LMFDB - Embedded newform 504.2.bs.a.257.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(257,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))

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

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

chi := DirichletCharacter("504.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.20
Character	$\chi$	$=$	504.257
Dual form			504.2.bs.a.353.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29769 - 1.14717i) q^{3} +(-0.643917 - 1.11530i) q^{5} +(-2.63392 - 0.249885i) q^{7} +(0.368015 - 2.97734i) q^{9} +O(q^{10})$	\(q+(1.29769 - 1.14717i) q^{3} +(-0.643917 - 1.11530i) q^{5} +(-2.63392 - 0.249885i) q^{7} +(0.368015 - 2.97734i) q^{9} +(-3.13384 - 1.80932i) q^{11} +(-3.48808 - 2.01385i) q^{13} +(-2.11504 - 0.708633i) q^{15} +(-0.828246 - 1.43456i) q^{17} +(5.15603 + 2.97683i) q^{19} +(-3.70469 + 2.69728i) q^{21} +(0.372292 - 0.214943i) q^{23} +(1.67074 - 2.89381i) q^{25} +(-2.93794 - 4.28585i) q^{27} +(6.39192 - 3.69038i) q^{29} +0.971739i q^{31} +(-6.14236 + 1.24709i) q^{33} +(1.41733 + 3.09851i) q^{35} +(-5.16236 + 8.94147i) q^{37} +(-6.83668 + 1.38806i) q^{39} +(5.15230 - 8.92404i) q^{41} +(3.67982 + 6.37363i) q^{43} +(-3.55759 + 1.50672i) q^{45} -8.03262 q^{47} +(6.87511 + 1.31636i) q^{49} +(-2.72049 - 0.911487i) q^{51} +(10.4907 - 6.05681i) q^{53} +4.66021i q^{55} +(10.1059 - 2.05181i) q^{57} -1.23719 q^{59} -6.64381i q^{61} +(-1.71332 + 7.75013i) q^{63} +5.18700i q^{65} -2.20562 q^{67} +(0.236545 - 0.706010i) q^{69} -3.66832i q^{71} +(-1.67314 + 0.965987i) q^{73} +(-1.15157 - 5.67190i) q^{75} +(7.80217 + 5.54872i) q^{77} -4.52649 q^{79} +(-8.72913 - 2.19141i) q^{81} +(-0.701322 - 1.21472i) q^{83} +(-1.06664 + 1.84748i) q^{85} +(4.06127 - 12.1216i) q^{87} +(4.81741 - 8.34400i) q^{89} +(8.68412 + 6.17594i) q^{91} +(1.11475 + 1.26102i) q^{93} -7.66734i q^{95} +(8.20853 - 4.73920i) q^{97} +(-6.54027 + 8.66465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.29769	−	1.14717i	0.749223	−	0.662317i
$3$	1.29769	−	1.14717i	0.749223	−	0.662317i
$4$		0			0
$5$	−0.643917	−	1.11530i	−0.287968	−	0.498776i	0.685356	−	0.728208i	$-0.259646\pi$
$5$	−0.643917	−	1.11530i	−0.287968	−	0.498776i	−0.973325	+	0.229432i	$0.926313\pi$
$6$		0			0
$7$	−2.63392	−	0.249885i	−0.995530	−	0.0944478i
$7$	−2.63392	−	0.249885i	−0.995530	−	0.0944478i
$8$		0			0
$9$	0.368015	−	2.97734i	0.122672	−	0.992447i
$10$		0			0
$11$	−3.13384	−	1.80932i	−0.944888	−	0.545531i	−0.0533987	−	0.998573i	$-0.517005\pi$
$11$	−3.13384	−	1.80932i	−0.944888	−	0.545531i	−0.891489	+	0.453042i	$0.850339\pi$
$12$		0			0
$13$	−3.48808	−	2.01385i	−0.967420	−	0.558540i	−0.0689715	−	0.997619i	$-0.521972\pi$
$13$	−3.48808	−	2.01385i	−0.967420	−	0.558540i	−0.898449	+	0.439078i	$0.855305\pi$
$14$		0			0
$15$	−2.11504	−	0.708633i	−0.546101	−	0.182968i
$16$		0			0
$17$	−0.828246	−	1.43456i	−0.200879	−	0.347933i	0.747933	−	0.663774i	$-0.231047\pi$
$17$	−0.828246	−	1.43456i	−0.200879	−	0.347933i	−0.948812	+	0.315842i	$0.897713\pi$
$18$		0			0
$19$	5.15603	+	2.97683i	1.18287	+	0.682933i	0.956678	−	0.291149i	$-0.0940376\pi$
$19$	5.15603	+	2.97683i	1.18287	+	0.682933i	0.226196	+	0.974082i	$0.427371\pi$
$20$		0			0
$21$	−3.70469	+	2.69728i	−0.808429	+	0.588594i
$22$		0			0
$23$	0.372292	−	0.214943i	0.0776282	−	0.0448186i	−0.460683	−	0.887564i	$-0.652396\pi$
$23$	0.372292	−	0.214943i	0.0776282	−	0.0448186i	0.538312	+	0.842746i	$0.319062\pi$
$24$		0			0
$25$	1.67074	−	2.89381i	0.334148	−	0.578762i
$26$		0			0
$27$	−2.93794	−	4.28585i	−0.565407	−	0.824812i
$28$		0			0
$29$	6.39192	−	3.69038i	1.18695	−	0.685286i	0.229338	−	0.973347i	$-0.426344\pi$
$29$	6.39192	−	3.69038i	1.18695	−	0.685286i	0.957612	+	0.288061i	$0.0930105\pi$
$30$		0			0
$31$			0.971739i			0.174530i	0.996185	+	0.0872648i	$0.0278126\pi$
$31$			0.971739i			0.174530i	−0.996185	+	0.0872648i	$0.972187\pi$
$32$		0			0
$33$	−6.14236	+	1.24709i	−1.06925	+	0.217091i
$34$		0			0
$35$	1.41733	+	3.09851i	0.239573	+	0.523744i
$36$		0			0
$37$	−5.16236	+	8.94147i	−0.848687	+	1.46997i	0.0336934	+	0.999432i	$0.489273\pi$
$37$	−5.16236	+	8.94147i	−0.848687	+	1.46997i	−0.882380	+	0.470537i	$0.844060\pi$
$38$		0			0
$39$	−6.83668	+	1.38806i	−1.09475	+	0.222268i
$40$		0			0
$41$	5.15230	−	8.92404i	0.804654	−	1.39370i	−0.111871	−	0.993723i	$-0.535684\pi$
$41$	5.15230	−	8.92404i	0.804654	−	1.39370i	0.916524	−	0.399979i	$-0.130982\pi$
$42$		0			0
$43$	3.67982	+	6.37363i	0.561167	+	0.971969i	0.997395	+	0.0721330i	$0.0229806\pi$
$43$	3.67982	+	6.37363i	0.561167	+	0.971969i	−0.436228	+	0.899836i	$0.643686\pi$
$44$		0			0
$45$	−3.55759	+	1.50672i	−0.530334	+	0.224608i
$46$		0			0
$47$	−8.03262			−1.17168			−0.585839	−	0.810427i	$-0.699235\pi$
$47$	−8.03262			−1.17168			−0.585839	+	0.810427i	$0.699235\pi$
$48$		0			0
$49$	6.87511	+	1.31636i	0.982159	+	0.188051i
$50$		0			0
$51$	−2.72049	−	0.911487i	−0.380945	−	0.127634i
$52$		0			0
$53$	10.4907	−	6.05681i	1.44101	−	0.831967i	0.443093	−	0.896476i	$-0.353881\pi$
$53$	10.4907	−	6.05681i	1.44101	−	0.831967i	0.997917	+	0.0645084i	$0.0205479\pi$
$54$		0			0
$55$			4.66021i			0.628383i
$56$		0			0
$57$	10.1059	−	2.05181i	1.33856	−	0.271769i
$58$		0			0
$59$	−1.23719			−0.161069			−0.0805343	−	0.996752i	$-0.525663\pi$
$59$	−1.23719			−0.161069			−0.0805343	+	0.996752i	$0.525663\pi$
$60$		0			0
$61$		−	6.64381i		−	0.850652i	−0.905040	−	0.425326i	$-0.860159\pi$
$61$		−	6.64381i		−	0.850652i	0.905040	−	0.425326i	$-0.139841\pi$
$62$		0			0
$63$	−1.71332	+	7.75013i	−0.215858	+	0.976425i
$64$		0			0
$65$			5.18700i			0.643368i
$66$		0			0
$67$	−2.20562			−0.269459			−0.134729	−	0.990882i	$-0.543017\pi$
$67$	−2.20562			−0.269459			−0.134729	+	0.990882i	$0.543017\pi$
$68$		0			0
$69$	0.236545	−	0.706010i	0.0284767	−	0.0849936i
$70$		0			0
$71$		−	3.66832i		−	0.435349i	−0.976021	−	0.217674i	$-0.930153\pi$
$71$		−	3.66832i		−	0.435349i	0.976021	−	0.217674i	$-0.0698471\pi$
$72$		0			0
$73$	−1.67314	+	0.965987i	−0.195826	+	0.113060i	−0.594707	−	0.803942i	$-0.702732\pi$
$73$	−1.67314	+	0.965987i	−0.195826	+	0.113060i	0.398881	+	0.917003i	$0.369399\pi$
$74$		0			0
$75$	−1.15157	−	5.67190i	−0.132972	−	0.654934i
$76$		0			0
$77$	7.80217	+	5.54872i	0.889140	+	0.632335i
$78$		0			0
$79$	−4.52649			−0.509270			−0.254635	−	0.967037i	$-0.581955\pi$
$79$	−4.52649			−0.509270			−0.254635	+	0.967037i	$0.581955\pi$
$80$		0			0
$81$	−8.72913	−	2.19141i	−0.969903	−	0.243490i
$82$		0			0
$83$	−0.701322	−	1.21472i	−0.0769800	−	0.133333i	0.824966	−	0.565183i	$-0.191194\pi$
$83$	−0.701322	−	1.21472i	−0.0769800	−	0.133333i	−0.901946	+	0.431850i	$0.857861\pi$
$84$		0			0
$85$	−1.06664	+	1.84748i	−0.115694	+	0.200387i
$86$		0			0
$87$	4.06127	−	12.1216i	0.435414	−	1.29957i
$88$		0			0
$89$	4.81741	−	8.34400i	0.510644	−	0.884462i	−0.489280	−	0.872127i	$-0.662740\pi$
$89$	4.81741	−	8.34400i	0.510644	−	0.884462i	0.999924	−	0.0123349i	$-0.00392643\pi$
$90$		0			0
$91$	8.68412	+	6.17594i	0.910343	+	0.647414i
$92$		0			0
$93$	1.11475	+	1.26102i	0.115594	+	0.130762i
$94$		0			0
$95$		−	7.66734i		−	0.786652i
$96$		0			0
$97$	8.20853	−	4.73920i	0.833450	−	0.481193i	−0.0215824	−	0.999767i	$-0.506870\pi$
$97$	8.20853	−	4.73920i	0.833450	−	0.481193i	0.855032	+	0.518574i	$0.173537\pi$
$98$		0			0
$99$	−6.54027	+	8.66465i	−0.657322	+	0.870830i
$100$		0			0
$101$	−2.54141	+	4.40185i	−0.252879	+	0.438000i	−0.964317	−	0.264749i	$-0.914711\pi$
$101$	−2.54141	+	4.40185i	−0.252879	+	0.438000i	0.711438	+	0.702749i	$0.248044\pi$
$102$		0			0
$103$	−6.91475	+	3.99223i	−0.681331	+	0.393366i	−0.800356	−	0.599525i	$-0.795356\pi$
$103$	−6.91475	+	3.99223i	−0.681331	+	0.393366i	0.119026	+	0.992891i	$0.462023\pi$
$104$		0			0
$105$	5.39377	+	2.39500i	0.526378	+	0.233728i
$106$		0			0
$107$	12.0233	+	6.94167i	1.16234	+	0.671077i	0.951863	−	0.306523i	$-0.0991655\pi$
$107$	12.0233	+	6.94167i	1.16234	+	0.671077i	0.210475	+	0.977599i	$0.432499\pi$
$108$		0			0
$109$	8.64546	+	14.9744i	0.828085	+	1.43429i	0.899538	+	0.436842i	$0.143903\pi$
$109$	8.64546	+	14.9744i	0.828085	+	1.43429i	−0.0714532	+	0.997444i	$0.522764\pi$
$110$		0			0
$111$	3.55820	+	17.5254i	0.337730	+	1.66344i
$112$		0			0
$113$	−2.21507	−	1.27887i	−0.208377	−	0.120306i	0.392180	−	0.919888i	$-0.371721\pi$
$113$	−2.21507	−	1.27887i	−0.208377	−	0.120306i	−0.600557	+	0.799582i	$0.705054\pi$
$114$		0			0
$115$	−0.479450	−	0.276810i	−0.0447089	−	0.0258127i
$116$		0			0
$117$	−7.27957	+	9.64409i	−0.672997	+	0.891597i
$118$		0			0
$119$	1.82306	+	3.98550i	0.167120	+	0.365350i
$120$		0			0
$121$	1.04730	+	1.81397i	0.0952087	+	0.164906i
$122$		0			0
$123$	−3.55127	−	17.4912i	−0.320207	−	1.57713i
$124$		0			0
$125$	−10.7424			−0.960834
$126$		0			0
$127$	14.8517			1.31788			0.658938	−	0.752197i	$-0.271006\pi$
$127$	14.8517			1.31788			0.658938	+	0.752197i	$0.271006\pi$
$128$		0			0
$129$	12.0869	+	4.04965i	1.06419	+	0.356552i
$130$		0			0
$131$	−3.92019	−	6.78997i	−0.342508	−	0.593242i	0.642389	−	0.766378i	$-0.277943\pi$
$131$	−3.92019	−	6.78997i	−0.342508	−	0.593242i	−0.984898	+	0.173136i	$0.944610\pi$
$132$		0			0
$133$	−12.8367	−	9.12917i	−1.11308	−	0.791600i
$134$		0			0
$135$	−2.88821	+	6.03641i	−0.248577	+	0.519531i
$136$		0			0
$137$	11.2380	+	6.48825i	0.960125	+	0.554328i	0.896211	−	0.443627i	$-0.146309\pi$
$137$	11.2380	+	6.48825i	0.960125	+	0.554328i	0.0639135	+	0.997955i	$0.479642\pi$
$138$		0			0
$139$	13.0039	+	7.50782i	1.10298	+	0.636805i	0.937002	−	0.349324i	$-0.113589\pi$
$139$	13.0039	+	7.50782i	1.10298	+	0.636805i	0.165977	+	0.986130i	$0.446922\pi$
$140$		0			0
$141$	−10.4239	+	9.21476i	−0.877849	+	0.776023i
$142$		0			0
$143$	7.28739	+	12.6221i	0.609403	+	1.05552i
$144$		0			0
$145$	−8.23174	−	4.75259i	−0.683608	−	0.394681i
$146$		0			0
$147$	10.4319	−	6.17868i	0.860406	−	0.509609i
$148$		0			0
$149$	−6.97082	+	4.02461i	−0.571072	+	0.329709i	−0.757577	−	0.652745i	$-0.773617\pi$
$149$	−6.97082	+	4.02461i	−0.571072	+	0.329709i	0.186505	+	0.982454i	$0.440284\pi$
$150$		0			0
$151$	4.94879	−	8.57156i	0.402727	−	0.697543i	−0.591327	−	0.806432i	$-0.701396\pi$
$151$	4.94879	−	8.57156i	0.402727	−	0.697543i	0.994054	+	0.108888i	$0.0347291\pi$
$152$		0			0
$153$	−4.57600	+	1.93803i	−0.369947	+	0.156681i
$154$		0			0
$155$	1.08378	−	0.625719i	0.0870511	−	0.0502590i
$156$		0			0
$157$			4.45628i			0.355650i	0.984062	+	0.177825i	$0.0569060\pi$
$157$			4.45628i			0.355650i	−0.984062	+	0.177825i	$0.943094\pi$
$158$		0			0
$159$	6.66554	−	19.8945i	0.528612	−	1.57774i
$160$		0			0
$161$	−1.03430	+	0.473112i	−0.0815142	+	0.0372865i
$162$		0			0
$163$	−10.1860	+	17.6426i	−0.797827	+	1.38188i	0.123202	+	0.992382i	$0.460684\pi$
$163$	−10.1860	+	17.6426i	−0.797827	+	1.38188i	−0.921029	+	0.389495i	$0.872650\pi$
$164$		0			0
$165$	5.34604	+	6.04753i	0.416189	+	0.470799i
$166$		0			0
$167$	4.32517	−	7.49141i	0.334692	−	0.579703i	−0.648734	−	0.761015i	$-0.724701\pi$
$167$	4.32517	−	7.49141i	0.334692	−	0.579703i	0.983426	+	0.181312i	$0.0580345\pi$
$168$		0			0
$169$	1.61115	+	2.79060i	0.123935	+	0.214661i
$170$		0			0
$171$	10.7605	−	14.2557i	0.822880	−	1.09016i
$172$		0			0
$173$	−6.83446			−0.519614			−0.259807	−	0.965661i	$-0.583659\pi$
$173$	−6.83446			−0.519614			−0.259807	+	0.965661i	$0.583659\pi$
$174$		0			0
$175$	−5.12373	+	7.20458i	−0.387317	+	0.544615i
$176$		0			0
$177$	−1.60549	+	1.41926i	−0.120676	+	0.106678i
$178$		0			0
$179$	−17.4620	+	10.0817i	−1.30517	+	0.753541i	−0.981286	−	0.192555i	$-0.938322\pi$
$179$	−17.4620	+	10.0817i	−1.30517	+	0.753541i	−0.323885	+	0.946096i	$0.604989\pi$
$180$		0			0
$181$		−	18.7298i		−	1.39218i	−0.717957	−	0.696088i	$-0.754922\pi$
$181$		−	18.7298i		−	1.39218i	0.717957	−	0.696088i	$-0.245078\pi$
$182$		0			0
$183$	−7.62156	−	8.62162i	−0.563402	−	0.637329i
$184$		0			0
$185$	13.2965			0.977580
$186$		0			0
$187$			5.99426i			0.438344i
$188$		0			0
$189$	6.66734	+	12.0228i	0.484977	+	0.874527i
$190$		0			0
$191$			4.71883i			0.341442i	0.985319	+	0.170721i	$0.0546097\pi$
$191$			4.71883i			0.341442i	−0.985319	+	0.170721i	$0.945390\pi$
$192$		0			0
$193$	−18.2693			−1.31506			−0.657528	−	0.753430i	$-0.728398\pi$
$193$	−18.2693			−1.31506			−0.657528	+	0.753430i	$0.728398\pi$
$194$		0			0
$195$	5.95035	+	6.73113i	0.426114	+	0.482026i
$196$		0			0
$197$		−	1.06267i		−	0.0757119i	−0.999283	−	0.0378560i	$-0.987947\pi$
$197$		−	1.06267i		−	0.0757119i	0.999283	−	0.0378560i	$-0.0120528\pi$
$198$		0			0
$199$	20.2137	−	11.6704i	1.43291	−	0.827292i	0.435570	−	0.900155i	$-0.356547\pi$
$199$	20.2137	−	11.6704i	1.43291	−	0.827292i	0.997342	+	0.0728629i	$0.0232136\pi$
$200$		0			0
$201$	−2.86221	+	2.53021i	−0.201885	+	0.178467i
$202$		0			0
$203$	−17.7580	+	8.12293i	−1.24637	+	0.570118i
$204$		0			0
$205$	−13.2706			−0.926860
$206$		0			0
$207$	−0.502949	−	1.18754i	−0.0349574	−	0.0825398i
$208$		0			0
$209$	−10.7721	−	18.6578i	−0.745122	−	1.29059i
$210$		0			0
$211$	−0.160679	+	0.278305i	−0.0110616	+	0.0191593i	−0.871503	−	0.490390i	$-0.836854\pi$
$211$	−0.160679	+	0.278305i	−0.0110616	+	0.0191593i	0.860442	+	0.509549i	$0.170188\pi$
$212$		0			0
$213$	−4.20817	−	4.76035i	−0.288339	−	0.326174i
$214$		0			0
$215$	4.73899	−	8.20817i	0.323196	−	0.559793i
$216$		0			0
$217$	0.242823	−	2.55949i	0.0164839	−	0.173749i
$218$		0			0
$219$	−1.06307	+	3.17293i	−0.0718358	+	0.214406i
$220$		0			0
$221$			6.67184i			0.448797i
$222$		0			0
$223$	9.64603	−	5.56914i	0.645946	−	0.372937i	−0.140955	−	0.990016i	$-0.545017\pi$
$223$	9.64603	−	5.56914i	0.645946	−	0.372937i	0.786901	+	0.617079i	$0.211684\pi$
$224$		0			0
$225$	−8.00100	−	6.03933i	−0.533400	−	0.402622i
$226$		0			0
$227$	13.6176	−	23.5864i	0.903833	−	1.56549i	0.0813580	−	0.996685i	$-0.474074\pi$
$227$	13.6176	−	23.5864i	0.903833	−	1.56549i	0.822475	−	0.568801i	$-0.192592\pi$
$228$		0			0
$229$	−14.2363	+	8.21931i	−0.940758	+	0.543147i	−0.890198	−	0.455574i	$-0.849434\pi$
$229$	−14.2363	+	8.21931i	−0.940758	+	0.543147i	−0.0505603	+	0.998721i	$0.516101\pi$
$230$		0			0
$231$	16.4901	−	1.74986i	1.08497	−	0.115132i
$232$		0			0
$233$	3.35682	+	1.93806i	0.219912	+	0.126966i	0.605910	−	0.795533i	$-0.292809\pi$
$233$	3.35682	+	1.93806i	0.219912	+	0.126966i	−0.385997	+	0.922500i	$0.626143\pi$
$234$		0			0
$235$	5.17234	+	8.95876i	0.337406	+	0.584405i
$236$		0			0
$237$	−5.87400	+	5.19264i	−0.381557	+	0.337298i
$238$		0			0
$239$	−12.3125	−	7.10864i	−0.796431	−	0.459820i	0.0457904	−	0.998951i	$-0.485419\pi$
$239$	−12.3125	−	7.10864i	−0.796431	−	0.459820i	−0.842222	+	0.539131i	$0.818753\pi$
$240$		0			0
$241$	6.09481	+	3.51884i	0.392601	+	0.226668i	0.683287	−	0.730150i	$-0.260550\pi$
$241$	6.09481	+	3.51884i	0.392601	+	0.226668i	−0.290685	+	0.956819i	$0.593883\pi$
$242$		0			0
$243$	−13.8416	+	7.16999i	−0.887942	+	0.459955i
$244$		0			0
$245$	−2.95887	−	8.51542i	−0.189035	−	0.544030i
$246$		0			0
$247$	−11.9898	−	20.7669i	−0.762891	−	1.32137i
$248$		0			0
$249$	−2.30359	−	0.771807i	−0.145984	−	0.0489113i
$250$		0			0
$251$	−19.6045			−1.23742			−0.618712	−	0.785618i	$-0.712345\pi$
$251$	−19.6045			−1.23742			−0.618712	+	0.785618i	$0.712345\pi$
$252$		0			0
$253$	−1.55560			−0.0977999
$254$		0			0
$255$	0.735193	+	3.62108i	0.0460396	+	0.226761i
$256$		0			0
$257$	7.41651	+	12.8458i	0.462629	+	0.801297i	0.999091	−	0.0426275i	$-0.0135729\pi$
$257$	7.41651	+	12.8458i	0.462629	+	0.801297i	−0.536462	+	0.843924i	$0.680240\pi$
$258$		0			0
$259$	15.8316	−	22.2612i	0.983729	−	1.38324i
$260$		0			0
$261$	−8.63520	−	20.3891i	−0.534505	−	1.26205i
$262$		0			0
$263$	10.6985	+	6.17678i	0.659698	+	0.380877i	0.792162	−	0.610311i	$-0.208956\pi$
$263$	10.6985	+	6.17678i	0.659698	+	0.380877i	−0.132464	+	0.991188i	$0.542289\pi$
$264$		0			0
$265$	−13.5103	−	7.80017i	−0.829931	−	0.479161i
$266$		0			0
$267$	−3.32044	−	16.3543i	−0.203208	−	1.00087i
$268$		0			0
$269$	−9.97197	−	17.2720i	−0.608002	−	1.05309i	−0.991569	−	0.129577i	$-0.958638\pi$
$269$	−9.97197	−	17.2720i	−0.608002	−	1.05309i	0.383568	−	0.923513i	$-0.374695\pi$
$270$		0			0
$271$	−12.8078	−	7.39458i	−0.778018	−	0.449189i	0.0577095	−	0.998333i	$-0.481620\pi$
$271$	−12.8078	−	7.39458i	−0.778018	−	0.449189i	−0.835727	+	0.549145i	$0.814954\pi$
$272$		0			0
$273$	18.3542	−	1.94766i	1.11084	−	0.117878i
$274$		0			0
$275$	−10.4717	+	6.04582i	−0.631465	+	0.364577i
$276$		0			0
$277$	4.47662	−	7.75374i	0.268974	−	0.465877i	−0.699623	−	0.714512i	$-0.746649\pi$
$277$	4.47662	−	7.75374i	0.268974	−	0.465877i	0.968597	+	0.248635i	$0.0799821\pi$
$278$		0			0
$279$	2.89320	+	0.357614i	0.173211	+	0.0214098i
$280$		0			0
$281$	18.3412	−	10.5893i	1.09414	−	0.631703i	0.159466	−	0.987203i	$-0.449023\pi$
$281$	18.3412	−	10.5893i	1.09414	−	0.631703i	0.934676	+	0.355500i	$0.115689\pi$
$282$		0			0
$283$		−	25.5208i		−	1.51706i	−0.651640	−	0.758528i	$-0.725919\pi$
$283$		−	25.5208i		−	1.51706i	0.651640	−	0.758528i	$-0.274081\pi$
$284$		0			0
$285$	−8.79572	−	9.94985i	−0.521013	−	0.589378i
$286$		0			0
$287$	−15.8008	+	22.2178i	−0.932689	+	1.31147i
$288$		0			0
$289$	7.12802	−	12.3461i	0.419295	−	0.726240i
$290$		0			0
$291$	5.21550	−	15.5666i	0.305738	−	0.912529i
$292$		0			0
$293$	−11.0921	+	19.2121i	−0.648009	+	1.12238i	0.335589	+	0.942008i	$0.391065\pi$
$293$	−11.0921	+	19.2121i	−0.648009	+	1.12238i	−0.983598	+	0.180375i	$0.942269\pi$
$294$		0			0
$295$	0.796648	+	1.37984i	0.0463827	+	0.0803371i
$296$		0			0
$297$	1.45254	+	18.7468i	0.0842850	+	1.08780i
$298$		0			0
$299$	−1.73145			−0.100132
$300$		0			0
$301$	−8.09968	−	17.7072i	−0.466858	−	1.02063i
$302$		0			0
$303$	1.75169	+	8.62766i	0.100632	+	0.495646i
$304$		0			0
$305$	−7.40982	+	4.27806i	−0.424285	+	0.244961i
$306$		0			0
$307$		−	15.8798i		−	0.906309i	−0.891432	−	0.453155i	$-0.850299\pi$
$307$		−	15.8798i		−	0.906309i	0.891432	−	0.453155i	$-0.149701\pi$
$308$		0			0
$309$	−4.39346	+	13.1131i	−0.249935	+	0.745976i
$310$		0			0
$311$	6.35781			0.360518			0.180259	−	0.983619i	$-0.442306\pi$
$311$	6.35781			0.360518			0.180259	+	0.983619i	$0.442306\pi$
$312$		0			0
$313$		−	17.7635i		−	1.00405i	−0.864853	−	0.502025i	$-0.832589\pi$
$313$		−	17.7635i		−	1.00405i	0.864853	−	0.502025i	$-0.167411\pi$
$314$		0			0
$315$	9.74693	−	3.07958i	0.549177	−	0.173515i
$316$		0			0
$317$			30.8018i			1.73000i	0.501771	+	0.865000i	$0.332682\pi$
$317$			30.8018i			1.73000i	−0.501771	+	0.865000i	$0.667318\pi$
$318$		0			0
$319$	−26.7083			−1.49538
$320$		0			0
$321$	23.5658	−	4.78461i	1.31532	−	0.267051i
$322$		0			0
$323$		−	9.86221i		−	0.548748i
$324$		0			0
$325$	−11.6554	+	6.72923i	−0.646524	+	0.373271i
$326$		0			0
$327$	28.3973	+	9.51436i	1.57037	+	0.526145i
$328$		0			0
$329$	21.1573	+	2.00724i	1.16644	+	0.110662i
$330$		0			0
$331$	−17.6062			−0.967726			−0.483863	−	0.875144i	$-0.660767\pi$
$331$	−17.6062			−0.967726			−0.483863	+	0.875144i	$0.660767\pi$
$332$		0			0
$333$	24.7220	+	18.6607i	1.35476	+	1.02260i
$334$		0			0
$335$	1.42023	+	2.45992i	0.0775956	+	0.134400i
$336$		0			0
$337$	−8.76938	+	15.1890i	−0.477699	+	0.827399i	−0.999673	−	0.0255625i	$-0.991862\pi$
$337$	−8.76938	+	15.1890i	−0.477699	+	0.827399i	0.521974	+	0.852961i	$0.325196\pi$
$338$		0			0
$339$	−4.34157	+	0.881474i	−0.235801	+	0.0478751i
$340$		0			0
$341$	1.75819	−	3.04527i	0.0952113	−	0.164911i
$342$		0			0
$343$	−17.7796	−	5.18518i	−0.960008	−	0.279973i
$344$		0			0
$345$	−0.939726	+	0.190794i	−0.0505932	+	0.0102720i
$346$		0			0
$347$			14.1875i			0.761623i	0.924653	+	0.380812i	$0.124355\pi$
$347$			14.1875i			0.761623i	−0.924653	+	0.380812i	$0.875645\pi$
$348$		0			0
$349$	20.9072	−	12.0708i	1.11914	−	0.646135i	0.177958	−	0.984038i	$-0.443051\pi$
$349$	20.9072	−	12.0708i	1.11914	−	0.646135i	0.941181	+	0.337903i	$0.109718\pi$
$350$		0			0
$351$	1.61673	+	20.8660i	0.0862949	+	1.11374i
$352$		0			0
$353$	−18.1502	+	31.4371i	−0.966038	+	1.67323i	−0.259240	+	0.965813i	$0.583472\pi$
$353$	−18.1502	+	31.4371i	−0.966038	+	1.67323i	−0.706799	+	0.707415i	$0.749861\pi$
$354$		0			0
$355$	−4.09126	+	2.36209i	−0.217142	+	0.125367i
$356$		0			0
$357$	6.93781	+	3.08060i	0.367188	+	0.163043i
$358$		0			0
$359$	13.1940	+	7.61756i	0.696353	+	0.402040i	0.805988	−	0.591932i	$-0.201635\pi$
$359$	13.1940	+	7.61756i	0.696353	+	0.402040i	−0.109635	+	0.993972i	$0.534968\pi$
$360$		0			0
$361$	8.22308	+	14.2428i	0.432794	+	0.749621i
$362$		0			0
$363$	3.43999	+	1.15255i	0.180553	+	0.0604933i
$364$		0			0
$365$	2.15473	+	1.24403i	0.112783	+	0.0651156i
$366$		0			0
$367$	3.69966	+	2.13600i	0.193120	+	0.111498i	0.593443	−	0.804876i	$-0.297768\pi$
$367$	3.69966	+	2.13600i	0.193120	+	0.111498i	−0.400322	+	0.916374i	$0.631102\pi$
$368$		0			0
$369$	−24.6738	−	18.6243i	−1.28447	−	0.969544i
$370$		0			0
$371$	−29.1452	+	13.3317i	−1.51315	+	0.692148i
$372$		0			0
$373$	7.69254	+	13.3239i	0.398305	+	0.689884i	0.993517	−	0.113685i	$-0.0362653\pi$
$373$	7.69254	+	13.3239i	0.398305	+	0.689884i	−0.595212	+	0.803569i	$0.702932\pi$
$374$		0			0
$375$	−13.9404	+	12.3234i	−0.719879	+	0.636377i
$376$		0			0
$377$	−29.7274			−1.53104
$378$		0			0
$379$	19.5146			1.00240			0.501200	−	0.865331i	$-0.332892\pi$
$379$	19.5146			1.00240			0.501200	+	0.865331i	$0.332892\pi$
$380$		0			0
$381$	19.2730	−	17.0374i	0.987383	−	0.872852i
$382$		0			0
$383$	−5.91247	−	10.2407i	−0.302113	−	0.523275i	0.674501	−	0.738274i	$-0.264359\pi$
$383$	−5.91247	−	10.2407i	−0.302113	−	0.523275i	−0.976614	+	0.214998i	$0.931025\pi$
$384$		0			0
$385$	1.16452	−	12.2746i	0.0593494	−	0.625574i
$386$		0			0
$387$	20.3307	−	8.61048i	1.03347	−	0.437695i
$388$		0			0
$389$	−12.2574	−	7.07680i	−0.621474	−	0.358808i	0.155969	−	0.987762i	$-0.450150\pi$
$389$	−12.2574	−	7.07680i	−0.621474	−	0.358808i	−0.777443	+	0.628954i	$0.783483\pi$
$390$		0			0
$391$	−0.616698	−	0.356051i	−0.0311878	−	0.0180063i
$392$		0			0
$393$	−12.8764	−	4.31418i	−0.649530	−	0.217622i
$394$		0			0
$395$	2.91468	+	5.04838i	0.146654	+	0.254012i
$396$		0			0
$397$	12.8297	+	7.40726i	0.643907	+	0.371760i	0.786118	−	0.618077i	$-0.212088\pi$
$397$	12.8297	+	7.40726i	0.643907	+	0.371760i	−0.142211	+	0.989836i	$0.545421\pi$
$398$		0			0
$399$	−27.1308	+	2.87900i	−1.35824	+	0.144130i
$400$		0			0
$401$	−6.88527	+	3.97521i	−0.343834	+	0.198513i	−0.661966	−	0.749534i	$-0.730278\pi$
$401$	−6.88527	+	3.97521i	−0.343834	+	0.198513i	0.318132	+	0.948046i	$0.396944\pi$
$402$		0			0
$403$	1.95693	−	3.38951i	0.0974818	−	0.168843i
$404$		0			0
$405$	3.17676	+	11.1467i	0.157855	+	0.553882i
$406$		0			0
$407$	32.3560	−	18.6808i	1.60383	−	0.925971i
$408$		0			0
$409$		−	9.53614i		−	0.471532i	−0.971810	−	0.235766i	$-0.924240\pi$
$409$		−	9.53614i		−	0.471532i	0.971810	−	0.235766i	$-0.0757599\pi$
$410$		0			0
$411$	22.0265	−	4.47208i	1.08649	−	0.220592i
$412$		0			0
$413$	3.25867	+	0.309156i	0.160349	+	0.0152126i
$414$		0			0
$415$	−0.903186	+	1.56436i	−0.0443356	+	0.0767916i
$416$		0			0
$417$	25.4878	−	5.17483i	1.24815	−	0.253413i
$418$		0			0
$419$	−16.0896	+	27.8680i	−0.786029	+	1.36144i	0.142354	+	0.989816i	$0.454533\pi$
$419$	−16.0896	+	27.8680i	−0.786029	+	1.36144i	−0.928383	+	0.371626i	$0.878800\pi$
$420$		0			0
$421$	19.5022	+	33.7789i	0.950481	+	1.64628i	0.744385	+	0.667750i	$0.232743\pi$
$421$	19.5022	+	33.7789i	0.950481	+	1.64628i	0.206096	+	0.978532i	$0.433924\pi$
$422$		0			0
$423$	−2.95612	+	23.9159i	−0.143732	+	1.16283i
$424$		0			0
$425$	−5.53514			−0.268494
$426$		0			0
$427$	−1.66019	+	17.4993i	−0.0803422	+	0.846850i
$428$		0			0
$429$	23.9365	+	8.01980i	1.15567	+	0.387200i
$430$		0			0
$431$	28.4988	−	16.4538i	1.37274	−	0.792551i	0.381466	−	0.924383i	$-0.375419\pi$
$431$	28.4988	−	16.4538i	1.37274	−	0.792551i	0.991272	+	0.131832i	$0.0420859\pi$
$432$		0			0
$433$		−	9.33359i		−	0.448544i	−0.974527	−	0.224272i	$-0.928000\pi$
$433$		−	9.33359i		−	0.448544i	0.974527	−	0.224272i	$-0.0720004\pi$
$434$		0			0
$435$	−16.1343	+	3.27577i	−0.773580	+	0.157061i
$436$		0			0
$437$	2.55939			0.122432
$438$		0			0
$439$			12.8595i			0.613749i	0.951750	+	0.306874i	$0.0992832\pi$
$439$			12.8595i			0.613749i	−0.951750	+	0.306874i	$0.900717\pi$
$440$		0			0
$441$	6.44939	−	19.9851i	0.307114	−	0.951673i
$442$		0			0
$443$		−	13.1076i		−	0.622759i	−0.950286	−	0.311380i	$-0.899209\pi$
$443$		−	13.1076i		−	0.622759i	0.950286	−	0.311380i	$-0.100791\pi$
$444$		0			0
$445$	−12.4080			−0.588198
$446$		0			0
$447$	−4.42909	+	13.2194i	−0.209489	+	0.625256i
$448$		0			0
$449$		−	32.7885i		−	1.54738i	−0.633562	−	0.773692i	$-0.718408\pi$
$449$		−	32.7885i		−	1.54738i	0.633562	−	0.773692i	$-0.281592\pi$
$450$		0			0
$451$	−32.2929	+	18.6443i	−1.52062	+	0.877928i
$452$		0			0
$453$	−3.41100	−	16.8003i	−0.160263	−	0.789349i
$454$		0			0
$455$	1.29615	−	13.6622i	0.0607647	−	0.640492i
$456$		0			0
$457$	−2.12533			−0.0994188			−0.0497094	−	0.998764i	$-0.515830\pi$
$457$	−2.12533			−0.0994188			−0.0497094	+	0.998764i	$0.515830\pi$
$458$		0			0
$459$	−3.71499	+	7.76440i	−0.173401	+	0.362411i
$460$		0			0
$461$	−2.85188	−	4.93960i	−0.132825	−	0.230060i	0.791939	−	0.610600i	$-0.209072\pi$
$461$	−2.85188	−	4.93960i	−0.132825	−	0.230060i	−0.924765	+	0.380540i	$0.875738\pi$
$462$		0			0
$463$	−8.05230	+	13.9470i	−0.374222	+	0.648171i	−0.990210	−	0.139584i	$-0.955424\pi$
$463$	−8.05230	+	13.9470i	−0.374222	+	0.648171i	0.615988	+	0.787755i	$0.288757\pi$
$464$		0			0
$465$	0.688606	−	2.05527i	0.0319333	−	0.0953107i
$466$		0			0
$467$	−15.8271	+	27.4133i	−0.732390	+	1.26854i	0.223470	+	0.974711i	$0.428262\pi$
$467$	−15.8271	+	27.4133i	−0.732390	+	1.26854i	−0.955859	+	0.293825i	$0.905072\pi$
$468$		0			0
$469$	5.80942	+	0.551151i	0.268254	+	0.0254498i
$470$		0			0
$471$	5.11209	+	5.78288i	0.235553	+	0.266461i
$472$		0			0
$473$		−	26.6319i		−	1.22454i
$474$		0			0
$475$	17.2288	−	9.94704i	0.790511	−	0.456402i
$476$		0			0
$477$	−14.1725	−	33.4634i	−0.648913	−	1.53219i
$478$		0			0
$479$	−0.421286	+	0.729689i	−0.0192490	+	0.0333403i	−0.875489	−	0.483237i	$-0.839461\pi$
$479$	−0.421286	+	0.729689i	−0.0192490	+	0.0333403i	0.856240	+	0.516578i	$0.172794\pi$
$480$		0			0
$481$	36.0135	−	20.7924i	1.64207	−	0.948052i
$482$		0			0
$483$	−0.799463	+	1.80047i	−0.0363768	+	0.0819241i
$484$		0			0
$485$	−10.5712	−	6.10330i	−0.480015	−	0.277137i
$486$		0			0
$487$	−7.66039	−	13.2682i	−0.347125	−	0.601239i	0.638612	−	0.769529i	$-0.279509\pi$
$487$	−7.66039	−	13.2682i	−0.347125	−	0.601239i	−0.985738	+	0.168290i	$0.946175\pi$
$488$		0			0
$489$	7.02077	+	34.5797i	0.317490	+	1.56375i
$490$		0			0
$491$	33.0568	+	19.0854i	1.49183	+	0.861311i	0.999956	−	0.00935358i	$-0.00297738\pi$
$491$	33.0568	+	19.0854i	1.49183	+	0.861311i	0.491878	+	0.870664i	$0.336311\pi$
$492$		0			0
$493$	−10.5882	−	6.11308i	−0.476867	−	0.275319i
$494$		0			0
$495$	13.8750	+	1.71503i	0.623637	+	0.0770847i
$496$		0			0
$497$	−0.916658	+	9.66206i	−0.0411177	+	0.433403i
$498$		0			0
$499$	15.7425	+	27.2667i	0.704729	+	1.22063i	0.966789	+	0.255575i	$0.0822648\pi$
$499$	15.7425	+	27.2667i	0.704729	+	1.22063i	−0.262060	+	0.965052i	$0.584402\pi$
$500$		0			0
$501$	−2.98116	−	14.6832i	−0.133188	−	0.655999i
$502$		0			0
$503$	8.17333			0.364431			0.182215	−	0.983259i	$-0.441673\pi$
$503$	8.17333			0.364431			0.182215	+	0.983259i	$0.441673\pi$
$504$		0			0
$505$	6.54582			0.291285
$506$		0			0
$507$	5.29206	+	1.77308i	0.235029	+	0.0787452i
$508$		0			0
$509$	17.0070	+	29.4571i	0.753824	+	1.30566i	0.945957	+	0.324293i	$0.105126\pi$
$509$	17.0070	+	29.4571i	0.753824	+	1.30566i	−0.192133	+	0.981369i	$0.561540\pi$
$510$		0			0
$511$	4.64831	−	2.12624i	0.205629	−	0.0940595i
$512$		0			0
$513$	−2.38983	−	30.8437i	−0.105514	−	1.36178i
$514$		0			0
$515$	8.90505	+	5.14133i	0.392403	+	0.226554i
$516$		0			0
$517$	25.1729	+	14.5336i	1.10710	+	0.639187i
$518$		0			0
$519$	−8.86903	+	7.84027i	−0.389307	+	0.344150i
$520$		0			0
$521$	19.4829	+	33.7453i	0.853560	+	1.47841i	0.877975	+	0.478707i	$0.158894\pi$
$521$	19.4829	+	33.7453i	0.853560	+	1.47841i	−0.0244152	+	0.999702i	$0.507772\pi$
$522$		0			0
$523$	10.7099	+	6.18335i	0.468311	+	0.270379i	0.715532	−	0.698580i	$-0.246184\pi$
$523$	10.7099	+	6.18335i	0.468311	+	0.270379i	−0.247222	+	0.968959i	$0.579518\pi$
$524$		0			0
$525$	1.61583	+	15.2271i	0.0705208	+	0.664566i
$526$		0			0
$527$	1.39402	−	0.804839i	0.0607246	−	0.0350594i
$528$		0			0
$529$	−11.4076	+	19.7585i	−0.495983	+	0.859067i
$530$		0			0
$531$	−0.455304	+	3.68354i	−0.0197585	+	0.159852i
$532$		0			0
$533$	−35.9433	+	20.7519i	−1.55688	+	0.898863i
$534$		0			0
$535$		−	17.8794i		−	0.772995i
$536$		0			0
$537$	−11.0949	+	33.1148i	−0.478782	+	1.42901i
$538$		0			0
$539$	−19.1638	−	16.5646i	−0.825443	−	0.713486i
$540$		0			0
$541$	11.0001	−	19.0528i	0.472932	−	0.819143i	−0.526588	−	0.850121i	$-0.676529\pi$
$541$	11.0001	−	19.0528i	0.472932	−	0.819143i	0.999520	+	0.0309781i	$0.00986222\pi$
$542$		0			0
$543$	−21.4862	−	24.3055i	−0.922062	−	1.04305i
$544$		0			0
$545$	11.1339	−	19.2845i	0.476925	−	0.826058i
$546$		0			0
$547$	−8.74089	−	15.1397i	−0.373733	−	0.647325i	0.616403	−	0.787431i	$-0.288589\pi$
$547$	−8.74089	−	15.1397i	−0.373733	−	0.647325i	−0.990137	+	0.140105i	$0.955256\pi$
$548$		0			0
$549$	−19.7809	−	2.44502i	−0.844228	−	0.104351i
$550$		0			0
$551$	43.9426			1.87202
$552$		0			0
$553$	11.9224	+	1.13110i	0.506993	+	0.0480994i
$554$		0			0
$555$	17.2548	−	15.2533i	0.732426	−	0.647468i
$556$		0			0
$557$	26.1236	−	15.0825i	1.10689	−	0.639065i	0.168870	−	0.985638i	$-0.445988\pi$
$557$	26.1236	−	15.0825i	1.10689	−	0.639065i	0.938023	+	0.346574i	$0.112655\pi$
$558$		0			0
$559$		−	29.6423i		−	1.25374i
$560$		0			0
$561$	6.87642	+	7.77871i	0.290322	+	0.328417i
$562$		0			0
$563$	−24.3050			−1.02433			−0.512167	−	0.858886i	$-0.671157\pi$
$563$	−24.3050			−1.02433			−0.512167	+	0.858886i	$0.671157\pi$
$564$		0			0
$565$			3.29395i			0.138578i
$566$		0			0
$567$	22.4443	+	7.95329i	0.942571	+	0.334007i
$568$		0			0
$569$		−	3.72023i		−	0.155960i	−0.996955	−	0.0779800i	$-0.975153\pi$
$569$		−	3.72023i		−	0.155960i	0.996955	−	0.0779800i	$-0.0248470\pi$
$570$		0			0
$571$	9.14578			0.382739			0.191370	−	0.981518i	$-0.438707\pi$
$571$	9.14578			0.382739			0.191370	+	0.981518i	$0.438707\pi$
$572$		0			0
$573$	5.41328	+	6.12359i	0.226143	+	0.255817i
$574$		0			0
$575$		−	1.43645i		−	0.0599043i
$576$		0			0
$577$	−21.2849	+	12.2888i	−0.886102	+	0.511591i	−0.872665	−	0.488319i	$-0.837610\pi$
$577$	−21.2849	+	12.2888i	−0.886102	+	0.511591i	−0.0134362	+	0.999910i	$0.504277\pi$
$578$		0			0
$579$	−23.7080	+	20.9580i	−0.985271	+	0.870984i
$580$		0			0
$581$	1.54369	+	3.37474i	0.0640429	+	0.140008i
$582$		0			0
$583$	−43.8349			−1.81546
$584$		0			0
$585$	15.4435	+	1.90889i	0.638509	+	0.0789230i
$586$		0			0
$587$	−12.9573	−	22.4427i	−0.534804	−	0.926308i	−0.999173	−	0.0406661i	$-0.987052\pi$
$587$	−12.9573	−	22.4427i	−0.534804	−	0.926308i	0.464369	−	0.885642i	$-0.346281\pi$
$588$		0			0
$589$	−2.89271	+	5.01032i	−0.119192	+	0.206446i
$590$		0			0
$591$	−1.21906	−	1.37902i	−0.0501453	−	0.0567252i
$592$		0			0
$593$	−3.69371	+	6.39770i	−0.151683	+	0.262722i	−0.931846	−	0.362854i	$-0.881803\pi$
$593$	−3.69371	+	6.39770i	−0.151683	+	0.262722i	0.780164	+	0.625576i	$0.215136\pi$
$594$		0			0
$595$	3.27112	−	4.59959i	0.134103	−	0.188565i
$596$		0			0
$597$	12.8433	−	38.3331i	0.525641	−	1.56887i
$598$		0			0
$599$		−	9.46757i		−	0.386834i	−0.981117	−	0.193417i	$-0.938043\pi$
$599$		−	9.46757i		−	0.386834i	0.981117	−	0.193417i	$-0.0619571\pi$
$600$		0			0
$601$	−22.5792	+	13.0361i	−0.921026	+	0.531754i	−0.883962	−	0.467559i	$-0.845134\pi$
$601$	−22.5792	+	13.0361i	−0.921026	+	0.531754i	−0.0370635	+	0.999313i	$0.511800\pi$
$602$		0			0
$603$	−0.811699	+	6.56687i	−0.0330549	+	0.267424i
$604$		0			0
$605$	1.34874	−	2.33609i	0.0548342	−	0.0949756i
$606$		0			0
$607$	6.67114	−	3.85158i	0.270773	−	0.156331i	−0.358466	−	0.933543i	$-0.616700\pi$
$607$	6.67114	−	3.85158i	0.270773	−	0.156331i	0.629239	+	0.777212i	$0.283367\pi$
$608$		0			0
$609$	−13.7261	+	30.9125i	−0.556209	+	1.25264i
$610$		0			0
$611$	28.0185	+	16.1765i	1.13351	+	0.654430i
$612$		0			0
$613$	10.5402	+	18.2561i	0.425713	+	0.737357i	0.996487	−	0.0837506i	$-0.0266899\pi$
$613$	10.5402	+	18.2561i	0.425713	+	0.737357i	−0.570774	+	0.821108i	$0.693357\pi$
$614$		0			0
$615$	−17.2212	+	15.2236i	−0.694425	+	0.613875i
$616$		0			0
$617$	−36.0311	−	20.8026i	−1.45056	−	0.837480i	−0.452045	−	0.891995i	$-0.649305\pi$
$617$	−36.0311	−	20.8026i	−1.45056	−	0.837480i	−0.998513	+	0.0545150i	$0.982639\pi$
$618$		0			0
$619$	6.84409	+	3.95144i	0.275087	+	0.158822i	0.631197	−	0.775622i	$-0.282564\pi$
$619$	6.84409	+	3.95144i	0.275087	+	0.158822i	−0.356110	+	0.934444i	$0.615897\pi$
$620$		0			0
$621$	−2.01498	−	0.964098i	−0.0808584	−	0.0386879i
$622$		0			0
$623$	−14.7737	+	20.7737i	−0.591897	+	0.832279i
$624$		0			0
$625$	−1.43647	−	2.48803i	−0.0574587	−	0.0995214i
$626$		0			0
$627$	−35.3825	−	11.8547i	−1.41304	−	0.473433i
$628$		0			0
$629$	17.1028			0.681934
$630$		0			0
$631$	−6.17105			−0.245666			−0.122833	−	0.992427i	$-0.539198\pi$
$631$	−6.17105			−0.245666			−0.122833	+	0.992427i	$0.539198\pi$
$632$		0			0
$633$	0.110750	+	0.545481i	0.00440191	+	0.0216809i
$634$		0			0
$635$	−9.56326	−	16.5641i	−0.379506	−	0.657325i
$636$		0			0
$637$	−21.3300	−	18.4370i	−0.845127	−	0.730500i
$638$		0			0
$639$	−10.9218	−	1.34999i	−0.432061	−	0.0534049i
$640$		0			0
$641$	14.1897	+	8.19244i	0.560461	+	0.323582i	0.753330	−	0.657642i	$-0.228446\pi$
$641$	14.1897	+	8.19244i	0.560461	+	0.323582i	−0.192870	+	0.981224i	$0.561779\pi$
$642$		0			0
$643$	32.0125	+	18.4824i	1.26245	+	0.728875i	0.973548	−	0.228484i	$-0.0733769\pi$
$643$	32.0125	+	18.4824i	1.26245	+	0.728875i	0.288901	+	0.957359i	$0.406710\pi$
$644$		0			0
$645$	−3.26639	−	16.0881i	−0.128614	−	0.633468i
$646$		0			0
$647$	−2.45759	−	4.25667i	−0.0966179	−	0.167347i	0.813665	−	0.581334i	$-0.197469\pi$
$647$	−2.45759	−	4.25667i	−0.0966179	−	0.167347i	−0.910283	+	0.413987i	$0.864136\pi$
$648$		0			0
$649$	3.87716	+	2.23848i	0.152192	+	0.0878679i
$650$		0			0
$651$	−2.62105	−	3.59999i	−0.102727	−	0.141095i
$652$		0			0
$653$	29.9198	−	17.2742i	1.17085	−	0.675991i	0.216970	−	0.976178i	$-0.430383\pi$
$653$	29.9198	−	17.2742i	1.17085	−	0.675991i	0.953880	+	0.300187i	$0.0970492\pi$
$654$		0			0
$655$	−5.04855	+	8.74435i	−0.197263	+	0.341670i
$656$		0			0
$657$	2.26033	+	5.33700i	0.0881841	+	0.208216i
$658$		0			0
$659$	15.7392	−	9.08706i	0.613114	−	0.353982i	−0.161069	−	0.986943i	$-0.551494\pi$
$659$	15.7392	−	9.08706i	0.613114	−	0.353982i	0.774183	+	0.632962i	$0.218161\pi$
$660$		0			0
$661$		−	6.74459i		−	0.262334i	−0.991360	−	0.131167i	$-0.958128\pi$
$661$		−	6.74459i		−	0.262334i	0.991360	−	0.131167i	$-0.0418724\pi$
$662$		0			0
$663$	7.65372	+	8.65800i	0.297246	+	0.336249i
$664$		0			0
$665$	−1.91595	+	20.1952i	−0.0742975	+	0.783136i
$666$		0			0
$667$	1.58644	−	2.74779i	0.0614272	−	0.106395i
$668$		0			0
$669$	6.12886	−	18.2926i	0.236955	−	0.707235i
$670$		0			0
$671$	−12.0208	+	20.8206i	−0.464057	+	0.803771i
$672$		0			0
$673$	11.0845	+	19.1990i	0.427277	+	0.740066i	0.996630	−	0.0820274i	$-0.0261395\pi$
$673$	11.0845	+	19.1990i	0.427277	+	0.740066i	−0.569353	+	0.822093i	$0.692806\pi$
$674$		0			0
$675$	−17.3110	+	1.34129i	−0.666300	+	0.0516262i
$676$		0			0
$677$	2.79838			0.107551			0.0537753	−	0.998553i	$-0.482875\pi$
$677$	2.79838			0.107551			0.0537753	+	0.998553i	$0.482875\pi$
$678$		0			0
$679$	−22.8049	+	10.4315i	−0.875172	+	0.400324i
$680$		0			0
$681$	−9.38607	−	46.2296i	−0.359675	−	1.77152i
$682$		0			0
$683$	−21.9835	+	12.6922i	−0.841175	+	0.485653i	−0.857663	−	0.514211i	$-0.828085\pi$
$683$	−21.9835	+	12.6922i	−0.841175	+	0.485653i	0.0164884	+	0.999864i	$0.494751\pi$
$684$		0			0
$685$		−	16.7116i		−	0.638516i
$686$		0			0
$687$	−9.04537	+	26.9975i	−0.345102	+	1.03002i
$688$		0			0
$689$	−48.7900			−1.85875
$690$		0			0
$691$			49.7094i			1.89103i	0.325574	+	0.945517i	$0.394442\pi$
$691$			49.7094i			1.89103i	−0.325574	+	0.945517i	$0.605558\pi$
$692$		0			0
$693$	19.3917	−	21.1877i	0.736632	−	0.804855i
$694$		0			0
$695$		−	19.3377i		−	0.733519i
$696$		0			0
$697$	−17.0695			−0.646553
$698$		0			0
$699$	6.57939	−	1.33582i	0.248855	−	0.0505255i
$700$		0			0
$701$		−	12.5554i		−	0.474212i	−0.971484	−	0.237106i	$-0.923801\pi$
$701$		−	12.5554i		−	0.474212i	0.971484	−	0.237106i	$-0.0761988\pi$
$702$		0			0
$703$	−53.2346	+	30.7350i	−2.00778	+	1.15919i
$704$		0			0
$705$	16.9893	+	5.69218i	0.639854	+	0.214380i
$706$		0			0
$707$	7.79383	−	10.9591i	0.293117	−	0.412158i
$708$		0			0
$709$	30.9465			1.16222			0.581110	−	0.813825i	$-0.302619\pi$
$709$	30.9465			1.16222			0.581110	+	0.813825i	$0.302619\pi$
$710$		0			0
$711$	−1.66582	+	13.4769i	−0.0624729	+	0.505424i
$712$		0			0
$713$	0.208868	+	0.361770i	0.00782218	+	0.0135484i
$714$		0			0
$715$	9.38495	−	16.2552i	0.350977	−	0.607911i
$716$		0			0
$717$	−24.1327	+	4.89970i	−0.901252	+	0.182982i
$718$		0			0
$719$	25.2520	−	43.7377i	0.941740	−	1.63114i	0.179591	−	0.983741i	$-0.442523\pi$
$719$	25.2520	−	43.7377i	0.941740	−	1.63114i	0.762150	−	0.647401i	$-0.224144\pi$
$720$		0			0
$721$	19.2105	−	8.78734i	0.715437	−	0.327258i
$722$		0			0
$723$	11.9459	−	2.42539i	0.444272	−	0.0902013i
$724$		0			0
$725$		−	24.6627i		−	0.915949i
$726$		0			0
$727$	3.87884	−	2.23945i	0.143858	−	0.0830565i	−0.426343	−	0.904561i	$-0.640198\pi$
$727$	3.87884	−	2.23945i	0.143858	−	0.0830565i	0.570201	+	0.821505i	$0.306865\pi$
$728$		0			0
$729$	−9.73703	+	25.1831i	−0.360631	+	0.932709i
$730$		0			0
$731$	6.09559	−	10.5579i	0.225453	−	0.390497i
$732$		0			0
$733$	15.6407	−	9.03013i	0.577701	−	0.333536i	−0.182518	−	0.983202i	$-0.558425\pi$
$733$	15.6407	−	9.03013i	0.577701	−	0.333536i	0.760219	+	0.649667i	$0.225092\pi$
$734$		0			0
$735$	−13.6083	−	7.65608i	−0.501950	−	0.282399i
$736$		0			0
$737$	6.91204	+	3.99067i	0.254608	+	0.146998i
$738$		0			0
$739$	−0.816296	−	1.41387i	−0.0300279	−	0.0520099i	0.850621	−	0.525779i	$-0.176226\pi$
$739$	−0.816296	−	1.41387i	−0.0300279	−	0.0520099i	−0.880649	+	0.473770i	$0.842893\pi$
$740$		0			0
$741$	−39.3821	−	13.1948i	−1.44674	−	0.484722i
$742$		0			0
$743$	4.79074	+	2.76593i	0.175755	+	0.101472i	0.585297	−	0.810819i	$-0.300978\pi$
$743$	4.79074	+	2.76593i	0.175755	+	0.101472i	−0.409542	+	0.912291i	$0.634311\pi$
$744$		0			0
$745$	8.97726	+	5.18302i	0.328901	+	0.189891i
$746$		0			0
$747$	−3.87475	+	1.64104i	−0.141770	+	0.0600424i
$748$		0			0
$749$	−29.9339	−	21.2883i	−1.09376	−	0.777857i
$750$		0			0
$751$	−24.1359	−	41.8046i	−0.880731	−	1.52547i	−0.850530	−	0.525927i	$-0.823719\pi$
$751$	−24.1359	−	41.8046i	−0.880731	−	1.52547i	−0.0302009	−	0.999544i	$-0.509615\pi$
$752$		0			0
$753$	−25.4406	+	22.4896i	−0.927107	+	0.819568i
$754$		0			0
$755$	−12.7464			−0.463891
$756$		0			0
$757$	27.5867			1.00266			0.501328	−	0.865257i	$-0.332845\pi$
$757$	27.5867			1.00266			0.501328	+	0.865257i	$0.332845\pi$
$758$		0			0
$759$	−2.01869	+	1.78454i	−0.0732740	+	0.0647745i
$760$		0			0
$761$	10.9302	+	18.9317i	0.396221	+	0.686274i	0.993256	−	0.115941i	$-0.0369882\pi$
$761$	10.9302	+	18.9317i	0.396221	+	0.686274i	−0.597036	+	0.802215i	$0.703655\pi$
$762$		0			0
$763$	−19.0296	−	41.6018i	−0.688918	−	1.50608i
$764$		0			0
$765$	5.10804	+	3.85566i	0.184682	+	0.139402i
$766$		0			0
$767$	4.31543	+	2.49151i	0.155821	+	0.0899633i
$768$		0			0
$769$	39.0087	+	22.5217i	1.40669	+	0.812153i	0.995067	−	0.0992014i	$-0.0316288\pi$
$769$	39.0087	+	22.5217i	1.40669	+	0.812153i	0.411623	+	0.911354i	$0.364962\pi$
$770$		0			0
$771$	24.3606	+	8.16189i	0.877325	+	0.293943i
$772$		0			0
$773$	0.810759	+	1.40428i	0.0291610	+	0.0505083i	0.880238	−	0.474533i	$-0.157383\pi$
$773$	0.810759	+	1.40428i	0.0291610	+	0.0505083i	−0.851077	+	0.525041i	$0.824050\pi$
$774$		0			0
$775$	2.81203	+	1.62353i	0.101011	+	0.0583188i
$776$		0			0
$777$	−4.99270	−	47.0497i	−0.179112	−	1.68790i
$778$		0			0
$779$	53.1308	−	30.6751i	1.90361	−	1.09905i
$780$		0			0
$781$	−6.63716	+	11.4959i	−0.237496	+	0.411356i
$782$		0			0
$783$	−34.5955	−	16.5527i	−1.23634	−	0.591546i
$784$		0			0
$785$	4.97007	−	2.86947i	0.177389	−	0.102416i
$786$		0			0
$787$		−	16.1931i		−	0.577223i	−0.957446	−	0.288612i	$-0.906806\pi$
$787$		−	16.1931i		−	0.577223i	0.957446	−	0.288612i	$-0.0931937\pi$
$788$		0			0
$789$	20.9692	−	4.25740i	0.746522	−	0.151567i
$790$		0			0
$791$	5.51476	+	3.92197i	0.196082	+	0.139449i
$792$		0			0
$793$	−13.3796	+	23.1742i	−0.475124	+	0.822939i
$794$		0			0
$795$	−26.4803	+	5.37634i	−0.939160	+	0.190679i
$796$		0			0
$797$	20.7822	−	35.9958i	0.736142	−	1.27504i	−0.218078	−	0.975931i	$-0.569979\pi$
$797$	20.7822	−	35.9958i	0.736142	−	1.27504i	0.954220	−	0.299105i	$-0.0966880\pi$
$798$		0			0
$799$	6.65299	+	11.5233i	0.235366	+	0.407666i
$800$		0			0
$801$	−23.0701	−	17.4138i	−0.815140	−	0.615286i
$802$		0			0
$803$	6.99113			0.246712
$804$		0			0
$805$	1.19366	+	0.848905i	0.0420711	+	0.0299200i
$806$		0			0
$807$	−32.7544	−	10.9742i	−1.15301	−	0.386310i
$808$		0			0
$809$	−5.22143	+	3.01459i	−0.183576	+	0.105987i	−0.588972	−	0.808154i	$-0.700467\pi$
$809$	−5.22143	+	3.01459i	−0.183576	+	0.105987i	0.405396	+	0.914141i	$0.367134\pi$
$810$		0			0
$811$			21.4651i			0.753741i	0.926266	+	0.376870i	$0.123000\pi$
$811$			21.4651i			0.753741i	−0.926266	+	0.376870i	$0.877000\pi$
$812$		0			0
$813$	−25.1034	+	5.09678i	−0.880415	+	0.178752i
$814$		0			0
$815$	26.2357			0.918996
$816$		0			0
$817$			43.8168i			1.53296i
$818$		0			0
$819$	21.5838	−	23.5828i	0.754198	−	0.824048i
$820$		0			0
$821$		−	10.8900i		−	0.380064i	−0.981778	−	0.190032i	$-0.939141\pi$
$821$		−	10.8900i		−	0.380064i	0.981778	−	0.190032i	$-0.0608592\pi$
$822$		0			0
$823$	40.2819			1.40414			0.702070	−	0.712108i	$-0.252259\pi$
$823$	40.2819			1.40414			0.702070	+	0.712108i	$0.252259\pi$
$824$		0			0
$825$	−6.65345	+	19.8584i	−0.231643	+	0.691380i
$826$		0			0
$827$		−	42.1373i		−	1.46526i	−0.680628	−	0.732630i	$-0.738293\pi$
$827$		−	42.1373i		−	1.46526i	0.680628	−	0.732630i	$-0.261707\pi$
$828$		0			0
$829$	0.335936	−	0.193953i	0.0116675	−	0.00673626i	−0.494155	−	0.869374i	$-0.664522\pi$
$829$	0.335936	−	0.193953i	0.0116675	−	0.00673626i	0.505822	+	0.862638i	$0.331189\pi$
$830$		0			0
$831$	−3.08555	−	15.1974i	−0.107037	−	0.527192i
$832$		0			0
$833$	−3.80589	−	10.9531i	−0.131866	−	0.379501i
$834$		0			0
$835$	−11.1402			−0.385522
$836$		0			0
$837$	4.16473	−	2.85491i	0.143954	−	0.0986802i
$838$		0			0
$839$	−12.5586	−	21.7522i	−0.433572	−	0.750969i	0.563606	−	0.826044i	$-0.309414\pi$
$839$	−12.5586	−	21.7522i	−0.433572	−	0.750969i	−0.997178	+	0.0750750i	$0.976080\pi$
$840$		0			0
$841$	12.7378	−	22.0625i	0.439234	−	0.760776i
$842$		0			0
$843$	11.6535	−	34.7820i	0.401369	−	1.19796i
$844$		0			0
$845$	2.07490	−	3.59383i	0.0713786	−	0.123631i
$846$		0			0
$847$	−2.30521	−	5.03956i	−0.0792080	−	0.173161i
$848$		0			0
$849$	−29.2767	−	33.1182i	−1.00477	−	1.13661i
$850$		0			0
$851$			4.43845i			0.152148i
$852$		0			0
$853$	−43.7344	+	25.2501i	−1.49744	+	0.864546i	−0.999996	−	0.00295209i	$-0.999060\pi$
$853$	−43.7344	+	25.2501i	−1.49744	+	0.864546i	−0.497441	+	0.867498i	$0.665727\pi$
$854$		0			0
$855$	−22.8283	−	2.82169i	−0.780711	−	0.0964998i
$856$		0			0
$857$	−3.90851	+	6.76974i	−0.133512	+	0.231250i	−0.925028	−	0.379899i	$-0.875959\pi$
$857$	−3.90851	+	6.76974i	−0.133512	+	0.231250i	0.791516	+	0.611149i	$0.209292\pi$
$858$		0			0
$859$	−0.649739	+	0.375127i	−0.0221688	+	0.0127992i	−0.511043	−	0.859555i	$-0.670741\pi$
$859$	−0.649739	+	0.375127i	−0.0221688	+	0.0127992i	0.488875	+	0.872354i	$0.337408\pi$
$860$		0			0
$861$	4.98297	+	46.9580i	0.169819	+	1.60032i
$862$		0			0
$863$	19.7963	+	11.4294i	0.673873	+	0.389061i	0.797543	−	0.603263i	$-0.206133\pi$
$863$	19.7963	+	11.4294i	0.673873	+	0.389061i	−0.123669	+	0.992323i	$0.539466\pi$
$864$		0			0
$865$	4.40083	+	7.62245i	0.149633	+	0.259171i
$866$		0			0
$867$	−4.91305	−	24.1985i	−0.166856	−	0.821823i
$868$		0			0
$869$	14.1853	+	8.18988i	0.481203	+	0.277823i
$870$		0			0
$871$	7.69337	+	4.44177i	0.260680	+	0.150504i
$872$		0			0
$873$	−11.0894	−	26.1837i	−0.375318	−	0.886184i
$874$		0			0
$875$	28.2948	+	2.68438i	0.956538	+	0.0907486i
$876$		0			0
$877$	−7.09473	−	12.2884i	−0.239572	−	0.414951i	0.721020	−	0.692915i	$-0.243674\pi$
$877$	−7.09473	−	12.2884i	−0.239572	−	0.414951i	−0.960592	+	0.277964i	$0.910340\pi$
$878$		0			0
$879$	7.64534	+	37.6559i	0.257871	+	1.27010i
$880$		0			0
$881$	−51.9677			−1.75084			−0.875419	−	0.483365i	$-0.839414\pi$
$881$	−51.9677			−1.75084			−0.875419	+	0.483365i	$0.839414\pi$
$882$		0			0
$883$	−32.7479			−1.10205			−0.551027	−	0.834487i	$-0.685764\pi$
$883$	−32.7479			−1.10205			−0.551027	+	0.834487i	$0.685764\pi$
$884$		0			0
$885$	2.61671	+	0.876714i	0.0879596	+	0.0294704i
$886$		0			0
$887$	−20.7391	−	35.9212i	−0.696351	−	1.20612i	−0.969723	−	0.244207i	$-0.921472\pi$
$887$	−20.7391	−	35.9212i	−0.696351	−	1.20612i	0.273372	−	0.961908i	$-0.411861\pi$
$888$		0			0
$889$	−39.1183	−	3.71122i	−1.31198	−	0.124470i
$890$		0			0
$891$	23.3907	+	22.6613i	0.783618	+	0.759183i
$892$		0			0
$893$	−41.4164	−	23.9118i	−1.38595	−	0.800178i
$894$		0			0
$895$	22.4882	+	12.9835i	0.751696	+	0.433992i
$896$		0			0
$897$	−2.24688	+	1.98626i	−0.0750213	+	0.0663192i
$898$		0			0
$899$	3.58609	+	6.21128i	0.119603	+	0.207158i
$900$		0			0
$901$	−17.3778	−	10.0331i	−0.578938	−	0.334250i
$902$		0			0
$903$	−30.8240	−	13.6868i	−1.02576	−	0.455468i
$904$		0			0
$905$	−20.8893	+	12.0604i	−0.694384	+	0.400903i
$906$		0			0
$907$	18.5974	−	32.2116i	0.617515	−	1.06957i	−0.372423	−	0.928063i	$-0.621473\pi$
$907$	18.5974	−	32.2116i	0.617515	−	1.06957i	0.989938	−	0.141504i	$-0.0451939\pi$
$908$		0			0
$909$	12.1705	+	9.18658i	0.403671	+	0.304700i
$910$		0			0
$911$	−17.4555	+	10.0780i	−0.578328	+	0.333898i	−0.760468	−	0.649375i	$-0.775031\pi$
$911$	−17.4555	+	10.0780i	−0.578328	+	0.333898i	0.182141	+	0.983272i	$0.441697\pi$
$912$		0			0
$913$			5.07567i			0.167980i
$914$		0			0
$915$	−4.70802	+	14.0519i	−0.155642	+	0.464542i
$916$		0			0
$917$	8.62877	+	18.8639i	0.284947	+	0.622939i
$918$		0			0
$919$	17.0665	−	29.5601i	0.562972	−	0.975097i	−0.434263	−	0.900786i	$-0.642991\pi$
$919$	17.0665	−	29.5601i	0.562972	−	0.975097i	0.997235	−	0.0743104i	$-0.0236755\pi$
$920$		0			0
$921$	−18.2168	−	20.6071i	−0.600264	−	0.679028i
$922$		0			0
$923$	−7.38742	+	12.7954i	−0.243160	+	0.421165i
$924$		0			0
$925$	17.2499	+	29.8778i	0.567175	+	0.982376i
$926$		0			0
$927$	9.34151	+	22.0568i	0.306815	+	0.724439i
$928$		0			0
$929$	26.3923			0.865905			0.432952	−	0.901417i	$-0.357472\pi$
$929$	26.3923			0.865905			0.432952	+	0.901417i	$0.357472\pi$
$930$		0			0
$931$	31.5297	+	27.2533i	1.03334	+	0.893189i
$932$		0			0
$933$	8.25049	−	7.29347i	0.270109	−	0.238778i
$934$		0			0
$935$	6.68538	−	3.85980i	0.218635	−	0.126229i
$936$		0			0
$937$			37.8276i			1.23577i	0.786267	+	0.617887i	$0.212011\pi$
$937$			37.8276i			1.23577i	−0.786267	+	0.617887i	$0.787989\pi$
$938$		0			0
$939$	−20.3777	−	23.0515i	−0.665000	−	0.752258i
$940$		0			0
$941$	33.7504			1.10023			0.550115	−	0.835089i	$-0.314584\pi$
$941$	33.7504			1.10023			0.550115	+	0.835089i	$0.314584\pi$
$942$		0			0
$943$		−	4.42979i		−	0.144254i
$944$		0			0
$945$	9.11573	−	15.1777i	0.296535	−	0.493731i
$946$		0			0
$947$			9.40083i			0.305486i	0.988266	+	0.152743i	$0.0488106\pi$
$947$			9.40083i			0.305486i	−0.988266	+	0.152743i	$0.951189\pi$
$948$		0			0
$949$	7.78140			0.252595
$950$		0			0
$951$	35.3348	+	39.9713i	1.14581	+	1.29616i
$952$		0			0
$953$			29.9023i			0.968630i	0.874894	+	0.484315i	$0.160931\pi$
$953$			29.9023i			0.968630i	−0.874894	+	0.484315i	$0.839069\pi$
$954$		0			0
$955$	5.26289	−	3.03853i	0.170303	−	0.0983246i
$956$		0			0
$957$	−34.6592	+	30.6389i	−1.12037	+	0.990416i
$958$		0			0
$959$	−27.9787	−	19.8978i	−0.903478	−	0.642532i
$960$		0			0
$961$	30.0557			0.969539
$962$		0			0
$963$	25.0925	−	33.2429i	0.808594	−	1.07124i
$964$		0			0
$965$	11.7639	+	20.3757i	0.378695	+	0.655918i
$966$		0			0
$967$	2.77164	−	4.80062i	0.0891300	−	0.154378i	−0.818014	−	0.575199i	$-0.804925\pi$
$967$	2.77164	−	4.80062i	0.0891300	−	0.154378i	0.907144	+	0.420821i	$0.138258\pi$
$968$		0			0
$969$	−11.3136	−	12.7981i	−0.363445	−	0.411135i
$970$		0			0
$971$	−7.73537	+	13.3981i	−0.248240	+	0.429964i	−0.963038	−	0.269367i	$-0.913185\pi$
$971$	−7.73537	+	13.3981i	−0.248240	+	0.429964i	0.714798	+	0.699331i	$0.246519\pi$
$972$		0			0
$973$	−32.3753	−	23.0245i	−1.03790	−	0.738133i
$974$		0			0
$975$	−7.40554	+	22.1031i	−0.237167	+	0.707867i
$976$		0			0
$977$			19.0544i			0.609605i	0.952416	+	0.304802i	$0.0985904\pi$
$977$			19.0544i			0.609605i	−0.952416	+	0.304802i	$0.901410\pi$
$978$		0			0
$979$	−30.1940	+	17.4325i	−0.965003	+	0.557145i
$980$		0			0
$981$	47.7655	−	20.2297i	1.52504	−	0.645885i
$982$		0			0
$983$	−17.2586	+	29.8927i	−0.550463	+	0.953430i	0.447778	+	0.894145i	$0.352215\pi$
$983$	−17.2586	+	29.8927i	−0.550463	+	0.953430i	−0.998241	+	0.0592852i	$0.981118\pi$
$984$		0			0
$985$	−1.18519	+	0.684270i	−0.0377633	+	0.0218026i
$986$		0			0
$987$	29.7583	−	21.6662i	0.947219	−	0.689643i
$988$		0			0
$989$	2.73993	+	1.58190i	0.0871246	+	0.0503014i
$990$		0			0
$991$	20.2633	+	35.0971i	0.643685	+	1.11490i	0.984603	+	0.174803i	$0.0559288\pi$
$991$	20.2633	+	35.0971i	0.643685	+	1.11490i	−0.340918	+	0.940093i	$0.610738\pi$
$992$		0			0
$993$	−22.8475	+	20.1973i	−0.725043	+	0.640942i
$994$		0			0
$995$	−26.0319	−	15.0295i	−0.825267	−	0.476468i
$996$		0			0
$997$	35.8376	+	20.6908i	1.13499	+	0.655285i	0.945184	−	0.326537i	$-0.105882\pi$
$997$	35.8376	+	20.6908i	1.13499	+	0.655285i	0.189803	+	0.981822i	$0.439215\pi$
$998$		0			0
$999$	53.4885	−	4.14439i	1.69230	−	0.131123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.257.20	✓	48
3.2	odd	2		1512.2.bs.a.1097.17		48
4.3	odd	2		1008.2.ca.e.257.5		48
7.3	odd	6		504.2.cx.a.185.21	yes	48
9.2	odd	6		504.2.cx.a.425.21	yes	48
9.7	even	3		1512.2.cx.a.89.17		48
12.11	even	2		3024.2.ca.e.2609.17		48
21.17	even	6		1512.2.cx.a.17.17		48
28.3	even	6		1008.2.df.e.689.4		48
36.7	odd	6		3024.2.df.e.1601.17		48
36.11	even	6		1008.2.df.e.929.4		48
63.38	even	6	inner	504.2.bs.a.353.20	yes	48
63.52	odd	6		1512.2.bs.a.521.17		48
84.59	odd	6		3024.2.df.e.17.17		48
252.115	even	6		3024.2.ca.e.2033.17		48
252.227	odd	6		1008.2.ca.e.353.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.20	✓	48	1.1	even	1	trivial
504.2.bs.a.353.20	yes	48	63.38	even	6	inner
504.2.cx.a.185.21	yes	48	7.3	odd	6
504.2.cx.a.425.21	yes	48	9.2	odd	6
1008.2.ca.e.257.5		48	4.3	odd	2
1008.2.ca.e.353.5		48	252.227	odd	6
1008.2.df.e.689.4		48	28.3	even	6
1008.2.df.e.929.4		48	36.11	even	6
1512.2.bs.a.521.17		48	63.52	odd	6
1512.2.bs.a.1097.17		48	3.2	odd	2
1512.2.cx.a.17.17		48	21.17	even	6
1512.2.cx.a.89.17		48	9.7	even	3
3024.2.ca.e.2033.17		48	252.115	even	6
3024.2.ca.e.2609.17		48	12.11	even	2
3024.2.df.e.17.17		48	84.59	odd	6
3024.2.df.e.1601.17		48	36.7	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29769 - 1.14717i) q^{3} +(-0.643917 - 1.11530i) q^{5} +(-2.63392 - 0.249885i) q^{7} +(0.368015 - 2.97734i) q^{9} +O(q^{10})\)	\(q+(1.29769 - 1.14717i) q^{3} +(-0.643917 - 1.11530i) q^{5} +(-2.63392 - 0.249885i) q^{7} +(0.368015 - 2.97734i) q^{9} +(-3.13384 - 1.80932i) q^{11} +(-3.48808 - 2.01385i) q^{13} +(-2.11504 - 0.708633i) q^{15} +(-0.828246 - 1.43456i) q^{17} +(5.15603 + 2.97683i) q^{19} +(-3.70469 + 2.69728i) q^{21} +(0.372292 - 0.214943i) q^{23} +(1.67074 - 2.89381i) q^{25} +(-2.93794 - 4.28585i) q^{27} +(6.39192 - 3.69038i) q^{29} +0.971739i q^{31} +(-6.14236 + 1.24709i) q^{33} +(1.41733 + 3.09851i) q^{35} +(-5.16236 + 8.94147i) q^{37} +(-6.83668 + 1.38806i) q^{39} +(5.15230 - 8.92404i) q^{41} +(3.67982 + 6.37363i) q^{43} +(-3.55759 + 1.50672i) q^{45} -8.03262 q^{47} +(6.87511 + 1.31636i) q^{49} +(-2.72049 - 0.911487i) q^{51} +(10.4907 - 6.05681i) q^{53} +4.66021i q^{55} +(10.1059 - 2.05181i) q^{57} -1.23719 q^{59} -6.64381i q^{61} +(-1.71332 + 7.75013i) q^{63} +5.18700i q^{65} -2.20562 q^{67} +(0.236545 - 0.706010i) q^{69} -3.66832i q^{71} +(-1.67314 + 0.965987i) q^{73} +(-1.15157 - 5.67190i) q^{75} +(7.80217 + 5.54872i) q^{77} -4.52649 q^{79} +(-8.72913 - 2.19141i) q^{81} +(-0.701322 - 1.21472i) q^{83} +(-1.06664 + 1.84748i) q^{85} +(4.06127 - 12.1216i) q^{87} +(4.81741 - 8.34400i) q^{89} +(8.68412 + 6.17594i) q^{91} +(1.11475 + 1.26102i) q^{93} -7.66734i q^{95} +(8.20853 - 4.73920i) q^{97} +(-6.54027 + 8.66465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

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