118	−	0.954841i	$-0.403975\pi$
$617$	−16.3375	−	16.3375i	−0.657723	−	0.657723i	−0.954841	+	0.297118i	$0.903975\pi$
$618$		0			0
$619$	0.207481	−	0.0859413i	0.00833935	−	0.00345427i	−0.378510	−	0.925597i	$-0.623563\pi$
$619$	0.207481	−	0.0859413i	0.00833935	−	0.00345427i	0.386849	+	0.922143i	$0.373563\pi$
$620$		0			0
$621$	8.07630	−	19.4979i	0.324091	−	0.782424i
$622$		0			0
$623$		−	2.98625i		−	0.119642i
$624$		0			0
$625$		−	0.465782i		−	0.0186313i
$626$		0			0
$627$	1.32783	−	3.20567i	0.0530285	−	0.128022i
$628$		0			0
$629$	−13.6202	+	5.64168i	−0.543074	+	0.224949i
$630$		0			0
$631$	17.4310	+	17.4310i	0.693919	+	0.693919i	0.963092	−	0.269173i	$-0.0867503\pi$
$631$	17.4310	+	17.4310i	0.693919	+	0.693919i	−0.269173	+	0.963092i	$0.586750\pi$
$632$		0			0
$633$	5.72041	−	5.72041i	0.227366	−	0.227366i
$634$		0			0
$635$	8.94209	+	21.5881i	0.354856	+	0.856698i
$636$		0			0
$637$	−1.04006	−	0.430806i	−0.0412086	−	0.0170692i
$638$		0			0
$639$	1.43207			0.0566517
$640$		0			0
$641$	3.65877			0.144513			0.0722563	−	0.997386i	$-0.476980\pi$
$641$	3.65877			0.144513			0.0722563	+	0.997386i	$0.476980\pi$
$642$		0			0
$643$	27.8166	+	11.5220i	1.09698	+	0.454383i	0.856435	−	0.516255i	$-0.172674\pi$
$643$	27.8166	+	11.5220i	1.09698	+	0.454383i	0.240543	+	0.970638i	$0.422674\pi$
$644$		0			0
$645$	0.552449	+	1.33373i	0.0217527	+	0.0525156i
$646$		0			0
$647$	14.7046	−	14.7046i	0.578098	−	0.578098i	−0.356281	−	0.934379i	$-0.615955\pi$
$647$	14.7046	−	14.7046i	0.578098	−	0.578098i	0.934379	+	0.356281i	$0.115955\pi$
$648$		0			0
$649$	−1.01880	−	1.01880i	−0.0399913	−	0.0399913i
$650$		0			0
$651$	5.90497	−	2.44592i	0.231434	−	0.0958631i
$652$		0			0
$653$	1.49385	−	3.60648i	0.0584590	−	0.141133i	−0.891951	−	0.452132i	$-0.850664\pi$
$653$	1.49385	−	3.60648i	0.0584590	−	0.141133i	0.950410	+	0.310999i	$0.100664\pi$
$654$		0			0
$655$		−	23.8301i		−	0.931118i
$656$		0			0
$657$			17.5070i			0.683013i
$658$		0			0
$659$	−3.58812	+	8.66248i	−0.139773	+	0.337442i	−0.978229	−	0.207527i	$-0.933459\pi$
$659$	−3.58812	+	8.66248i	−0.139773	+	0.337442i	0.838456	+	0.544969i	$0.183459\pi$
$660$		0			0
$661$	4.73950	−	1.96317i	0.184345	−	0.0763583i	−0.288602	−	0.957449i	$-0.593190\pi$
$661$	4.73950	−	1.96317i	0.184345	−	0.0763583i	0.472947	+	0.881091i	$0.343190\pi$
$662$		0			0
$663$	2.85091	+	2.85091i	0.110720	+	0.110720i
$664$		0			0
$665$	−3.16711	+	3.16711i	−0.122815	+	0.122815i
$666$		0			0
$667$	−11.7796	−	28.4385i	−0.456108	−	1.10114i
$668$		0			0
$669$	9.84264	+	4.07696i	0.380538	+	0.157624i
$670$		0			0
$671$	0.0946637			0.00365445
$672$		0			0
$673$	−20.7432			−0.799592			−0.399796	−	0.916604i	$-0.630919\pi$
$673$	−20.7432			−0.799592			−0.399796	+	0.916604i	$0.630919\pi$
$674$		0			0
$675$	15.1146	+	6.26066i	0.581760	+	0.240973i
$676$		0			0
$677$	−15.2136	−	36.7288i	−0.584706	−	1.41160i	−0.888504	−	0.458868i	$-0.848255\pi$
$677$	−15.2136	−	36.7288i	−0.584706	−	1.41160i	0.303799	−	0.952736i	$-0.401745\pi$
$678$		0			0
$679$	4.32865	−	4.32865i	0.166118	−	0.166118i
$680$		0			0
$681$	13.0224	+	13.0224i	0.499021	+	0.499021i
$682$		0			0
$683$	−6.12378	+	2.53655i	−0.234320	+	0.0970585i	−0.496754	−	0.867891i	$-0.665475\pi$
$683$	−6.12378	+	2.53655i	−0.234320	+	0.0970585i	0.262434	+	0.964950i	$0.415475\pi$
$684$		0			0
$685$	7.45816	−	18.0056i	0.284962	−	0.687958i
$686$		0			0
$687$			21.0558i			0.803328i
$688$		0			0
$689$		−	6.45535i		−	0.245929i
$690$		0			0
$691$	−15.3357	+	37.0236i	−0.583397	+	1.40844i	0.306319	+	0.951929i	$0.400903\pi$
$691$	−15.3357	+	37.0236i	−0.583397	+	1.40844i	−0.889716	+	0.456515i	$0.849097\pi$
$692$		0			0
$693$	−1.65571	+	0.685819i	−0.0628954	+	0.0260521i
$694$		0			0
$695$	10.4694	+	10.4694i	0.397127	+	0.397127i
$696$		0			0
$697$	−24.2289	+	24.2289i	−0.917737	+	0.917737i
$698$		0			0
$699$	1.90947	+	4.60988i	0.0722229	+	0.174362i
$700$		0			0
$701$	31.5541	+	13.0701i	1.19178	+	0.493652i	0.888335	−	0.459196i	$-0.151862\pi$
$701$	31.5541	+	13.0701i	1.19178	+	0.493652i	0.303447	+	0.952848i	$0.401862\pi$
$702$		0			0
$703$	−14.5877			−0.550185
$704$		0			0
$705$	−15.8633			−0.597448
$706$		0			0
$707$	6.08466	+	2.52035i	0.228837	+	0.0947874i
$708$		0			0
$709$	15.9191	+	38.4322i	0.597856	+	1.44335i	0.875762	+	0.482743i	$0.160359\pi$
$709$	15.9191	+	38.4322i	0.597856	+	1.44335i	−0.277907	+	0.960608i	$0.589641\pi$
$710$		0			0
$711$	−15.3868	+	15.3868i	−0.577051	+	0.577051i
$712$		0			0
$713$	−16.8824	−	16.8824i	−0.632251	−	0.632251i
$714$		0			0
$715$	−1.39191	+	0.576549i	−0.0520546	+	0.0215617i
$716$		0			0
$717$	1.17279	−	2.83136i	0.0437985	−	0.105739i
$718$		0			0
$719$		−	1.68899i		−	0.0629887i	−0.999504	−	0.0314943i	$-0.989973\pi$
$719$		−	1.68899i		−	0.0629887i	0.999504	−	0.0314943i	$-0.0100266\pi$
$720$		0			0
$721$			12.0614i			0.449188i
$722$		0			0
$723$	−9.32070	+	22.5021i	−0.346640	+	0.836864i
$724$		0			0
$725$	22.0452	−	9.13142i	0.818738	−	0.339132i
$726$		0			0
$727$	−9.22518	−	9.22518i	−0.342143	−	0.342143i	0.515029	−	0.857173i	$-0.327781\pi$
$727$	−9.22518	−	9.22518i	−0.342143	−	0.342143i	−0.857173	+	0.515029i	$0.827781\pi$
$728$		0			0
$729$	−12.1901	+	12.1901i	−0.451484	+	0.451484i
$730$		0			0
$731$	1.23759	+	2.98782i	0.0457741	+	0.110508i
$732$		0			0
$733$	44.9627	+	18.6241i	1.66073	+	0.687898i	0.998133	−	0.0610744i	$-0.0194527\pi$
$733$	44.9627	+	18.6241i	1.66073	+	0.687898i	0.662601	+	0.748973i	$0.269453\pi$
$734$		0			0
$735$	−1.47825			−0.0545261
$736$		0			0
$737$	−5.22371			−0.192418
$738$		0			0
$739$	36.8745	+	15.2739i	1.35645	+	0.561861i	0.938081	−	0.346415i	$-0.112601\pi$
$739$	36.8745	+	15.2739i	1.35645	+	0.561861i	0.418371	+	0.908276i	$0.362601\pi$
$740$		0			0
$741$	1.52671	+	3.68580i	0.0560851	+	0.135401i
$742$		0			0
$743$	16.9537	−	16.9537i	0.621972	−	0.621972i	−0.324063	−	0.946035i	$-0.605049\pi$
$743$	16.9537	−	16.9537i	0.621972	−	0.621972i	0.946035	+	0.324063i	$0.105049\pi$
$744$		0			0
$745$	18.6519	+	18.6519i	0.683354	+	0.683354i
$746$		0			0
$747$	−10.9256	+	4.52553i	−0.399747	+	0.165581i
$748$		0			0
$749$	4.54336	−	10.9686i	0.166011	−	0.400785i
$750$		0			0
$751$		−	4.46547i		−	0.162947i	−0.996675	−	0.0814737i	$-0.974037\pi$
$751$		−	4.46547i		−	0.162947i	0.996675	−	0.0814737i	$-0.0259626\pi$
$752$		0			0
$753$		−	24.2484i		−	0.883661i
$754$		0			0
$755$	−4.71483	+	11.3826i	−0.171590	+	0.414255i
$756$		0			0
$757$	−32.9773	+	13.6596i	−1.19858	+	0.496468i	−0.890540	−	0.454905i	$-0.849673\pi$
$757$	−32.9773	+	13.6596i	−1.19858	+	0.496468i	−0.308040	+	0.951373i	$0.599673\pi$
$758$		0			0
$759$	−3.02486	−	3.02486i	−0.109795	−	0.109795i
$760$		0			0
$761$	32.2143	−	32.2143i	1.16777	−	1.16777i	0.185034	−	0.982732i	$-0.440761\pi$
$761$	32.2143	−	32.2143i	1.16777	−	1.16777i	0.982732	−	0.185034i	$-0.0592395\pi$
$762$		0			0
$763$	−4.93652	−	11.9178i	−0.178714	−	0.431454i
$764$		0			0
$765$	−7.65450	−	3.17060i	−0.276749	−	0.114633i
$766$		0			0
$767$	1.65660			0.0598163
$768$		0			0
$769$	−46.4889			−1.67643			−0.838217	−	0.545337i	$-0.816402\pi$
$769$	−46.4889			−1.67643			−0.838217	+	0.545337i	$0.816402\pi$
$770$		0			0
$771$	−7.99463	−	3.31148i	−0.287920	−	0.119260i
$772$		0			0
$773$	19.4635	+	46.9890i	0.700053	+	1.69008i	0.723474	+	0.690352i	$0.242544\pi$
$773$	19.4635	+	46.9890i	0.700053	+	1.69008i	−0.0234209	+	0.999726i	$0.507456\pi$
$774$		0			0
$775$	13.0871	−	13.0871i	0.470101	−	0.470101i
$776$		0			0
$777$	−3.40441	−	3.40441i	−0.122133	−	0.122133i
$778$		0			0
$779$	−31.3244	+	12.9750i	−1.12231	+	0.464877i
$780$		0			0
$781$	0.293150	−	0.707727i	0.0104897	−	0.0253245i
$782$		0			0
$783$			39.8039i			1.42247i
$784$		0			0
$785$		−	1.11198i		−	0.0396884i
$786$		0			0
$787$	−18.8857	+	45.5941i	−0.673202	+	1.62525i	0.102934	+	0.994688i	$0.467177\pi$
$787$	−18.8857	+	45.5941i	−0.673202	+	1.62525i	−0.776136	+	0.630565i	$0.782823\pi$
$788$		0			0
$789$	21.4797	−	8.89719i	0.764699	−	0.316749i
$790$		0			0
$791$	−11.2368	−	11.2368i	−0.399535	−	0.399535i
$792$		0			0
$793$	−0.0769631	+	0.0769631i	−0.00273304	+	0.00273304i
$794$		0			0
$795$	−3.24389	−	7.83143i	−0.115049	−	0.277752i
$796$		0			0
$797$	5.80787	+	2.40570i	0.205725	+	0.0852142i	0.483167	−	0.875528i	$-0.339486\pi$
$797$	5.80787	+	2.40570i	0.205725	+	0.0852142i	−0.277442	+	0.960743i	$0.589486\pi$
$798$		0			0
$799$	−35.5370			−1.25721
$800$		0			0
$801$	5.46597			0.193131
$802$		0			0
$803$	8.65196	+	3.58376i	0.305321	+	0.126468i
$804$		0			0
$805$	2.11317	+	5.10165i	0.0744795	+	0.179809i
$806$		0			0
$807$	6.86039	−	6.86039i	0.241497	−	0.241497i
$808$		0			0
$809$	−9.41608	−	9.41608i	−0.331052	−	0.331052i	0.521934	−	0.852986i	$-0.325211\pi$
$809$	−9.41608	−	9.41608i	−0.331052	−	0.331052i	−0.852986	+	0.521934i	$0.825211\pi$
$810$		0			0
$811$	45.3813	−	18.7976i	1.59355	−	0.660072i	0.603068	−	0.797690i	$-0.293945\pi$
$811$	45.3813	−	18.7976i	1.59355	−	0.660072i	0.990485	+	0.137618i	$0.0439447\pi$
$812$		0			0
$813$	6.72164	−	16.2275i	0.235738	−	0.569122i
$814$		0			0
$815$		−	1.54114i		−	0.0539838i
$816$		0			0
$817$			3.20005i			0.111956i
$818$		0			0
$819$	0.788539	−	1.90370i	0.0275538	−	0.0665207i
$820$		0			0
$821$	−30.8653	+	12.7848i	−1.07721	+	0.446194i	−0.849528	−	0.527543i	$-0.823113\pi$
$821$	−30.8653	+	12.7848i	−1.07721	+	0.446194i	−0.227678	+	0.973736i	$0.573113\pi$
$822$		0			0
$823$	−0.854721	−	0.854721i	−0.0297937	−	0.0297937i	0.692053	−	0.721847i	$-0.256706\pi$
$823$	−0.854721	−	0.854721i	−0.0297937	−	0.0297937i	−0.721847	+	0.692053i	$0.756706\pi$
$824$		0			0
$825$	2.34484	−	2.34484i	0.0816368	−	0.0816368i
$826$		0			0
$827$	8.18409	+	19.7581i	0.284589	+	0.687058i	0.999931	−	0.0117158i	$-0.00372935\pi$
$827$	8.18409	+	19.7581i	0.284589	+	0.687058i	−0.715343	+	0.698774i	$0.753729\pi$
$828$		0			0
$829$	22.1565	+	9.17751i	0.769526	+	0.318748i	0.732680	−	0.680573i	$-0.238269\pi$
$829$	22.1565	+	9.17751i	0.769526	+	0.318748i	0.0368457	+	0.999321i	$0.488269\pi$
$830$		0			0
$831$	−9.58014			−0.332331
$832$		0			0
$833$	−3.31157			−0.114739
$834$		0			0
$835$	−13.5728	−	5.62206i	−0.469708	−	0.194559i
$836$		0			0
$837$	11.8147	+	28.5233i	0.408376	+	0.985908i
$838$		0			0
$839$	−7.72755	+	7.72755i	−0.266785	+	0.266785i	−0.827803	−	0.561018i	$-0.810410\pi$
$839$	−7.72755	+	7.72755i	−0.266785	+	0.266785i	0.561018	+	0.827803i	$0.310410\pi$
$840$		0			0
$841$	20.5454	+	20.5454i	0.708461	+	0.708461i
$842$		0			0
$843$	−13.4634	+	5.57671i	−0.463703	+	0.192072i
$844$		0			0
$845$	−6.13710	+	14.8163i	−0.211123	+	0.509695i
$846$		0			0
$847$		−	10.0414i		−	0.345025i
$848$		0			0
$849$			26.2556i			0.901090i
$850$		0			0
$851$	−6.88245	+	16.6157i	−0.235927	+	0.569579i
$852$		0			0
$853$	−13.6812	+	5.66694i	−0.468436	+	0.194032i	−0.604400	−	0.796681i	$-0.706587\pi$
$853$	−13.6812	+	5.66694i	−0.468436	+	0.194032i	0.135964	+	0.990714i	$0.456587\pi$
$854$		0			0
$855$	−5.79702	−	5.79702i	−0.198254	−	0.198254i
$856$		0			0
$857$	−27.6739	+	27.6739i	−0.945322	+	0.945322i	−0.998581	−	0.0532590i	$-0.983039\pi$
$857$	−27.6739	+	27.6739i	−0.945322	+	0.945322i	0.0532590	+	0.998581i	$0.483039\pi$
$858$		0			0
$859$	13.1026	+	31.6326i	0.447056	+	1.07929i	0.973419	+	0.229030i	$0.0735553\pi$
$859$	13.1026	+	31.6326i	0.447056	+	1.07929i	−0.526363	+	0.850260i	$0.676445\pi$
$860$		0			0
$861$	−10.3384	−	4.28230i	−0.352331	−	0.145940i
$862$		0			0
$863$	42.2413			1.43791			0.718955	−	0.695056i	$-0.244620\pi$
$863$	42.2413			1.43791			0.718955	+	0.695056i	$0.244620\pi$
$864$		0			0
$865$	−30.0203			−1.02072
$866$		0			0
$867$	−6.02845	−	2.49707i	−0.204737	−	0.0848048i
$868$		0			0
$869$	4.45442	+	10.7539i	0.151106	+	0.364801i
$870$		0			0
$871$	4.24696	−	4.24696i	0.143903	−	0.143903i
$872$		0			0
$873$	7.92308	+	7.92308i	0.268156	+	0.268156i
$874$		0			0
$875$	−10.2688	+	4.25349i	−0.347150	+	0.143794i
$876$		0			0
$877$	1.49656	−	3.61301i	0.0505352	−	0.122003i	−0.896596	−	0.442850i	$-0.853968\pi$
$877$	1.49656	−	3.61301i	0.0505352	−	0.122003i	0.947131	+	0.320847i	$0.103968\pi$
$878$		0			0
$879$		−	24.1465i		−	0.814440i
$880$		0			0
$881$		−	46.9294i		−	1.58109i	−0.612403	−	0.790546i	$-0.709797\pi$
$881$		−	46.9294i		−	1.58109i	0.612403	−	0.790546i	$-0.290203\pi$
$882$		0			0
$883$	−9.05346	+	21.8570i	−0.304673	+	0.735546i	0.695187	+	0.718829i	$0.255322\pi$
$883$	−9.05346	+	21.8570i	−0.304673	+	0.735546i	−0.999860	+	0.0167174i	$0.994678\pi$
$884$		0			0
$885$	2.00973	−	0.832459i	0.0675564	−	0.0279828i
$886$		0			0
$887$	3.55140	+	3.55140i	0.119244	+	0.119244i	0.764211	−	0.644967i	$-0.223129\pi$
$887$	3.55140	+	3.55140i	0.119244	+	0.119244i	−0.644967	+	0.764211i	$0.723129\pi$
$888$		0			0
$889$	−12.0881	+	12.0881i	−0.405422	+	0.405422i
$890$		0			0
$891$	0.0594133	+	0.143436i	0.00199042	+	0.00480530i
$892$		0			0
$893$	−32.4873	−	13.4567i	−1.08715	−	0.450311i
$894$		0			0
$895$	−28.3506			−0.947655
$896$		0			0
$897$	4.91851			0.164224
$898$		0			0
$899$	41.6023	+	17.2322i	1.38751	+	0.574727i
$900$		0			0
$901$	−7.26694	−	17.5439i	−0.242097	−	0.584474i
$902$		0			0
$903$	−0.746813	+	0.746813i	−0.0248524	+	0.0248524i
$904$		0			0
$905$	−0.365489	−	0.365489i	−0.0121493	−	0.0121493i
$906$		0			0
$907$	14.4344	−	5.97893i	0.479287	−	0.198527i	−0.129942	−	0.991522i	$-0.541479\pi$
$907$	14.4344	−	5.97893i	0.479287	−	0.198527i	0.609229	+	0.792994i	$0.291479\pi$
$908$		0			0
$909$	−4.61319	+	11.1372i	−0.153010	+	0.369399i
$910$		0			0
$911$		−	5.65334i		−	0.187303i	−0.995605	−	0.0936517i	$-0.970146\pi$
$911$		−	5.65334i		−	0.187303i	0.995605	−	0.0936517i	$-0.0298540\pi$
$912$		0			0
$913$			6.32583i			0.209354i
$914$		0			0
$915$	−0.0546944	+	0.132044i	−0.00180814	+	0.00436524i
$916$		0			0
$917$	16.1070	−	6.67174i	0.531900	−	0.220320i
$918$		0			0
$919$	−3.33146	−	3.33146i	−0.109895	−	0.109895i	0.650021	−	0.759916i	$-0.274760\pi$
$919$	−3.33146	−	3.33146i	−0.109895	−	0.109895i	−0.759916	+	0.650021i	$0.774760\pi$
$920$		0			0
$921$	−25.1308	+	25.1308i	−0.828087	+	0.828087i
$922$		0			0
$923$	0.337057	+	0.813729i	0.0110944	+	0.0267842i
$924$		0			0
$925$	−12.8803	−	5.33520i	−0.423502	−	0.175420i
$926$		0			0
$927$	−22.0769			−0.725099
$928$		0			0
$929$	−56.0336			−1.83840			−0.919202	−	0.393787i	$-0.871165\pi$
$929$	−56.0336			−1.83840			−0.919202	+	0.393787i	$0.871165\pi$
$930$		0			0
$931$	−3.02738	−	1.25398i	−0.0992185	−	0.0410977i
$932$		0			0
$933$	5.60782	+	13.5385i	0.183592	+	0.443230i
$934$		0			0
$935$	−3.13382	+	3.13382i	−0.102487	+	0.102487i
$936$		0			0
$937$	−19.6625	−	19.6625i	−0.642345	−	0.642345i	0.308787	−	0.951131i	$-0.400077\pi$
$937$	−19.6625	−	19.6625i	−0.642345	−	0.642345i	−0.951131	+	0.308787i	$0.900077\pi$
$938$		0			0
$939$	−13.3980	+	5.54962i	−0.437226	+	0.181105i
$940$		0			0
$941$	−8.94829	+	21.6031i	−0.291706	+	0.704240i	−0.999999	−	0.00167870i	$-0.999466\pi$
$941$	−8.94829	+	21.6031i	−0.291706	+	0.704240i	0.708293	+	0.705919i	$0.249466\pi$
$942$		0			0
$943$			41.8008i			1.36122i
$944$		0			0
$945$		−	7.14052i		−	0.232281i
$946$		0			0
$947$	2.96135	−	7.14933i	0.0962309	−	0.232322i	−0.868432	−	0.495808i	$-0.834872\pi$
$947$	2.96135	−	7.14933i	0.0962309	−	0.232322i	0.964663	+	0.263486i	$0.0848721\pi$
$948$		0			0
$949$	−9.94783	+	4.12052i	−0.322920	+	0.133758i
$950$		0			0
$951$	21.3602	+	21.3602i	0.692653	+	0.692653i
$952$		0			0
$953$	22.9816	−	22.9816i	0.744448	−	0.744448i	−0.228983	−	0.973431i	$-0.573540\pi$
$953$	22.9816	−	22.9816i	0.744448	−	0.744448i	0.973431	+	0.228983i	$0.0735399\pi$
$954$		0			0
$955$	3.98258	+	9.61479i	0.128873	+	0.311127i
$956$		0			0
$957$	7.45398	+	3.08754i	0.240953	+	0.0998059i
$958$		0			0
$959$	14.2582			0.460422
$960$		0			0
$961$	3.92690			0.126674
$962$		0			0
$963$	20.0768	+	8.31607i	0.646965	+	0.267982i
$964$		0			0
$965$	12.4200	+	29.9846i	0.399815	+	0.965239i
$966$		0			0
$967$	37.6861	−	37.6861i	1.21190	−	1.21190i	0.241503	−	0.970400i	$-0.422360\pi$
$967$	37.6861	−	37.6861i	1.21190	−	1.21190i	0.970400	−	0.241503i	$-0.0776402\pi$
$968$		0			0
$969$	8.29839	+	8.29839i	0.266583	+	0.266583i
$970$		0			0
$971$	−4.96890	+	2.05819i	−0.159460	+	0.0660504i	−0.460986	−	0.887408i	$-0.652504\pi$
$971$	−4.96890	+	2.05819i	−0.159460	+	0.0660504i	0.301526	+	0.953458i	$0.402504\pi$
$972$		0			0
$973$	−4.14525	+	10.0075i	−0.132891	+	0.320826i
$974$		0			0
$975$			3.81278i			0.122107i
$976$		0			0
$977$		−	28.1908i		−	0.901905i	−0.892548	−	0.450952i	$-0.851084\pi$
$977$		−	28.1908i		−	0.901905i	0.892548	−	0.450952i	$-0.148916\pi$
$978$		0			0
$979$	1.11891	−	2.70128i	0.0357605	−	0.0863334i
$980$		0			0
$981$	21.8141	−	9.03570i	0.696471	−	0.288488i
$982$		0			0
$983$	20.6985	+	20.6985i	0.660179	+	0.660179i	0.955422	−	0.295243i	$-0.0954007\pi$
$983$	20.6985	+	20.6985i	0.660179	+	0.660179i	−0.295243	+	0.955422i	$0.595401\pi$
$984$		0			0
$985$	1.25196	−	1.25196i	0.0398906	−	0.0398906i
$986$		0			0
$987$	−4.44128	−	10.7222i	−0.141368	−	0.341292i
$988$		0			0
$989$	3.64493	+	1.50978i	0.115902	+	0.0480082i
$990$		0			0
$991$	−13.1949			−0.419149			−0.209575	−	0.977793i	$-0.567208\pi$
$991$	−13.1949			−0.419149			−0.209575	+	0.977793i	$0.567208\pi$
$992$		0			0
$993$	−13.5360			−0.429553
$994$		0			0
$995$	−18.1471	−	7.51676i	−0.575301	−	0.238297i
$996$		0			0
$997$	11.0248	+	26.6162i	0.349158	+	0.842942i	0.996720	+	0.0809291i	$0.0257887\pi$
$997$	11.0248	+	26.6162i	0.349158	+	0.842942i	−0.647562	+	0.762013i	$0.724211\pi$
$998$		0			0
$999$	16.4446	−	16.4446i	0.520284	−	0.520284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.337.5		52
4.3	odd	2		224.2.u.c.29.11	✓	52
32.11	odd	8		224.2.u.c.85.11	yes	52
32.21	even	8	inner	896.2.u.c.561.5		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.11	✓	52	4.3	odd	2
224.2.u.c.85.11	yes	52	32.11	odd	8
896.2.u.c.337.5		52	1.1	even	1	trivial
896.2.u.c.561.5		52	32.21	even	8	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.u (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.999166 - 0.413868i) q^{3} +(0.523077 + 1.26282i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-1.29427 - 1.29427i) q^{9} +O(q^{10})\)	\(q+(-0.999166 - 0.413868i) q^{3} +(0.523077 + 1.26282i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-1.29427 - 1.29427i) q^{9} +(-0.904574 + 0.374687i) q^{11} +(0.430806 - 1.04006i) q^{13} -1.47825i q^{15} -3.31157i q^{17} +(1.25398 - 3.02738i) q^{19} +(0.999166 - 0.413868i) q^{21} +(-2.85663 - 2.85663i) q^{23} +(2.21443 - 2.21443i) q^{25} +(1.99914 + 4.82635i) q^{27} +(7.03942 + 2.91582i) q^{29} +5.90990 q^{31} +1.05889 q^{33} +(-1.26282 - 0.523077i) q^{35} +(-1.70363 - 4.11292i) q^{37} +(-0.860894 + 0.860894i) q^{39} +(-7.31644 - 7.31644i) q^{41} +(-0.902235 + 0.373718i) q^{43} +(0.957430 - 2.31144i) q^{45} -10.7312i q^{47} -1.00000i q^{49} +(-1.37055 + 3.30881i) q^{51} +(5.29777 - 2.19441i) q^{53} +(-0.946323 - 0.946323i) q^{55} +(-2.50588 + 2.50588i) q^{57} +(0.563137 + 1.35953i) q^{59} +(-0.0893244 - 0.0369994i) q^{61} +1.83038 q^{63} +1.53875 q^{65} +(4.92908 + 2.04169i) q^{67} +(1.67198 + 4.03652i) q^{69} +(-0.553232 + 0.553232i) q^{71} +(-6.76325 - 6.76325i) q^{73} +(-3.12907 + 1.29610i) q^{75} +(0.374687 - 0.904574i) q^{77} -11.8884i q^{79} -0.158568i q^{81} +(2.47245 - 5.96903i) q^{83} +(4.18192 - 1.73221i) q^{85} +(-5.82679 - 5.82679i) q^{87} +(-2.11160 + 2.11160i) q^{89} +(0.430806 + 1.04006i) q^{91} +(-5.90497 - 2.44592i) q^{93} +4.47897 q^{95} -6.12164 q^{97} +(1.65571 + 0.685819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) \) 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Introduction

L-functions

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