LMFDB - Embedded newform 896.2.x.b.111.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(111,896)]

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([4, 7, 4]))

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

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

chi := DirichletCharacter("896.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.x (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.28
Character	$\chi$	$=$	896.111
Dual form			896.2.x.b.783.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25862 - 3.03857i) q^{3} +(-0.824079 - 1.98950i) q^{5} +(0.0837494 - 2.64443i) q^{7} +(-5.52747 - 5.52747i) q^{9} +O(q^{10})$	\(q+(1.25862 - 3.03857i) q^{3} +(-0.824079 - 1.98950i) q^{5} +(0.0837494 - 2.64443i) q^{7} +(-5.52747 - 5.52747i) q^{9} +(0.623399 - 0.258220i) q^{11} +(-1.24310 + 3.00110i) q^{13} -7.08245 q^{15} +2.68128 q^{17} +(4.54495 + 1.88258i) q^{19} +(-7.92987 - 3.58280i) q^{21} +(0.871276 - 0.871276i) q^{23} +(0.256515 - 0.256515i) q^{25} +(-14.6369 + 6.06280i) q^{27} +(-2.60571 + 6.29073i) q^{29} +4.75214 q^{31} -2.21924i q^{33} +(-5.33011 + 2.01260i) q^{35} +(-5.97522 + 2.47502i) q^{37} +(7.55448 + 7.55448i) q^{39} +(3.37920 - 3.37920i) q^{41} +(11.8871 - 4.92381i) q^{43} +(-6.44185 + 15.5520i) q^{45} -3.01477i q^{47} +(-6.98597 - 0.442938i) q^{49} +(3.37471 - 8.14727i) q^{51} +(1.62665 + 3.92708i) q^{53} +(-1.02746 - 1.02746i) q^{55} +(11.4407 - 11.4407i) q^{57} +(-2.08390 + 0.863180i) q^{59} +(5.36260 + 2.22126i) q^{61} +(-15.0799 + 14.1541i) q^{63} +6.99512 q^{65} +(-6.52791 - 2.70395i) q^{67} +(-1.55083 - 3.74404i) q^{69} +(-9.16414 - 9.16414i) q^{71} +(3.68420 - 3.68420i) q^{73} +(-0.456585 - 1.10229i) q^{75} +(-0.630635 - 1.67016i) q^{77} -5.81800 q^{79} +28.6549i q^{81} +(-4.18900 - 1.73514i) q^{83} +(-2.20959 - 5.33442i) q^{85} +(15.8352 + 15.8352i) q^{87} +(0.872091 + 0.872091i) q^{89} +(7.83209 + 3.53862i) q^{91} +(5.98113 - 14.4397i) q^{93} -10.5936i q^{95} +16.0201i q^{97} +(-4.87313 - 2.01852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 112 * q + 4 * q^7 - 8 * q^9	$ 112 q + 4 q^{7} - 8 q^{9} + 8 q^{11} + 16 q^{15} - 4 q^{21} + 48 q^{23} - 8 q^{25} - 8 q^{29} - 20 q^{35} - 8 q^{37} + 8 q^{39} - 32 q^{43} + 32 q^{51} - 32 q^{53} - 8 q^{57} - 16 q^{65} + 64 q^{67} - 56 q^{71} + 52 q^{77} + 16 q^{79} - 48 q^{85} + 52 q^{91} - 32 q^{93} - 16 q^{99}+O(q^{100}) $ 112 * q + 4 * q^7 - 8 * q^9 + 8 * q^11 + 16 * q^15 - 4 * q^21 + 48 * q^23 - 8 * q^25 - 8 * q^29 - 20 * q^35 - 8 * q^37 + 8 * q^39 - 32 * q^43 + 32 * q^51 - 32 * q^53 - 8 * q^57 - 16 * q^65 + 64 * q^67 - 56 * q^71 + 52 * q^77 + 16 * q^79 - 48 * q^85 + 52 * q^91 - 32 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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
$3$	1.25862	−	3.03857i	0.726663	−	1.75432i	0.0732556	−	0.997313i	$-0.476661\pi$
$3$	1.25862	−	3.03857i	0.726663	−	1.75432i	0.653407	−	0.757006i	$-0.273339\pi$
$4$		0			0
$5$	−0.824079	−	1.98950i	−0.368540	−	0.889733i	−0.993990	−	0.109469i	$-0.965085\pi$
$5$	−0.824079	−	1.98950i	−0.368540	−	0.889733i	0.625451	−	0.780264i	$-0.284915\pi$
$6$		0			0
$7$	0.0837494	−	2.64443i	0.0316543	−	0.999499i
$7$	0.0837494	−	2.64443i	0.0316543	−	0.999499i
$8$		0			0
$9$	−5.52747	−	5.52747i	−1.84249	−	1.84249i
$10$		0			0
$11$	0.623399	−	0.258220i	0.187962	−	0.0778564i	−0.286717	−	0.958015i	$-0.592564\pi$
$11$	0.623399	−	0.258220i	0.187962	−	0.0778564i	0.474679	+	0.880159i	$0.342564\pi$
$12$		0			0
$13$	−1.24310	+	3.00110i	−0.344773	+	0.832356i	0.652446	+	0.757835i	$0.273743\pi$
$13$	−1.24310	+	3.00110i	−0.344773	+	0.832356i	−0.997219	+	0.0745212i	$0.976257\pi$
$14$		0			0
$15$	−7.08245			−1.82868
$16$		0			0
$17$	2.68128			0.650307			0.325153	−	0.945661i	$-0.394584\pi$
$17$	2.68128			0.650307			0.325153	+	0.945661i	$0.394584\pi$
$18$		0			0
$19$	4.54495	+	1.88258i	1.04268	+	0.431894i	0.837275	−	0.546782i	$-0.184147\pi$
$19$	4.54495	+	1.88258i	1.04268	+	0.431894i	0.205409	+	0.978676i	$0.434147\pi$
$20$		0			0
$21$	−7.92987	−	3.58280i	−1.73044	−	0.781831i
$22$		0			0
$23$	0.871276	−	0.871276i	0.181674	−	0.181674i	−0.610411	−	0.792085i	$-0.708996\pi$
$23$	0.871276	−	0.871276i	0.181674	−	0.181674i	0.792085	+	0.610411i	$0.208996\pi$
$24$		0			0
$25$	0.256515	−	0.256515i	0.0513031	−	0.0513031i
$26$		0			0
$27$	−14.6369	+	6.06280i	−2.81687	+	1.16679i
$28$		0			0
$29$	−2.60571	+	6.29073i	−0.483867	+	1.16816i	0.473891	+	0.880584i	$0.342849\pi$
$29$	−2.60571	+	6.29073i	−0.483867	+	1.16816i	−0.957758	+	0.287576i	$0.907151\pi$
$30$		0			0
$31$	4.75214			0.853510			0.426755	−	0.904367i	$-0.359657\pi$
$31$	4.75214			0.853510			0.426755	+	0.904367i	$0.359657\pi$
$32$		0			0
$33$		−	2.21924i		−	0.386321i
$34$		0			0
$35$	−5.33011	+	2.01260i	−0.900953	+	0.340191i
$36$		0			0
$37$	−5.97522	+	2.47502i	−0.982319	+	0.406890i	−0.815284	−	0.579061i	$-0.803419\pi$
$37$	−5.97522	+	2.47502i	−0.982319	+	0.406890i	−0.167035	+	0.985951i	$0.553419\pi$
$38$		0			0
$39$	7.55448	+	7.55448i	1.20969	+	1.20969i
$40$		0			0
$41$	3.37920	−	3.37920i	0.527742	−	0.527742i	−0.392156	−	0.919899i	$-0.628271\pi$
$41$	3.37920	−	3.37920i	0.527742	−	0.527742i	0.919899	+	0.392156i	$0.128271\pi$
$42$		0			0
$43$	11.8871	−	4.92381i	1.81277	−	0.750874i	0.832265	−	0.554378i	$-0.187044\pi$
$43$	11.8871	−	4.92381i	1.81277	−	0.750874i	0.980505	−	0.196496i	$-0.0629563\pi$
$44$		0			0
$45$	−6.44185	+	15.5520i	−0.960295	+	2.31836i
$46$		0			0
$47$		−	3.01477i		−	0.439750i	−0.975528	−	0.219875i	$-0.929435\pi$
$47$		−	3.01477i		−	0.439750i	0.975528	−	0.219875i	$-0.0705649\pi$
$48$		0			0
$49$	−6.98597	−	0.442938i	−0.997996	−	0.0632769i
$50$		0			0
$51$	3.37471	−	8.14727i	0.472554	−	1.14085i
$52$		0			0
$53$	1.62665	+	3.92708i	0.223437	+	0.539425i	0.995352	−	0.0963004i	$-0.0307010\pi$
$53$	1.62665	+	3.92708i	0.223437	+	0.539425i	−0.771915	+	0.635726i	$0.780701\pi$
$54$		0			0
$55$	−1.02746	−	1.02746i	−0.138543	−	0.138543i
$56$		0			0
$57$	11.4407	−	11.4407i	1.51536	−	1.51536i
$58$		0			0
$59$	−2.08390	+	0.863180i	−0.271301	+	0.112376i	−0.514186	−	0.857678i	$-0.671906\pi$
$59$	−2.08390	+	0.863180i	−0.271301	+	0.112376i	0.242886	+	0.970055i	$0.421906\pi$
$60$		0			0
$61$	5.36260	+	2.22126i	0.686611	+	0.284403i	0.698587	−	0.715525i	$-0.253812\pi$
$61$	5.36260	+	2.22126i	0.686611	+	0.284403i	−0.0119767	+	0.999928i	$0.503812\pi$
$62$		0			0
$63$	−15.0799	+	14.1541i	−1.89989	+	1.78325i
$64$		0			0
$65$	6.99512			0.867638
$66$		0			0
$67$	−6.52791	−	2.70395i	−0.797511	−	0.330340i	−0.0535518	−	0.998565i	$-0.517054\pi$
$67$	−6.52791	−	2.70395i	−0.797511	−	0.330340i	−0.743959	+	0.668225i	$0.767054\pi$
$68$		0			0
$69$	−1.55083	−	3.74404i	−0.186698	−	0.450729i
$70$		0			0
$71$	−9.16414	−	9.16414i	−1.08758	−	1.08758i	−0.995777	−	0.0918067i	$-0.970736\pi$
$71$	−9.16414	−	9.16414i	−1.08758	−	1.08758i	−0.0918067	−	0.995777i	$-0.529264\pi$
$72$		0			0
$73$	3.68420	−	3.68420i	0.431203	−	0.431203i	−0.457835	−	0.889037i	$-0.651375\pi$
$73$	3.68420	−	3.68420i	0.431203	−	0.431203i	0.889037	+	0.457835i	$0.151375\pi$
$74$		0			0
$75$	−0.456585	−	1.10229i	−0.0527219	−	0.127282i
$76$		0			0
$77$	−0.630635	−	1.67016i	−0.0718676	−	0.190332i
$78$		0			0
$79$	−5.81800			−0.654576			−0.327288	−	0.944925i	$-0.606135\pi$
$79$	−5.81800			−0.654576			−0.327288	+	0.944925i	$0.606135\pi$
$80$		0			0
$81$			28.6549i			3.18387i
$82$		0			0
$83$	−4.18900	−	1.73514i	−0.459803	−	0.190457i	0.140744	−	0.990046i	$-0.455050\pi$
$83$	−4.18900	−	1.73514i	−0.459803	−	0.190457i	−0.600547	+	0.799589i	$0.705050\pi$
$84$		0			0
$85$	−2.20959	−	5.33442i	−0.239664	−	0.578599i
$86$		0			0
$87$	15.8352	+	15.8352i	1.69772	+	1.69772i
$88$		0			0
$89$	0.872091	+	0.872091i	0.0924415	+	0.0924415i	0.751815	−	0.659374i	$-0.229179\pi$
$89$	0.872091	+	0.872091i	0.0924415	+	0.0924415i	−0.659374	+	0.751815i	$0.729179\pi$
$90$		0			0
$91$	7.83209	+	3.53862i	0.821026	+	0.370948i
$92$		0			0
$93$	5.98113	−	14.4397i	0.620214	−	1.49733i
$94$		0			0
$95$		−	10.5936i		−	1.08688i
$96$		0			0
$97$			16.0201i			1.62660i	0.581845	+	0.813300i	$0.302331\pi$
$97$			16.0201i			1.62660i	−0.581845	+	0.813300i	$0.697669\pi$
$98$		0			0
$99$	−4.87313	−	2.01852i	−0.489768	−	0.202869i
$100$		0			0
$101$	0.555956	+	1.34220i	0.0553197	+	0.133554i	0.949123	−	0.314906i	$-0.101973\pi$
$101$	0.555956	+	1.34220i	0.0553197	+	0.133554i	−0.893803	+	0.448459i	$0.851973\pi$
$102$		0			0
$103$	4.23866	−	4.23866i	0.417647	−	0.417647i	−0.466745	−	0.884392i	$-0.654573\pi$
$103$	4.23866	−	4.23866i	0.417647	−	0.417647i	0.884392	+	0.466745i	$0.154573\pi$
$104$		0			0
$105$	−0.593151	+	18.7290i	−0.0578856	+	1.82776i
$106$		0			0
$107$	−7.88751	+	3.26711i	−0.762514	+	0.315844i	−0.729836	−	0.683622i	$-0.760404\pi$
$107$	−7.88751	+	3.26711i	−0.762514	+	0.315844i	−0.0326782	+	0.999466i	$0.510404\pi$
$108$		0			0
$109$	−4.75970	−	1.97153i	−0.455897	−	0.188839i	0.142904	−	0.989737i	$-0.454356\pi$
$109$	−4.75970	−	1.97153i	−0.455897	−	0.188839i	−0.598801	+	0.800898i	$0.704356\pi$
$110$		0			0
$111$			21.2712i			2.01897i
$112$		0			0
$113$		−	10.2261i		−	0.961993i	−0.876723	−	0.480996i	$-0.840275\pi$
$113$		−	10.2261i		−	0.961993i	0.876723	−	0.480996i	$-0.159725\pi$
$114$		0			0
$115$	−2.45141	−	1.01541i	−0.228595	−	0.0946872i
$116$		0			0
$117$	23.4597	−	9.71733i	2.16885	−	0.898368i
$118$		0			0
$119$	0.224556	−	7.09045i	0.0205850	−	0.649981i
$120$		0			0
$121$	−7.45623	+	7.45623i	−0.677839	+	0.677839i
$122$		0			0
$123$	−6.01482	−	14.5210i	−0.542338	−	1.30932i
$124$		0			0
$125$	−10.6692	−	4.41935i	−0.954286	−	0.395278i
$126$		0			0
$127$		−	3.43170i		−	0.304514i	−0.988341	−	0.152257i	$-0.951346\pi$
$127$		−	3.43170i		−	0.304514i	0.988341	−	0.152257i	$-0.0486542\pi$
$128$		0			0
$129$		−	42.3171i		−	3.72581i
$130$		0			0
$131$	2.16614	−	5.22953i	0.189257	−	0.456906i	−0.800560	−	0.599252i	$-0.795465\pi$
$131$	2.16614	−	5.22953i	0.189257	−	0.456906i	0.989817	+	0.142346i	$0.0454647\pi$
$132$		0			0
$133$	5.35898	−	11.8611i	0.464683	−	1.02849i
$134$		0			0
$135$	24.1239	+	24.1239i	2.07626	+	2.07626i
$136$		0			0
$137$	−6.07189	−	6.07189i	−0.518757	−	0.518757i	0.398438	−	0.917195i	$-0.369552\pi$
$137$	−6.07189	−	6.07189i	−0.518757	−	0.518757i	−0.917195	+	0.398438i	$0.869552\pi$
$138$		0			0
$139$	−1.49929	−	3.61960i	−0.127168	−	0.307011i	0.847454	−	0.530869i	$-0.178135\pi$
$139$	−1.49929	−	3.61960i	−0.127168	−	0.307011i	−0.974622	+	0.223859i	$0.928135\pi$
$140$		0			0
$141$	−9.16060	−	3.79444i	−0.771461	−	0.319550i
$142$		0			0
$143$			2.19188i			0.183294i
$144$		0			0
$145$	14.6627			1.21767
$146$		0			0
$147$	−10.1386	+	20.6699i	−0.836215	+	1.70482i
$148$		0			0
$149$	−0.328004	−	0.791871i	−0.0268711	−	0.0648726i	0.909874	−	0.414884i	$-0.136178\pi$
$149$	−0.328004	−	0.791871i	−0.0268711	−	0.0648726i	−0.936746	+	0.350011i	$0.886178\pi$
$150$		0			0
$151$	−5.36290	+	5.36290i	−0.436427	+	0.436427i	−0.890808	−	0.454381i	$-0.849861\pi$
$151$	−5.36290	+	5.36290i	−0.436427	+	0.436427i	0.454381	+	0.890808i	$0.349861\pi$
$152$		0			0
$153$	−14.8207	−	14.8207i	−1.19818	−	1.19818i
$154$		0			0
$155$	−3.91614	−	9.45440i	−0.314552	−	0.759396i
$156$		0			0
$157$	17.5449	+	7.26734i	1.40024	+	0.579996i	0.949813	−	0.312819i	$-0.101273\pi$
$157$	17.5449	+	7.26734i	1.40024	+	0.579996i	0.450423	+	0.892815i	$0.351273\pi$
$158$		0			0
$159$	13.9800			1.10869
$160$		0			0
$161$	−2.23106	−	2.37699i	−0.175832	−	0.187333i
$162$		0			0
$163$	14.6269	+	6.05865i	1.14567	+	0.474550i	0.873078	−	0.487581i	$-0.162121\pi$
$163$	14.6269	+	6.05865i	1.14567	+	0.474550i	0.272587	+	0.962131i	$0.412121\pi$
$164$		0			0
$165$	−4.41519	+	1.82883i	−0.343722	+	0.142374i
$166$		0			0
$167$	12.5015	−	12.5015i	0.967399	−	0.967399i	−0.0320865	−	0.999485i	$-0.510215\pi$
$167$	12.5015	−	12.5015i	0.967399	−	0.967399i	0.999485	+	0.0320865i	$0.0102152\pi$
$168$		0			0
$169$	1.73106	+	1.73106i	0.133158	+	0.133158i
$170$		0			0
$171$	−14.7162	−	35.5280i	−1.12538	−	2.71690i
$172$		0			0
$173$	3.90765	−	9.43391i	0.297093	−	0.717247i	−0.702889	−	0.711300i	$-0.748107\pi$
$173$	3.90765	−	9.43391i	0.297093	−	0.717247i	0.999982	−	0.00594710i	$-0.00189303\pi$
$174$		0			0
$175$	−0.656853	−	0.699819i	−0.0496534	−	0.0529013i
$176$		0			0
$177$			7.41849i			0.557608i
$178$		0			0
$179$	−0.689085	+	1.66360i	−0.0515046	+	0.124343i	−0.947538	−	0.319644i	$-0.896437\pi$
$179$	−0.689085	+	1.66360i	−0.0515046	+	0.124343i	0.896033	+	0.443988i	$0.146437\pi$
$180$		0			0
$181$	−1.09010	+	0.451534i	−0.0810264	+	0.0335623i	−0.422829	−	0.906210i	$-0.638963\pi$
$181$	−1.09010	+	0.451534i	−0.0810264	+	0.0335623i	0.341802	+	0.939772i	$0.388963\pi$
$182$		0			0
$183$	13.4989	−	13.4989i	0.997869	−	0.997869i
$184$		0			0
$185$	9.84811	+	9.84811i	0.724047	+	0.724047i
$186$		0			0
$187$	1.67151	−	0.692362i	0.122233	−	0.0506305i
$188$		0			0
$189$	14.8068	+	39.2139i	1.07703	+	2.85239i
$190$		0			0
$191$			4.49592i			0.325313i	0.986683	+	0.162657i	$0.0520063\pi$
$191$			4.49592i			0.325313i	−0.986683	+	0.162657i	$0.947994\pi$
$192$		0			0
$193$	12.6862			0.913170			0.456585	−	0.889680i	$-0.349072\pi$
$193$	12.6862			0.913170			0.456585	+	0.889680i	$0.349072\pi$
$194$		0			0
$195$	8.80418	−	21.2552i	0.630480	−	1.52211i
$196$		0			0
$197$	11.0548	−	4.57904i	0.787620	−	0.326243i	0.0476337	−	0.998865i	$-0.484832\pi$
$197$	11.0548	−	4.57904i	0.787620	−	0.326243i	0.739986	+	0.672622i	$0.234832\pi$
$198$		0			0
$199$	7.36746	−	7.36746i	0.522265	−	0.522265i	−0.395990	−	0.918255i	$-0.629598\pi$
$199$	7.36746	−	7.36746i	0.522265	−	0.522265i	0.918255	+	0.395990i	$0.129598\pi$
$200$		0			0
$201$	−16.4323	+	16.4323i	−1.15904	+	1.15904i
$202$		0			0
$203$	16.4171	+	7.41744i	1.15226	+	0.520602i
$204$		0			0
$205$	−9.50765	−	3.93820i	−0.664043	−	0.275056i
$206$		0			0
$207$	−9.63192			−0.669465
$208$		0			0
$209$	3.31944			0.229611
$210$		0			0
$211$	−6.69674	+	16.1673i	−0.461022	+	1.11301i	0.506956	+	0.861972i	$0.330771\pi$
$211$	−6.69674	+	16.1673i	−0.461022	+	1.11301i	−0.967978	+	0.251034i	$0.919229\pi$
$212$		0			0
$213$	−39.3800	+	16.3117i	−2.69828	+	1.11766i
$214$		0			0
$215$	−19.5919	−	19.5919i	−1.33615	−	1.33615i
$216$		0			0
$217$	0.397989	−	12.5667i	0.0270173	−	0.853082i
$218$		0			0
$219$	−6.55770	−	15.8317i	−0.443128	−	1.06981i
$220$		0			0
$221$	−3.33310	+	8.04681i	−0.224208	+	0.541287i
$222$		0			0
$223$	25.1684			1.68540			0.842700	−	0.538383i	$-0.180965\pi$
$223$	25.1684			1.68540			0.842700	+	0.538383i	$0.180965\pi$
$224$		0			0
$225$	−2.83576			−0.189051
$226$		0			0
$227$	−11.3017	+	27.2846i	−0.750118	+	1.81095i	−0.191559	+	0.981481i	$0.561354\pi$
$227$	−11.3017	+	27.2846i	−0.750118	+	1.81095i	−0.558560	+	0.829464i	$0.688646\pi$
$228$		0			0
$229$	−2.33071	−	5.62684i	−0.154018	−	0.371832i	0.827971	−	0.560771i	$-0.189495\pi$
$229$	−2.33071	−	5.62684i	−0.154018	−	0.371832i	−0.981989	+	0.188939i	$0.939495\pi$
$230$		0			0
$231$	−5.86862	−	0.185860i	−0.386127	−	0.0122287i
$232$		0			0
$233$	−5.98323	−	5.98323i	−0.391974	−	0.391974i	0.483416	−	0.875391i	$-0.339396\pi$
$233$	−5.98323	−	5.98323i	−0.391974	−	0.391974i	−0.875391	+	0.483416i	$0.839396\pi$
$234$		0			0
$235$	−5.99790	+	2.48441i	−0.391260	+	0.162065i
$236$		0			0
$237$	−7.32263	+	17.6784i	−0.475656	+	1.14834i
$238$		0			0
$239$	15.7731			1.02028			0.510138	−	0.860092i	$-0.329594\pi$
$239$	15.7731			1.02028			0.510138	+	0.860092i	$0.329594\pi$
$240$		0			0
$241$	28.0178			1.80479			0.902394	−	0.430912i	$-0.141808\pi$
$241$	28.0178			1.80479			0.902394	+	0.430912i	$0.141808\pi$
$242$		0			0
$243$	43.1592	+	17.8771i	2.76866	+	1.14682i
$244$		0			0
$245$	4.87577	+	14.2636i	0.311501	+	0.911270i
$246$		0			0
$247$	−11.2996	+	11.2996i	−0.718979	+	0.718979i
$248$		0			0
$249$	−10.5447	+	10.5447i	−0.668243	+	0.668243i
$250$		0			0
$251$	−10.8704	+	4.50269i	−0.686137	+	0.284207i	−0.698390	−	0.715718i	$-0.746100\pi$
$251$	−10.8704	+	4.50269i	−0.686137	+	0.284207i	0.0122529	+	0.999925i	$0.496100\pi$
$252$		0			0
$253$	0.318172	−	0.768134i	0.0200033	−	0.0482922i
$254$		0			0
$255$	−18.9900			−1.18920
$256$		0			0
$257$			17.4070i			1.08582i	0.839791	+	0.542910i	$0.182678\pi$
$257$			17.4070i			1.08582i	−0.839791	+	0.542910i	$0.817322\pi$
$258$		0			0
$259$	6.04457	+	16.0083i	0.375591	+	0.994707i
$260$		0			0
$261$	49.1748	−	20.3689i	3.04385	−	1.26080i
$262$		0			0
$263$	−0.439018	−	0.439018i	−0.0270710	−	0.0270710i	0.693442	−	0.720513i	$-0.256093\pi$
$263$	−0.439018	−	0.439018i	−0.0270710	−	0.0270710i	−0.720513	+	0.693442i	$0.756093\pi$
$264$		0			0
$265$	6.47244	−	6.47244i	0.397599	−	0.397599i
$266$		0			0
$267$	3.74754	−	1.55228i	0.229346	−	0.0949981i
$268$		0			0
$269$	7.83216	−	18.9085i	0.477535	−	1.15287i	−0.483226	−	0.875496i	$-0.660535\pi$
$269$	7.83216	−	18.9085i	0.477535	−	1.15287i	0.960761	−	0.277377i	$-0.0894650\pi$
$270$		0			0
$271$		−	0.819802i		−	0.0497994i	−0.999690	−	0.0248997i	$-0.992073\pi$
$271$		−	0.819802i		−	0.0497994i	0.999690	−	0.0248997i	$-0.00792664\pi$
$272$		0			0
$273$	20.6099	−	19.3446i	1.24737	−	1.17079i
$274$		0			0
$275$	0.0936740	−	0.226149i	0.00564875	−	0.0136373i
$276$		0			0
$277$	11.8718	+	28.6611i	0.713308	+	1.72208i	0.691566	+	0.722314i	$0.256921\pi$
$277$	11.8718	+	28.6611i	0.713308	+	1.72208i	0.0217422	+	0.999764i	$0.493079\pi$
$278$		0			0
$279$	−26.2673	−	26.2673i	−1.57258	−	1.57258i
$280$		0			0
$281$	−0.733988	+	0.733988i	−0.0437861	+	0.0437861i	−0.728661	−	0.684875i	$-0.759857\pi$
$281$	−0.733988	+	0.733988i	−0.0437861	+	0.0437861i	0.684875	+	0.728661i	$0.259857\pi$
$282$		0			0
$283$	13.4762	−	5.58204i	0.801079	−	0.331818i	0.0556903	−	0.998448i	$-0.482264\pi$
$283$	13.4762	−	5.58204i	0.801079	−	0.331818i	0.745388	+	0.666630i	$0.232264\pi$
$284$		0			0
$285$	−32.1894	−	13.3333i	−1.90674	−	0.789796i
$286$		0			0
$287$	−8.65303	−	9.21904i	−0.510772	−	0.544183i
$288$		0			0
$289$	−9.81072			−0.577101
$290$		0			0
$291$	48.6783	+	20.1632i	2.85357	+	1.18199i
$292$		0			0
$293$	5.69443	+	13.7476i	0.332672	+	0.803141i	0.998378	+	0.0569272i	$0.0181303\pi$
$293$	5.69443	+	13.7476i	0.332672	+	0.803141i	−0.665706	+	0.746214i	$0.731870\pi$
$294$		0			0
$295$	3.43460	+	3.43460i	0.199970	+	0.199970i
$296$		0			0
$297$	−7.55909	+	7.55909i	−0.438623	+	0.438623i
$298$		0			0
$299$	1.53171	+	3.69787i	0.0885810	+	0.213853i
$300$		0			0
$301$	−12.0251	−	31.8470i	−0.693116	−	1.83563i
$302$		0			0
$303$	4.77810			0.274494
$304$		0			0
$305$		−	12.4994i		−	0.715714i
$306$		0			0
$307$	11.8291	+	4.89978i	0.675123	+	0.279645i	0.693787	−	0.720181i	$-0.255941\pi$
$307$	11.8291	+	4.89978i	0.675123	+	0.279645i	−0.0186633	+	0.999826i	$0.505941\pi$
$308$		0			0
$309$	−7.54461	−	18.2143i	−0.429198	−	1.03618i
$310$		0			0
$311$	3.93148	+	3.93148i	0.222934	+	0.222934i	0.809733	−	0.586799i	$-0.199612\pi$
$311$	3.93148	+	3.93148i	0.222934	+	0.222934i	−0.586799	+	0.809733i	$0.699612\pi$
$312$		0			0
$313$	2.30964	+	2.30964i	0.130548	+	0.130548i	0.769362	−	0.638813i	$-0.220574\pi$
$313$	2.30964	+	2.30964i	0.130548	+	0.130548i	−0.638813	+	0.769362i	$0.720574\pi$
$314$		0			0
$315$	40.5866	+	18.3375i	2.28680	+	1.03320i
$316$		0			0
$317$	2.05636	−	4.96449i	0.115497	−	0.278834i	−0.855551	−	0.517718i	$-0.826782\pi$
$317$	2.05636	−	4.96449i	0.115497	−	0.278834i	0.971048	+	0.238884i	$0.0767816\pi$
$318$		0			0
$319$			4.59448i			0.257242i
$320$		0			0
$321$			28.0788i			1.56721i
$322$		0			0
$323$	12.1863	+	5.04773i	0.678064	+	0.280863i
$324$		0			0
$325$	0.450955	+	1.08870i	0.0250145	+	0.0603904i
$326$		0			0
$327$	−11.9813	+	11.9813i	−0.662566	+	0.662566i
$328$		0			0
$329$	−7.97234	−	0.252485i	−0.439529	−	0.0139200i
$330$		0			0
$331$	7.57759	−	3.13874i	0.416502	−	0.172521i	−0.164584	−	0.986363i	$-0.552628\pi$
$331$	7.57759	−	3.13874i	0.416502	−	0.172521i	0.581086	+	0.813842i	$0.302628\pi$
$332$		0			0
$333$	46.7084	+	19.3473i	2.55961	+	1.06022i
$334$		0			0
$335$			15.2156i			0.831315i
$336$		0			0
$337$			3.17787i			0.173110i	0.996247	+	0.0865549i	$0.0275858\pi$
$337$			3.17787i			0.173110i	−0.996247	+	0.0865549i	$0.972414\pi$
$338$		0			0
$339$	−31.0728	−	12.8708i	−1.68764	−	0.699045i
$340$		0			0
$341$	2.96248	−	1.22710i	0.160427	−	0.0664512i
$342$		0			0
$343$	−1.75639	+	18.4368i	−0.0948361	+	0.995493i
$344$		0			0
$345$	−6.17077	+	6.17077i	−0.332223	+	0.332223i
$346$		0			0
$347$	3.90004	+	9.41553i	0.209365	+	0.505452i	0.993324	−	0.115361i	$-0.0368025\pi$
$347$	3.90004	+	9.41553i	0.209365	+	0.505452i	−0.783959	+	0.620813i	$0.786803\pi$
$348$		0			0
$349$	−19.8320	−	8.21468i	−1.06158	−	0.439722i	−0.217570	−	0.976045i	$-0.569813\pi$
$349$	−19.8320	−	8.21468i	−1.06158	−	0.439722i	−0.844013	+	0.536323i	$0.819813\pi$
$350$		0			0
$351$		−	51.4635i		−	2.74692i
$352$		0			0
$353$			8.47471i			0.451063i	0.974236	+	0.225532i	$0.0724119\pi$
$353$			8.47471i			0.451063i	−0.974236	+	0.225532i	$0.927588\pi$
$354$		0			0
$355$	−10.6801	+	25.7841i	−0.566842	+	1.36848i
$356$		0			0
$357$	−21.2622	−	9.60649i	−1.12532	−	0.508430i
$358$		0			0
$359$	−16.7952	−	16.7952i	−0.886414	−	0.886414i	0.107762	−	0.994177i	$-0.465631\pi$
$359$	−16.7952	−	16.7952i	−0.886414	−	0.886414i	−0.994177	+	0.107762i	$0.965631\pi$
$360$		0			0
$361$	3.67747	+	3.67747i	0.193551	+	0.193551i
$362$		0			0
$363$	13.2717	+	32.0408i	0.696585	+	1.68171i
$364$		0			0
$365$	−10.3658	−	4.29365i	−0.542570	−	0.224740i
$366$		0			0
$367$			0.399698i			0.0208641i	0.999946	+	0.0104320i	$0.00332068\pi$
$367$			0.399698i			0.0208641i	−0.999946	+	0.0104320i	$0.996679\pi$
$368$		0			0
$369$	−37.3569			−1.94472
$370$		0			0
$371$	10.5211	−	3.97266i	0.546228	−	0.206250i
$372$		0			0
$373$	2.30682	+	5.56916i	0.119443	+	0.288360i	0.972281	−	0.233815i	$-0.0751209\pi$
$373$	2.30682	+	5.56916i	0.119443	+	0.288360i	−0.852839	+	0.522175i	$0.825121\pi$
$374$		0			0
$375$	−26.8570	+	26.8570i	−1.38689	+	1.38689i
$376$		0			0
$377$	−15.6400	−	15.6400i	−0.805500	−	0.805500i
$378$		0			0
$379$	−4.69148	−	11.3262i	−0.240985	−	0.581790i	0.756396	−	0.654114i	$-0.226958\pi$
$379$	−4.69148	−	11.3262i	−0.240985	−	0.581790i	−0.997381	+	0.0723241i	$0.976958\pi$
$380$		0			0
$381$	−10.4275	−	4.31920i	−0.534215	−	0.221279i
$382$		0			0
$383$	−24.8644			−1.27051			−0.635255	−	0.772303i	$-0.719105\pi$
$383$	−24.8644			−1.27051			−0.635255	+	0.772303i	$0.719105\pi$
$384$		0			0
$385$	−2.80309	+	2.63099i	−0.142859	+	0.134088i
$386$		0			0
$387$	−92.9220	−	38.4896i	−4.72349	−	1.95653i
$388$		0			0
$389$	−27.6691	+	11.4609i	−1.40288	+	0.581091i	−0.950497	−	0.310735i	$-0.899425\pi$
$389$	−27.6691	+	11.4609i	−1.40288	+	0.581091i	−0.452380	+	0.891825i	$0.649425\pi$
$390$		0			0
$391$	2.33614	−	2.33614i	0.118144	−	0.118144i
$392$		0			0
$393$	−13.1639	−	13.1639i	−0.664033	−	0.664033i
$394$		0			0
$395$	4.79449	+	11.5749i	0.241237	+	0.582398i
$396$		0			0
$397$	−5.84792	+	14.1181i	−0.293499	+	0.708569i	0.706501	+	0.707712i	$0.250273\pi$
$397$	−5.84792	+	14.1181i	−0.293499	+	0.708569i	−1.00000		0.000856758i	$0.999727\pi$
$398$		0			0
$399$	−29.2960	−	31.2123i	−1.46663	−	1.56257i
$400$		0			0
$401$		−	25.4029i		−	1.26856i	−0.773103	−	0.634281i	$-0.781296\pi$
$401$		−	25.4029i		−	1.26856i	0.773103	−	0.634281i	$-0.218704\pi$
$402$		0			0
$403$	−5.90737	+	14.2617i	−0.294267	+	0.710424i
$404$		0			0
$405$	57.0090	−	23.6139i	2.83280	−	1.17338i
$406$		0			0
$407$	−3.08585	+	3.08585i	−0.152960	+	0.152960i
$408$		0			0
$409$	−15.1589	−	15.1589i	−0.749562	−	0.749562i	0.224835	−	0.974397i	$-0.427816\pi$
$409$	−15.1589	−	15.1589i	−0.749562	−	0.749562i	−0.974397	+	0.224835i	$0.927816\pi$
$410$		0			0
$411$	−26.0921	+	10.8077i	−1.28703	+	0.533104i
$412$		0			0
$413$	2.10809	+	5.58301i	0.103732	+	0.274722i
$414$		0			0
$415$			9.76393i			0.479293i
$416$		0			0
$417$	−12.8855			−0.631003
$418$		0			0
$419$	12.8383	−	30.9945i	0.627194	−	1.51418i	−0.215900	−	0.976415i	$-0.569269\pi$
$419$	12.8383	−	30.9945i	0.627194	−	1.51418i	0.843095	−	0.537765i	$-0.180731\pi$
$420$		0			0
$421$	−11.9570	+	4.95276i	−0.582749	+	0.241383i	−0.654528	−	0.756038i	$-0.727132\pi$
$421$	−11.9570	+	4.95276i	−0.582749	+	0.241383i	0.0717787	+	0.997421i	$0.477132\pi$
$422$		0			0
$423$	−16.6641	+	16.6641i	−0.810235	+	0.810235i
$424$		0			0
$425$	0.687790	−	0.687790i	0.0333627	−	0.0333627i
$426$		0			0
$427$	6.32308	−	13.9950i	0.305995	−	0.677264i
$428$		0			0
$429$	6.66018	+	2.75874i	0.321556	+	0.133193i
$430$		0			0
$431$	37.7600			1.81883			0.909417	−	0.415885i	$-0.136528\pi$
$431$	37.7600			1.81883			0.909417	+	0.415885i	$0.136528\pi$
$432$		0			0
$433$	24.2606			1.16589			0.582945	−	0.812512i	$-0.301900\pi$
$433$	24.2606			1.16589			0.582945	+	0.812512i	$0.301900\pi$
$434$		0			0
$435$	18.4548	−	44.5538i	0.884839	−	2.13619i
$436$		0			0
$437$	5.60016	−	2.31966i	0.267892	−	0.110965i
$438$		0			0
$439$	−3.09504	−	3.09504i	−0.147718	−	0.147718i	0.629380	−	0.777098i	$-0.283309\pi$
$439$	−3.09504	−	3.09504i	−0.147718	−	0.147718i	−0.777098	+	0.629380i	$0.783309\pi$
$440$		0			0
$441$	36.1665	+	41.0631i	1.72221	+	1.95539i
$442$		0			0
$443$	−1.34081	−	3.23699i	−0.0637036	−	0.153794i	0.888822	−	0.458253i	$-0.151524\pi$
$443$	−1.34081	−	3.23699i	−0.0637036	−	0.153794i	−0.952526	+	0.304459i	$0.901524\pi$
$444$		0			0
$445$	1.01636	−	2.45370i	0.0481799	−	0.116317i
$446$		0			0
$447$	−2.81899			−0.133334
$448$		0			0
$449$	28.9280			1.36519			0.682597	−	0.730795i	$-0.260850\pi$
$449$	28.9280			1.36519			0.682597	+	0.730795i	$0.260850\pi$
$450$		0			0
$451$	1.23401	−	2.97917i	0.0581073	−	0.140283i
$452$		0			0
$453$	9.54571	+	23.0454i	0.448497	+	1.08277i
$454$		0			0
$455$	0.585837	−	18.4981i	0.0274645	−	0.867203i
$456$		0			0
$457$	8.25491	+	8.25491i	0.386149	+	0.386149i	0.873311	−	0.487163i	$-0.161968\pi$
$457$	8.25491	+	8.25491i	0.386149	+	0.386149i	−0.487163	+	0.873311i	$0.661968\pi$
$458$		0			0
$459$	−39.2456	+	16.2561i	−1.83183	+	0.758768i
$460$		0			0
$461$	7.76886	−	18.7557i	0.361832	−	0.873540i	−0.633200	−	0.773988i	$-0.718259\pi$
$461$	7.76886	−	18.7557i	0.361832	−	0.873540i	0.995032	−	0.0995519i	$-0.0317409\pi$
$462$		0			0
$463$	−12.5010			−0.580969			−0.290484	−	0.956880i	$-0.593816\pi$
$463$	−12.5010			−0.580969			−0.290484	+	0.956880i	$0.593816\pi$
$464$		0			0
$465$	−33.6568			−1.56080
$466$		0			0
$467$	−33.4570	−	13.8584i	−1.54821	−	0.641288i	−0.565216	−	0.824943i	$-0.691207\pi$
$467$	−33.4570	−	13.8584i	−1.54821	−	0.641288i	−0.982991	+	0.183655i	$0.941207\pi$
$468$		0			0
$469$	−7.69710	+	17.0361i	−0.355419	+	0.786654i
$470$		0			0
$471$	44.1646	−	44.1646i	2.03500	−	2.03500i
$472$		0			0
$473$	6.13900	−	6.13900i	0.282271	−	0.282271i
$474$		0			0
$475$	1.64876	−	0.682939i	0.0756504	−	0.0313354i
$476$		0			0
$477$	12.7156	−	30.6981i	0.582205	−	1.40557i
$478$		0			0
$479$	18.5273			0.846535			0.423267	−	0.906005i	$-0.360883\pi$
$479$	18.5273			0.846535			0.423267	+	0.906005i	$0.360883\pi$
$480$		0			0
$481$		−	21.0089i		−	0.957925i
$482$		0			0
$483$	−10.0307	+	3.78750i	−0.456413	+	0.172337i
$484$		0			0
$485$	31.8721	−	13.2019i	1.44724	−	0.599466i
$486$		0			0
$487$	0.307533	+	0.307533i	0.0139356	+	0.0139356i	0.714040	−	0.700105i	$-0.246863\pi$
$487$	0.307533	+	0.307533i	0.0139356	+	0.0139356i	−0.700105	+	0.714040i	$0.746863\pi$
$488$		0			0
$489$	36.8193	−	36.8193i	1.66503	−	1.66503i
$490$		0			0
$491$	−36.5287	+	15.1307i	−1.64852	+	0.682838i	−0.997116	−	0.0758970i	$-0.975818\pi$
$491$	−36.5287	+	15.1307i	−1.64852	+	0.682838i	−0.651400	+	0.758735i	$0.725818\pi$
$492$		0			0
$493$	−6.98663	+	16.8672i	−0.314662	+	0.759662i
$494$		0			0
$495$			11.3585i			0.510528i
$496$		0			0
$497$	−25.0014	+	23.4664i	−1.12147	+	1.05261i
$498$		0			0
$499$	−11.4771	+	27.7082i	−0.513786	+	1.24039i	0.427879	+	0.903836i	$0.359261\pi$
$499$	−11.4771	+	27.7082i	−0.513786	+	1.24039i	−0.941665	+	0.336552i	$0.890739\pi$
$500$		0			0
$501$	−22.2522	−	53.7215i	−0.994154	−	2.40010i
$502$		0			0
$503$	−21.5299	−	21.5299i	−0.959969	−	0.959969i	0.0392600	−	0.999229i	$-0.487500\pi$
$503$	−21.5299	−	21.5299i	−0.959969	−	0.959969i	−0.999229	+	0.0392600i	$0.987500\pi$
$504$		0			0
$505$	2.21215	−	2.21215i	0.0984395	−	0.0984395i
$506$		0			0
$507$	7.43868	−	3.08120i	0.330364	−	0.136841i
$508$		0			0
$509$	12.7961	+	5.30030i	0.567176	+	0.234932i	0.647797	−	0.761813i	$-0.275690\pi$
$509$	12.7961	+	5.30030i	0.567176	+	0.234932i	−0.0806214	+	0.996745i	$0.525690\pi$
$510$		0			0
$511$	−9.43403	−	10.0511i	−0.417337	−	0.444636i
$512$		0			0
$513$	−77.9377			−3.44103
$514$		0			0
$515$	−11.9258	−	4.93983i	−0.525514	−	0.217675i
$516$		0			0
$517$	−0.778475	−	1.87941i	−0.0342373	−	0.0826562i
$518$		0			0
$519$	−23.7474	−	23.7474i	−1.04239	−	1.04239i
$520$		0			0
$521$	−26.1575	+	26.1575i	−1.14598	+	1.14598i	−0.158645	+	0.987336i	$0.550713\pi$
$521$	−26.1575	+	26.1575i	−1.14598	+	1.14598i	−0.987336	+	0.158645i	$0.949287\pi$
$522$		0			0
$523$	−7.83184	−	18.9077i	−0.342463	−	0.826778i	−0.997466	−	0.0711514i	$-0.977333\pi$
$523$	−7.83184	−	18.9077i	−0.342463	−	0.826778i	0.655003	−	0.755626i	$-0.272667\pi$
$524$		0			0
$525$	−2.95317	+	1.11509i	−0.128887	+	0.0486665i
$526$		0			0
$527$	12.7418			0.555043
$528$		0			0
$529$			21.4818i			0.933989i
$530$		0			0
$531$	16.2899	+	6.74750i	0.706922	+	0.292817i
$532$		0			0
$533$	5.94065	+	14.3420i	0.257318	+	0.621221i
$534$		0			0
$535$	12.9999	+	12.9999i	0.562033	+	0.562033i
$536$		0			0
$537$	4.18767	+	4.18767i	0.180711	+	0.180711i
$538$		0			0
$539$	−4.46943	+	1.52779i	−0.192512	+	0.0658067i
$540$		0			0
$541$	−8.04425	+	19.4205i	−0.345849	+	0.834954i	0.651251	+	0.758862i	$0.274244\pi$
$541$	−8.04425	+	19.4205i	−0.345849	+	0.834954i	−0.997101	+	0.0760921i	$0.975756\pi$
$542$		0			0
$543$			3.88065i			0.166535i
$544$		0			0
$545$			11.0941i			0.475221i
$546$		0			0
$547$	18.9194	+	7.83669i	0.808937	+	0.335073i	0.748530	−	0.663101i	$-0.230760\pi$
$547$	18.9194	+	7.83669i	0.808937	+	0.335073i	0.0604073	+	0.998174i	$0.480760\pi$
$548$		0			0
$549$	−17.3637	−	41.9196i	−0.741063	−	1.78909i
$550$		0			0
$551$	−23.6856	+	23.6856i	−1.00904	+	1.00904i
$552$		0			0
$553$	−0.487254	+	15.3853i	−0.0207202	+	0.654248i
$554$		0			0
$555$	42.3192	−	17.5292i	1.79635	−	0.744072i
$556$		0			0
$557$	−2.22340	−	0.920962i	−0.0942085	−	0.0390224i	0.335081	−	0.942189i	$-0.391236\pi$
$557$	−2.22340	−	0.920962i	−0.0942085	−	0.0390224i	−0.429290	+	0.903167i	$0.641236\pi$
$558$		0			0
$559$			41.7953i			1.76775i
$560$		0			0
$561$		−	5.95042i		−	0.251227i
$562$		0			0
$563$	16.9952	+	7.03966i	0.716264	+	0.296686i	0.710894	−	0.703299i	$-0.248291\pi$
$563$	16.9952	+	7.03966i	0.716264	+	0.296686i	0.00537035	+	0.999986i	$0.498291\pi$
$564$		0			0
$565$	−20.3449	+	8.42714i	−0.855917	+	0.354532i
$566$		0			0
$567$	75.7757	+	2.39983i	3.18228	+	0.100783i
$568$		0			0
$569$	−10.3726	+	10.3726i	−0.434843	+	0.434843i	−0.890272	−	0.455429i	$-0.849486\pi$
$569$	−10.3726	+	10.3726i	−0.434843	+	0.434843i	0.455429	+	0.890272i	$0.349486\pi$
$570$		0			0
$571$	−4.51061	−	10.8896i	−0.188763	−	0.455715i	0.800959	−	0.598719i	$-0.204324\pi$
$571$	−4.51061	−	10.8896i	−0.188763	−	0.455715i	−0.989722	+	0.143005i	$0.954324\pi$
$572$		0			0
$573$	13.6612	+	5.65864i	0.570703	+	0.236393i
$574$		0			0
$575$		−	0.446992i		−	0.0186408i
$576$		0			0
$577$			23.0622i			0.960093i	0.877243	+	0.480046i	$0.159380\pi$
$577$			23.0622i			0.960093i	−0.877243	+	0.480046i	$0.840620\pi$
$578$		0			0
$579$	15.9670	−	38.5478i	0.663567	−	1.60199i
$580$		0			0
$581$	−4.93928	+	10.9322i	−0.204916	+	0.453544i
$582$		0			0
$583$	2.02810	+	2.02810i	0.0839954	+	0.0839954i
$584$		0			0
$585$	−38.6653	−	38.6653i	−1.59861	−	1.59861i
$586$		0			0
$587$	5.83675	+	14.0912i	0.240908	+	0.581604i	0.997374	−	0.0724299i	$-0.0230754\pi$
$587$	5.83675	+	14.0912i	0.240908	+	0.581604i	−0.756465	+	0.654034i	$0.773075\pi$
$588$		0			0
$589$	21.5983	+	8.94629i	0.889941	+	0.368626i
$590$		0			0
$591$		−	39.3540i		−	1.61881i
$592$		0			0
$593$	−23.0448			−0.946335			−0.473168	−	0.880972i	$-0.656890\pi$
$593$	−23.0448			−0.946335			−0.473168	+	0.880972i	$0.656890\pi$
$594$		0			0
$595$	−14.2915	+	5.39634i	−0.585896	+	0.221228i
$596$		0			0
$597$	−13.1137	−	31.6594i	−0.536709	−	1.29573i
$598$		0			0
$599$	15.8621	−	15.8621i	0.648108	−	0.648108i	−0.304427	−	0.952536i	$-0.598465\pi$
$599$	15.8621	−	15.8621i	0.648108	−	0.648108i	0.952536	+	0.304427i	$0.0984650\pi$
$600$		0			0
$601$	7.79999	+	7.79999i	0.318168	+	0.318168i	0.848063	−	0.529895i	$-0.177769\pi$
$601$	7.79999	+	7.79999i	0.318168	+	0.318168i	−0.529895	+	0.848063i	$0.677769\pi$
$602$		0			0
$603$	21.1368	+	51.0288i	0.860759	+	2.07806i
$604$		0			0
$605$	20.9787	+	8.68967i	0.852906	+	0.353285i
$606$		0			0
$607$	−31.8826			−1.29408			−0.647038	−	0.762458i	$-0.723993\pi$
$607$	−31.8826			−1.29408			−0.647038	+	0.762458i	$0.723993\pi$
$608$		0			0
$609$	43.2013	−	40.5489i	1.75061	−	1.64313i
$610$		0			0
$611$	9.04764	+	3.74766i	0.366028	+	0.151614i
$612$		0			0
$613$	16.6544	−	6.89848i	0.672665	−	0.278627i	−0.0200918	−	0.999798i	$-0.506396\pi$
$613$	16.6544	−	6.89848i	0.672665	−	0.278627i	0.692757	+	0.721171i	$0.256396\pi$
$614$		0			0
$615$	−23.9330	+	23.9330i	−0.965072	+	0.965072i
$616$		0			0
$617$	−20.2465	−	20.2465i	−0.815093	−	0.815093i	0.170300	−	0.985392i	$-0.445526\pi$
$617$	−20.2465	−	20.2465i	−0.815093	−	0.815093i	−0.985392	+	0.170300i	$0.945526\pi$
$618$		0			0
$619$	14.1434	+	34.1451i	0.568469	+	1.37241i	0.902845	+	0.429966i	$0.141475\pi$
$619$	14.1434	+	34.1451i	0.568469	+	1.37241i	−0.334376	+	0.942440i	$0.608525\pi$
$620$		0			0
$621$	−7.47040	+	18.0351i	−0.299777	+	0.723726i
$622$		0			0
$623$	2.37922	−	2.23314i	0.0953214	−	0.0894690i
$624$		0			0
$625$			23.0546i			0.922182i
$626$		0			0
$627$	4.17791	−	10.0864i	0.166850	−	0.402810i
$628$		0			0
$629$	−16.0212	+	6.63622i	−0.638809	+	0.264603i
$630$		0			0
$631$	4.35670	−	4.35670i	0.173437	−	0.173437i	−0.615050	−	0.788488i	$-0.710864\pi$
$631$	4.35670	−	4.35670i	0.173437	−	0.173437i	0.788488	+	0.615050i	$0.210864\pi$
$632$		0			0
$633$	40.6970	+	40.6970i	1.61756	+	1.61756i
$634$		0			0
$635$	−6.82738	+	2.82799i	−0.270936	+	0.112226i
$636$		0			0
$637$	10.0135	−	20.4150i	0.396751	−	0.808872i
$638$		0			0
$639$			101.309i			4.00773i
$640$		0			0
$641$	−5.51270			−0.217739			−0.108869	−	0.994056i	$-0.534723\pi$
$641$	−5.51270			−0.217739			−0.108869	+	0.994056i	$0.534723\pi$
$642$		0			0
$643$	6.12039	−	14.7759i	0.241365	−	0.582706i	−0.756054	−	0.654509i	$-0.772875\pi$
$643$	6.12039	−	14.7759i	0.241365	−	0.582706i	0.997419	+	0.0718033i	$0.0228754\pi$
$644$		0			0
$645$	−84.1900	+	34.8726i	−3.31498	+	1.37311i
$646$		0			0
$647$	7.12879	−	7.12879i	0.280262	−	0.280262i	−0.552952	−	0.833213i	$-0.686499\pi$
$647$	7.12879	−	7.12879i	0.280262	−	0.280262i	0.833213	+	0.552952i	$0.186499\pi$
$648$		0			0
$649$	−1.07621	+	1.07621i	−0.0422450	+	0.0422450i
$650$		0			0
$651$	−37.6838	−	17.0260i	−1.47695	−	0.667300i
$652$		0			0
$653$	36.0059	+	14.9141i	1.40902	+	0.583635i	0.952076	−	0.305860i	$-0.0989440\pi$
$653$	36.0059	+	14.9141i	1.40902	+	0.583635i	0.456944	+	0.889496i	$0.348944\pi$
$654$		0			0
$655$	−12.1892			−0.476273
$656$		0			0
$657$	−40.7286			−1.58897
$658$		0			0
$659$	−12.9689	+	31.3096i	−0.505196	+	1.21965i	0.441424	+	0.897299i	$0.354473\pi$
$659$	−12.9689	+	31.3096i	−0.505196	+	1.21965i	−0.946620	+	0.322352i	$0.895527\pi$
$660$		0			0
$661$	6.99080	−	2.89568i	0.271911	−	0.112629i	−0.242562	−	0.970136i	$-0.577988\pi$
$661$	6.99080	−	2.89568i	0.271911	−	0.112629i	0.514473	+	0.857507i	$0.327988\pi$
$662$		0			0
$663$	20.2557	+	20.2557i	0.786666	+	0.786666i
$664$		0			0
$665$	−28.0140	−	0.887208i	−1.08634	−	0.0344045i
$666$		0			0
$667$	3.21068	+	7.75126i	0.124318	+	0.300130i
$668$		0			0
$669$	31.6774	−	76.4759i	1.22472	−	2.95673i
$670$		0			0
$671$	3.91662			0.151199
$672$		0			0
$673$	28.3567			1.09307			0.546536	−	0.837436i	$-0.315946\pi$
$673$	28.3567			1.09307			0.546536	+	0.837436i	$0.315946\pi$
$674$		0			0
$675$	−2.19939	+	5.30979i	−0.0846544	+	0.204374i
$676$		0			0
$677$	−9.12470	−	22.0290i	−0.350691	−	0.846642i	−0.996535	−	0.0831730i	$-0.973495\pi$
$677$	−9.12470	−	22.0290i	−0.350691	−	0.846642i	0.645845	−	0.763469i	$-0.276505\pi$
$678$		0			0
$679$	42.3641	+	1.34168i	1.62578	+	0.0514889i
$680$		0			0
$681$	68.6819	+	68.6819i	2.63189	+	2.63189i
$682$		0			0
$683$	−7.72775	+	3.20094i	−0.295694	+	0.122481i	−0.525599	−	0.850733i	$-0.676159\pi$
$683$	−7.72775	+	3.20094i	−0.295694	+	0.122481i	0.229904	+	0.973213i	$0.426159\pi$
$684$		0			0
$685$	−7.07633	+	17.0838i	−0.270373	+	0.652737i
$686$		0			0
$687$	−20.0310			−0.764231
$688$		0			0
$689$	−13.8076			−0.526029
$690$		0			0
$691$	−28.9600	−	11.9956i	−1.10169	−	0.456336i	−0.243623	−	0.969870i	$-0.578336\pi$
$691$	−28.9600	−	11.9956i	−1.10169	−	0.456336i	−0.858069	+	0.513534i	$0.828336\pi$
$692$		0			0
$693$	−5.74594	+	12.7176i	−0.218270	+	0.483101i
$694$		0			0
$695$	−5.96568	+	5.96568i	−0.226291	+	0.226291i
$696$		0			0
$697$	9.06058	−	9.06058i	0.343194	−	0.343194i
$698$		0			0
$699$	−25.7111	+	10.6499i	−0.972482	+	0.402815i
$700$		0			0
$701$	−3.06015	+	7.38785i	−0.115580	+	0.279035i	−0.971074	−	0.238777i	$-0.923253\pi$
$701$	−3.06015	+	7.38785i	−0.115580	+	0.279035i	0.855494	+	0.517812i	$0.173253\pi$
$702$		0			0
$703$	−31.8165			−1.19998
$704$		0			0
$705$			21.3520i			0.804162i
$706$		0			0
$707$	3.59590	−	1.35778i	0.135238	−	0.0510644i
$708$		0			0
$709$	−0.607077	+	0.251460i	−0.0227993	+	0.00944377i	−0.394054	−	0.919087i	$-0.628928\pi$
$709$	−0.607077	+	0.251460i	−0.0227993	+	0.00944377i	0.371255	+	0.928531i	$0.378928\pi$
$710$		0			0
$711$	32.1588	+	32.1588i	1.20605	+	1.20605i
$712$		0			0
$713$	4.14043	−	4.14043i	0.155060	−	0.155060i
$714$		0			0
$715$	4.36075	−	1.80628i	0.163083	−	0.0675511i
$716$		0			0
$717$	19.8523	−	47.9277i	0.741397	−	1.78989i
$718$		0			0
$719$		−	16.3413i		−	0.609428i	−0.952444	−	0.304714i	$-0.901439\pi$
$719$		−	16.3413i		−	0.609428i	0.952444	−	0.304714i	$-0.0985609\pi$
$720$		0			0
$721$	−10.8538	−	11.5638i	−0.404217	−	0.430658i
$722$		0			0
$723$	35.2637	−	85.1342i	1.31147	−	3.16617i
$724$		0			0
$725$	0.945265	+	2.28207i	0.0351063	+	0.0847540i
$726$		0			0
$727$	28.8831	+	28.8831i	1.07122	+	1.07122i	0.997262	+	0.0739549i	$0.0235621\pi$
$727$	28.8831	+	28.8831i	1.07122	+	1.07122i	0.0739549	+	0.997262i	$0.476438\pi$
$728$		0			0
$729$	47.8556	−	47.8556i	1.77243	−	1.77243i
$730$		0			0
$731$	31.8727	−	13.2021i	1.17886	−	0.488298i
$732$		0			0
$733$	−20.4499	−	8.47062i	−0.755334	−	0.312869i	−0.0284180	−	0.999596i	$-0.509047\pi$
$733$	−20.4499	−	8.47062i	−0.755334	−	0.312869i	−0.726916	+	0.686727i	$0.759047\pi$
$734$		0			0
$735$	49.4778	+	3.13709i	1.82502	+	0.115713i
$736$		0			0
$737$	−4.76771			−0.175621
$738$		0			0
$739$	−24.7778	−	10.2633i	−0.911465	−	0.377541i	−0.122848	−	0.992426i	$-0.539203\pi$
$739$	−24.7778	−	10.2633i	−0.911465	−	0.377541i	−0.788617	+	0.614884i	$0.789203\pi$
$740$		0			0
$741$	20.1128	+	48.5567i	0.738864	+	1.78377i
$742$		0			0
$743$	14.7349	+	14.7349i	0.540573	+	0.540573i	0.923697	−	0.383124i	$-0.125152\pi$
$743$	14.7349	+	14.7349i	0.540573	+	0.540573i	−0.383124	+	0.923697i	$0.625152\pi$
$744$		0			0
$745$	−1.30513	+	1.30513i	−0.0478162	+	0.0478162i
$746$		0			0
$747$	13.5637	+	32.7456i	0.496268	+	1.19810i
$748$		0			0
$749$	7.97906	+	21.1315i	0.291549	+	0.772130i
$750$		0			0
$751$	16.7817			0.612375			0.306187	−	0.951971i	$-0.400947\pi$
$751$	16.7817			0.612375			0.306187	+	0.951971i	$0.400947\pi$
$752$		0			0
$753$			38.6978i			1.41023i
$754$		0			0
$755$	15.0890	+	6.25006i	0.549144	+	0.227463i
$756$		0			0
$757$	11.3417	+	27.3812i	0.412220	+	0.995186i	0.984541	+	0.175157i	$0.0560432\pi$
$757$	11.3417	+	27.3812i	0.412220	+	0.995186i	−0.572321	+	0.820030i	$0.693957\pi$
$758$		0			0
$759$	−1.93357	−	1.93357i	−0.0701843	−	0.0701843i
$760$		0			0
$761$	−26.1478	−	26.1478i	−0.947857	−	0.947857i	0.0508495	−	0.998706i	$-0.483807\pi$
$761$	−26.1478	−	26.1478i	−0.947857	−	0.947857i	−0.998706	+	0.0508495i	$0.983807\pi$
$762$		0			0
$763$	−5.61219	+	12.4216i	−0.203175	+	0.449691i
$764$		0			0
$765$	−17.2724	+	41.6993i	−0.624486	+	1.50764i
$766$		0			0
$767$		−	7.32702i		−	0.264563i
$768$		0			0
$769$		−	0.182902i		−	0.00659561i	−0.999995	−	0.00329780i	$-0.998950\pi$
$769$		−	0.182902i		−	0.00659561i	0.999995	−	0.00329780i	$-0.00104973\pi$
$770$		0			0
$771$	52.8925	+	21.9088i	1.90488	+	0.789025i
$772$		0			0
$773$	17.4127	+	42.0379i	0.626290	+	1.51200i	0.844200	+	0.536028i	$0.180076\pi$
$773$	17.4127	+	42.0379i	0.626290	+	1.51200i	−0.217911	+	0.975969i	$0.569924\pi$
$774$		0			0
$775$	1.21900	−	1.21900i	0.0437877	−	0.0437877i
$776$		0			0
$777$	56.2501	+	1.78145i	2.01796	+	0.0639092i
$778$		0			0
$779$	21.7199	−	8.99668i	0.778197	−	0.322340i
$780$		0			0
$781$	−8.07929	−	3.34655i	−0.289100	−	0.119749i
$782$		0			0
$783$		−	107.875i		−	3.85512i
$784$		0			0
$785$		−	40.8945i		−	1.45959i
$786$		0			0
$787$	7.61027	+	3.15228i	0.271277	+	0.112367i	0.514175	−	0.857685i	$-0.328098\pi$
$787$	7.61027	+	3.15228i	0.271277	+	0.112367i	−0.242898	+	0.970052i	$0.578098\pi$
$788$		0			0
$789$	−1.88654	+	0.781432i	−0.0671627	+	0.0278197i
$790$		0			0
$791$	−27.0422	−	0.856432i	−0.961511	−	0.0304512i
$792$		0			0
$793$	−13.3325	+	13.3325i	−0.473450	+	0.473450i
$794$		0			0
$795$	−11.5207	−	27.8133i	−0.408595	−	0.986436i
$796$		0			0
$797$	−34.3958	−	14.2472i	−1.21836	−	0.504663i	−0.321474	−	0.946918i	$-0.604178\pi$
$797$	−34.3958	−	14.2472i	−1.21836	−	0.504663i	−0.896889	+	0.442256i	$0.854178\pi$
$798$		0			0
$799$		−	8.08345i		−	0.285972i
$800$		0			0
$801$		−	9.64093i		−	0.340645i
$802$		0			0
$803$	1.34539	−	3.24806i	0.0474778	−	0.114622i
$804$		0			0
$805$	−2.89047	+	6.39753i	−0.101876	+	0.225483i
$806$		0			0
$807$	−47.5972	−	47.5972i	−1.67550	−	1.67550i
$808$		0			0
$809$	9.80000	+	9.80000i	0.344550	+	0.344550i	0.858075	−	0.513525i	$-0.171661\pi$
$809$	9.80000	+	9.80000i	0.344550	+	0.344550i	−0.513525	+	0.858075i	$0.671661\pi$
$810$		0			0
$811$	−17.5923	−	42.4717i	−0.617751	−	1.49138i	−0.854309	−	0.519765i	$-0.826019\pi$
$811$	−17.5923	−	42.4717i	−0.617751	−	1.49138i	0.236558	−	0.971617i	$-0.423981\pi$
$812$		0			0
$813$	−2.49103	−	1.03182i	−0.0873641	−	0.0361874i
$814$		0			0
$815$		−	34.0930i		−	1.19423i
$816$		0			0
$817$	63.2959			2.21444
$818$		0			0
$819$	−23.7320	−	62.8513i	−0.829264	−	2.19620i
$820$		0			0
$821$	1.02804	+	2.48190i	0.0358787	+	0.0866189i	0.940803	−	0.338953i	$-0.110073\pi$
$821$	1.02804	+	2.48190i	0.0358787	+	0.0866189i	−0.904924	+	0.425572i	$0.860073\pi$
$822$		0			0
$823$	−37.1905	+	37.1905i	−1.29638	+	1.29638i	−0.365611	+	0.930768i	$0.619140\pi$
$823$	−37.1905	+	37.1905i	−1.29638	+	1.29638i	−0.930768	+	0.365611i	$0.880860\pi$
$824$		0			0
$825$	−0.569270	−	0.569270i	−0.0198194	−	0.0198194i
$826$		0			0
$827$	10.7657	+	25.9908i	0.374361	+	0.903787i	0.993000	+	0.118112i	$0.0376843\pi$
$827$	10.7657	+	25.9908i	0.374361	+	0.903787i	−0.618639	+	0.785675i	$0.712316\pi$
$828$		0			0
$829$	38.4490	+	15.9261i	1.33539	+	0.553136i	0.932187	−	0.361976i	$-0.117898\pi$
$829$	38.4490	+	15.9261i	1.33539	+	0.553136i	0.403200	+	0.915112i	$0.367898\pi$
$830$		0			0
$831$	102.031			3.53941
$832$		0			0
$833$	−18.7314	−	1.18764i	−0.649003	−	0.0411494i
$834$		0			0
$835$	−35.1741	−	14.5696i	−1.21725	−	0.504202i
$836$		0			0
$837$	−69.5565	+	28.8113i	−2.40423	+	0.995863i
$838$		0			0
$839$	−4.92466	+	4.92466i	−0.170018	+	0.170018i	−0.786987	−	0.616969i	$-0.788360\pi$
$839$	−4.92466	+	4.92466i	−0.170018	+	0.170018i	0.616969	+	0.786987i	$0.288360\pi$
$840$		0			0
$841$	−12.2775	−	12.2775i	−0.423362	−	0.423362i
$842$		0			0
$843$	1.30647	+	3.15409i	0.0449971	+	0.108632i
$844$		0			0
$845$	2.01742	−	4.87048i	0.0694013	−	0.167550i
$846$		0			0
$847$	19.0930	+	20.3419i	0.656043	+	0.698956i
$848$		0			0
$849$		−	47.9741i		−	1.64647i
$850$		0			0
$851$	−3.04964	+	7.36249i	−0.104540	+	0.252383i
$852$		0			0
$853$	30.4737	−	12.6226i	1.04340	−	0.432191i	0.205869	−	0.978580i	$-0.433998\pi$
$853$	30.4737	−	12.6226i	1.04340	−	0.432191i	0.837531	+	0.546389i	$0.183998\pi$
$854$		0			0
$855$	−58.5559	+	58.5559i	−2.00257	+	2.00257i
$856$		0			0
$857$	8.71179	+	8.71179i	0.297589	+	0.297589i	0.840069	−	0.542480i	$-0.182514\pi$
$857$	8.71179	+	8.71179i	0.297589	+	0.297589i	−0.542480	+	0.840069i	$0.682514\pi$
$858$		0			0
$859$	24.6028	−	10.1908i	0.839436	−	0.347706i	0.0788051	−	0.996890i	$-0.474890\pi$
$859$	24.6028	−	10.1908i	0.839436	−	0.347706i	0.760631	+	0.649184i	$0.224890\pi$
$860$		0			0
$861$	−38.9036	+	14.6896i	−1.32583	+	0.500620i
$862$		0			0
$863$			17.7600i			0.604556i	0.953220	+	0.302278i	$0.0977472\pi$
$863$			17.7600i			0.604556i	−0.953220	+	0.302278i	$0.902253\pi$
$864$		0			0
$865$	−21.9890			−0.747649
$866$		0			0
$867$	−12.3479	+	29.8106i	−0.419358	+	1.01242i
$868$		0			0
$869$	−3.62694	+	1.50233i	−0.123035	+	0.0509629i
$870$		0			0
$871$	16.2297	−	16.2297i	0.549921	−	0.549921i
$872$		0			0
$873$	88.5509	−	88.5509i	2.99700	−	2.99700i
$874$		0			0
$875$	−12.5802	+	27.8439i	−0.425288	+	0.941296i
$876$		0			0
$877$	−45.4844	−	18.8403i	−1.53590	−	0.636190i	−0.555201	−	0.831716i	$-0.687359\pi$
$877$	−45.4844	−	18.8403i	−1.53590	−	0.636190i	−0.980699	+	0.195526i	$0.937359\pi$
$878$		0			0
$879$	48.9400			1.65071
$880$		0			0
$881$	−30.5234			−1.02836			−0.514180	−	0.857683i	$-0.671904\pi$
$881$	−30.5234			−1.02836			−0.514180	+	0.857683i	$0.671904\pi$
$882$		0			0
$883$	13.5867	−	32.8013i	0.457230	−	1.10385i	−0.512284	−	0.858816i	$-0.671200\pi$
$883$	13.5867	−	32.8013i	0.457230	−	1.10385i	0.969514	−	0.245035i	$-0.0787995\pi$
$884$		0			0
$885$	14.7591	−	6.11343i	0.496122	−	0.205501i
$886$		0			0
$887$	21.8427	+	21.8427i	0.733407	+	0.733407i	0.971293	−	0.237886i	$-0.0764544\pi$
$887$	21.8427	+	21.8427i	0.733407	+	0.733407i	−0.237886	+	0.971293i	$0.576454\pi$
$888$		0			0
$889$	−9.07488	−	0.287403i	−0.304362	−	0.00963919i
$890$		0			0
$891$	7.39927	+	17.8634i	0.247885	+	0.598447i
$892$		0			0
$893$	5.67555	−	13.7020i	0.189925	−	0.458520i
$894$		0			0
$895$	3.87759			0.129614
$896$		0			0
$897$	13.1641			0.439536
$898$		0			0
$899$	−12.3827	+	29.8944i	−0.412985	+	0.997035i
$900$		0			0
$901$	4.36150	+	10.5296i	0.145303	+	0.350792i
$902$		0			0
$903$	−111.904	−	3.54403i	−3.72394	−	0.117938i
$904$		0			0
$905$	1.79666	+	1.79666i	0.0597229	+	0.0597229i
$906$		0			0
$907$	44.2914	−	18.3461i	1.47067	−	0.609172i	0.503660	−	0.863902i	$-0.331986\pi$
$907$	44.2914	−	18.3461i	1.47067	−	0.609172i	0.967012	+	0.254730i	$0.0819865\pi$
$908$		0			0
$909$	4.34593	−	10.4920i	0.144145	−	0.347997i
$910$		0			0
$911$	−28.0080			−0.927946			−0.463973	−	0.885849i	$-0.653577\pi$
$911$	−28.0080			−0.927946			−0.463973	+	0.885849i	$0.653577\pi$
$912$		0			0
$913$	−3.05947			−0.101254
$914$		0			0
$915$	−37.9803	−	15.7320i	−1.25559	−	0.520083i
$916$		0			0
$917$	−13.6477	−	6.16617i	−0.450686	−	0.203625i
$918$		0			0
$919$	11.0504	−	11.0504i	0.364520	−	0.364520i	−0.500954	−	0.865474i	$-0.667017\pi$
$919$	11.0504	−	11.0504i	0.364520	−	0.364520i	0.865474	+	0.500954i	$0.167017\pi$
$920$		0			0
$921$	29.7767	−	29.7767i	0.981174	−	0.981174i
$922$		0			0
$923$	38.8945	−	16.1106i	1.28023	−	0.530287i
$924$		0			0
$925$	−0.897855	+	2.16761i	−0.0295213	+	0.0712707i
$926$		0			0
$927$	−46.8581			−1.53902
$928$		0			0
$929$			3.46522i			0.113690i	0.998383	+	0.0568451i	$0.0181041\pi$
$929$			3.46522i			0.113690i	−0.998383	+	0.0568451i	$0.981896\pi$
$930$		0			0
$931$	−30.9171	−	15.1648i	−1.01327	−	0.497006i
$932$		0			0
$933$	16.8943	−	6.99786i	0.553096	−	0.229100i
$934$		0			0
$935$	−2.75491	−	2.75491i	−0.0900953	−	0.0900953i
$936$		0			0
$937$	10.2285	−	10.2285i	0.334149	−	0.334149i	−0.520011	−	0.854160i	$-0.674072\pi$
$937$	10.2285	−	10.2285i	0.334149	−	0.334149i	0.854160	+	0.520011i	$0.174072\pi$
$938$		0			0
$939$	9.92495	−	4.11105i	0.323888	−	0.134159i
$940$		0			0
$941$	17.9086	−	43.2352i	0.583804	−	1.40943i	−0.305536	−	0.952180i	$-0.598836\pi$
$941$	17.9086	−	43.2352i	0.583804	−	1.40943i	0.889340	−	0.457246i	$-0.151164\pi$
$942$		0			0
$943$		−	5.88843i		−	0.191754i
$944$		0			0
$945$	65.8143	−	61.7735i	2.14094	−	2.00949i
$946$		0			0
$947$	−4.53360	+	10.9451i	−0.147322	+	0.355667i	−0.980264	−	0.197694i	$-0.936655\pi$
$947$	−4.53360	+	10.9451i	−0.147322	+	0.355667i	0.832942	+	0.553361i	$0.186655\pi$
$948$		0			0
$949$	6.47684	+	15.6365i	0.210247	+	0.507581i
$950$		0			0
$951$	−12.4968	−	12.4968i	−0.405236	−	0.405236i
$952$		0			0
$953$	−23.1515	+	23.1515i	−0.749952	+	0.749952i	−0.974470	−	0.224518i	$-0.927919\pi$
$953$	−23.1515	+	23.1515i	−0.749952	+	0.749952i	0.224518	+	0.974470i	$0.427919\pi$
$954$		0			0
$955$	8.94465	−	3.70499i	0.289442	−	0.119891i
$956$		0			0
$957$	13.9607	+	5.78270i	0.451284	+	0.186928i
$958$		0			0
$959$	−16.5652	+	15.5481i	−0.534918	+	0.502076i
$960$		0			0
$961$	−8.41717			−0.271522
$962$		0			0
$963$	61.6569	+	25.5391i	1.98687	+	0.822987i
$964$		0			0
$965$	−10.4544	−	25.2392i	−0.336539	−	0.812478i
$966$		0			0
$967$	−13.5816	−	13.5816i	−0.436755	−	0.436755i	0.454163	−	0.890918i	$-0.349938\pi$
$967$	−13.5816	−	13.5816i	−0.436755	−	0.436755i	−0.890918	+	0.454163i	$0.849938\pi$
$968$		0			0
$969$	30.6758	−	30.6758i	0.985448	−	0.985448i
$970$		0			0
$971$	4.71036	+	11.3718i	0.151163	+	0.364939i	0.981262	−	0.192676i	$-0.0617166\pi$
$971$	4.71036	+	11.3718i	0.151163	+	0.364939i	−0.830100	+	0.557615i	$0.811717\pi$
$972$		0			0
$973$	−9.69734	+	3.66162i	−0.310882	+	0.117386i
$974$		0			0
$975$	3.87568			0.124121
$976$		0			0
$977$			16.3145i			0.521946i	0.965346	+	0.260973i	$0.0840434\pi$
$977$			16.3145i			0.521946i	−0.965346	+	0.260973i	$0.915957\pi$
$978$		0			0
$979$	0.768853	+	0.318469i	0.0245726	+	0.0101783i
$980$		0			0
$981$	15.4115	+	37.2067i	0.492052	+	1.18792i
$982$		0			0
$983$	−25.5491	−	25.5491i	−0.814890	−	0.814890i	0.170472	−	0.985363i	$-0.445471\pi$
$983$	−25.5491	−	25.5491i	−0.814890	−	0.814890i	−0.985363	+	0.170472i	$0.945471\pi$
$984$		0			0
$985$	−18.2200	−	18.2200i	−0.580538	−	0.580538i
$986$		0			0
$987$	−10.8013	+	23.9067i	−0.343810	+	0.760960i
$988$		0			0
$989$	6.06697	−	14.6470i	0.192919	−	0.465747i
$990$		0			0
$991$		−	14.7714i		−	0.469227i	−0.972089	−	0.234614i	$-0.924617\pi$
$991$		−	14.7714i		−	0.469227i	0.972089	−	0.234614i	$-0.0753825\pi$
$992$		0			0
$993$		−	26.9755i		−	0.856042i
$994$		0			0
$995$	−20.7290	−	8.58622i	−0.657152	−	0.272201i
$996$		0			0
$997$	−10.1843	−	24.5872i	−0.322542	−	0.778684i	−0.999105	−	0.0422998i	$-0.986532\pi$
$997$	−10.1843	−	24.5872i	−0.322542	−	0.778684i	0.676563	−	0.736384i	$-0.263468\pi$
$998$		0			0
$999$	72.4530	−	72.4530i	2.29231	−	2.29231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.x.b.111.28		112
4.3	odd	2		224.2.x.b.83.13	yes	112
7.6	odd	2	inner	896.2.x.b.111.1		112
28.27	even	2		224.2.x.b.83.14	yes	112
32.5	even	8		224.2.x.b.27.14	yes	112
32.27	odd	8	inner	896.2.x.b.783.1		112
224.27	even	8	inner	896.2.x.b.783.28		112
224.69	odd	8		224.2.x.b.27.13	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.x.b.27.13	✓	112	224.69	odd	8
224.2.x.b.27.14	yes	112	32.5	even	8
224.2.x.b.83.13	yes	112	4.3	odd	2
224.2.x.b.83.14	yes	112	28.27	even	2
896.2.x.b.111.1		112	7.6	odd	2	inner
896.2.x.b.111.28		112	1.1	even	1	trivial
896.2.x.b.783.1		112	32.27	odd	8	inner
896.2.x.b.783.28		112	224.27	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.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25862 - 3.03857i) q^{3} +(-0.824079 - 1.98950i) q^{5} +(0.0837494 - 2.64443i) q^{7} +(-5.52747 - 5.52747i) q^{9} +O(q^{10})\)	\(q+(1.25862 - 3.03857i) q^{3} +(-0.824079 - 1.98950i) q^{5} +(0.0837494 - 2.64443i) q^{7} +(-5.52747 - 5.52747i) q^{9} +(0.623399 - 0.258220i) q^{11} +(-1.24310 + 3.00110i) q^{13} -7.08245 q^{15} +2.68128 q^{17} +(4.54495 + 1.88258i) q^{19} +(-7.92987 - 3.58280i) q^{21} +(0.871276 - 0.871276i) q^{23} +(0.256515 - 0.256515i) q^{25} +(-14.6369 + 6.06280i) q^{27} +(-2.60571 + 6.29073i) q^{29} +4.75214 q^{31} -2.21924i q^{33} +(-5.33011 + 2.01260i) q^{35} +(-5.97522 + 2.47502i) q^{37} +(7.55448 + 7.55448i) q^{39} +(3.37920 - 3.37920i) q^{41} +(11.8871 - 4.92381i) q^{43} +(-6.44185 + 15.5520i) q^{45} -3.01477i q^{47} +(-6.98597 - 0.442938i) q^{49} +(3.37471 - 8.14727i) q^{51} +(1.62665 + 3.92708i) q^{53} +(-1.02746 - 1.02746i) q^{55} +(11.4407 - 11.4407i) q^{57} +(-2.08390 + 0.863180i) q^{59} +(5.36260 + 2.22126i) q^{61} +(-15.0799 + 14.1541i) q^{63} +6.99512 q^{65} +(-6.52791 - 2.70395i) q^{67} +(-1.55083 - 3.74404i) q^{69} +(-9.16414 - 9.16414i) q^{71} +(3.68420 - 3.68420i) q^{73} +(-0.456585 - 1.10229i) q^{75} +(-0.630635 - 1.67016i) q^{77} -5.81800 q^{79} +28.6549i q^{81} +(-4.18900 - 1.73514i) q^{83} +(-2.20959 - 5.33442i) q^{85} +(15.8352 + 15.8352i) q^{87} +(0.872091 + 0.872091i) q^{89} +(7.83209 + 3.53862i) q^{91} +(5.98113 - 14.4397i) q^{93} -10.5936i q^{95} +16.0201i q^{97} +(-4.87313 - 2.01852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 112 * q + 4 * q^7 - 8 * q^9	\( 112 q + 4 q^{7} - 8 q^{9} + 8 q^{11} + 16 q^{15} - 4 q^{21} + 48 q^{23} - 8 q^{25} - 8 q^{29} - 20 q^{35} - 8 q^{37} + 8 q^{39} - 32 q^{43} + 32 q^{51} - 32 q^{53} - 8 q^{57} - 16 q^{65} + 64 q^{67} - 56 q^{71} + 52 q^{77} + 16 q^{79} - 48 q^{85} + 52 q^{91} - 32 q^{93} - 16 q^{99}+O(q^{100}) \) 112 * q + 4 * q^7 - 8 * q^9 + 8 * q^11 + 16 * q^15 - 4 * q^21 + 48 * q^23 - 8 * q^25 - 8 * q^29 - 20 * q^35 - 8 * q^37 + 8 * q^39 - 32 * q^43 + 32 * q^51 - 32 * q^53 - 8 * q^57 - 16 * q^65 + 64 * q^67 - 56 * q^71 + 52 * q^77 + 16 * q^79 - 48 * q^85 + 52 * q^91 - 32 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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