LMFDB - Embedded newform 220.2.u.a.57.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(13,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

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

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

chi := DirichletCharacter("220.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.u (of order $20$, degree $8$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.4
Character	$\chi$	$=$	220.57
Dual form			220.2.u.a.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0307474 - 0.194131i) q^{3} +(-2.23602 - 0.0146855i) q^{5} +(3.21432 - 0.509098i) q^{7} +(2.81643 + 0.915113i) q^{9} +(2.95000 - 1.51575i) q^{11} +(4.74775 - 2.41910i) q^{13} +(-0.0716027 + 0.433630i) q^{15} +(-3.57446 - 1.82128i) q^{17} +(-4.43615 + 3.22305i) q^{19} -0.639653i q^{21} +(-2.60297 + 2.60297i) q^{23} +(4.99957 + 0.0656742i) q^{25} +(0.531947 - 1.04400i) q^{27} +(-3.79815 - 2.75952i) q^{29} +(-2.52450 + 7.76962i) q^{31} +(-0.203550 - 0.619293i) q^{33} +(-7.19476 + 1.09115i) q^{35} +(-1.76715 - 11.1573i) q^{37} +(-0.323642 - 0.996068i) q^{39} +(5.80437 + 7.98904i) q^{41} +(5.17742 + 5.17742i) q^{43} +(-6.28415 - 2.08757i) q^{45} +(-0.662035 - 0.104856i) q^{47} +(3.41527 - 1.10969i) q^{49} +(-0.463472 + 0.637915i) q^{51} +(-2.88788 - 5.66778i) q^{53} +(-6.61852 + 3.34592i) q^{55} +(0.489295 + 0.960296i) q^{57} +(-4.44597 + 6.11936i) q^{59} +(-7.85138 + 2.55107i) q^{61} +(9.51878 + 1.50763i) q^{63} +(-10.6516 + 5.33943i) q^{65} +(-7.99503 - 7.99503i) q^{67} +(0.425284 + 0.585353i) q^{69} +(-3.11574 - 9.58925i) q^{71} +(0.177831 + 1.12278i) q^{73} +(0.166473 - 0.968554i) q^{75} +(8.71058 - 6.37394i) q^{77} +(-1.14340 + 3.51903i) q^{79} +(7.00107 + 5.08658i) q^{81} +(-0.851148 + 1.67047i) q^{83} +(7.96581 + 4.12490i) q^{85} +(-0.652493 + 0.652493i) q^{87} +1.02792i q^{89} +(14.0292 - 10.1928i) q^{91} +(1.43071 + 0.728981i) q^{93} +(9.96665 - 7.14166i) q^{95} +(-3.00091 + 1.52904i) q^{97} +(9.69555 - 1.56941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.0307474	−	0.194131i	0.0177520	−	0.112082i	−0.977221	−	0.212223i	$-0.931930\pi$
$3$	0.0307474	−	0.194131i	0.0177520	−	0.112082i	0.994973	+	0.100142i	$0.0319296\pi$
$4$		0			0
$5$	−2.23602	−	0.0146855i	−0.999978	−	0.00656756i
$5$	−2.23602	−	0.0146855i	−0.999978	−	0.00656756i
$6$		0			0
$7$	3.21432	−	0.509098i	1.21490	−	0.192421i	0.484099	−	0.875013i	$-0.339148\pi$
$7$	3.21432	−	0.509098i	1.21490	−	0.192421i	0.730799	+	0.682592i	$0.239148\pi$
$8$		0			0
$9$	2.81643	+	0.915113i	0.938809	+	0.305038i
$10$		0			0
$11$	2.95000	−	1.51575i	0.889459	−	0.457015i
$11$	2.95000	−	1.51575i	0.889459	−	0.457015i
$12$		0			0
$13$	4.74775	−	2.41910i	1.31679	−	0.670938i	0.352506	−	0.935810i	$-0.385330\pi$
$13$	4.74775	−	2.41910i	1.31679	−	0.670938i	0.964284	+	0.264872i	$0.0853297\pi$
$14$		0			0
$15$	−0.0716027	+	0.433630i	−0.0184877	+	0.111963i
$16$		0			0
$17$	−3.57446	−	1.82128i	−0.866933	−	0.441724i	−0.0368214	−	0.999322i	$-0.511723\pi$
$17$	−3.57446	−	1.82128i	−0.866933	−	0.441724i	−0.830111	+	0.557597i	$0.811723\pi$
$18$		0			0
$19$	−4.43615	+	3.22305i	−1.01772	+	0.739418i	−0.965815	−	0.259233i	$-0.916530\pi$
$19$	−4.43615	+	3.22305i	−1.01772	+	0.739418i	−0.0519075	+	0.998652i	$0.516530\pi$
$20$		0			0
$21$		−	0.639653i		−	0.139584i
$22$		0			0
$23$	−2.60297	+	2.60297i	−0.542757	+	0.542757i	−0.924336	−	0.381579i	$-0.875380\pi$
$23$	−2.60297	+	2.60297i	−0.542757	+	0.542757i	0.381579	+	0.924336i	$0.375380\pi$
$24$		0			0
$25$	4.99957	+	0.0656742i	0.999914	+	0.0131348i
$26$		0			0
$27$	0.531947	−	1.04400i	0.102373	−	0.200919i
$28$		0			0
$29$	−3.79815	−	2.75952i	−0.705299	−	0.512430i	0.176354	−	0.984327i	$-0.443570\pi$
$29$	−3.79815	−	2.75952i	−0.705299	−	0.512430i	−0.881654	+	0.471897i	$0.843570\pi$
$30$		0			0
$31$	−2.52450	+	7.76962i	−0.453414	+	1.39547i	0.419573	+	0.907722i	$0.362180\pi$
$31$	−2.52450	+	7.76962i	−0.453414	+	1.39547i	−0.872987	+	0.487744i	$0.837820\pi$
$32$		0			0
$33$	−0.203550	−	0.619293i	−0.0354334	−	0.107805i
$34$		0			0
$35$	−7.19476	+	1.09115i	−1.21614	+	0.184438i
$36$		0			0
$37$	−1.76715	−	11.1573i	−0.290518	−	1.83426i	−0.511870	−	0.859063i	$-0.671047\pi$
$37$	−1.76715	−	11.1573i	−0.290518	−	1.83426i	0.221353	−	0.975194i	$-0.428953\pi$
$38$		0			0
$39$	−0.323642	−	0.996068i	−0.0518242	−	0.159499i
$40$		0			0
$41$	5.80437	+	7.98904i	0.906491	+	1.24768i	0.968351	+	0.249593i	$0.0802968\pi$
$41$	5.80437	+	7.98904i	0.906491	+	1.24768i	−0.0618598	+	0.998085i	$0.519703\pi$
$42$		0			0
$43$	5.17742	+	5.17742i	0.789549	+	0.789549i	0.981420	−	0.191871i	$-0.0614556\pi$
$43$	5.17742	+	5.17742i	0.789549	+	0.789549i	−0.191871	+	0.981420i	$0.561456\pi$
$44$		0			0
$45$	−6.28415	−	2.08757i	−0.936786	−	0.311197i
$46$		0			0
$47$	−0.662035	−	0.104856i	−0.0965678	−	0.0152948i	0.107964	−	0.994155i	$-0.465567\pi$
$47$	−0.662035	−	0.104856i	−0.0965678	−	0.0152948i	−0.204531	+	0.978860i	$0.565567\pi$
$48$		0			0
$49$	3.41527	−	1.10969i	0.487895	−	0.158527i
$50$		0			0
$51$	−0.463472	+	0.637915i	−0.0648991	+	0.0893259i
$52$		0			0
$53$	−2.88788	−	5.66778i	−0.396681	−	0.778530i	0.603137	−	0.797638i	$-0.293917\pi$
$53$	−2.88788	−	5.66778i	−0.396681	−	0.778530i	−0.999817	+	0.0191079i	$0.993917\pi$
$54$		0			0
$55$	−6.61852	+	3.34592i	−0.892441	+	0.451164i
$56$		0			0
$57$	0.489295	+	0.960296i	0.0648087	+	0.127194i
$58$		0			0
$59$	−4.44597	+	6.11936i	−0.578817	+	0.796673i	−0.993565	−	0.113263i	$-0.963870\pi$
$59$	−4.44597	+	6.11936i	−0.578817	+	0.796673i	0.414748	+	0.909936i	$0.363870\pi$
$60$		0			0
$61$	−7.85138	+	2.55107i	−1.00527	+	0.326631i	−0.764968	−	0.644068i	$-0.777245\pi$
$61$	−7.85138	+	2.55107i	−1.00527	+	0.326631i	−0.240298	+	0.970699i	$0.577245\pi$
$62$		0			0
$63$	9.51878	+	1.50763i	1.19925	+	0.189943i
$64$		0			0
$65$	−10.6516	+	5.33943i	−1.32117	+	0.662275i
$66$		0			0
$67$	−7.99503	−	7.99503i	−0.976748	−	0.976748i	0.0229875	−	0.999736i	$-0.492682\pi$
$67$	−7.99503	−	7.99503i	−0.976748	−	0.976748i	−0.999736	+	0.0229875i	$0.992682\pi$
$68$		0			0
$69$	0.425284	+	0.585353i	0.0511982	+	0.0704682i
$70$		0			0
$71$	−3.11574	−	9.58925i	−0.369770	−	1.13803i	−0.946940	−	0.321410i	$-0.895843\pi$
$71$	−3.11574	−	9.58925i	−0.369770	−	1.13803i	0.577170	−	0.816624i	$-0.304157\pi$
$72$		0			0
$73$	0.177831	+	1.12278i	0.0208136	+	0.131412i	0.995907	−	0.0903820i	$-0.0288088\pi$
$73$	0.177831	+	1.12278i	0.0208136	+	0.131412i	−0.975094	+	0.221794i	$0.928809\pi$
$74$		0			0
$75$	0.166473	−	0.968554i	0.0192227	−	0.111839i
$76$		0			0
$77$	8.71058	−	6.37394i	0.992662	−	0.726378i
$78$		0			0
$79$	−1.14340	+	3.51903i	−0.128643	+	0.395922i	−0.994547	−	0.104288i	$-0.966744\pi$
$79$	−1.14340	+	3.51903i	−0.128643	+	0.395922i	0.865904	+	0.500210i	$0.166744\pi$
$80$		0			0
$81$	7.00107	+	5.08658i	0.777897	+	0.565175i
$82$		0			0
$83$	−0.851148	+	1.67047i	−0.0934256	+	0.183358i	−0.932990	−	0.359902i	$-0.882810\pi$
$83$	−0.851148	+	1.67047i	−0.0934256	+	0.183358i	0.839565	+	0.543260i	$0.182810\pi$
$84$		0			0
$85$	7.96581	+	4.12490i	0.864013	+	0.447408i
$86$		0			0
$87$	−0.652493	+	0.652493i	−0.0699546	+	0.0699546i
$88$		0			0
$89$			1.02792i			0.108959i	0.998515	+	0.0544795i	$0.0173500\pi$
$89$			1.02792i			0.108959i	−0.998515	+	0.0544795i	$0.982650\pi$
$90$		0			0
$91$	14.0292	−	10.1928i	1.47066	−	1.06850i
$92$		0			0
$93$	1.43071	+	0.728981i	0.148357	+	0.0755918i
$94$		0			0
$95$	9.96665	−	7.14166i	1.02256	−	0.732719i
$96$		0			0
$97$	−3.00091	+	1.52904i	−0.304696	+	0.155250i	−0.599653	−	0.800260i	$-0.704695\pi$
$97$	−3.00091	+	1.52904i	−0.304696	+	0.155250i	0.294957	+	0.955511i	$0.404695\pi$
$98$		0			0
$99$	9.69555	−	1.56941i	0.974439	−	0.157732i
$100$		0			0
$101$	0.104950	+	0.0341002i	0.0104429	+	0.00339310i	0.314234	−	0.949346i	$-0.398252\pi$
$101$	0.104950	+	0.0341002i	0.0104429	+	0.00339310i	−0.303791	+	0.952739i	$0.598252\pi$
$102$		0			0
$103$	0.101767	−	0.0161183i	0.0100274	−	0.00158818i	−0.151419	−	0.988470i	$-0.548384\pi$
$103$	0.101767	−	0.0161183i	0.0100274	−	0.00158818i	0.161446	+	0.986882i	$0.448384\pi$
$104$		0			0
$105$	−0.00939364	+	1.43028i	−0.000916725	+	0.139581i
$106$		0			0
$107$	−2.49553	+	15.7562i	−0.241252	+	1.52321i	0.508252	+	0.861208i	$0.330292\pi$
$107$	−2.49553	+	15.7562i	−0.241252	+	1.52321i	−0.749505	+	0.661999i	$0.769708\pi$
$108$		0			0
$109$	0.774585			0.0741918			0.0370959	−	0.999312i	$-0.488189\pi$
$109$	0.774585			0.0741918			0.0370959	+	0.999312i	$0.488189\pi$
$110$		0			0
$111$	−2.22033			−0.210744
$112$		0			0
$113$	1.37656	−	8.69124i	0.129496	−	0.817603i	−0.834368	−	0.551207i	$-0.814167\pi$
$113$	1.37656	−	8.69124i	0.129496	−	0.817603i	0.963864	−	0.266395i	$-0.0858327\pi$
$114$		0			0
$115$	5.85852	−	5.78207i	0.546310	−	0.539181i
$116$		0			0
$117$	15.5855	−	2.46849i	1.44088	−	0.228212i
$118$		0			0
$119$	−12.4166	−	4.03441i	−1.13823	−	0.369834i
$120$		0			0
$121$	6.40501	−	8.94292i	0.582274	−	0.812993i
$122$		0			0
$123$	1.72939	−	0.881169i	0.155934	−	0.0794523i
$124$		0			0
$125$	−11.1782	−	0.220270i	−0.999806	−	0.0197015i
$126$		0			0
$127$	3.66110	+	1.86542i	0.324870	+	0.165529i	0.608817	−	0.793310i	$-0.291644\pi$
$127$	3.66110	+	1.86542i	0.324870	+	0.165529i	−0.283948	+	0.958840i	$0.591644\pi$
$128$		0			0
$129$	1.16429	−	0.845907i	0.102510	−	0.0744780i
$130$		0			0
$131$			8.42076i			0.735725i	0.929880	+	0.367863i	$0.119910\pi$
$131$			8.42076i			0.735725i	−0.929880	+	0.367863i	$0.880090\pi$
$132$		0			0
$133$	−12.6183	+	12.6183i	−1.09415	+	1.09415i
$134$		0			0
$135$	−1.20478	+	2.32660i	−0.103691	+	0.200242i
$136$		0			0
$137$	−1.67147	+	3.28044i	−0.142803	+	0.280267i	−0.951319	−	0.308207i	$-0.900271\pi$
$137$	−1.67147	+	3.28044i	−0.142803	+	0.280267i	0.808516	+	0.588474i	$0.200271\pi$
$138$		0			0
$139$	−2.79197	−	2.02848i	−0.236811	−	0.172054i	0.463050	−	0.886332i	$-0.346755\pi$
$139$	−2.79197	−	2.02848i	−0.236811	−	0.172054i	−0.699862	+	0.714279i	$0.746755\pi$
$140$		0			0
$141$	−0.0407117	+	0.125298i	−0.00342854	+	0.0105520i
$142$		0			0
$143$	10.3391	−	14.3327i	0.864601	−	1.19856i
$144$		0			0
$145$	8.45222	+	6.22612i	0.701919	+	0.517051i
$146$		0			0
$147$	−0.110415	−	0.697130i	−0.00910684	−	0.0574983i
$148$		0			0
$149$	1.65385	+	5.09001i	0.135488	+	0.416990i	0.995666	−	0.0930049i	$-0.0296472\pi$
$149$	1.65385	+	5.09001i	0.135488	+	0.416990i	−0.860177	+	0.509995i	$0.829647\pi$
$150$		0			0
$151$	2.65450	+	3.65361i	0.216020	+	0.297326i	0.903251	−	0.429113i	$-0.141174\pi$
$151$	2.65450	+	3.65361i	0.216020	+	0.297326i	−0.687231	+	0.726439i	$0.741174\pi$
$152$		0			0
$153$	−8.40052	−	8.40052i	−0.679142	−	0.679142i
$154$		0			0
$155$	5.75894	−	17.3360i	0.462569	−	1.39246i
$156$		0			0
$157$	5.75059	+	0.910804i	0.458947	+	0.0726901i	0.381627	−	0.924316i	$-0.375364\pi$
$157$	5.75059	+	0.910804i	0.458947	+	0.0726901i	0.0773197	+	0.997006i	$0.475364\pi$
$158$		0			0
$159$	−1.18909	+	0.386359i	−0.0943009	+	0.0306402i
$160$		0			0
$161$	−7.04161	+	9.69195i	−0.554957	+	0.763832i
$162$		0			0
$163$	5.64816	+	11.0851i	0.442398	+	0.868255i	0.999290	+	0.0376700i	$0.0119936\pi$
$163$	5.64816	+	11.0851i	0.442398	+	0.868255i	−0.556892	+	0.830585i	$0.688006\pi$
$164$		0			0
$165$	0.446046	+	1.38774i	0.0347246	+	0.108035i
$166$		0			0
$167$	−2.85138	−	5.59615i	−0.220646	−	0.433043i	0.753975	−	0.656903i	$-0.228134\pi$
$167$	−2.85138	−	5.59615i	−0.220646	−	0.433043i	−0.974621	+	0.223861i	$0.928134\pi$
$168$		0			0
$169$	9.04789	−	12.4534i	0.695992	−	0.957950i
$170$		0			0
$171$	−15.4435	+	5.01791i	−1.18100	+	0.383729i
$172$		0			0
$173$	−15.0136	−	2.37792i	−1.14146	−	0.180790i	−0.443058	−	0.896493i	$-0.646106\pi$
$173$	−15.0136	−	2.37792i	−1.14146	−	0.180790i	−0.698405	+	0.715703i	$0.746106\pi$
$174$		0			0
$175$	16.1036	−	2.33417i	1.21732	−	0.176447i
$176$		0			0
$177$	1.05126	+	1.05126i	0.0790173	+	0.0790173i
$178$		0			0
$179$	4.23571	+	5.82995i	0.316592	+	0.435751i	0.937423	−	0.348193i	$-0.113205\pi$
$179$	4.23571	+	5.82995i	0.316592	+	0.435751i	−0.620831	+	0.783944i	$0.713205\pi$
$180$		0			0
$181$	−3.59279	−	11.0575i	−0.267050	−	0.821896i	−0.991214	−	0.132268i	$-0.957774\pi$
$181$	−3.59279	−	11.0575i	−0.267050	−	0.821896i	0.724164	−	0.689628i	$-0.242226\pi$
$182$		0			0
$183$	0.253833	+	1.60264i	0.0187639	+	0.118470i
$184$		0			0
$185$	3.78753	+	24.9740i	0.278465	+	1.83612i
$186$		0			0
$187$	−13.3052	+	0.0452105i	−0.972976	+	0.00330612i
$188$		0			0
$189$	1.17835	−	3.62658i	0.0857121	−	0.263795i
$190$		0			0
$191$	−13.0699	−	9.49582i	−0.945703	−	0.687094i	0.00408349	−	0.999992i	$-0.498700\pi$
$191$	−13.0699	−	9.49582i	−0.945703	−	0.687094i	−0.949787	+	0.312898i	$0.898700\pi$
$192$		0			0
$193$	−3.65910	+	7.18138i	−0.263388	+	0.516927i	−0.984389	−	0.176006i	$-0.943682\pi$
$193$	−3.65910	+	7.18138i	−0.263388	+	0.516927i	0.721001	+	0.692934i	$0.243682\pi$
$194$		0			0
$195$	0.709043	+	2.23198i	0.0507756	+	0.159836i
$196$		0			0
$197$	−7.99806	+	7.99806i	−0.569838	+	0.569838i	−0.932083	−	0.362245i	$-0.882010\pi$
$197$	−7.99806	+	7.99806i	−0.569838	+	0.569838i	0.362245	+	0.932083i	$0.382010\pi$
$198$		0			0
$199$		−	7.97776i		−	0.565529i	−0.959189	−	0.282764i	$-0.908749\pi$
$199$		−	7.97776i		−	0.565529i	0.959189	−	0.282764i	$-0.0912514\pi$
$200$		0			0
$201$	−1.79791	+	1.30626i	−0.126815	+	0.0921365i
$202$		0			0
$203$	−13.6133	−	6.93634i	−0.955469	−	0.486836i
$204$		0			0
$205$	−12.8614	−	17.9489i	−0.898277	−	1.25360i
$206$		0			0
$207$	−9.71309	+	4.94907i	−0.675107	+	0.343984i
$208$		0			0
$209$	−8.20131	+	16.2321i	−0.567296	+	1.12280i
$210$		0			0
$211$	4.86478	+	1.58066i	0.334905	+	0.108817i	0.471642	−	0.881790i	$-0.343661\pi$
$211$	4.86478	+	1.58066i	0.334905	+	0.108817i	−0.136737	+	0.990607i	$0.543661\pi$
$212$		0			0
$213$	−1.95737	+	0.310018i	−0.134117	+	0.0212421i
$214$		0			0
$215$	−11.5008	−	11.6528i	−0.784346	−	0.794717i
$216$		0			0
$217$	−4.15906	+	26.2593i	−0.282335	+	1.78259i
$218$		0			0
$219$	0.223435			0.0150984
$220$		0			0
$221$	−21.3765			−1.43794
$222$		0			0
$223$	−1.51284	+	9.55172i	−0.101308	+	0.639631i	0.883823	+	0.467822i	$0.154961\pi$
$223$	−1.51284	+	9.55172i	−0.101308	+	0.639631i	−0.985130	+	0.171809i	$0.945039\pi$
$224$		0			0
$225$	14.0208	+	4.76014i	0.934722	+	0.317342i
$226$		0			0
$227$	12.0925	−	1.91526i	0.802607	−	0.127120i	0.258363	−	0.966048i	$-0.416817\pi$
$227$	12.0925	−	1.91526i	0.802607	−	0.127120i	0.544243	+	0.838927i	$0.316817\pi$
$228$		0			0
$229$	9.71729	+	3.15734i	0.642137	+	0.208643i	0.611944	−	0.790901i	$-0.290388\pi$
$229$	9.71729	+	3.15734i	0.642137	+	0.208643i	0.0301930	+	0.999544i	$0.490388\pi$
$230$		0			0
$231$	−0.969554	−	1.88698i	−0.0637920	−	0.124154i
$232$		0			0
$233$	−1.27644	+	0.650378i	−0.0836222	+	0.0426077i	−0.495301	−	0.868721i	$-0.664942\pi$
$233$	−1.27644	+	0.650378i	−0.0836222	+	0.0426077i	0.411679	+	0.911329i	$0.364942\pi$
$234$		0			0
$235$	1.47878	+	0.244183i	0.0964653	+	0.0159287i
$236$		0			0
$237$	0.647998	+	0.330171i	0.0420920	+	0.0214469i
$238$		0			0
$239$	22.4095	−	16.2815i	1.44955	−	1.05316i	0.463617	−	0.886036i	$-0.346552\pi$
$239$	22.4095	−	16.2815i	1.44955	−	1.05316i	0.985936	−	0.167125i	$-0.0534485\pi$
$240$		0			0
$241$		−	6.65481i		−	0.428674i	−0.976760	−	0.214337i	$-0.931241\pi$
$241$		−	6.65481i		−	0.428674i	0.976760	−	0.214337i	$-0.0687591\pi$
$242$		0			0
$243$	3.68831	−	3.68831i	0.236605	−	0.236605i
$244$		0			0
$245$	−7.65290	+	2.43113i	−0.488926	+	0.155319i
$246$		0			0
$247$	−13.2648	+	26.0337i	−0.844022	+	1.65649i
$248$		0			0
$249$	0.298120	+	0.216597i	0.0188926	+	0.0137263i
$250$		0			0
$251$	7.36460	−	22.6659i	0.464849	−	1.43066i	−0.394323	−	0.918972i	$-0.629021\pi$
$251$	7.36460	−	22.6659i	0.464849	−	1.43066i	0.859172	−	0.511687i	$-0.170979\pi$
$252$		0			0
$253$	−3.73332	+	11.6242i	−0.234712	+	0.730808i
$254$		0			0
$255$	1.04570	−	1.41958i	0.0654843	−	0.0888977i
$256$		0			0
$257$	0.685639	+	4.32895i	0.0427690	+	0.270033i	0.999801	−	0.0199496i	$-0.00635059\pi$
$257$	0.685639	+	4.32895i	0.0427690	+	0.270033i	−0.957032	+	0.289982i	$0.906351\pi$
$258$		0			0
$259$	−11.3604	−	34.9636i	−0.705899	−	2.17253i
$260$		0			0
$261$	−8.17195	−	11.2477i	−0.505831	−	0.696217i
$262$		0			0
$263$	12.6404	+	12.6404i	0.779442	+	0.779442i	0.979736	−	0.200294i	$-0.0641897\pi$
$263$	12.6404	+	12.6404i	0.779442	+	0.779442i	−0.200294	+	0.979736i	$0.564190\pi$
$264$		0			0
$265$	6.37412	+	12.7157i	0.391559	+	0.781119i
$266$		0			0
$267$	0.199551	+	0.0316058i	0.0122123	+	0.00193424i
$268$		0			0
$269$	19.6421	−	6.38211i	1.19760	−	0.389124i	0.358723	−	0.933444i	$-0.383212\pi$
$269$	19.6421	−	6.38211i	1.19760	−	0.389124i	0.838878	+	0.544320i	$0.183212\pi$
$270$		0			0
$271$	−3.67960	+	5.06454i	−0.223520	+	0.307649i	−0.906018	−	0.423238i	$-0.860893\pi$
$271$	−3.67960	+	5.06454i	−0.223520	+	0.307649i	0.682499	+	0.730887i	$0.260893\pi$
$272$		0			0
$273$	−1.54739	−	3.03692i	−0.0936520	−	0.183802i
$274$		0			0
$275$	14.8483	−	7.38435i	0.895385	−	0.445293i
$276$		0			0
$277$	−10.6368	−	20.8758i	−0.639102	−	1.25431i	−0.952457	−	0.304672i	$-0.901453\pi$
$277$	−10.6368	−	20.8758i	−0.639102	−	1.25431i	0.313356	−	0.949636i	$-0.398547\pi$
$278$		0			0
$279$	−14.2202	+	19.5724i	−0.851339	+	1.17177i
$280$		0			0
$281$	9.65989	−	3.13869i	0.576261	−	0.187238i	−0.00636405	−	0.999980i	$-0.502026\pi$
$281$	9.65989	−	3.13869i	0.576261	−	0.187238i	0.582625	+	0.812741i	$0.302026\pi$
$282$		0			0
$283$	−13.0076	−	2.06021i	−0.773225	−	0.122467i	−0.242660	−	0.970111i	$-0.578020\pi$
$283$	−13.0076	−	2.06021i	−0.773225	−	0.122467i	−0.530564	+	0.847645i	$0.678020\pi$
$284$		0			0
$285$	−1.07997	−	2.15443i	−0.0639720	−	0.127617i
$286$		0			0
$287$	22.7243	+	22.7243i	1.34137	+	1.34137i
$288$		0			0
$289$	−0.532661	−	0.733145i	−0.0313330	−	0.0431262i
$290$		0			0
$291$	0.204564	+	0.629584i	0.0119918	+	0.0369069i
$292$		0			0
$293$	1.22817	+	7.75437i	0.0717506	+	0.453015i	0.997240	+	0.0742424i	$0.0236539\pi$
$293$	1.22817	+	7.75437i	0.0717506	+	0.453015i	−0.925490	+	0.378773i	$0.876346\pi$
$294$		0			0
$295$	10.0312	−	13.6177i	0.584036	−	0.792854i
$296$		0			0
$297$	−0.0132048	−	3.88611i	−0.000766221	−	0.225495i
$298$		0			0
$299$	−6.06141	+	18.6551i	−0.350541	+	1.07885i
$300$		0			0
$301$	19.2777	+	14.0061i	1.11115	+	0.807296i
$302$		0			0
$303$	0.00984686	−	0.0193255i	0.000565687	−	0.00111022i
$304$		0			0
$305$	17.5933	−	5.58894i	1.00739	−	0.320022i
$306$		0			0
$307$	6.65300	−	6.65300i	0.379707	−	0.379707i	−0.491289	−	0.870996i	$-0.663474\pi$
$307$	6.65300	−	6.65300i	0.379707	−	0.379707i	0.870996	+	0.491289i	$0.163474\pi$
$308$		0			0
$309$		−	0.0202518i		−	0.00115208i
$310$		0			0
$311$	6.20361	−	4.50719i	0.351774	−	0.255579i	−0.397839	−	0.917455i	$-0.630240\pi$
$311$	6.20361	−	4.50719i	0.351774	−	0.255579i	0.749613	+	0.661876i	$0.230240\pi$
$312$		0			0
$313$	−28.2126	−	14.3750i	−1.59467	−	0.812526i	−0.999963	−	0.00858451i	$-0.997267\pi$
$313$	−28.2126	−	14.3750i	−1.59467	−	0.812526i	−0.594709	−	0.803941i	$-0.702733\pi$
$314$		0			0
$315$	−21.2620	−	3.51087i	−1.19798	−	0.197815i
$316$		0			0
$317$	7.62587	−	3.88557i	0.428311	−	0.218236i	−0.226526	−	0.974005i	$-0.572737\pi$
$317$	7.62587	−	3.88557i	0.428311	−	0.218236i	0.654838	+	0.755769i	$0.272737\pi$
$318$		0			0
$319$	−15.3873	−	2.38354i	−0.861523	−	0.133453i
$320$		0			0
$321$	2.98204	+	0.968923i	0.166441	+	0.0540800i
$322$		0			0
$323$	21.7269	−	3.44120i	1.20892	−	0.191473i
$324$		0			0
$325$	23.8956	−	11.7827i	1.32549	−	0.653584i
$326$		0			0
$327$	0.0238165	−	0.150371i	0.00131705	−	0.00831555i
$328$		0			0
$329$	−2.18137			−0.120263
$330$		0			0
$331$	−16.9166			−0.929820			−0.464910	−	0.885358i	$-0.653913\pi$
$331$	−16.9166			−0.929820			−0.464910	+	0.885358i	$0.653913\pi$
$332$		0			0
$333$	5.23318	−	33.0410i	0.286777	−	1.81064i
$334$		0			0
$335$	17.7596	+	17.9945i	0.970312	+	0.983142i
$336$		0			0
$337$	16.9422	−	2.68338i	0.922901	−	0.146173i	0.323139	−	0.946352i	$-0.395262\pi$
$337$	16.9422	−	2.68338i	0.922901	−	0.146173i	0.599762	+	0.800178i	$0.295262\pi$
$338$		0			0
$339$	−1.64492	−	0.534466i	−0.0893396	−	0.0290282i
$340$		0			0
$341$	4.32951	+	26.7469i	0.234456	+	1.44843i
$342$		0			0
$343$	−9.88494	+	5.03663i	−0.533736	+	0.271952i
$344$		0			0
$345$	−0.942347	−	1.31511i	−0.0507342	−	0.0708029i
$346$		0			0
$347$	22.3812	+	11.4038i	1.20149	+	0.612187i	0.936025	−	0.351934i	$-0.114476\pi$
$347$	22.3812	+	11.4038i	1.20149	+	0.612187i	0.265461	+	0.964122i	$0.414476\pi$
$348$		0			0
$349$	−4.91014	+	3.56743i	−0.262834	+	0.190960i	−0.711395	−	0.702792i	$-0.751936\pi$
$349$	−4.91014	+	3.56743i	−0.262834	+	0.190960i	0.448562	+	0.893752i	$0.351936\pi$
$350$		0			0
$351$		−	6.24351i		−	0.333254i
$352$		0			0
$353$	17.8379	−	17.8379i	0.949413	−	0.949413i	−0.0493677	−	0.998781i	$-0.515721\pi$
$353$	17.8379	−	17.8379i	0.949413	−	0.949413i	0.998781	+	0.0493677i	$0.0157206\pi$
$354$		0			0
$355$	6.82602	+	21.4875i	0.362288	+	1.14044i
$356$		0			0
$357$	−1.16499	+	2.28641i	−0.0616576	+	0.121010i
$358$		0			0
$359$	7.65250	+	5.55987i	0.403883	+	0.293439i	0.771121	−	0.636689i	$-0.219696\pi$
$359$	7.65250	+	5.55987i	0.403883	+	0.293439i	−0.367237	+	0.930127i	$0.619696\pi$
$360$		0			0
$361$	3.42003	−	10.5258i	0.180002	−	0.553989i
$362$		0			0
$363$	−1.53916	−	1.51838i	−0.0807852	−	0.0796945i
$364$		0			0
$365$	−0.381146	−	2.51318i	−0.0199501	−	0.131546i
$366$		0			0
$367$	−2.74867	−	17.3544i	−0.143480	−	0.905895i	−0.949445	−	0.313932i	$-0.898353\pi$
$367$	−2.74867	−	17.3544i	−0.143480	−	0.905895i	0.805966	−	0.591962i	$-0.201647\pi$
$368$		0			0
$369$	9.03673	+	27.8122i	0.470434	+	1.44785i
$370$		0			0
$371$	−12.1680	−	16.7478i	−0.631732	−	0.869505i
$372$		0			0
$373$	−10.6232	−	10.6232i	−0.550050	−	0.550050i	0.376405	−	0.926455i	$-0.377160\pi$
$373$	−10.6232	−	10.6232i	−0.550050	−	0.550050i	−0.926455	+	0.376405i	$0.877160\pi$
$374$		0			0
$375$	−0.386461	+	2.16326i	−0.0199568	+	0.111710i
$376$		0			0
$377$	−24.7082	−	3.91340i	−1.27254	−	0.201550i
$378$		0			0
$379$	0.421294	−	0.136887i	0.0216404	−	0.00703139i	−0.298177	−	0.954511i	$-0.596379\pi$
$379$	0.421294	−	0.136887i	0.0216404	−	0.00703139i	0.319817	+	0.947479i	$0.396379\pi$
$380$		0			0
$381$	0.474706	−	0.653377i	0.0243199	−	0.0334735i
$382$		0			0
$383$	−6.26658	−	12.2989i	−0.320207	−	0.628442i	0.673658	−	0.739044i	$-0.264722\pi$
$383$	−6.26658	−	12.2989i	−0.320207	−	0.628442i	−0.993865	+	0.110602i	$0.964722\pi$
$384$		0			0
$385$	−19.5706	+	14.1243i	−0.997412	+	0.719843i
$386$		0			0
$387$	9.84390	+	19.3197i	0.500394	+	0.982078i
$388$		0			0
$389$	10.4451	−	14.3765i	0.529588	−	0.728915i	−0.457480	−	0.889220i	$-0.651248\pi$
$389$	10.4451	−	14.3765i	0.529588	−	0.728915i	0.987068	+	0.160305i	$0.0512478\pi$
$390$		0			0
$391$	14.0449	−	4.56348i	0.710283	−	0.230785i
$392$		0			0
$393$	1.63473	+	0.258916i	0.0824614	+	0.0130606i
$394$		0			0
$395$	2.60835	−	7.85183i	0.131240	−	0.395069i
$396$		0			0
$397$	21.6616	+	21.6616i	1.08717	+	1.08717i	0.995819	+	0.0913478i	$0.0291175\pi$
$397$	21.6616	+	21.6616i	1.08717	+	1.08717i	0.0913478	+	0.995819i	$0.470883\pi$
$398$		0			0
$399$	2.06164	+	2.83760i	0.103211	+	0.142058i
$400$		0			0
$401$	1.10249	+	3.39310i	0.0550555	+	0.169444i	0.974803	−	0.223067i	$-0.0716068\pi$
$401$	1.10249	+	3.39310i	0.0550555	+	0.169444i	−0.919748	+	0.392510i	$0.871607\pi$
$402$		0			0
$403$	6.80978	+	42.9953i	0.339219	+	2.14175i
$404$		0			0
$405$	−15.5798	−	11.4765i	−0.774168	−	0.570272i
$406$		0			0
$407$	−22.1248	−	30.2356i	−1.09669	−	1.49872i
$408$		0			0
$409$	7.83663	−	24.1187i	0.387497	−	1.19259i	−0.547156	−	0.837030i	$-0.684290\pi$
$409$	7.83663	−	24.1187i	0.387497	−	1.19259i	0.934653	−	0.355561i	$-0.115710\pi$
$410$		0			0
$411$	0.585443	+	0.425349i	0.0288778	+	0.0209809i
$412$		0			0
$413$	−11.1754	+	21.9330i	−0.549907	+	1.07925i
$414$		0			0
$415$	1.92772	−	3.72271i	0.0946278	−	0.182741i
$416$		0			0
$417$	−0.479638	+	0.479638i	−0.0234880	+	0.0234880i
$418$		0			0
$419$		−	18.4358i		−	0.900648i	−0.892865	−	0.450324i	$-0.851308\pi$
$419$		−	18.4358i		−	0.900648i	0.892865	−	0.450324i	$-0.148692\pi$
$420$		0			0
$421$	−21.0494	+	15.2933i	−1.02589	+	0.745351i	−0.967481	−	0.252942i	$-0.918602\pi$
$421$	−21.0494	+	15.2933i	−1.02589	+	0.745351i	−0.0584058	+	0.998293i	$0.518602\pi$
$422$		0			0
$423$	−1.76862	−	0.901157i	−0.0859932	−	0.0438157i
$424$		0			0
$425$	−17.7511	−	9.34035i	−0.861056	−	0.453073i
$426$		0			0
$427$	−23.9381	+	12.1971i	−1.15845	+	0.590258i
$428$		0			0
$429$	−2.46453	−	2.44784i	−0.118989	−	0.118183i
$430$		0			0
$431$	8.15236	+	2.64886i	0.392685	+	0.127591i	0.498703	−	0.866773i	$-0.333810\pi$
$431$	8.15236	+	2.64886i	0.392685	+	0.127591i	−0.106018	+	0.994364i	$0.533810\pi$
$432$		0			0
$433$	21.3177	−	3.37639i	1.02446	−	0.162259i	0.378478	−	0.925610i	$-0.376447\pi$
$433$	21.3177	−	3.37639i	1.02446	−	0.162259i	0.645983	+	0.763351i	$0.276447\pi$
$434$		0			0
$435$	1.46857	−	1.44940i	0.0704125	−	0.0694936i
$436$		0			0
$437$	3.15766	−	19.9367i	0.151051	−	0.953700i
$438$		0			0
$439$	−12.2003			−0.582288			−0.291144	−	0.956679i	$-0.594036\pi$
$439$	−12.2003			−0.582288			−0.291144	+	0.956679i	$0.594036\pi$
$440$		0			0
$441$	10.6343			0.506397
$442$		0			0
$443$	−1.73420	+	10.9493i	−0.0823944	+	0.520218i	0.911626	+	0.411021i	$0.134828\pi$
$443$	−1.73420	+	10.9493i	−0.0823944	+	0.520218i	−0.994020	+	0.109197i	$0.965172\pi$
$444$		0			0
$445$	0.0150955	−	2.29844i	0.000715595	−	0.108957i
$446$		0			0
$447$	1.03898	−	0.164559i	0.0491422	−	0.00778336i
$448$		0			0
$449$	8.90862	+	2.89459i	0.420424	+	0.136604i	0.511586	−	0.859232i	$-0.329058\pi$
$449$	8.90862	+	2.89459i	0.420424	+	0.136604i	−0.0911622	+	0.995836i	$0.529058\pi$
$450$		0			0
$451$	29.2323	+	14.7697i	1.37649	+	0.695478i
$452$		0			0
$453$	0.790899	−	0.402983i	0.0371597	−	0.0189338i
$454$		0			0
$455$	−31.5193	+	22.5853i	−1.47765	+	1.05882i
$456$		0			0
$457$	−11.7148	−	5.96901i	−0.547997	−	0.279218i	0.157993	−	0.987440i	$-0.449498\pi$
$457$	−11.7148	−	5.96901i	−0.547997	−	0.279218i	−0.705990	+	0.708222i	$0.749498\pi$
$458$		0			0
$459$	−3.80284	+	2.76293i	−0.177502	+	0.128962i
$460$		0			0
$461$			12.4764i			0.581084i	0.956862	+	0.290542i	$0.0938355\pi$
$461$			12.4764i			0.581084i	−0.956862	+	0.290542i	$0.906164\pi$
$462$		0			0
$463$	0.334220	−	0.334220i	0.0155325	−	0.0155325i	−0.699298	−	0.714830i	$-0.746504\pi$
$463$	0.334220	−	0.334220i	0.0155325	−	0.0155325i	0.714830	+	0.699298i	$0.246504\pi$
$464$		0			0
$465$	−3.18838	−	1.65103i	−0.147858	−	0.0765645i
$466$		0			0
$467$	0.468732	−	0.919938i	0.0216903	−	0.0425697i	−0.879907	−	0.475146i	$-0.842395\pi$
$467$	0.468732	−	0.919938i	0.0216903	−	0.0425697i	0.901597	+	0.432576i	$0.142395\pi$
$468$		0			0
$469$	−29.7688	−	21.6283i	−1.37460	−	0.998703i
$470$		0			0
$471$	0.353631	−	1.08836i	0.0162945	−	0.0501492i
$472$		0			0
$473$	23.1211	+	7.42572i	1.06311	+	0.341435i
$474$		0			0
$475$	−22.3905	+	15.8225i	−1.02735	+	0.725987i
$476$		0			0
$477$	−2.94684	−	18.6056i	−0.134927	−	0.851894i
$478$		0			0
$479$	12.2212	+	37.6130i	0.558401	+	1.71858i	0.686789	+	0.726857i	$0.259020\pi$
$479$	12.2212	+	37.6130i	0.558401	+	1.71858i	−0.128388	+	0.991724i	$0.540980\pi$
$480$		0			0
$481$	−35.3807	−	48.6974i	−1.61322	−	2.22041i
$482$		0			0
$483$	1.66500	+	1.66500i	0.0757601	+	0.0757601i
$484$		0			0
$485$	6.73254	−	3.37489i	0.305709	−	0.153246i
$486$		0			0
$487$	−36.2263	−	5.73768i	−1.64157	−	0.259999i	−0.733769	−	0.679399i	$-0.762241\pi$
$487$	−36.2263	−	5.73768i	−1.64157	−	0.259999i	−0.907802	+	0.419400i	$0.862241\pi$
$488$		0			0
$489$	2.32564	−	0.755646i	0.105169	−	0.0341715i
$490$		0			0
$491$	−24.5974	+	33.8554i	−1.11006	+	1.52787i	−0.288742	+	0.957407i	$0.593237\pi$
$491$	−24.5974	+	33.8554i	−1.11006	+	1.52787i	−0.821322	+	0.570465i	$0.806763\pi$
$492$		0			0
$493$	8.55048	+	16.7813i	0.385094	+	0.755790i
$494$		0			0
$495$	−21.7025	+	3.36686i	−0.975454	+	0.151329i
$496$		0			0
$497$	−14.8968	−	29.2367i	−0.668214	−	1.31144i
$498$		0			0
$499$	−25.8822	+	35.6238i	−1.15865	+	1.59474i	−0.442537	+	0.896750i	$0.645921\pi$
$499$	−25.8822	+	35.6238i	−1.15865	+	1.59474i	−0.716109	+	0.697989i	$0.754079\pi$
$500$		0			0
$501$	−1.17406	+	0.381475i	−0.0524531	+	0.0170431i
$502$		0			0
$503$	−19.3133	−	3.05893i	−0.861137	−	0.136391i	−0.289781	−	0.957093i	$-0.593583\pi$
$503$	−19.3133	−	3.05893i	−0.861137	−	0.136391i	−0.571356	+	0.820702i	$0.693583\pi$
$504$		0			0
$505$	−0.234169	−	0.0777901i	−0.0104204	−	0.00346161i
$506$		0			0
$507$	−2.13939	−	2.13939i	−0.0950135	−	0.0950135i
$508$		0			0
$509$	−2.50898	−	3.45331i	−0.111208	−	0.153065i	0.749785	−	0.661682i	$-0.230157\pi$
$509$	−2.50898	−	3.45331i	−0.111208	−	0.153065i	−0.860993	+	0.508617i	$0.830157\pi$
$510$		0			0
$511$	1.14321	+	3.51845i	0.0505728	+	0.155647i
$512$		0			0
$513$	1.00508	+	6.34585i	0.0443756	+	0.280176i
$514$		0			0
$515$	−0.227790	+	0.0345464i	−0.0100376	+	0.00152229i
$516$		0			0
$517$	−2.11194	+	0.694154i	−0.0928830	+	0.0305288i
$518$		0			0
$519$	−0.923258	+	2.84149i	−0.0405265	+	0.124728i
$520$		0			0
$521$	7.92382	+	5.75699i	0.347149	+	0.252218i	0.747672	−	0.664068i	$-0.231172\pi$
$521$	7.92382	+	5.75699i	0.347149	+	0.252218i	−0.400523	+	0.916287i	$0.631172\pi$
$522$		0			0
$523$	13.5045	−	26.5041i	0.590511	−	1.15894i	−0.381580	−	0.924336i	$-0.624620\pi$
$523$	13.5045	−	26.5041i	0.590511	−	1.15894i	0.972090	−	0.234607i	$-0.0753802\pi$
$524$		0			0
$525$	0.0420087	−	3.19799i	0.00183341	−	0.139572i
$526$		0			0
$527$	23.1744	−	23.1744i	1.00949	−	1.00949i
$528$		0			0
$529$			9.44908i			0.410830i
$530$		0			0
$531$	−18.1217	+	13.1662i	−0.786414	+	0.571363i
$532$		0			0
$533$	46.8840	+	23.8886i	2.03077	+	1.03473i
$534$		0			0
$535$	5.81145	−	35.1945i	0.251251	−	1.52159i
$536$		0			0
$537$	1.26201	−	0.643028i	0.0544599	−	0.0277487i
$538$		0			0
$539$	8.39303	−	8.45026i	0.361513	−	0.363979i
$540$		0			0
$541$	37.2531	+	12.1043i	1.60164	+	0.520404i	0.967512	−	0.252826i	$-0.0813601\pi$
$541$	37.2531	+	12.1043i	1.60164	+	0.520404i	0.634126	+	0.773230i	$0.281360\pi$
$542$		0			0
$543$	−2.25707	+	0.357485i	−0.0968602	+	0.0153412i
$544$		0			0
$545$	−1.73199	−	0.0113752i	−0.0741902	−	0.000487259i
$546$		0			0
$547$	6.13688	−	38.7467i	0.262394	−	1.65669i	−0.406737	−	0.913545i	$-0.633333\pi$
$547$	6.13688	−	38.7467i	0.262394	−	1.65669i	0.669131	−	0.743144i	$-0.266667\pi$
$548$		0			0
$549$	−24.4474			−1.04339
$550$		0			0
$551$	25.7432			1.09670
$552$		0			0
$553$	−1.88373	+	11.8934i	−0.0801043	+	0.505759i
$554$		0			0
$555$	4.96469	+	0.0326066i	0.210739	+	0.00138407i
$556$		0			0
$557$	19.7334	−	3.12546i	0.836131	−	0.132430i	0.276336	−	0.961061i	$-0.410880\pi$
$557$	19.7334	−	3.12546i	0.836131	−	0.132430i	0.559795	+	0.828631i	$0.310880\pi$
$558$		0			0
$559$	37.1058	+	12.0564i	1.56941	+	0.509931i
$560$		0			0
$561$	−0.400325	+	2.58436i	−0.0169017	+	0.109112i
$562$		0			0
$563$	26.2573	−	13.3788i	1.10661	−	0.563848i	0.197462	−	0.980311i	$-0.436730\pi$
$563$	26.2573	−	13.3788i	1.10661	−	0.563848i	0.909153	+	0.416462i	$0.136730\pi$
$564$		0			0
$565$	−3.20564	+	19.4136i	−0.134862	+	0.816735i
$566$		0			0
$567$	25.0932	+	12.7856i	1.05382	+	0.536947i
$568$		0			0
$569$	12.5719	−	9.13401i	0.527041	−	0.382918i	−0.292209	−	0.956355i	$-0.594390\pi$
$569$	12.5719	−	9.13401i	0.527041	−	0.382918i	0.819250	+	0.573437i	$0.194390\pi$
$570$		0			0
$571$			0.662428i			0.0277217i	0.999904	+	0.0138609i	$0.00441219\pi$
$571$			0.662428i			0.0277217i	−0.999904	+	0.0138609i	$0.995588\pi$
$572$		0			0
$573$	−2.24530	+	2.24530i	−0.0937988	+	0.0937988i
$574$		0			0
$575$	−13.1847	+	12.8428i	−0.549839	+	0.535581i
$576$		0			0
$577$	−17.6530	+	34.6459i	−0.734903	+	1.44233i	0.155822	+	0.987785i	$0.450197\pi$
$577$	−17.6530	+	34.6459i	−0.734903	+	1.44233i	−0.890725	+	0.454543i	$0.849803\pi$
$578$		0			0
$579$	1.28162	+	0.931154i	0.0532625	+	0.0386974i
$580$		0			0
$581$	−1.88543	+	5.80275i	−0.0782207	+	0.240739i
$582$		0			0
$583$	−17.1102	−	12.3427i	−0.708632	−	0.511181i
$584$		0			0
$585$	−34.8856	+	5.29072i	−1.44234	+	0.218744i
$586$		0			0
$587$	−0.375602	−	2.37146i	−0.0155027	−	0.0978805i	0.978724	−	0.205183i	$-0.0657788\pi$
$587$	−0.375602	−	2.37146i	−0.0155027	−	0.0978805i	−0.994226	+	0.107302i	$0.965779\pi$
$588$		0			0
$589$	−13.8428	−	42.6038i	−0.570383	−	1.75546i
$590$		0			0
$591$	1.30675	+	1.79859i	0.0537527	+	0.0739842i
$592$		0			0
$593$	−31.9523	−	31.9523i	−1.31213	−	1.31213i	−0.919846	−	0.392280i	$-0.871687\pi$
$593$	−31.9523	−	31.9523i	−1.31213	−	1.31213i	−0.392280	−	0.919846i	$-0.628313\pi$
$594$		0			0
$595$	27.7046	+	9.20337i	1.13578	+	0.377301i
$596$		0			0
$597$	−1.54873	−	0.245295i	−0.0633855	−	0.0100393i
$598$		0			0
$599$	−15.0927	+	4.90391i	−0.616670	+	0.200368i	−0.600661	−	0.799504i	$-0.705096\pi$
$599$	−15.0927	+	4.90391i	−0.616670	+	0.200368i	−0.0160087	+	0.999872i	$0.505096\pi$
$600$		0			0
$601$	−4.48148	+	6.16823i	−0.182803	+	0.251607i	−0.890578	−	0.454831i	$-0.849699\pi$
$601$	−4.48148	+	6.16823i	−0.182803	+	0.251607i	0.707774	+	0.706439i	$0.249699\pi$
$602$		0			0
$603$	−15.2011	−	29.8338i	−0.619035	−	1.21493i
$604$		0			0
$605$	−14.4531	+	19.9025i	−0.587601	+	0.809151i
$606$		0			0
$607$	−8.10055	−	15.8982i	−0.328791	−	0.645289i	0.666142	−	0.745825i	$-0.267944\pi$
$607$	−8.10055	−	15.8982i	−0.328791	−	0.645289i	−0.994933	+	0.100536i	$0.967944\pi$
$608$		0			0
$609$	−1.76514	+	2.42950i	−0.0715269	+	0.0984484i
$610$		0			0
$611$	−3.39684	+	1.10370i	−0.137421	+	0.0446509i
$612$		0			0
$613$	1.32799	+	0.210333i	0.0536370	+	0.00849527i	0.183195	−	0.983077i	$-0.441356\pi$
$613$	1.32799	+	0.210333i	0.0536370	+	0.00849527i	−0.129558	+	0.991572i	$0.541356\pi$
$614$		0			0
$615$	−3.87989	+	1.94491i	−0.156452	+	0.0784265i
$616$		0			0
$617$	2.91978	+	2.91978i	0.117546	+	0.117546i	0.763433	−	0.645887i	$-0.223512\pi$
$617$	2.91978	+	2.91978i	0.117546	+	0.117546i	−0.645887	+	0.763433i	$0.723512\pi$
$618$		0			0
$619$	3.15329	+	4.34013i	0.126741	+	0.174445i	0.867672	−	0.497137i	$-0.165615\pi$
$619$	3.15329	+	4.34013i	0.126741	+	0.174445i	−0.740931	+	0.671582i	$0.765615\pi$
$620$		0			0
$621$	1.33287	+	4.10216i	0.0534863	+	0.164614i
$622$		0			0
$623$	0.523311	+	3.30405i	0.0209660	+	0.132374i
$624$		0			0
$625$	24.9914	+	0.656685i	0.999655	+	0.0262674i
$626$		0			0
$627$	2.89899	+	2.09123i	0.115774	+	0.0835155i
$628$		0			0
$629$	−14.0040	+	43.0999i	−0.558376	+	1.71851i
$630$		0			0
$631$	28.0962	+	20.4131i	1.11849	+	0.812631i	0.983980	−	0.178281i	$-0.0570535\pi$
$631$	28.0962	+	20.4131i	1.11849	+	0.812631i	0.134511	+	0.990912i	$0.457054\pi$
$632$		0			0
$633$	0.456435	−	0.895805i	0.0181417	−	0.0356050i
$634$		0			0
$635$	−8.15889	−	4.22489i	−0.323776	−	0.167659i
$636$		0			0
$637$	13.5304	−	13.5304i	0.536093	−	0.536093i
$638$		0			0
$639$		−	29.8587i		−	1.18119i
$640$		0			0
$641$	37.5802	−	27.3036i	1.48433	−	1.07843i	0.508200	−	0.861239i	$-0.330311\pi$
$641$	37.5802	−	27.3036i	1.48433	−	1.07843i	0.976130	−	0.217189i	$-0.0696888\pi$
$642$		0			0
$643$	−23.8844	−	12.1697i	−0.941911	−	0.479927i	−0.0855661	−	0.996332i	$-0.527270\pi$
$643$	−23.8844	−	12.1697i	−0.941911	−	0.479927i	−0.856344	+	0.516405i	$0.827270\pi$
$644$		0			0
$645$	−2.61580	+	1.87437i	−0.102997	+	0.0738031i
$646$		0			0
$647$	7.02618	−	3.58002i	0.276228	−	0.140745i	−0.310389	−	0.950610i	$-0.600459\pi$
$647$	7.02618	−	3.58002i	0.276228	−	0.140745i	0.586617	+	0.809865i	$0.300459\pi$
$648$		0			0
$649$	−3.84022	+	24.7911i	−0.150742	+	0.973136i
$650$		0			0
$651$	4.96987	+	1.61481i	0.194784	+	0.0632893i
$652$		0			0
$653$	18.8247	−	2.98154i	0.736668	−	0.116677i	0.223185	−	0.974776i	$-0.428355\pi$
$653$	18.8247	−	2.98154i	0.736668	−	0.116677i	0.513483	+	0.858099i	$0.328355\pi$
$654$		0			0
$655$	0.123663	−	18.8290i	0.00483192	−	0.735709i
$656$		0			0
$657$	−0.526624	+	3.32497i	−0.0205456	+	0.129720i
$658$		0			0
$659$	42.2869			1.64726			0.823632	−	0.567125i	$-0.191944\pi$
$659$	42.2869			1.64726			0.823632	+	0.567125i	$0.191944\pi$
$660$		0			0
$661$	25.4299			0.989109			0.494555	−	0.869147i	$-0.335331\pi$
$661$	25.4299			0.989109			0.494555	+	0.869147i	$0.335331\pi$
$662$		0			0
$663$	−0.657271	+	4.14984i	−0.0255263	+	0.161167i
$664$		0			0
$665$	28.4002	−	28.0296i	1.10131	−	1.08694i
$666$		0			0
$667$	17.0694	−	2.70353i	0.660931	−	0.104681i
$668$		0			0
$669$	1.80777	+	0.587381i	0.0698925	+	0.0227095i
$670$		0			0
$671$	−19.2948	+	19.4264i	−0.744868	+	0.749947i
$672$		0			0
$673$	19.1313	−	9.74788i	0.737457	−	0.375753i	−0.0445627	−	0.999007i	$-0.514189\pi$
$673$	19.1313	−	9.74788i	0.737457	−	0.375753i	0.782020	+	0.623253i	$0.214189\pi$
$674$		0			0
$675$	2.72807	−	5.18464i	0.105003	−	0.199557i
$676$		0			0
$677$	38.1118	+	19.4189i	1.46475	+	0.746330i	0.990941	−	0.134296i	$-0.0428771\pi$
$677$	38.1118	+	19.4189i	1.46475	+	0.746330i	0.473813	+	0.880625i	$0.342877\pi$
$678$		0			0
$679$	−8.86744	+	6.44257i	−0.340301	+	0.247243i
$680$		0			0
$681$		−	2.40642i		−	0.0922142i
$682$		0			0
$683$	−7.18559	+	7.18559i	−0.274949	+	0.274949i	−0.831089	−	0.556140i	$-0.812282\pi$
$683$	−7.18559	+	7.18559i	−0.274949	+	0.274949i	0.556140	+	0.831089i	$0.312282\pi$
$684$		0			0
$685$	3.78561	−	7.31058i	0.144641	−	0.279323i
$686$		0			0
$687$	0.911720	−	1.78935i	0.0347843	−	0.0682680i
$688$		0			0
$689$	−27.4219	−	19.9232i	−1.04469	−	0.759012i
$690$		0			0
$691$	5.61862	−	17.2923i	0.213742	−	0.657831i	−0.785498	−	0.618864i	$-0.787593\pi$
$691$	5.61862	−	17.2923i	0.213742	−	0.657831i	0.999240	−	0.0389674i	$-0.0124068\pi$
$692$		0			0
$693$	30.3656	−	9.98058i	1.15349	−	0.379131i
$694$		0			0
$695$	6.21310	+	4.57673i	0.235676	+	0.173605i
$696$		0			0
$697$	−6.19724	−	39.1278i	−0.234737	−	1.48207i
$698$		0			0
$699$	0.0870116	+	0.267794i	0.00329108	+	0.0101289i
$700$		0			0
$701$	6.05920	+	8.33978i	0.228853	+	0.314989i	0.907965	−	0.419045i	$-0.137635\pi$
$701$	6.05920	+	8.33978i	0.228853	+	0.314989i	−0.679112	+	0.734034i	$0.737635\pi$
$702$		0			0
$703$	43.8000	+	43.8000i	1.65195	+	1.65195i
$704$		0			0
$705$	0.0928723	−	0.279570i	0.00349777	−	0.0105292i
$706$		0			0
$707$	0.354702	+	0.0561793i	0.0133400	+	0.00211284i
$708$		0			0
$709$	−31.6001	+	10.2675i	−1.18677	+	0.385604i	−0.834877	−	0.550437i	$-0.814461\pi$
$709$	−31.6001	+	10.2675i	−1.18677	+	0.385604i	−0.351891	+	0.936041i	$0.614461\pi$
$710$		0			0
$711$	−6.44062	+	8.86476i	−0.241542	+	0.332454i
$712$		0			0
$713$	−13.6529	−	26.7953i	−0.511305	−	1.00349i
$714$		0			0
$715$	−23.3290	+	31.8965i	−0.872454	+	1.19286i
$716$		0			0
$717$	−2.47171	−	4.85101i	−0.0923077	−	0.181164i
$718$		0			0
$719$	14.2160	−	19.5667i	0.530169	−	0.729715i	−0.456987	−	0.889473i	$-0.651072\pi$
$719$	14.2160	−	19.5667i	0.530169	−	0.729715i	0.987156	+	0.159758i	$0.0510715\pi$
$720$		0			0
$721$	0.318906	−	0.103619i	0.0118767	−	0.00385896i
$722$		0			0
$723$	−1.29191	−	0.204618i	−0.0480466	−	0.00760983i
$724$		0			0
$725$	−18.8079	−	14.0459i	−0.698508	−	0.521650i
$726$		0			0
$727$	−0.348445	−	0.348445i	−0.0129231	−	0.0129231i	0.700616	−	0.713539i	$-0.252909\pi$
$727$	−0.348445	−	0.348445i	−0.0129231	−	0.0129231i	−0.713539	+	0.700616i	$0.752909\pi$
$728$		0			0
$729$	14.6571	+	20.1738i	0.542856	+	0.747178i
$730$		0			0
$731$	−9.07694	−	27.9360i	−0.335723	−	1.03325i
$732$		0			0
$733$	6.36801	+	40.2060i	0.235208	+	1.48504i	0.768902	+	0.639366i	$0.220803\pi$
$733$	6.36801	+	40.2060i	0.235208	+	1.48504i	−0.533694	+	0.845677i	$0.679197\pi$
$734$		0			0
$735$	0.236651	+	1.56042i	0.00872902	+	0.0575569i
$736$		0			0
$737$	−35.7038	−	11.4669i	−1.31517	−	0.422388i
$738$		0			0
$739$	3.05832	−	9.41255i	0.112502	−	0.346246i	−0.878916	−	0.476977i	$-0.841732\pi$
$739$	3.05832	−	9.41255i	0.112502	−	0.346246i	0.991418	+	0.130731i	$0.0417324\pi$
$740$		0			0
$741$	4.64610	+	3.37559i	0.170679	+	0.124005i
$742$		0			0
$743$	12.2803	−	24.1015i	0.450521	−	0.884198i	−0.548329	−	0.836263i	$-0.684736\pi$
$743$	12.2803	−	24.1015i	0.450521	−	0.884198i	0.998850	−	0.0479352i	$-0.0152641\pi$
$744$		0			0
$745$	−3.62328	−	11.4057i	−0.132747	−	0.417871i
$746$		0			0
$747$	−3.92587	+	3.92587i	−0.143640	+	0.143640i
$748$		0			0
$749$			51.9159i			1.89696i
$750$		0			0
$751$	4.69796	−	3.41327i	0.171431	−	0.124552i	−0.498761	−	0.866739i	$-0.666212\pi$
$751$	4.69796	−	3.41327i	0.171431	−	0.124552i	0.670192	+	0.742187i	$0.266212\pi$
$752$		0			0
$753$	−4.17372	−	2.12662i	−0.152099	−	0.0774982i
$754$		0			0
$755$	−5.88186	−	8.20852i	−0.214063	−	0.298739i
$756$		0			0
$757$	31.9778	−	16.2935i	1.16225	−	0.592197i	0.236985	−	0.971513i	$-0.423841\pi$
$757$	31.9778	−	16.2935i	1.16225	−	0.592197i	0.925267	+	0.379316i	$0.123841\pi$
$758$		0			0
$759$	2.14184	+	1.08217i	0.0777437	+	0.0392802i
$760$		0			0
$761$	−18.4521	−	5.99545i	−0.668888	−	0.217335i	−0.0451642	−	0.998980i	$-0.514381\pi$
$761$	−18.4521	−	5.99545i	−0.668888	−	0.217335i	−0.623724	+	0.781645i	$0.714381\pi$
$762$		0			0
$763$	2.48976	−	0.394340i	0.0901354	−	0.0142761i
$764$		0			0
$765$	18.6604	+	18.9071i	0.674667	+	0.683588i
$766$		0			0
$767$	−6.30504	+	39.8085i	−0.227662	+	1.43740i
$768$		0			0
$769$	23.1799			0.835887			0.417944	−	0.908473i	$-0.362751\pi$
$769$	23.1799			0.835887			0.417944	+	0.908473i	$0.362751\pi$
$770$		0			0
$771$	0.861467			0.0310250
$772$		0			0
$773$	−3.70509	+	23.3930i	−0.133263	+	0.841389i	0.826982	+	0.562229i	$0.190056\pi$
$773$	−3.70509	+	23.3930i	−0.133263	+	0.841389i	−0.960245	+	0.279160i	$0.909944\pi$
$774$		0			0
$775$	−13.1317	+	38.6790i	−0.471704	+	1.38939i
$776$		0			0
$777$	−7.13683	+	1.13036i	−0.256033	+	0.0405516i
$778$		0			0
$779$	−51.4981	−	16.7328i	−1.84511	−	0.599513i
$780$		0			0
$781$	−23.7263	−	23.5656i	−0.848994	−	0.843244i
$782$		0			0
$783$	−4.90137	+	2.49737i	−0.175161	+	0.0892488i
$784$		0			0
$785$	−12.8451	−	2.12103i	−0.458460	−	0.0757027i
$786$		0			0
$787$	−36.0798	−	18.3836i	−1.28611	−	0.655304i	−0.328806	−	0.944398i	$-0.606646\pi$
$787$	−36.0798	−	18.3836i	−1.28611	−	0.655304i	−0.957301	+	0.289094i	$0.906646\pi$
$788$		0			0
$789$	2.84256	−	2.06524i	0.101198	−	0.0735246i
$790$		0			0
$791$		−	28.6372i		−	1.01822i
$792$		0			0
$793$	−31.1051	+	31.1051i	−1.10458	+	1.10458i
$794$		0			0
$795$	2.66450	−	0.846443i	0.0945001	−	0.0300202i
$796$		0			0
$797$	−22.1104	+	43.3942i	−0.783192	+	1.53710i	0.0592071	+	0.998246i	$0.481143\pi$
$797$	−22.1104	+	43.3942i	−0.783192	+	1.53710i	−0.842399	+	0.538855i	$0.818857\pi$
$798$		0			0
$799$	2.17544	+	1.58055i	0.0769617	+	0.0559159i
$800$		0			0
$801$	−0.940661	+	2.89506i	−0.0332366	+	0.102292i
$802$		0			0
$803$	2.22646	+	3.04266i	0.0785700	+	0.107373i
$804$		0			0
$805$	15.8875	−	21.5680i	0.559961	−	0.760171i
$806$		0			0
$807$	−0.635024	−	4.00938i	−0.0223539	−	0.141137i
$808$		0			0
$809$	−8.36499	−	25.7448i	−0.294097	−	0.905138i	−0.983523	−	0.180782i	$-0.942137\pi$
$809$	−8.36499	−	25.7448i	−0.294097	−	0.905138i	0.689426	−	0.724356i	$-0.257863\pi$
$810$		0			0
$811$	−5.42770	−	7.47059i	−0.190592	−	0.262328i	0.703017	−	0.711173i	$-0.251836\pi$
$811$	−5.42770	−	7.47059i	−0.190592	−	0.262328i	−0.893610	+	0.448845i	$0.851836\pi$
$812$		0			0
$813$	0.870047	+	0.870047i	0.0305139	+	0.0305139i
$814$		0			0
$815$	−12.4666	−	24.8695i	−0.436686	−	0.871141i
$816$		0			0
$817$	−39.6549	−	6.28072i	−1.38735	−	0.219734i
$818$		0			0
$819$	48.8399	−	15.8690i	1.70660	−	0.554509i
$820$		0			0
$821$	−18.4645	+	25.4142i	−0.644416	+	0.886962i	−0.998841	−	0.0481218i	$-0.984676\pi$
$821$	−18.4645	+	25.4142i	−0.644416	+	0.886962i	0.354426	+	0.935084i	$0.384676\pi$
$822$		0			0
$823$	9.70553	+	19.0482i	0.338313	+	0.663977i	0.996004	−	0.0893109i	$-0.0284665\pi$
$823$	9.70553	+	19.0482i	0.338313	+	0.663977i	−0.657690	+	0.753288i	$0.728466\pi$
$824$		0			0
$825$	−0.976988	−	3.10957i	−0.0340144	−	0.108261i
$826$		0			0
$827$	1.76115	+	3.45645i	0.0612412	+	0.120193i	0.919598	−	0.392860i	$-0.128514\pi$
$827$	1.76115	+	3.45645i	0.0612412	+	0.120193i	−0.858357	+	0.513053i	$0.828514\pi$
$828$		0			0
$829$	3.49646	−	4.81246i	0.121437	−	0.167144i	−0.743970	−	0.668213i	$-0.767060\pi$
$829$	3.49646	−	4.81246i	0.121437	−	0.167144i	0.865407	+	0.501069i	$0.167060\pi$
$830$		0			0
$831$	−4.37971	+	1.42305i	−0.151930	+	0.0493652i
$832$		0			0
$833$	−14.2288	−	2.25361i	−0.492997	−	0.0780831i
$834$		0			0
$835$	6.29356	+	12.5550i	0.217797	+	0.434482i
$836$		0			0
$837$	6.76862	+	6.76862i	0.233958	+	0.233958i
$838$		0			0
$839$	−19.8076	−	27.2628i	−0.683834	−	0.941217i	0.316138	−	0.948713i	$-0.397614\pi$
$839$	−19.8076	−	27.2628i	−0.683834	−	0.941217i	−0.999972	+	0.00749608i	$0.997614\pi$
$840$		0			0
$841$	−2.15047	−	6.61847i	−0.0741542	−	0.228223i
$842$		0			0
$843$	−0.312301	−	1.97179i	−0.0107562	−	0.0679122i
$844$		0			0
$845$	−20.4141	+	27.7131i	−0.702268	+	0.953359i
$846$		0			0
$847$	16.0349	−	32.0062i	0.550966	−	1.09975i
$848$		0			0
$849$	−0.799902	+	2.46185i	−0.0274526	+	0.0844904i
$850$		0			0
$851$	33.6421	+	24.4424i	1.15324	+	0.837875i
$852$		0			0
$853$	−9.71522	+	19.0672i	−0.332643	+	0.652848i	−0.995381	−	0.0960029i	$-0.969394\pi$
$853$	−9.71522	+	19.0672i	−0.332643	+	0.652848i	0.662738	+	0.748851i	$0.269394\pi$
$854$		0			0
$855$	34.6058	−	10.9934i	1.18349	−	0.375965i
$856$		0			0
$857$	−18.6774	+	18.6774i	−0.638008	+	0.638008i	−0.950064	−	0.312056i	$-0.898982\pi$
$857$	−18.6774	+	18.6774i	−0.638008	+	0.638008i	0.312056	+	0.950064i	$0.398982\pi$
$858$		0			0
$859$			6.24532i			0.213088i	0.994308	+	0.106544i	$0.0339784\pi$
$859$			6.24532i			0.213088i	−0.994308	+	0.106544i	$0.966022\pi$
$860$		0			0
$861$	5.11021	−	3.71279i	0.174156	−	0.126531i
$862$		0			0
$863$	−15.6521	−	7.97514i	−0.532804	−	0.271477i	0.166822	−	0.985987i	$-0.446650\pi$
$863$	−15.6521	−	7.97514i	−0.532804	−	0.271477i	−0.699625	+	0.714510i	$0.746650\pi$
$864$		0			0
$865$	33.5358	+	5.53756i	1.14025	+	0.188283i
$866$		0			0
$867$	−0.158704	+	0.0808639i	−0.00538989	+	0.00274628i
$868$		0			0
$869$	1.96093	+	12.1143i	0.0665200	+	0.410948i
$870$		0			0
$871$	−57.2992	−	18.6176i	−1.94151	−	0.630835i
$872$		0			0
$873$	−9.85108	+	1.56026i	−0.333409	+	0.0528068i
$874$		0			0
$875$	−36.0423	+	4.98277i	−1.21845	+	0.168448i
$876$		0			0
$877$	−7.86105	+	49.6327i	−0.265449	+	1.67598i	0.390060	+	0.920789i	$0.372454\pi$
$877$	−7.86105	+	49.6327i	−0.265449	+	1.67598i	−0.655509	+	0.755188i	$0.727546\pi$
$878$		0			0
$879$	1.54313			0.0520485
$880$		0			0
$881$	−48.4041			−1.63077			−0.815387	−	0.578916i	$-0.803476\pi$
$881$	−48.4041			−1.63077			−0.815387	+	0.578916i	$0.803476\pi$
$882$		0			0
$883$	5.98949	−	37.8161i	0.201562	−	1.27261i	−0.654627	−	0.755952i	$-0.727174\pi$
$883$	5.98949	−	37.8161i	0.201562	−	1.27261i	0.856189	−	0.516662i	$-0.172826\pi$
$884$		0			0
$885$	−2.33519	−	2.36607i	−0.0784967	−	0.0795346i
$886$		0			0
$887$	43.4632	−	6.88389i	1.45935	−	0.231138i	0.624245	−	0.781228i	$-0.285407\pi$
$887$	43.4632	−	6.88389i	1.45935	−	0.231138i	0.835105	+	0.550090i	$0.185407\pi$
$888$		0			0
$889$	12.7176	+	4.13220i	0.426535	+	0.138590i
$890$		0			0
$891$	28.3631	+	4.39354i	0.950201	+	0.147189i
$892$		0			0
$893$	3.27484	−	1.66862i	0.109588	−	0.0558381i
$894$		0			0
$895$	−9.38551	−	13.0981i	−0.313723	−	0.437821i
$896$		0			0
$897$	3.43517	+	1.75031i	0.114697	+	0.0584410i
$898$		0			0
$899$	31.0289	−	22.5438i	1.03487	−	0.751878i
$900$		0			0
$901$			25.5189i			0.850157i
$902$		0			0
$903$	3.31175	−	3.31175i	0.110208	−	0.110208i
$904$		0			0
$905$	7.87117	+	24.7775i	0.261646	+	0.823632i
$906$		0			0
$907$	4.88315	−	9.58372i	0.162142	−	0.318222i	−0.795614	−	0.605804i	$-0.792851\pi$
$907$	4.88315	−	9.58372i	0.162142	−	0.318222i	0.957756	+	0.287582i	$0.0928514\pi$
$908$		0			0
$909$	0.264378	+	0.192082i	0.00876886	+	0.00637095i
$910$		0			0
$911$	−5.83452	+	17.9568i	−0.193306	+	0.594936i	0.806686	+	0.590981i	$0.201259\pi$
$911$	−5.83452	+	17.9568i	−0.193306	+	0.594936i	−0.999992	+	0.00395526i	$0.998741\pi$
$912$		0			0
$913$	0.0211285	+	6.21802i	0.000699252	+	0.205786i
$914$		0			0
$915$	−0.544040	−	3.58726i	−0.0179854	−	0.118591i
$916$		0			0
$917$	4.28699	+	27.0670i	0.141569	+	0.893831i
$918$		0			0
$919$	−5.20310	−	16.0135i	−0.171634	−	0.528236i	0.827829	−	0.560980i	$-0.189576\pi$
$919$	−5.20310	−	16.0135i	−0.171634	−	0.528236i	−0.999464	+	0.0327436i	$0.989576\pi$
$920$		0			0
$921$	−1.08699	−	1.49612i	−0.0358177	−	0.0492988i
$922$		0			0
$923$	−37.9901	−	37.9901i	−1.25046	−	1.25046i
$924$		0			0
$925$	−8.10224	−	55.8980i	−0.266400	−	1.83791i
$926$		0			0
$927$	0.301370	+	0.0477322i	0.00989827	+	0.00156773i
$928$		0			0
$929$	14.0294	−	4.55842i	0.460289	−	0.149557i	−0.0696882	−	0.997569i	$-0.522200\pi$
$929$	14.0294	−	4.55842i	0.460289	−	0.149557i	0.529977	+	0.848012i	$0.322200\pi$
$930$		0			0
$931$	−11.5740	+	15.9303i	−0.379324	+	0.522095i
$932$		0			0
$933$	−0.684241	−	1.34290i	−0.0224011	−	0.0439646i
$934$		0			0
$935$	29.7515	+	0.0943027i	0.972977	+	0.00308403i
$936$		0			0
$937$	18.0760	+	35.4761i	0.590517	+	1.15895i	0.972088	+	0.234615i	$0.0753830\pi$
$937$	18.0760	+	35.4761i	0.590517	+	1.15895i	−0.381571	+	0.924339i	$0.624617\pi$
$938$		0			0
$939$	−3.65811	+	5.03496i	−0.119378	+	0.164310i
$940$		0			0
$941$	−22.5807	+	7.33691i	−0.736110	+	0.239177i	−0.652994	−	0.757363i	$-0.726487\pi$
$941$	−22.5807	+	7.33691i	−0.736110	+	0.239177i	−0.0831160	+	0.996540i	$0.526487\pi$
$942$		0			0
$943$	−35.9039	−	5.68661i	−1.16919	−	0.185182i
$944$		0			0
$945$	−2.68806	+	8.09179i	−0.0874427	+	0.263226i
$946$		0			0
$947$	−22.9342	−	22.9342i	−0.745261	−	0.745261i	0.228324	−	0.973585i	$-0.426675\pi$
$947$	−22.9342	−	22.9342i	−0.745261	−	0.745261i	−0.973585	+	0.228324i	$0.926675\pi$
$948$		0			0
$949$	3.56042	+	4.90050i	0.115576	+	0.159077i
$950$		0			0
$951$	−0.519836	−	1.59989i	−0.0168568	−	0.0518800i
$952$		0			0
$953$	−5.01286	−	31.6499i	−0.162382	−	1.02524i	−0.925435	−	0.378906i	$-0.876300\pi$
$953$	−5.01286	−	31.6499i	−0.162382	−	1.02524i	0.763053	−	0.646336i	$-0.223700\pi$
$954$		0			0
$955$	29.0851	+	21.4248i	0.941170	+	0.693290i
$956$		0			0
$957$	−0.935839	+	2.91387i	−0.0302514	+	0.0941920i
$958$		0			0
$959$	−3.70256	+	11.3953i	−0.119562	+	0.367974i
$960$		0			0
$961$	−28.9144	−	21.0075i	−0.932722	−	0.677662i
$962$		0			0
$963$	−21.4472	+	42.0925i	−0.691126	+	1.35641i
$964$		0			0
$965$	8.28728	−	16.0040i	0.266777	−	0.515186i
$966$		0			0
$967$	−20.9981	+	20.9981i	−0.675253	+	0.675253i	−0.958922	−	0.283669i	$-0.908448\pi$
$967$	−20.9981	+	20.9981i	−0.675253	+	0.675253i	0.283669	+	0.958922i	$0.408448\pi$
$968$		0			0
$969$		−	4.32368i		−	0.138897i
$970$		0			0
$971$	0.106113	−	0.0770954i	0.00340532	−	0.00247411i	−0.586081	−	0.810252i	$-0.699330\pi$
$971$	0.106113	−	0.0770954i	0.00340532	−	0.00247411i	0.589487	+	0.807778i	$0.299330\pi$
$972$		0			0
$973$	−10.0070	−	5.09880i	−0.320808	−	0.163460i
$974$		0			0
$975$	−1.55266	−	5.00117i	−0.0497248	−	0.160166i
$976$		0			0
$977$	−14.4170	+	7.34581i	−0.461240	+	0.235013i	−0.669140	−	0.743137i	$-0.733337\pi$
$977$	−14.4170	+	7.34581i	−0.461240	+	0.235013i	0.207900	+	0.978150i	$0.433337\pi$
$978$		0			0
$979$	1.55807	+	3.03236i	0.0497960	+	0.0969146i
$980$		0			0
$981$	2.18156	+	0.708833i	0.0696519	+	0.0226313i
$982$		0			0
$983$	−40.1054	+	6.35207i	−1.27916	+	0.202600i	−0.758788	−	0.651338i	$-0.774208\pi$
$983$	−40.1054	+	6.35207i	−1.27916	+	0.202600i	−0.520376	+	0.853937i	$0.674208\pi$
$984$		0			0
$985$	18.0013	−	17.7664i	0.573568	−	0.566083i
$986$		0			0
$987$	−0.0670716	+	0.423473i	−0.00213491	+	0.0134793i
$988$		0			0
$989$	−26.9533			−0.857066
$990$		0			0
$991$	23.5944			0.749502			0.374751	−	0.927126i	$-0.377728\pi$
$991$	23.5944			0.749502			0.374751	+	0.927126i	$0.377728\pi$
$992$		0			0
$993$	−0.520141	+	3.28404i	−0.0165062	+	0.104216i
$994$		0			0
$995$	−0.117158	+	17.8384i	−0.00371414	+	0.565517i
$996$		0			0
$997$	3.22469	−	0.510741i	0.102127	−	0.0161753i	−0.105162	−	0.994455i	$-0.533536\pi$
$997$	3.22469	−	0.510741i	0.102127	−	0.0161753i	0.207289	+	0.978280i	$0.433536\pi$
$998$		0			0
$999$	−12.5884	−	4.09020i	−0.398278	−	0.129408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.u.a.57.4	yes	48
4.3	odd	2		880.2.cm.b.497.3		48
5.3	odd	4	inner	220.2.u.a.13.4	✓	48
11.6	odd	10	inner	220.2.u.a.17.4	yes	48
20.3	even	4		880.2.cm.b.673.3		48
44.39	even	10		880.2.cm.b.17.3		48
55.28	even	20	inner	220.2.u.a.193.4	yes	48
220.83	odd	20		880.2.cm.b.193.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.13.4	✓	48	5.3	odd	4	inner
220.2.u.a.17.4	yes	48	11.6	odd	10	inner
220.2.u.a.57.4	yes	48	1.1	even	1	trivial
220.2.u.a.193.4	yes	48	55.28	even	20	inner
880.2.cm.b.17.3		48	44.39	even	10
880.2.cm.b.193.3		48	220.83	odd	20
880.2.cm.b.497.3		48	4.3	odd	2
880.2.cm.b.673.3		48	20.3	even	4

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0307474 - 0.194131i) q^{3} +(-2.23602 - 0.0146855i) q^{5} +(3.21432 - 0.509098i) q^{7} +(2.81643 + 0.915113i) q^{9} +(2.95000 - 1.51575i) q^{11} +(4.74775 - 2.41910i) q^{13} +(-0.0716027 + 0.433630i) q^{15} +(-3.57446 - 1.82128i) q^{17} +(-4.43615 + 3.22305i) q^{19} -0.639653i q^{21} +(-2.60297 + 2.60297i) q^{23} +(4.99957 + 0.0656742i) q^{25} +(0.531947 - 1.04400i) q^{27} +(-3.79815 - 2.75952i) q^{29} +(-2.52450 + 7.76962i) q^{31} +(-0.203550 - 0.619293i) q^{33} +(-7.19476 + 1.09115i) q^{35} +(-1.76715 - 11.1573i) q^{37} +(-0.323642 - 0.996068i) q^{39} +(5.80437 + 7.98904i) q^{41} +(5.17742 + 5.17742i) q^{43} +(-6.28415 - 2.08757i) q^{45} +(-0.662035 - 0.104856i) q^{47} +(3.41527 - 1.10969i) q^{49} +(-0.463472 + 0.637915i) q^{51} +(-2.88788 - 5.66778i) q^{53} +(-6.61852 + 3.34592i) q^{55} +(0.489295 + 0.960296i) q^{57} +(-4.44597 + 6.11936i) q^{59} +(-7.85138 + 2.55107i) q^{61} +(9.51878 + 1.50763i) q^{63} +(-10.6516 + 5.33943i) q^{65} +(-7.99503 - 7.99503i) q^{67} +(0.425284 + 0.585353i) q^{69} +(-3.11574 - 9.58925i) q^{71} +(0.177831 + 1.12278i) q^{73} +(0.166473 - 0.968554i) q^{75} +(8.71058 - 6.37394i) q^{77} +(-1.14340 + 3.51903i) q^{79} +(7.00107 + 5.08658i) q^{81} +(-0.851148 + 1.67047i) q^{83} +(7.96581 + 4.12490i) q^{85} +(-0.652493 + 0.652493i) q^{87} +1.02792i q^{89} +(14.0292 - 10.1928i) q^{91} +(1.43071 + 0.728981i) q^{93} +(9.96665 - 7.14166i) q^{95} +(-3.00091 + 1.52904i) q^{97} +(9.69555 - 1.56941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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