LMFDB - Embedded newform 220.3.q.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(29,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.q (of order $10$, degree $4$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	220.29
Dual form			220.3.q.a.129.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.83667 - 1.24661i) q^{3} +(-4.92332 + 0.872318i) q^{5} +(-0.101776 - 0.313235i) q^{7} +(5.88485 + 4.27559i) q^{9} +(7.92623 + 7.62725i) q^{11} +(-5.19406 - 3.77371i) q^{13} +(19.9766 + 2.79066i) q^{15} +(18.3110 - 13.3037i) q^{17} +(26.2028 + 8.51380i) q^{19} +1.32865i q^{21} +26.5778i q^{23} +(23.4781 - 8.58940i) q^{25} +(4.09250 + 5.63285i) q^{27} +(-0.693449 + 0.225315i) q^{29} +(-7.02505 - 5.10400i) q^{31} +(-20.9021 - 39.1441i) q^{33} +(0.774317 + 1.45337i) q^{35} +(-2.92359 + 0.949933i) q^{37} +(15.2236 + 20.9534i) q^{39} +(27.5889 + 8.96419i) q^{41} -53.5197 q^{43} +(-32.7027 - 15.9166i) q^{45} +(62.5341 + 20.3186i) q^{47} +(39.5541 - 28.7377i) q^{49} +(-86.8376 + 28.2152i) q^{51} +(-40.5229 + 55.7749i) q^{53} +(-45.6767 - 30.6372i) q^{55} +(-89.9181 - 65.3293i) q^{57} +(17.7615 + 54.6642i) q^{59} +(-47.9102 - 65.9427i) q^{61} +(0.740328 - 2.27849i) q^{63} +(28.8639 + 14.0483i) q^{65} +65.6000i q^{67} +(33.1321 - 101.970i) q^{69} +(-24.8061 + 18.0227i) q^{71} +(12.8287 + 39.4826i) q^{73} +(-100.785 + 3.68662i) q^{75} +(1.58242 - 3.25904i) q^{77} +(41.8643 - 57.6213i) q^{79} +(-28.9099 - 88.9756i) q^{81} +(90.6212 - 65.8402i) q^{83} +(-78.5456 + 81.4713i) q^{85} +2.94141 q^{87} +76.2467 q^{89} +(-0.653425 + 2.01104i) q^{91} +(20.5901 + 28.3399i) q^{93} +(-136.431 - 19.0590i) q^{95} +(-31.4114 + 43.2341i) q^{97} +(14.0337 + 78.7745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 5 q^{5} + 20 q^{9} - 23 q^{15} - 7 q^{25} - 74 q^{31} + 155 q^{35} + 80 q^{39} - 20 q^{41} + 12 q^{45} + 102 q^{49} + 220 q^{51} - 69 q^{55} + 40 q^{59} - 290 q^{61} - 234 q^{69} - 406 q^{71} + 153 q^{75}+ \cdots - 382 q^{99}+O(q^{100}) $ 48 * q + 5 * q^5 + 20 * q^9 - 23 * q^15 - 7 * q^25 - 74 * q^31 + 155 * q^35 + 80 * q^39 - 20 * q^41 + 12 * q^45 + 102 * q^49 + 220 * q^51 - 69 * q^55 + 40 * q^59 - 290 * q^61 - 234 * q^69 - 406 * q^71 + 153 * q^75 - 280 * q^79 + 230 * q^81 - 465 * q^85 - 636 * q^89 + 512 * q^91 - 495 * q^95 - 382 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$-1$

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
$3$	−3.83667	−	1.24661i	−1.27889	−	0.415537i	−0.410701	−	0.911770i	$-0.634716\pi$
$3$	−3.83667	−	1.24661i	−1.27889	−	0.415537i	−0.868189	+	0.496234i	$0.834716\pi$
$4$		0			0
$5$	−4.92332	+	0.872318i	−0.984664	+	0.174464i
$5$	−4.92332	+	0.872318i	−0.984664	+	0.174464i
$6$		0			0
$7$	−0.101776	−	0.313235i	−0.0145395	−	0.0447479i	0.943524	−	0.331305i	$-0.107489\pi$
$7$	−0.101776	−	0.313235i	−0.0145395	−	0.0447479i	−0.958063	+	0.286558i	$0.907489\pi$
$8$		0			0
$9$	5.88485	+	4.27559i	0.653872	+	0.475066i
$10$		0			0
$11$	7.92623	+	7.62725i	0.720566	+	0.693386i
$11$	7.92623	+	7.62725i	0.720566	+	0.693386i
$12$		0			0
$13$	−5.19406	−	3.77371i	−0.399543	−	0.290285i	0.369812	−	0.929107i	$-0.379422\pi$
$13$	−5.19406	−	3.77371i	−0.399543	−	0.290285i	−0.769355	+	0.638822i	$0.779422\pi$
$14$		0			0
$15$	19.9766	+	2.79066i	1.33177	+	0.186044i
$16$		0			0
$17$	18.3110	−	13.3037i	1.07712	−	0.782570i	0.0999374	−	0.994994i	$-0.468136\pi$
$17$	18.3110	−	13.3037i	1.07712	−	0.782570i	0.977178	+	0.212424i	$0.0681358\pi$
$18$		0			0
$19$	26.2028	+	8.51380i	1.37909	+	0.448095i	0.902372	−	0.430959i	$-0.141825\pi$
$19$	26.2028	+	8.51380i	1.37909	+	0.448095i	0.476723	+	0.879054i	$0.341825\pi$
$20$		0			0
$21$			1.32865i			0.0632693i
$22$		0			0
$23$			26.5778i			1.15556i	0.816194	+	0.577778i	$0.196080\pi$
$23$			26.5778i			1.15556i	−0.816194	+	0.577778i	$0.803920\pi$
$24$		0			0
$25$	23.4781	−	8.58940i	0.939125	−	0.343576i
$26$		0			0
$27$	4.09250	+	5.63285i	0.151574	+	0.208624i
$28$		0			0
$29$	−0.693449	+	0.225315i	−0.0239120	+	0.00776949i	−0.320949	−	0.947097i	$-0.604002\pi$
$29$	−0.693449	+	0.225315i	−0.0239120	+	0.00776949i	0.297037	+	0.954866i	$0.404002\pi$
$30$		0			0
$31$	−7.02505	−	5.10400i	−0.226615	−	0.164645i	0.468685	−	0.883366i	$-0.344728\pi$
$31$	−7.02505	−	5.10400i	−0.226615	−	0.164645i	−0.695299	+	0.718720i	$0.744728\pi$
$32$		0			0
$33$	−20.9021	−	39.1441i	−0.633398	−	1.18619i
$34$		0			0
$35$	0.774317	+	1.45337i	0.0221233	+	0.0415250i
$36$		0			0
$37$	−2.92359	+	0.949933i	−0.0790160	+	0.0256739i	−0.348258	−	0.937399i	$-0.613227\pi$
$37$	−2.92359	+	0.949933i	−0.0790160	+	0.0256739i	0.269242	+	0.963072i	$0.413227\pi$
$38$		0			0
$39$	15.2236	+	20.9534i	0.390348	+	0.537268i
$40$		0			0
$41$	27.5889	+	8.96419i	0.672901	+	0.218639i	0.625485	−	0.780236i	$-0.284901\pi$
$41$	27.5889	+	8.96419i	0.672901	+	0.218639i	0.0474164	+	0.998875i	$0.484901\pi$
$42$		0			0
$43$	−53.5197			−1.24464			−0.622322	−	0.782761i	$-0.713811\pi$
$43$	−53.5197			−1.24464			−0.622322	+	0.782761i	$0.713811\pi$
$44$		0			0
$45$	−32.7027	−	15.9166i	−0.726726	−	0.353703i
$46$		0			0
$47$	62.5341	+	20.3186i	1.33051	+	0.432310i	0.886093	−	0.463508i	$-0.153410\pi$
$47$	62.5341	+	20.3186i	1.33051	+	0.432310i	0.444421	+	0.895818i	$0.353410\pi$
$48$		0			0
$49$	39.5541	−	28.7377i	0.807226	−	0.586484i
$50$		0			0
$51$	−86.8376	+	28.2152i	−1.70270	+	0.553240i
$52$		0			0
$53$	−40.5229	+	55.7749i	−0.764582	+	1.05236i	0.232237	+	0.972659i	$0.425396\pi$
$53$	−40.5229	+	55.7749i	−0.764582	+	1.05236i	−0.996819	+	0.0796979i	$0.974604\pi$
$54$		0			0
$55$	−45.6767	−	30.6372i	−0.830486	−	0.557040i
$56$		0			0
$57$	−89.9181	−	65.3293i	−1.57751	−	1.14613i
$58$		0			0
$59$	17.7615	+	54.6642i	0.301042	+	0.926512i	0.981125	+	0.193377i	$0.0619440\pi$
$59$	17.7615	+	54.6642i	0.301042	+	0.926512i	−0.680082	+	0.733136i	$0.738056\pi$
$60$		0			0
$61$	−47.9102	−	65.9427i	−0.785413	−	1.08103i	−0.994664	−	0.103166i	$-0.967103\pi$
$61$	−47.9102	−	65.9427i	−0.785413	−	1.08103i	0.209252	−	0.977862i	$-0.432897\pi$
$62$		0			0
$63$	0.740328	−	2.27849i	0.0117512	−	0.0361666i
$64$		0			0
$65$	28.8639	+	14.0483i	0.444060	+	0.216128i
$66$		0			0
$67$			65.6000i			0.979104i	0.871974	+	0.489552i	$0.162840\pi$
$67$			65.6000i			0.979104i	−0.871974	+	0.489552i	$0.837160\pi$
$68$		0			0
$69$	33.1321	−	101.970i	0.480176	−	1.47783i
$70$		0			0
$71$	−24.8061	+	18.0227i	−0.349382	+	0.253841i	−0.748610	−	0.663011i	$-0.769278\pi$
$71$	−24.8061	+	18.0227i	−0.349382	+	0.253841i	0.399228	+	0.916852i	$0.369278\pi$
$72$		0			0
$73$	12.8287	+	39.4826i	0.175735	+	0.540858i	0.999666	−	0.0258323i	$-0.00822361\pi$
$73$	12.8287	+	39.4826i	0.175735	+	0.540858i	−0.823931	+	0.566690i	$0.808224\pi$
$74$		0			0
$75$	−100.785	+	3.68662i	−1.34381	+	0.0491550i
$76$		0			0
$77$	1.58242	−	3.25904i	0.0205509	−	0.0423253i
$78$		0			0
$79$	41.8643	−	57.6213i	0.529928	−	0.729384i	−0.457191	−	0.889368i	$-0.651144\pi$
$79$	41.8643	−	57.6213i	0.529928	−	0.729384i	0.987120	+	0.159985i	$0.0511445\pi$
$80$		0			0
$81$	−28.9099	−	88.9756i	−0.356913	−	1.09846i
$82$		0			0
$83$	90.6212	−	65.8402i	1.09182	−	0.793255i	0.112116	−	0.993695i	$-0.464237\pi$
$83$	90.6212	−	65.8402i	1.09182	−	0.793255i	0.979706	+	0.200440i	$0.0642371\pi$
$84$		0			0
$85$	−78.5456	+	81.4713i	−0.924066	+	0.958485i
$86$		0			0
$87$	2.94141			0.0338094
$88$		0			0
$89$	76.2467			0.856704			0.428352	−	0.903612i	$-0.359094\pi$
$89$	76.2467			0.856704			0.428352	+	0.903612i	$0.359094\pi$
$90$		0			0
$91$	−0.653425	+	2.01104i	−0.00718050	+	0.0220993i
$92$		0			0
$93$	20.5901	+	28.3399i	0.221399	+	0.304730i
$94$		0			0
$95$	−136.431	−	19.0590i	−1.43612	−	0.200621i
$96$		0			0
$97$	−31.4114	+	43.2341i	−0.323829	+	0.445713i	−0.939632	−	0.342188i	$-0.888832\pi$
$97$	−31.4114	+	43.2341i	−0.323829	+	0.445713i	0.615802	+	0.787901i	$0.288832\pi$
$98$		0			0
$99$	14.0337	+	78.7745i	0.141754	+	0.795702i
$100$		0			0
$101$	46.3016	−	63.7287i	0.458432	−	0.630977i	−0.515751	−	0.856739i	$-0.672487\pi$
$101$	46.3016	−	63.7287i	0.458432	−	0.630977i	0.974183	+	0.225761i	$0.0724870\pi$
$102$		0			0
$103$	142.507	−	46.3033i	1.38356	−	0.449546i	0.479723	−	0.877420i	$-0.340737\pi$
$103$	142.507	−	46.3033i	1.38356	−	0.449546i	0.903838	+	0.427874i	$0.140737\pi$
$104$		0			0
$105$	−1.15901	−	6.54139i	−0.0110382	−	0.0622989i
$106$		0			0
$107$	−22.4926	+	69.2252i	−0.210212	+	0.646965i	0.789247	+	0.614075i	$0.210471\pi$
$107$	−22.4926	+	69.2252i	−0.210212	+	0.646965i	−0.999459	+	0.0328895i	$0.989529\pi$
$108$		0			0
$109$			71.8548i			0.659218i	0.944117	+	0.329609i	$0.106917\pi$
$109$			71.8548i			0.659218i	−0.944117	+	0.329609i	$0.893083\pi$
$110$		0			0
$111$	12.4011			0.111721
$112$		0			0
$113$	98.3423	+	31.9533i	0.870286	+	0.282773i	0.709918	−	0.704284i	$-0.248732\pi$
$113$	98.3423	+	31.9533i	0.870286	+	0.282773i	0.160368	+	0.987057i	$0.448732\pi$
$114$		0			0
$115$	−23.1843	−	130.851i	−0.201602	−	1.13783i
$116$		0			0
$117$	−14.4314	−	44.4154i	−0.123346	−	0.379619i
$118$		0			0
$119$	−6.03080	−	4.38163i	−0.0506790	−	0.0368204i
$120$		0			0
$121$	4.65019	+	120.911i	0.0384313	+	0.999261i
$122$		0			0
$123$	−94.6748	−	68.7853i	−0.769714	−	0.559230i
$124$		0			0
$125$	−108.098	+	62.7687i	−0.864781	+	0.502150i
$126$		0			0
$127$	105.663	−	76.7688i	0.831994	−	0.604479i	−0.0881289	−	0.996109i	$-0.528089\pi$
$127$	105.663	−	76.7688i	0.831994	−	0.604479i	0.920123	+	0.391630i	$0.128089\pi$
$128$		0			0
$129$	205.337	+	66.7182i	1.59176	+	0.517195i
$130$		0			0
$131$			225.296i			1.71982i	0.510447	+	0.859909i	$0.329480\pi$
$131$			225.296i			1.71982i	−0.510447	+	0.859909i	$0.670520\pi$
$132$		0			0
$133$		−	9.07413i		−	0.0682266i
$134$		0			0
$135$	−25.0623	−	24.1623i	−0.185647	−	0.178980i
$136$		0			0
$137$	−64.1439	−	88.2865i	−0.468203	−	0.644427i	0.507981	−	0.861368i	$-0.330392\pi$
$137$	−64.1439	−	88.2865i	−0.468203	−	0.644427i	−0.976185	+	0.216941i	$0.930392\pi$
$138$		0			0
$139$	8.20353	−	2.66549i	0.0590182	−	0.0191762i	−0.279359	−	0.960187i	$-0.590122\pi$
$139$	8.20353	−	2.66549i	0.0590182	−	0.0191762i	0.338377	+	0.941011i	$0.390122\pi$
$140$		0			0
$141$	−214.593	−	155.911i	−1.52194	−	1.10575i
$142$		0			0
$143$	−12.3863	−	69.5277i	−0.0866177	−	0.486207i
$144$		0			0
$145$	3.21752	−	1.71421i	0.0221898	−	0.0118221i
$146$		0			0
$147$	−187.581	+	60.9487i	−1.27606	+	0.414617i
$148$		0			0
$149$	157.379	+	216.614i	1.05624	+	1.45378i	0.883275	+	0.468856i	$0.155334\pi$
$149$	157.379	+	216.614i	1.05624	+	1.45378i	0.172962	+	0.984929i	$0.444666\pi$
$150$		0			0
$151$	16.2876	+	5.29217i	0.107865	+	0.0350475i	0.362452	−	0.932002i	$-0.381940\pi$
$151$	16.2876	+	5.29217i	0.107865	+	0.0350475i	−0.254587	+	0.967050i	$0.581940\pi$
$152$		0			0
$153$	164.638			1.07607
$154$		0			0
$155$	39.0389	+	19.0005i	0.251864	+	0.122584i
$156$		0			0
$157$	−100.632	−	32.6973i	−0.640967	−	0.208263i	−0.0295401	−	0.999564i	$-0.509404\pi$
$157$	−100.632	−	32.6973i	−0.640967	−	0.208263i	−0.611427	+	0.791301i	$0.709404\pi$
$158$		0			0
$159$	225.002	−	163.474i	1.41511	−	1.02814i
$160$		0			0
$161$	8.32509	−	2.70499i	0.0517087	−	0.0168012i
$162$		0			0
$163$	4.55107	−	6.26402i	0.0279207	−	0.0384295i	−0.794828	−	0.606834i	$-0.792439\pi$
$163$	4.55107	−	6.26402i	0.0279207	−	0.0384295i	0.822749	+	0.568405i	$0.192439\pi$
$164$		0			0
$165$	137.054	+	174.486i	0.830630	+	1.05749i
$166$		0			0
$167$	178.324	+	129.560i	1.06781	+	0.775810i	0.975517	−	0.219922i	$-0.0705804\pi$
$167$	178.324	+	129.560i	1.06781	+	0.775810i	0.0922930	+	0.995732i	$0.470580\pi$
$168$		0			0
$169$	−39.4865	−	121.527i	−0.233648	−	0.719094i
$170$		0			0
$171$	117.798	+	162.135i	0.688877	+	0.948157i
$172$		0			0
$173$	72.6938	−	223.728i	0.420195	−	1.29323i	−0.487326	−	0.873220i	$-0.662028\pi$
$173$	72.6938	−	223.728i	0.420195	−	1.29323i	0.907521	−	0.420007i	$-0.137972\pi$
$174$		0			0
$175$	−5.08001	−	6.47997i	−0.0290287	−	0.0370284i
$176$		0			0
$177$		−	231.870i		−	1.31000i
$178$		0			0
$179$	−8.11479	+	24.9748i	−0.0453340	+	0.139524i	−0.971161	−	0.238423i	$-0.923370\pi$
$179$	−8.11479	+	24.9748i	−0.0453340	+	0.139524i	0.925827	+	0.377946i	$0.123370\pi$
$180$		0			0
$181$	33.1864	−	24.1113i	0.183350	−	0.133212i	−0.492324	−	0.870412i	$-0.663853\pi$
$181$	33.1864	−	24.1113i	0.183350	−	0.133212i	0.675674	+	0.737200i	$0.263853\pi$
$182$		0			0
$183$	101.611	+	312.726i	0.555250	+	1.70888i
$184$		0			0
$185$	13.5651	−	7.22712i	0.0733250	−	0.0390655i
$186$		0			0
$187$	246.607	+	34.2141i	1.31876	+	0.182963i
$188$		0			0
$189$	1.34789	−	1.85520i	0.00713167	−	0.00981590i
$190$		0			0
$191$	47.4961	+	146.178i	0.248671	+	0.765330i	0.995011	+	0.0997652i	$0.0318092\pi$
$191$	47.4961	+	146.178i	0.248671	+	0.765330i	−0.746340	+	0.665565i	$0.768191\pi$
$192$		0			0
$193$	−191.005	+	138.774i	−0.989666	+	0.719034i	−0.959848	−	0.280521i	$-0.909493\pi$
$193$	−191.005	+	138.774i	−0.989666	+	0.719034i	−0.0298179	+	0.999555i	$0.509493\pi$
$194$		0			0
$195$	−93.2285	−	89.8807i	−0.478095	−	0.460926i
$196$		0			0
$197$	193.400			0.981725			0.490863	−	0.871237i	$-0.336682\pi$
$197$	193.400			0.981725			0.490863	+	0.871237i	$0.336682\pi$
$198$		0			0
$199$	−145.484			−0.731077			−0.365538	−	0.930796i	$-0.619115\pi$
$199$	−145.484			−0.731077			−0.365538	+	0.930796i	$0.619115\pi$
$200$		0			0
$201$	81.7775	−	251.685i	0.406853	−	1.25217i
$202$		0			0
$203$	0.141153	+	0.194281i	0.000695336	+	0.000957048i
$204$		0			0
$205$	−143.649	−	20.0672i	−0.700726	−	0.0978890i
$206$		0			0
$207$	−113.636	+	156.406i	−0.548965	+	0.755586i
$208$		0			0
$209$	142.752	+	267.337i	0.683026	+	1.27913i
$210$		0			0
$211$	148.470	−	204.352i	0.703651	−	0.968493i	−0.296259	−	0.955108i	$-0.595739\pi$
$211$	148.470	−	204.352i	0.703651	−	0.968493i	0.999910	−	0.0133852i	$-0.00426077\pi$
$212$		0			0
$213$	117.640	−	38.2236i	0.552301	−	0.179453i
$214$		0			0
$215$	263.495	−	46.6862i	1.22556	−	0.217145i
$216$		0			0
$217$	−0.883768	+	2.71996i	−0.00407266	+	0.0125344i
$218$		0			0
$219$		−	167.474i		−	0.764722i
$220$		0			0
$221$	−145.312			−0.657522
$222$		0			0
$223$	−379.770	−	123.395i	−1.70300	−	0.553339i	−0.713860	−	0.700289i	$-0.753055\pi$
$223$	−379.770	−	123.395i	−1.70300	−	0.553339i	−0.989144	+	0.146949i	$0.953055\pi$
$224$		0			0
$225$	174.890	+	49.8356i	0.777289	+	0.221492i
$226$		0			0
$227$	3.96727	+	12.2100i	0.0174770	+	0.0537886i	0.959415	−	0.281999i	$-0.0909975\pi$
$227$	3.96727	+	12.2100i	0.0174770	+	0.0537886i	−0.941938	+	0.335788i	$0.890998\pi$
$228$		0			0
$229$	−314.493	−	228.492i	−1.37333	−	0.997783i	−0.997469	−	0.0711075i	$-0.977347\pi$
$229$	−314.493	−	228.492i	−1.37333	−	0.997783i	−0.375862	−	0.926676i	$-0.622653\pi$
$230$		0			0
$231$	−10.1340	+	10.5312i	−0.0438700	+	0.0455897i
$232$		0			0
$233$	−319.338	−	232.012i	−1.37055	−	0.995761i	−0.997694	−	0.0678710i	$-0.978379\pi$
$233$	−319.338	−	232.012i	−1.37055	−	0.995761i	−0.372854	−	0.927890i	$-0.621621\pi$
$234$		0			0
$235$	−325.600	−	45.4851i	−1.38553	−	0.193554i
$236$		0			0
$237$	−232.451	+	168.886i	−0.980806	+	0.712597i
$238$		0			0
$239$	−249.429	−	81.0444i	−1.04364	−	0.339098i	−0.263468	−	0.964668i	$-0.584866\pi$
$239$	−249.429	−	81.0444i	−1.04364	−	0.339098i	−0.780168	+	0.625570i	$0.784866\pi$
$240$		0			0
$241$			153.597i			0.637334i	0.947867	+	0.318667i	$0.103235\pi$
$241$			153.597i			0.637334i	−0.947867	+	0.318667i	$0.896765\pi$
$242$		0			0
$243$			314.746i			1.29525i
$244$		0			0
$245$	−169.669	+	175.989i	−0.692526	+	0.718321i
$246$		0			0
$247$	−103.970	−	143.103i	−0.420932	−	0.579364i
$248$		0			0
$249$	−429.761	+	139.638i	−1.72595	+	0.560794i
$250$		0			0
$251$	−299.713	−	217.754i	−1.19408	−	0.867546i	−0.200386	−	0.979717i	$-0.564220\pi$
$251$	−299.713	−	217.754i	−1.19408	−	0.867546i	−0.993689	+	0.112171i	$0.964220\pi$
$252$		0			0
$253$	−202.715	+	210.662i	−0.801247	+	0.832655i
$254$		0			0
$255$	402.916	−	214.663i	1.58006	−	0.841814i
$256$		0			0
$257$	262.422	−	85.2662i	1.02110	−	0.331775i	0.249833	−	0.968289i	$-0.419624\pi$
$257$	262.422	−	85.2662i	1.02110	−	0.331775i	0.771265	+	0.636514i	$0.219624\pi$
$258$		0			0
$259$	0.595104	+	0.819091i	0.00229770	+	0.00316251i
$260$		0			0
$261$	−5.04420	−	1.63896i	−0.0193264	−	0.00627954i
$262$		0			0
$263$	−507.646			−1.93021			−0.965106	−	0.261861i	$-0.915664\pi$
$263$	−507.646			−1.93021			−0.965106	+	0.261861i	$0.915664\pi$
$264$		0			0
$265$	150.853	−	309.947i	0.569258	−	1.16961i
$266$		0			0
$267$	−292.533	−	95.0498i	−1.09563	−	0.355992i
$268$		0			0
$269$	−179.547	+	130.448i	−0.667460	+	0.484938i	−0.869174	−	0.494507i	$-0.835349\pi$
$269$	−179.547	+	130.448i	−0.667460	+	0.484938i	0.201714	+	0.979444i	$0.435349\pi$
$270$		0			0
$271$	−19.1301	+	6.21576i	−0.0705910	+	0.0229364i	−0.344100	−	0.938933i	$-0.611816\pi$
$271$	−19.1301	+	6.21576i	−0.0705910	+	0.0229364i	0.273509	+	0.961870i	$0.411816\pi$
$272$		0			0
$273$	5.01395	−	6.90112i	0.0183661	−	0.0252788i
$274$		0			0
$275$	251.606	+	110.992i	0.914932	+	0.403607i
$276$		0			0
$277$	134.590	+	97.7857i	0.485886	+	0.353017i	0.803600	−	0.595170i	$-0.202915\pi$
$277$	134.590	+	97.7857i	0.485886	+	0.353017i	−0.317714	+	0.948187i	$0.602915\pi$
$278$		0			0
$279$	−19.5188	−	60.0725i	−0.0699597	−	0.215314i
$280$		0			0
$281$	−10.1298	−	13.9425i	−0.0360491	−	0.0496173i	0.790612	−	0.612317i	$-0.209763\pi$
$281$	−10.1298	−	13.9425i	−0.0360491	−	0.0496173i	−0.826661	+	0.562700i	$0.809763\pi$
$282$		0			0
$283$	146.754	−	451.661i	0.518564	−	1.59598i	−0.258137	−	0.966108i	$-0.583109\pi$
$283$	146.754	−	451.661i	0.518564	−	1.59598i	0.776702	−	0.629869i	$-0.216891\pi$
$284$		0			0
$285$	499.683	+	243.200i	1.75327	+	0.853333i
$286$		0			0
$287$		−	9.55417i		−	0.0332898i
$288$		0			0
$289$	68.9971	−	212.351i	0.238744	−	0.734779i
$290$		0			0
$291$	174.411	−	126.717i	0.599352	−	0.435455i
$292$		0			0
$293$	167.468	+	515.412i	0.571562	+	1.75909i	0.647599	+	0.761981i	$0.275773\pi$
$293$	167.468	+	515.412i	0.571562	+	1.75909i	−0.0760375	+	0.997105i	$0.524227\pi$
$294$		0			0
$295$	−135.130	−	253.636i	−0.458068	−	0.859782i
$296$		0			0
$297$	−10.5250	+	75.8617i	−0.0354377	+	0.255427i
$298$		0			0
$299$	100.297	−	138.047i	0.335441	−	0.461695i
$300$		0			0
$301$	5.44703	+	16.7642i	0.0180965	+	0.0556952i
$302$		0			0
$303$	−257.089	+	186.786i	−0.848478	+	0.616455i
$304$		0			0
$305$	293.400	+	282.864i	0.961967	+	0.927423i
$306$		0			0
$307$	197.533			0.643429			0.321715	−	0.946837i	$-0.395741\pi$
$307$	197.533			0.643429			0.321715	+	0.946837i	$0.395741\pi$
$308$		0			0
$309$	−604.474			−1.95623
$310$		0			0
$311$	−144.391	+	444.389i	−0.464278	+	1.42890i	0.395609	+	0.918419i	$0.370533\pi$
$311$	−144.391	+	444.389i	−0.464278	+	1.42890i	−0.859888	+	0.510483i	$0.829467\pi$
$312$		0			0
$313$	27.3209	+	37.6040i	0.0872873	+	0.120141i	0.850427	−	0.526092i	$-0.176343\pi$
$313$	27.3209	+	37.6040i	0.0872873	+	0.120141i	−0.763140	+	0.646233i	$0.776343\pi$
$314$		0			0
$315$	−1.65730	+	11.8636i	−0.00526126	+	0.0376621i
$316$		0			0
$317$	45.5360	−	62.6749i	0.143647	−	0.197713i	−0.731131	−	0.682237i	$-0.761007\pi$
$317$	45.5360	−	62.6749i	0.143647	−	0.197713i	0.874778	+	0.484524i	$0.161007\pi$
$318$		0			0
$319$	−7.21497	−	3.50321i	−0.0226175	−	0.0109818i
$320$		0			0
$321$	172.594	−	237.555i	0.537675	−	0.740046i
$322$		0			0
$323$	593.063	−	192.698i	1.83611	−	0.596588i
$324$		0			0
$325$	−154.361	−	43.9857i	−0.474956	−	0.135341i
$326$		0			0
$327$	89.5749	−	275.683i	0.273929	−	0.843068i
$328$		0			0
$329$		−	21.6558i		−	0.0658232i
$330$		0			0
$331$	372.688			1.12594			0.562972	−	0.826476i	$-0.309658\pi$
$331$	372.688			1.12594			0.562972	+	0.826476i	$0.309658\pi$
$332$		0			0
$333$	−21.2664	−	6.90988i	−0.0638632	−	0.0207504i
$334$		0			0
$335$	−57.2240	−	322.969i	−0.170818	−	0.964088i
$336$		0			0
$337$	173.727	+	534.677i	0.515510	+	1.58658i	0.782352	+	0.622837i	$0.214020\pi$
$337$	173.727	+	534.677i	0.515510	+	1.58658i	−0.266841	+	0.963740i	$0.585980\pi$
$338$		0			0
$339$	−337.474	−	245.189i	−0.995497	−	0.723271i
$340$		0			0
$341$	−16.7527	−	94.0373i	−0.0491282	−	0.275769i
$342$		0			0
$343$	−26.0835	−	18.9508i	−0.0760453	−	0.0552502i
$344$		0			0
$345$	−74.1696	+	530.934i	−0.214984	+	1.53894i
$346$		0			0
$347$	156.720	−	113.864i	0.451644	−	0.328139i	−0.338600	−	0.940930i	$-0.609953\pi$
$347$	156.720	−	113.864i	0.451644	−	0.328139i	0.790245	+	0.612792i	$0.209953\pi$
$348$		0			0
$349$	246.547	+	80.1081i	0.706440	+	0.229536i	0.640134	−	0.768263i	$-0.278879\pi$
$349$	246.547	+	80.1081i	0.706440	+	0.229536i	0.0663055	+	0.997799i	$0.478879\pi$
$350$		0			0
$351$		−	44.7013i		−	0.127354i
$352$		0			0
$353$			313.093i			0.886949i	0.896287	+	0.443475i	$0.146254\pi$
$353$			313.093i			0.886949i	−0.896287	+	0.443475i	$0.853746\pi$
$354$		0			0
$355$	106.407	−	110.370i	0.299738	−	0.310902i
$356$		0			0
$357$	17.6760	+	24.3289i	0.0495126	+	0.0681483i
$358$		0			0
$359$	118.727	−	38.5767i	0.330716	−	0.107456i	−0.138953	−	0.990299i	$-0.544374\pi$
$359$	118.727	−	38.5767i	0.330716	−	0.107456i	0.469668	+	0.882843i	$0.344374\pi$
$360$		0			0
$361$	322.046	+	233.980i	0.892095	+	0.648145i
$362$		0			0
$363$	132.887	−	469.691i	0.366080	−	1.29391i
$364$		0			0
$365$	−97.6011	−	183.195i	−0.267400	−	0.501904i
$366$		0			0
$367$	−417.755	+	135.737i	−1.13830	+	0.369855i	−0.816723	−	0.577030i	$-0.804212\pi$
$367$	−417.755	+	135.737i	−1.13830	+	0.369855i	−0.321574	+	0.946885i	$0.604212\pi$
$368$		0			0
$369$	124.030	+	170.712i	0.336124	+	0.462634i
$370$		0			0
$371$	21.5949	+	7.01662i	0.0582073	+	0.0189127i
$372$		0			0
$373$	−29.9460			−0.0802841			−0.0401420	−	0.999194i	$-0.512781\pi$
$373$	−29.9460			−0.0802841			−0.0401420	+	0.999194i	$0.512781\pi$
$374$		0			0
$375$	492.983	−	106.067i	1.31462	−	0.282846i
$376$		0			0
$377$	4.45209	+	1.44657i	0.0118093	+	0.00383706i
$378$		0			0
$379$	−175.405	+	127.439i	−0.462810	+	0.336251i	−0.794632	−	0.607091i	$-0.792336\pi$
$379$	−175.405	+	127.439i	−0.462810	+	0.336251i	0.331823	+	0.943342i	$0.392336\pi$
$380$		0			0
$381$	−501.096	+	162.816i	−1.31521	+	0.427338i
$382$		0			0
$383$	43.5625	−	59.9586i	0.113740	−	0.156550i	−0.748351	−	0.663303i	$-0.769154\pi$
$383$	43.5625	−	59.9586i	0.113740	−	0.156550i	0.862091	+	0.506753i	$0.169154\pi$
$384$		0			0
$385$	−4.94783	+	17.4257i	−0.0128515	+	0.0452615i
$386$		0			0
$387$	−314.955	−	228.828i	−0.813838	−	0.591288i
$388$		0			0
$389$	13.4884	+	41.5130i	0.0346745	+	0.106717i	0.966896	−	0.255172i	$-0.0821320\pi$
$389$	13.4884	+	41.5130i	0.0346745	+	0.106717i	−0.932221	+	0.361889i	$0.882132\pi$
$390$		0			0
$391$	353.583	+	486.665i	0.904303	+	1.24467i
$392$		0			0
$393$	280.856	−	864.387i	0.714647	−	2.19946i
$394$		0			0
$395$	−155.847	+	320.207i	−0.394550	+	0.810651i
$396$		0			0
$397$		−	349.486i		−	0.880317i	−0.897920	−	0.440158i	$-0.854922\pi$
$397$		−	349.486i		−	0.880317i	0.897920	−	0.440158i	$-0.145078\pi$
$398$		0			0
$399$	−11.3119	+	34.8145i	−0.0283506	+	0.0872543i
$400$		0			0
$401$	374.461	−	272.062i	0.933818	−	0.678459i	−0.0131064	−	0.999914i	$-0.504172\pi$
$401$	374.461	−	272.062i	0.933818	−	0.678459i	0.946925	+	0.321455i	$0.104172\pi$
$402$		0			0
$403$	17.2276	+	53.0210i	0.0427483	+	0.131566i
$404$		0			0
$405$	219.948	+	412.837i	0.543081	+	1.01935i
$406$		0			0
$407$	−30.4184	−	14.7696i	−0.0747382	−	0.0362889i
$408$		0			0
$409$	−401.816	+	553.052i	−0.982435	+	1.35221i	−0.0469278	+	0.998898i	$0.514943\pi$
$409$	−401.816	+	553.052i	−0.982435	+	1.35221i	−0.935507	+	0.353308i	$0.885057\pi$
$410$		0			0
$411$	136.040	+	418.688i	0.330998	+	1.01871i
$412$		0			0
$413$	15.3151	−	11.1270i	0.0370825	−	0.0269420i
$414$		0			0
$415$	−388.724	+	403.203i	−0.936683	+	0.971573i
$416$		0			0
$417$	−34.7971			−0.0834462
$418$		0			0
$419$	−707.515			−1.68858			−0.844290	−	0.535887i	$-0.819977\pi$
$419$	−707.515			−1.68858			−0.844290	+	0.535887i	$0.819977\pi$
$420$		0			0
$421$	75.3508	−	231.906i	0.178980	−	0.550845i	−0.820812	−	0.571198i	$-0.806479\pi$
$421$	75.3508	−	231.906i	0.178980	−	0.550845i	0.999793	+	0.0203526i	$0.00647888\pi$
$422$		0			0
$423$	281.130	+	386.942i	0.664610	+	0.914757i
$424$		0			0
$425$	315.636	−	469.626i	0.742673	−	1.10500i
$426$		0			0
$427$	−15.7794	+	21.7185i	−0.0369542	+	0.0508631i
$428$		0			0
$429$	−39.1516	+	282.196i	−0.0912625	+	0.657799i
$430$		0			0
$431$	127.709	−	175.777i	0.296309	−	0.407834i	−0.634742	−	0.772724i	$-0.718893\pi$
$431$	127.709	−	175.777i	0.296309	−	0.407834i	0.931051	+	0.364890i	$0.118893\pi$
$432$		0			0
$433$	781.028	−	253.771i	1.80376	−	0.586077i	0.803799	−	0.594901i	$-0.202809\pi$
$433$	781.028	−	253.771i	1.80376	−	0.586077i	0.999961	+	0.00882412i	$0.00280884\pi$
$434$		0			0
$435$	−14.4815	+	2.56585i	−0.0332908	+	0.00589850i
$436$		0			0
$437$	−226.278	+	696.412i	−0.517799	+	1.59362i
$438$		0			0
$439$		−	148.110i		−	0.337381i	−0.985669	−	0.168690i	$-0.946046\pi$
$439$		−	148.110i		−	0.337381i	0.985669	−	0.168690i	$-0.0539538\pi$
$440$		0			0
$441$	355.641			0.806441
$442$		0			0
$443$	445.670	+	144.807i	1.00603	+	0.326878i	0.765271	−	0.643708i	$-0.222605\pi$
$443$	445.670	+	144.807i	1.00603	+	0.326878i	0.240756	+	0.970586i	$0.422605\pi$
$444$		0			0
$445$	−375.387	+	66.5113i	−0.843565	+	0.149464i
$446$		0			0
$447$	−333.779	−	1027.27i	−0.746710	−	2.29814i
$448$		0			0
$449$	29.1101	+	21.1497i	0.0648332	+	0.0471041i	0.619730	−	0.784815i	$-0.287242\pi$
$449$	29.1101	+	21.1497i	0.0648332	+	0.0471041i	−0.554897	+	0.831919i	$0.687242\pi$
$450$		0			0
$451$	150.304	+	281.480i	0.333269	+	0.624124i
$452$		0			0
$453$	−55.8929	−	40.6086i	−0.123384	−	0.0896437i
$454$		0			0
$455$	1.46276	−	10.4710i	0.00321485	−	0.0230131i
$456$		0			0
$457$	348.643	−	253.304i	0.762895	−	0.554276i	−0.136902	−	0.990585i	$-0.543714\pi$
$457$	348.643	−	253.304i	0.762895	−	0.554276i	0.899797	+	0.436309i	$0.143714\pi$
$458$		0			0
$459$	149.875	+	48.6974i	0.326526	+	0.106095i
$460$		0			0
$461$		−	575.058i		−	1.24742i	−0.781658	−	0.623708i	$-0.785626\pi$
$461$		−	575.058i		−	1.24742i	0.781658	−	0.623708i	$-0.214374\pi$
$462$		0			0
$463$			597.953i			1.29148i	0.763559	+	0.645738i	$0.223450\pi$
$463$			597.953i			1.29148i	−0.763559	+	0.645738i	$0.776550\pi$
$464$		0			0
$465$	−126.093	−	121.565i	−0.271168	−	0.261430i
$466$		0			0
$467$	144.452	+	198.821i	0.309319	+	0.425742i	0.935169	−	0.354202i	$-0.115248\pi$
$467$	144.452	+	198.821i	0.309319	+	0.425742i	−0.625849	+	0.779944i	$0.715248\pi$
$468$		0			0
$469$	20.5482	−	6.67652i	0.0438128	−	0.0142356i
$470$		0			0
$471$	345.331	+	250.897i	0.733186	+	0.532691i
$472$		0			0
$473$	−424.209	−	408.208i	−0.896849	−	0.863019i
$474$		0			0
$475$	688.321	−	25.1780i	1.44910	−	0.0530064i
$476$		0			0
$477$	−476.942	+	154.968i	−0.999878	+	0.324880i
$478$		0			0
$479$	−99.1187	−	136.425i	−0.206928	−	0.284812i	0.692921	−	0.721014i	$-0.256324\pi$
$479$	−99.1187	−	136.425i	−0.206928	−	0.284812i	−0.899849	+	0.436201i	$0.856324\pi$
$480$		0			0
$481$	18.7701	+	6.09877i	0.0390231	+	0.0126794i
$482$		0			0
$483$	−35.3127			−0.0731112
$484$		0			0
$485$	116.935	−	240.256i	0.241102	−	0.495374i
$486$		0			0
$487$	546.027	+	177.415i	1.12121	+	0.364302i	0.810228	−	0.586115i	$-0.199343\pi$
$487$	546.027	+	177.415i	1.12121	+	0.364302i	0.310978	+	0.950417i	$0.399343\pi$
$488$		0			0
$489$	−25.2698	+	18.3596i	−0.0516764	+	0.0375451i
$490$		0			0
$491$	−376.115	+	122.207i	−0.766018	+	0.248894i	−0.665860	−	0.746077i	$-0.731935\pi$
$491$	−376.115	+	122.207i	−0.766018	+	0.248894i	−0.100159	+	0.994971i	$0.531935\pi$
$492$		0			0
$493$	−9.70019	+	13.3512i	−0.0196758	+	0.0270815i
$494$		0			0
$495$	−137.809	−	375.590i	−0.278401	−	0.758768i
$496$		0			0
$497$	8.17001	+	5.93586i	0.0164386	+	0.0119434i
$498$		0			0
$499$	−269.630	−	829.836i	−0.540341	−	1.66300i	−0.731818	−	0.681500i	$-0.761328\pi$
$499$	−269.630	−	829.836i	−0.540341	−	1.66300i	0.191477	−	0.981497i	$-0.438672\pi$
$500$		0			0
$501$	−522.661	−	719.381i	−1.04323	−	1.43589i
$502$		0			0
$503$	−206.446	+	635.375i	−0.410429	+	1.26317i	0.505847	+	0.862623i	$0.331180\pi$
$503$	−206.446	+	635.375i	−0.410429	+	1.26317i	−0.916276	+	0.400548i	$0.868820\pi$
$504$		0			0
$505$	−172.366	+	354.146i	−0.341319	+	0.701280i
$506$		0			0
$507$			515.482i			1.01673i
$508$		0			0
$509$	291.921	−	898.441i	0.573519	−	1.76511i	−0.0676497	−	0.997709i	$-0.521550\pi$
$509$	291.921	−	898.441i	0.573519	−	1.76511i	0.641168	−	0.767400i	$-0.278450\pi$
$510$		0			0
$511$	11.0617	−	8.03679i	0.0216471	−	0.0157276i
$512$		0			0
$513$	59.2780	+	182.439i	0.115552	+	0.355632i
$514$		0			0
$515$	−661.215	+	352.277i	−1.28391	+	0.684033i
$516$		0			0
$517$	340.685	+	638.013i	0.658965	+	1.23407i
$518$		0			0
$519$	−557.804	+	767.751i	−1.07477	+	1.47929i
$520$		0			0
$521$	−235.542	−	724.923i	−0.452095	−	1.39141i	−0.874512	−	0.485005i	$-0.838818\pi$
$521$	−235.542	−	724.923i	−0.452095	−	1.39141i	0.422416	−	0.906402i	$-0.361182\pi$
$522$		0			0
$523$	668.203	−	485.478i	1.27763	−	0.928256i	0.278155	−	0.960536i	$-0.410277\pi$
$523$	668.203	−	485.478i	1.27763	−	0.928256i	0.999479	+	0.0322804i	$0.0102770\pi$
$524$		0			0
$525$	11.4123	+	31.1943i	0.0217378	+	0.0594177i
$526$		0			0
$527$	−196.537			−0.372936
$528$		0			0
$529$	−177.379			−0.335310
$530$		0			0
$531$	−129.198	+	397.632i	−0.243311	+	0.748836i
$532$		0			0
$533$	−109.470	−	150.673i	−0.205386	−	0.282689i
$534$		0			0
$535$	50.3520	−	360.439i	0.0941160	−	0.673717i
$536$		0			0
$537$	62.2675	−	85.7039i	0.115954	−	0.159598i
$538$		0			0
$539$	532.704	+	73.9070i	0.988320	+	0.137119i
$540$		0			0
$541$	−548.025	+	754.292i	−1.01299	+	1.39425i	−0.0959786	+	0.995383i	$0.530598\pi$
$541$	−548.025	+	754.292i	−1.01299	+	1.39425i	−0.917007	+	0.398871i	$0.869402\pi$
$542$		0			0
$543$	−157.383	+	51.1368i	−0.289839	+	0.0941745i
$544$		0			0
$545$	−62.6802	−	353.764i	−0.115010	−	0.649108i
$546$		0			0
$547$	−64.7653	+	199.327i	−0.118401	+	0.364401i	−0.992641	−	0.121093i	$-0.961360\pi$
$547$	−64.7653	+	199.327i	−0.118401	+	0.364401i	0.874240	+	0.485494i	$0.161360\pi$
$548$		0			0
$549$		−	592.907i		−	1.07998i
$550$		0			0
$551$	−20.0886			−0.0364584
$552$		0			0
$553$	−22.3098	−	7.24890i	−0.0403432	−	0.0131083i
$554$		0			0
$555$	−61.0543	+	10.8177i	−0.110008	+	0.0194913i
$556$		0			0
$557$	−108.478	−	333.860i	−0.194753	−	0.599389i	−0.999979	−	0.00642113i	$-0.997956\pi$
$557$	−108.478	−	333.860i	−0.194753	−	0.599389i	0.805226	−	0.592968i	$-0.202044\pi$
$558$		0			0
$559$	277.985	+	201.968i	0.497289	+	0.361302i
$560$		0			0
$561$	−903.499	−	438.691i	−1.61052	−	0.781981i
$562$		0			0
$563$	−218.952	−	159.078i	−0.388903	−	0.282555i	0.376103	−	0.926578i	$-0.377264\pi$
$563$	−218.952	−	159.078i	−0.388903	−	0.282555i	−0.765006	+	0.644023i	$0.777264\pi$
$564$		0			0
$565$	−512.044	−	71.5308i	−0.906272	−	0.126603i
$566$		0			0
$567$	−24.9279	+	18.1112i	−0.0439646	+	0.0319422i
$568$		0			0
$569$	397.866	+	129.274i	0.699237	+	0.227196i	0.636998	−	0.770866i	$-0.280176\pi$
$569$	397.866	+	129.274i	0.699237	+	0.227196i	0.0622388	+	0.998061i	$0.480176\pi$
$570$		0			0
$571$			711.709i			1.24643i	0.782052	+	0.623213i	$0.214173\pi$
$571$			711.709i			1.24643i	−0.782052	+	0.623213i	$0.785827\pi$
$572$		0			0
$573$		−	620.046i		−	1.08210i
$574$		0			0
$575$	228.287	+	623.997i	0.397021	+	1.08521i
$576$		0			0
$577$	−386.572	−	532.071i	−0.669969	−	0.922133i	0.329791	−	0.944054i	$-0.393022\pi$
$577$	−386.572	−	532.071i	−0.669969	−	0.922133i	−0.999760	+	0.0219209i	$0.993022\pi$
$578$		0			0
$579$	905.822	−	294.319i	1.56446	−	0.508323i
$580$		0			0
$581$	−29.8465	−	21.6848i	−0.0513710	−	0.0373232i
$582$		0			0
$583$	−746.603	+	133.007i	−1.28062	+	0.228142i
$584$		0			0
$585$	109.795	+	206.082i	0.187684	+	0.352278i
$586$		0			0
$587$	−304.789	+	99.0320i	−0.519232	+	0.168709i	−0.556897	−	0.830582i	$-0.688008\pi$
$587$	−304.789	+	99.0320i	−0.519232	+	0.168709i	0.0376647	+	0.999290i	$0.488008\pi$
$588$		0			0
$589$	−140.622	−	193.549i	−0.238746	−	0.328606i
$590$		0			0
$591$	−742.012	−	241.094i	−1.25552	−	0.407943i
$592$		0			0
$593$	−530.847			−0.895189			−0.447595	−	0.894237i	$-0.647719\pi$
$593$	−530.847			−0.895189			−0.447595	+	0.894237i	$0.647719\pi$
$594$		0			0
$595$	33.5137	+	16.3114i	0.0563256	+	0.0274141i
$596$		0			0
$597$	558.175	+	181.362i	0.934967	+	0.303789i
$598$		0			0
$599$	−602.735	+	437.912i	−1.00624	+	0.731073i	−0.963416	−	0.268010i	$-0.913634\pi$
$599$	−602.735	+	437.912i	−1.00624	+	0.731073i	−0.0428190	+	0.999083i	$0.513634\pi$
$600$		0			0
$601$	898.863	−	292.058i	1.49561	−	0.485954i	0.556878	−	0.830594i	$-0.311999\pi$
$601$	898.863	−	292.058i	1.49561	−	0.485954i	0.938735	+	0.344640i	$0.111999\pi$
$602$		0			0
$603$	−280.479	+	386.046i	−0.465139	+	0.640209i
$604$		0			0
$605$	−128.367	−	591.225i	−0.212177	−	0.977231i
$606$		0			0
$607$	−159.275	−	115.720i	−0.262398	−	0.190643i	0.448806	−	0.893629i	$-0.351850\pi$
$607$	−159.275	−	115.720i	−0.262398	−	0.190643i	−0.711203	+	0.702986i	$0.751850\pi$
$608$		0			0
$609$	−0.299366	−	0.921354i	−0.000491570	−	0.00151290i
$610$		0			0
$611$	−248.130	−	341.521i	−0.406104	−	0.558955i
$612$		0			0
$613$	−290.171	+	893.056i	−0.473363	+	1.45686i	0.374790	+	0.927110i	$0.377715\pi$
$613$	−290.171	+	893.056i	−0.473363	+	1.45686i	−0.848153	+	0.529751i	$0.822285\pi$
$614$		0			0
$615$	526.117	+	256.065i	0.855475	+	0.416366i
$616$		0			0
$617$			425.600i			0.689789i	0.938641	+	0.344895i	$0.112085\pi$
$617$			425.600i			0.689789i	−0.938641	+	0.344895i	$0.887915\pi$
$618$		0			0
$619$	−27.1880	+	83.6761i	−0.0439225	+	0.135179i	−0.970613	−	0.240646i	$-0.922641\pi$
$619$	−27.1880	+	83.6761i	−0.0439225	+	0.135179i	0.926691	+	0.375825i	$0.122641\pi$
$620$		0			0
$621$	−149.709	+	108.770i	−0.241077	+	0.175152i
$622$		0			0
$623$	−7.76010	−	23.8831i	−0.0124560	−	0.0383357i
$624$		0			0
$625$	477.445	−	403.326i	0.763911	−	0.645321i
$626$		0			0
$627$	−214.428	−	1203.64i	−0.341991	−	1.91968i
$628$		0			0
$629$	−40.8962	+	56.2887i	−0.0650178	+	0.0894893i
$630$		0			0
$631$	159.104	+	489.671i	0.252146	+	0.776024i	0.994379	+	0.105882i	$0.0337667\pi$
$631$	159.104	+	489.671i	0.252146	+	0.776024i	−0.742233	+	0.670142i	$0.766233\pi$
$632$		0			0
$633$	−824.379	+	598.946i	−1.30234	+	0.946203i
$634$		0			0
$635$	−453.247	+	470.129i	−0.713774	+	0.740361i
$636$		0			0
$637$	−313.894			−0.492769
$638$		0			0
$639$	−223.038			−0.349042
$640$		0			0
$641$	128.796	−	396.393i	0.200930	−	0.618398i	−0.798926	−	0.601429i	$-0.794598\pi$
$641$	128.796	−	396.393i	0.200930	−	0.618398i	0.999856	−	0.0169692i	$-0.00540174\pi$
$642$		0			0
$643$	−152.972	−	210.548i	−0.237903	−	0.327446i	0.673326	−	0.739346i	$-0.264865\pi$
$643$	−152.972	−	210.548i	−0.237903	−	0.327446i	−0.911229	+	0.411900i	$0.864865\pi$
$644$		0			0
$645$	−1069.14	−	149.355i	−1.65758	−	0.231559i
$646$		0			0
$647$	138.801	−	191.043i	0.214529	−	0.295274i	−0.688167	−	0.725552i	$-0.741584\pi$
$647$	138.801	−	191.043i	0.214529	−	0.295274i	0.902697	+	0.430278i	$0.141584\pi$
$648$		0			0
$649$	−276.156	+	568.752i	−0.425510	+	0.876352i
$650$		0			0
$651$	6.78145	−	9.33387i	0.0104170	−	0.0143377i
$652$		0			0
$653$	−335.701	+	109.076i	−0.514090	+	0.167038i	−0.554562	−	0.832143i	$-0.687114\pi$
$653$	−335.701	+	109.076i	−0.514090	+	0.167038i	0.0404715	+	0.999181i	$0.487114\pi$
$654$		0			0
$655$	−196.530	−	1109.20i	−0.300046	−	1.69344i
$656$		0			0
$657$	−93.3168	+	287.200i	−0.142035	+	0.437138i
$658$		0			0
$659$		−	1104.98i		−	1.67675i	−0.545097	−	0.838373i	$-0.683507\pi$
$659$		−	1104.98i		−	1.67675i	0.545097	−	0.838373i	$-0.316493\pi$
$660$		0			0
$661$	1002.47			1.51659			0.758295	−	0.651912i	$-0.226033\pi$
$661$	1002.47			1.51659			0.758295	+	0.651912i	$0.226033\pi$
$662$		0			0
$663$	557.516	+	181.148i	0.840899	+	0.273225i
$664$		0			0
$665$	7.91553	+	44.6748i	0.0119030	+	0.0671802i
$666$		0			0
$667$	−5.98838	−	18.4303i	−0.00897808	−	0.0276317i
$668$		0			0
$669$	1303.23	+	946.850i	1.94802	+	1.41532i
$670$		0			0
$671$	123.214	−	888.100i	0.183628	−	1.32355i
$672$		0			0
$673$	−186.414	−	135.438i	−0.276990	−	0.201245i	0.440613	−	0.897697i	$-0.354761\pi$
$673$	−186.414	−	135.438i	−0.276990	−	0.201245i	−0.717603	+	0.696452i	$0.754761\pi$
$674$		0			0
$675$	144.467	+	97.0965i	0.214025	+	0.143847i
$676$		0			0
$677$	573.766	−	416.865i	0.847512	−	0.615754i	−0.0769468	−	0.997035i	$-0.524517\pi$
$677$	573.766	−	416.865i	0.847512	−	0.615754i	0.924459	+	0.381282i	$0.124517\pi$
$678$		0			0
$679$	16.7394	+	5.43895i	0.0246530	+	0.00801024i
$680$		0			0
$681$		−	51.7914i		−	0.0760520i
$682$		0			0
$683$		−	448.387i		−	0.656497i	−0.944591	−	0.328248i	$-0.893542\pi$
$683$		−	448.387i		−	0.656497i	0.944591	−	0.328248i	$-0.106458\pi$
$684$		0			0
$685$	392.815	+	378.709i	0.573452	+	0.552859i
$686$		0			0
$687$	921.764	+	1268.70i	1.34172	+	1.84672i
$688$		0			0
$689$	420.957	−	136.777i	0.610967	−	0.198515i
$690$		0			0
$691$	386.122	+	280.534i	0.558788	+	0.405983i	0.831015	−	0.556250i	$-0.187760\pi$
$691$	386.122	+	280.534i	0.558788	+	0.405983i	−0.272227	+	0.962233i	$0.587760\pi$
$692$		0			0
$693$	23.2467	−	12.4132i	0.0335449	−	0.0179123i
$694$		0			0
$695$	−38.0634	+	20.2791i	−0.0547675	+	0.0291786i
$696$		0			0
$697$	624.437	−	202.892i	0.895892	−	0.291093i
$698$		0			0
$699$	935.964	+	1288.24i	1.33900	+	1.84298i
$700$		0			0
$701$	−305.767	−	99.3498i	−0.436187	−	0.141726i	0.0826886	−	0.996575i	$-0.473649\pi$
$701$	−305.767	−	99.3498i	−0.436187	−	0.141726i	−0.518876	+	0.854850i	$0.673649\pi$
$702$		0			0
$703$	−84.6938			−0.120475
$704$		0			0
$705$	1192.52	+	580.407i	1.69151	+	0.823273i
$706$		0			0
$707$	−24.6745	−	8.01722i	−0.0349002	−	0.0113398i
$708$		0			0
$709$	825.864	−	600.025i	1.16483	−	0.846298i	0.174448	−	0.984666i	$-0.444186\pi$
$709$	825.864	−	600.025i	1.16483	−	0.846298i	0.990381	+	0.138369i	$0.0441859\pi$
$710$		0			0
$711$	492.731	−	160.098i	0.693011	−	0.225173i
$712$		0			0
$713$	135.653	−	186.710i	0.190257	−	0.261866i
$714$		0			0
$715$	121.632	+	331.502i	0.170115	+	0.463639i
$716$		0			0
$717$	855.947	+	621.882i	1.19379	+	0.867338i
$718$		0			0
$719$	124.798	+	384.088i	0.173571	+	0.534197i	0.999565	−	0.0294817i	$-0.00938568\pi$
$719$	124.798	+	384.088i	0.173571	+	0.534197i	−0.825994	+	0.563679i	$0.809386\pi$
$720$		0			0
$721$	−29.0076	−	39.9255i	−0.0402325	−	0.0553752i
$722$		0			0
$723$	191.476	−	589.303i	0.264836	−	0.815080i
$724$		0			0
$725$	−14.3456	+	11.2463i	−0.0197870	+	0.0155121i
$726$		0			0
$727$		−	984.907i		−	1.35475i	−0.735636	−	0.677377i	$-0.763116\pi$
$727$		−	984.907i		−	1.35475i	0.735636	−	0.677377i	$-0.236884\pi$
$728$		0			0
$729$	132.176	−	406.797i	0.181312	−	0.558021i
$730$		0			0
$731$	−979.997	+	712.009i	−1.34062	+	0.974021i
$732$		0			0
$733$	−272.723	−	839.356i	−0.372065	−	1.14510i	−0.945438	−	0.325803i	$-0.894365\pi$
$733$	−272.723	−	839.356i	−0.372065	−	1.14510i	0.573373	−	0.819294i	$-0.305635\pi$
$734$		0			0
$735$	870.353	−	463.700i	1.18415	−	0.630884i
$736$		0			0
$737$	−500.347	+	519.960i	−0.678897	+	0.705509i
$738$		0			0
$739$	−599.010	+	824.467i	−0.810569	+	1.11565i	0.180667	+	0.983544i	$0.442174\pi$
$739$	−599.010	+	824.467i	−0.810569	+	1.11565i	−0.991235	+	0.132108i	$0.957826\pi$
$740$		0			0
$741$	220.506	+	678.649i	0.297580	+	0.915856i
$742$		0			0
$743$	−39.7064	+	28.8484i	−0.0534406	+	0.0388269i	−0.614185	−	0.789162i	$-0.710515\pi$
$743$	−39.7064	+	28.8484i	−0.0534406	+	0.0388269i	0.560744	+	0.827989i	$0.310515\pi$
$744$		0			0
$745$	−963.784	−	929.175i	−1.29367	−	1.24721i
$746$		0			0
$747$	814.798			1.09076
$748$		0			0
$749$	23.9730			0.0320067
$750$		0			0
$751$	−316.258	+	973.343i	−0.421116	+	1.29606i	0.485548	+	0.874210i	$0.338620\pi$
$751$	−316.258	+	973.343i	−0.421116	+	1.29606i	−0.906664	+	0.421853i	$0.861380\pi$
$752$		0			0
$753$	878.445	+	1209.08i	1.16659	+	1.60568i
$754$		0			0
$755$	−84.8056	−	11.8470i	−0.112325	−	0.0156914i
$756$		0			0
$757$	223.751	−	307.967i	0.295576	−	0.406826i	−0.635239	−	0.772315i	$-0.719098\pi$
$757$	223.751	−	307.967i	0.295576	−	0.406826i	0.930815	+	0.365490i	$0.119098\pi$
$758$		0			0
$759$	1040.36	−	555.532i	1.37070	−	0.731926i
$760$		0			0
$761$	236.882	−	326.039i	0.311277	−	0.428436i	−0.624502	−	0.781023i	$-0.714698\pi$
$761$	236.882	−	326.039i	0.311277	−	0.428436i	0.935779	+	0.352588i	$0.114698\pi$
$762$		0			0
$763$	22.5074	−	7.31311i	0.0294986	−	0.00958468i
$764$		0			0
$765$	−810.567	+	143.617i	−1.05956	+	0.187735i
$766$		0			0
$767$	114.033	−	350.956i	0.148673	−	0.457570i
$768$		0			0
$769$		−	157.816i		−	0.205223i	−0.994722	−	0.102611i	$-0.967280\pi$
$769$		−	157.816i		−	0.205223i	0.994722	−	0.102611i	$-0.0327198\pi$
$770$		0			0
$771$	−1113.12			−1.44374
$772$		0			0
$773$	−471.540	−	153.213i	−0.610013	−	0.198205i	−0.0123121	−	0.999924i	$-0.503919\pi$
$773$	−471.540	−	153.213i	−0.610013	−	0.198205i	−0.597701	+	0.801719i	$0.703919\pi$
$774$		0			0
$775$	−208.775	−	59.4914i	−0.269388	−	0.0767631i
$776$		0			0
$777$	−1.26213	−	3.88444i	−0.00162437	−	0.00499929i
$778$		0			0
$779$	646.588	+	469.774i	0.830023	+	0.603047i
$780$		0			0
$781$	−334.082	−	46.3503i	−0.427762	−	0.0593474i
$782$		0			0
$783$	−4.10711	−	2.98399i	−0.00524535	−	0.00381097i
$784$		0			0
$785$	523.965	+	73.1961i	0.667471	+	0.0932435i
$786$		0			0
$787$	−1214.36	+	882.282i	−1.54302	+	1.12107i	−0.594615	+	0.804011i	$0.702695\pi$
$787$	−1214.36	+	882.282i	−1.54302	+	1.12107i	−0.948406	+	0.317059i	$0.897305\pi$
$788$		0			0
$789$	1947.67	+	632.836i	2.46853	+	0.802073i
$790$		0			0
$791$		−	34.0563i		−	0.0430548i
$792$		0			0
$793$			523.309i			0.659911i
$794$		0			0
$795$	−965.157	+	1001.11i	−1.21403	+	1.25925i
$796$		0			0
$797$	−878.944	−	1209.76i	−1.10282	−	1.51790i	−0.831599	−	0.555377i	$-0.812574\pi$
$797$	−878.944	−	1209.76i	−1.10282	−	1.51790i	−0.271216	−	0.962518i	$-0.587426\pi$
$798$		0			0
$799$	1415.37	−	459.882i	1.77143	−	0.575572i
$800$		0			0
$801$	448.700	+	326.000i	0.560175	+	0.406991i
$802$		0			0
$803$	−199.461	+	410.796i	−0.248394	+	0.511576i
$804$		0			0
$805$	−38.6275	+	20.5796i	−0.0479844	+	0.0255648i
$806$		0			0
$807$	851.480	−	276.662i	1.05512	−	0.342828i
$808$		0			0
$809$	−229.935	−	316.478i	−0.284221	−	0.391197i	0.642905	−	0.765946i	$-0.277729\pi$
$809$	−229.935	−	316.478i	−0.284221	−	0.391197i	−0.927126	+	0.374749i	$0.877729\pi$
$810$		0			0
$811$	403.812	+	131.206i	0.497918	+	0.161783i	0.547201	−	0.837001i	$-0.315693\pi$
$811$	403.812	+	131.206i	0.497918	+	0.161783i	−0.0492825	+	0.998785i	$0.515693\pi$
$812$		0			0
$813$	81.1447			0.0998090
$814$		0			0
$815$	−16.9422	+	34.8097i	−0.0207879	+	0.0427113i
$816$		0			0
$817$	−1402.37	−	455.656i	−1.71648	−	0.557719i
$818$		0			0
$819$	−12.4437	+	9.04086i	−0.0151937	+	0.0110389i
$820$		0			0
$821$	−74.9621	+	24.3567i	−0.0913059	+	0.0296671i	−0.354314	−	0.935127i	$-0.615285\pi$
$821$	−74.9621	+	24.3567i	−0.0913059	+	0.0296671i	0.263008	+	0.964794i	$0.415285\pi$
$822$		0			0
$823$	417.453	−	574.575i	0.507234	−	0.698148i	−0.476216	−	0.879328i	$-0.657992\pi$
$823$	417.453	−	574.575i	0.507234	−	0.698148i	0.983450	+	0.181181i	$0.0579919\pi$
$824$		0			0
$825$	−826.967	−	739.495i	−1.00238	−	0.896357i
$826$		0			0
$827$	−8.41147	−	6.11129i	−0.0101711	−	0.00738971i	0.582688	−	0.812696i	$-0.302001\pi$
$827$	−8.41147	−	6.11129i	−0.0101711	−	0.00738971i	−0.592859	+	0.805306i	$0.702001\pi$
$828$		0			0
$829$	−168.549	−	518.739i	−0.203316	−	0.625741i	−0.999778	−	0.0210534i	$-0.993298\pi$
$829$	−168.549	−	518.739i	−0.203316	−	0.625741i	0.796463	−	0.604688i	$-0.206702\pi$
$830$		0			0
$831$	−394.479	−	542.953i	−0.474703	−	0.653373i
$832$		0			0
$833$	341.955	−	1052.43i	0.410511	−	1.26342i
$834$		0			0
$835$	−990.965	−	482.311i	−1.18678	−	0.577618i
$836$		0			0
$837$		−	60.4592i		−	0.0722332i
$838$		0			0
$839$	−87.0345	+	267.865i	−0.103736	+	0.319267i	−0.989432	−	0.145000i	$-0.953682\pi$
$839$	−87.0345	+	267.865i	−0.103736	+	0.319267i	0.885696	+	0.464266i	$0.153682\pi$
$840$		0			0
$841$	−679.953	+	494.015i	−0.808506	+	0.587414i
$842$		0			0
$843$	21.4838	+	66.1205i	0.0254850	+	0.0784347i
$844$		0			0
$845$	300.414	+	563.870i	0.355520	+	0.667302i
$846$		0			0
$847$	37.4002	−	13.7624i	0.0441560	−	0.0162484i
$848$		0			0
$849$	−1126.09	+	1549.93i	−1.32637	+	1.82560i
$850$		0			0
$851$	−25.2471	−	77.7026i	−0.0296676	−	0.0913074i
$852$		0			0
$853$	476.106	−	345.911i	0.558154	−	0.405523i	−0.272629	−	0.962119i	$-0.587893\pi$
$853$	476.106	−	345.911i	0.558154	−	0.405523i	0.830783	+	0.556596i	$0.187893\pi$
$854$		0			0
$855$	−721.390	−	695.485i	−0.843731	−	0.813432i
$856$		0			0
$857$	−1169.51			−1.36466			−0.682329	−	0.731045i	$-0.739033\pi$
$857$	−1169.51			−1.36466			−0.682329	+	0.731045i	$0.739033\pi$
$858$		0			0
$859$	−847.128			−0.986179			−0.493089	−	0.869979i	$-0.664132\pi$
$859$	−847.128			−0.986179			−0.493089	+	0.869979i	$0.664132\pi$
$860$		0			0
$861$	−11.9103	+	36.6562i	−0.0138331	+	0.0425740i
$862$		0			0
$863$	−346.990	−	477.591i	−0.402075	−	0.553408i	0.559189	−	0.829041i	$-0.311113\pi$
$863$	−346.990	−	477.591i	−0.402075	−	0.553408i	−0.961263	+	0.275632i	$0.911113\pi$
$864$		0			0
$865$	−162.732	+	1164.90i	−0.188130	+	1.34670i
$866$		0			0
$867$	−529.438	+	728.709i	−0.610655	+	0.840495i
$868$		0			0
$869$	771.318	−	137.410i	0.887593	−	0.158124i
$870$		0			0
$871$	247.555	−	340.730i	0.284219	−	0.391194i
$872$		0			0
$873$	−369.703	+	120.124i	−0.423486	+	0.137599i
$874$		0			0
$875$	30.6631	+	27.4716i	0.0350436	+	0.0313961i
$876$		0			0
$877$	116.074	−	357.238i	0.132353	−	0.407341i	−0.862816	−	0.505518i	$-0.831301\pi$
$877$	116.074	−	357.238i	0.132353	−	0.407341i	0.995169	+	0.0981776i	$0.0313013\pi$
$878$		0			0
$879$		−	2186.23i		−	2.48718i
$880$		0			0
$881$	−36.1533			−0.0410367			−0.0205183	−	0.999789i	$-0.506532\pi$
$881$	−36.1533			−0.0410367			−0.0205183	+	0.999789i	$0.506532\pi$
$882$		0			0
$883$	76.3685	+	24.8136i	0.0864876	+	0.0281015i	0.351941	−	0.936022i	$-0.385522\pi$
$883$	76.3685	+	24.8136i	0.0864876	+	0.0281015i	−0.265454	+	0.964124i	$0.585522\pi$
$884$		0			0
$885$	202.265	+	1141.57i	0.228548	+	1.28991i
$886$		0			0
$887$	211.476	+	650.855i	0.238417	+	0.733771i	0.996650	+	0.0817877i	$0.0260630\pi$
$887$	211.476	+	650.855i	0.238417	+	0.733771i	−0.758233	+	0.651984i	$0.773937\pi$
$888$		0			0
$889$	−34.8007	−	25.2842i	−0.0391459	−	0.0284411i
$890$		0			0
$891$	449.492	−	925.744i	0.504481	−	1.03899i
$892$		0			0
$893$	1465.58	+	1064.81i	1.64119	+	1.19239i
$894$		0			0
$895$	18.1658	−	130.037i	0.0202969	−	0.145293i
$896$		0			0
$897$	−556.896	+	404.609i	−0.620843	+	0.451069i
$898$		0			0
$899$	6.02152	+	1.95651i	0.00669802	+	0.00217632i
$900$		0			0
$901$			1560.40i			1.73185i
$902$		0			0
$903$		−	71.1092i		−	0.0787477i
$904$		0			0
$905$	−142.355	+	147.657i	−0.157298	+	0.163157i
$906$		0			0
$907$	93.2767	+	128.384i	0.102841	+	0.141548i	0.857336	−	0.514758i	$-0.172118\pi$
$907$	93.2767	+	128.384i	0.102841	+	0.141548i	−0.754495	+	0.656306i	$0.772118\pi$
$908$		0			0
$909$	544.956	−	177.067i	0.599512	−	0.194793i
$910$		0			0
$911$	−1015.13	−	737.536i	−1.11430	−	0.809589i	−0.130968	−	0.991387i	$-0.541808\pi$
$911$	−1015.13	−	737.536i	−1.11430	−	0.809589i	−0.983336	+	0.181798i	$0.941808\pi$
$912$		0			0
$913$	1220.46	+	169.326i	1.33676	+	0.185461i
$914$		0			0
$915$	−773.058	−	1451.01i	−0.844872	−	1.58580i
$916$		0			0
$917$	70.5707	−	22.9298i	0.0769582	−	0.0250052i
$918$		0			0
$919$	560.745	+	771.800i	0.610169	+	0.839825i	0.996591	−	0.0824965i	$-0.0262893\pi$
$919$	560.745	+	771.800i	0.610169	+	0.839825i	−0.386422	+	0.922322i	$0.626289\pi$
$920$		0			0
$921$	−757.868	−	246.246i	−0.822875	−	0.267368i
$922$		0			0
$923$	196.857			0.213279
$924$		0			0
$925$	−60.4811	+	47.4145i	−0.0653850	+	0.0512590i
$926$		0			0
$927$	1036.60	+	336.813i	1.11824	+	0.363337i
$928$		0			0
$929$	−593.886	+	431.484i	−0.639275	+	0.464460i	−0.859601	−	0.510966i	$-0.829288\pi$
$929$	−593.886	+	431.484i	−0.639275	+	0.464460i	0.220326	+	0.975426i	$0.429288\pi$
$930$		0			0
$931$	1281.09	−	416.253i	1.37604	−	0.447103i
$932$		0			0
$933$	1107.96	−	1524.97i	1.18752	−	1.63448i
$934$		0			0
$935$	−1243.97	+	46.6729i	−1.33045	+	0.0499176i
$936$		0			0
$937$	946.417	+	687.612i	1.01005	+	0.733844i	0.964220	−	0.265105i	$-0.0854067\pi$
$937$	946.417	+	687.612i	1.01005	+	0.733844i	0.0458302	+	0.998949i	$0.485407\pi$
$938$		0			0
$939$	−57.9439	−	178.333i	−0.0617080	−	0.189918i
$940$		0			0
$941$	−720.775	−	992.061i	−0.765967	−	1.05426i	−0.996694	−	0.0812442i	$-0.974111\pi$
$941$	−720.775	−	992.061i	−0.765967	−	1.05426i	0.230728	−	0.973018i	$-0.425889\pi$
$942$		0			0
$943$	−238.248	+	733.253i	−0.252649	+	0.777575i
$944$		0			0
$945$	−5.01774	+	10.3095i	−0.00530978	+	0.0109096i
$946$		0			0
$947$			287.197i			0.303270i	0.988437	+	0.151635i	$0.0484539\pi$
$947$			287.197i			0.303270i	−0.988437	+	0.151635i	$0.951546\pi$
$948$		0			0
$949$	82.3629	−	253.487i	0.0867891	−	0.267110i
$950$		0			0
$951$	−252.838	+	183.697i	−0.265865	+	0.193162i
$952$		0			0
$953$	245.100	+	754.339i	0.257187	+	0.791541i	0.993391	+	0.114781i	$0.0366167\pi$
$953$	245.100	+	754.339i	0.257187	+	0.791541i	−0.736203	+	0.676760i	$0.763383\pi$
$954$		0			0
$955$	−361.352	−	678.249i	−0.378379	−	0.710208i
$956$		0			0
$957$	23.3143	+	22.4349i	0.0243619	+	0.0234429i
$958$		0			0
$959$	−21.1261	+	29.0776i	−0.0220293	+	0.0303207i
$960$		0			0
$961$	−273.665	−	842.254i	−0.284771	−	0.876435i
$962$		0			0
$963$	−428.345	+	311.211i	−0.444803	+	0.323168i
$964$		0			0
$965$	819.326	−	849.844i	0.849043	−	0.880667i
$966$		0			0
$967$	141.449			0.146276			0.0731381	−	0.997322i	$-0.476699\pi$
$967$	141.449			0.146276			0.0731381	+	0.997322i	$0.476699\pi$
$968$		0			0
$969$	−2515.61			−2.59609
$970$		0			0
$971$	−47.2954	+	145.560i	−0.0487079	+	0.149908i	−0.972452	−	0.233102i	$-0.925112\pi$
$971$	−47.2954	+	145.560i	−0.0487079	+	0.149908i	0.923744	+	0.383010i	$0.125112\pi$
$972$		0			0
$973$	−1.66985	−	2.29835i	−0.00171619	−	0.00236213i
$974$		0			0
$975$	537.398	+	361.186i	0.551178	+	0.370447i
$976$		0			0
$977$	888.630	−	1223.09i	0.909550	−	1.25189i	−0.0577699	−	0.998330i	$-0.518399\pi$
$977$	888.630	−	1223.09i	0.909550	−	1.25189i	0.967320	−	0.253558i	$-0.0816010\pi$
$978$		0			0
$979$	604.348	+	581.552i	0.617312	+	0.594027i
$980$		0			0
$981$	−307.222	+	422.855i	−0.313172	+	0.431045i
$982$		0			0
$983$	1.50113	−	0.487748i	0.00152709	−	0.000496183i	−0.308253	−	0.951304i	$-0.599744\pi$
$983$	1.50113	−	0.487748i	0.00152709	−	0.000496183i	0.309780	+	0.950808i	$0.399744\pi$
$984$		0			0
$985$	−952.169	+	168.706i	−0.966669	+	0.171275i
$986$		0			0
$987$	−26.9964	+	83.0863i	−0.0273519	+	0.0841806i
$988$		0			0
$989$		−	1422.44i		−	1.43826i
$990$		0			0
$991$	860.757			0.868574			0.434287	−	0.900775i	$-0.357000\pi$
$991$	860.757			0.868574			0.434287	+	0.900775i	$0.357000\pi$
$992$		0			0
$993$	−1429.88	−	464.596i	−1.43996	−	0.467871i
$994$		0			0
$995$	716.265	−	126.909i	0.719865	−	0.127546i
$996$		0			0
$997$	12.1700	+	37.4555i	0.0122067	+	0.0375682i	0.956974	−	0.290173i	$-0.0937127\pi$
$997$	12.1700	+	37.4555i	0.0122067	+	0.0375682i	−0.944768	+	0.327741i	$0.893713\pi$
$998$		0			0
$999$	−17.3156	−	12.5805i	−0.0173330	−	0.0125931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.q.a.29.3	✓	48
5.4	even	2	inner	220.3.q.a.29.10	yes	48
11.8	odd	10	inner	220.3.q.a.129.10	yes	48
55.19	odd	10	inner	220.3.q.a.129.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.q.a.29.3	✓	48	1.1	even	1	trivial
220.3.q.a.29.10	yes	48	5.4	even	2	inner
220.3.q.a.129.3	yes	48	55.19	odd	10	inner
220.3.q.a.129.10	yes	48	11.8	odd	10	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.83667 - 1.24661i) q^{3} +(-4.92332 + 0.872318i) q^{5} +(-0.101776 - 0.313235i) q^{7} +(5.88485 + 4.27559i) q^{9} +(7.92623 + 7.62725i) q^{11} +(-5.19406 - 3.77371i) q^{13} +(19.9766 + 2.79066i) q^{15} +(18.3110 - 13.3037i) q^{17} +(26.2028 + 8.51380i) q^{19} +1.32865i q^{21} +26.5778i q^{23} +(23.4781 - 8.58940i) q^{25} +(4.09250 + 5.63285i) q^{27} +(-0.693449 + 0.225315i) q^{29} +(-7.02505 - 5.10400i) q^{31} +(-20.9021 - 39.1441i) q^{33} +(0.774317 + 1.45337i) q^{35} +(-2.92359 + 0.949933i) q^{37} +(15.2236 + 20.9534i) q^{39} +(27.5889 + 8.96419i) q^{41} -53.5197 q^{43} +(-32.7027 - 15.9166i) q^{45} +(62.5341 + 20.3186i) q^{47} +(39.5541 - 28.7377i) q^{49} +(-86.8376 + 28.2152i) q^{51} +(-40.5229 + 55.7749i) q^{53} +(-45.6767 - 30.6372i) q^{55} +(-89.9181 - 65.3293i) q^{57} +(17.7615 + 54.6642i) q^{59} +(-47.9102 - 65.9427i) q^{61} +(0.740328 - 2.27849i) q^{63} +(28.8639 + 14.0483i) q^{65} +65.6000i q^{67} +(33.1321 - 101.970i) q^{69} +(-24.8061 + 18.0227i) q^{71} +(12.8287 + 39.4826i) q^{73} +(-100.785 + 3.68662i) q^{75} +(1.58242 - 3.25904i) q^{77} +(41.8643 - 57.6213i) q^{79} +(-28.9099 - 88.9756i) q^{81} +(90.6212 - 65.8402i) q^{83} +(-78.5456 + 81.4713i) q^{85} +2.94141 q^{87} +76.2467 q^{89} +(-0.653425 + 2.01104i) q^{91} +(20.5901 + 28.3399i) q^{93} +(-136.431 - 19.0590i) q^{95} +(-31.4114 + 43.2341i) q^{97} +(14.0337 + 78.7745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 5 q^{5} + 20 q^{9} - 23 q^{15} - 7 q^{25} - 74 q^{31} + 155 q^{35} + 80 q^{39} - 20 q^{41} + 12 q^{45} + 102 q^{49} + 220 q^{51} - 69 q^{55} + 40 q^{59} - 290 q^{61} - 234 q^{69} - 406 q^{71} + 153 q^{75}+ \cdots - 382 q^{99}+O(q^{100}) \) 48 * q + 5 * q^5 + 20 * q^9 - 23 * q^15 - 7 * q^25 - 74 * q^31 + 155 * q^35 + 80 * q^39 - 20 * q^41 + 12 * q^45 + 102 * q^49 + 220 * q^51 - 69 * q^55 + 40 * q^59 - 290 * q^61 - 234 * q^69 - 406 * q^71 + 153 * q^75 - 280 * q^79 + 230 * q^81 - 465 * q^85 - 636 * q^89 + 512 * q^91 - 495 * q^95 - 382 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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