LMFDB - Embedded newform 880.2.cm.b.497.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(17,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))

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

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

chi := DirichletCharacter("880.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			497.3
Character	$\chi$	$=$	880.497
Dual form			880.2.cm.b.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0307474 + 0.194131i) q^{3} +(-2.23602 - 0.0146855i) q^{5} +(-3.21432 + 0.509098i) q^{7} +(2.81643 + 0.915113i) q^{9} +(-2.95000 + 1.51575i) q^{11} +(4.74775 - 2.41910i) q^{13} +(0.0716027 - 0.433630i) q^{15} +(-3.57446 - 1.82128i) q^{17} +(4.43615 - 3.22305i) q^{19} -0.639653i q^{21} +(2.60297 - 2.60297i) q^{23} +(4.99957 + 0.0656742i) q^{25} +(-0.531947 + 1.04400i) q^{27} +(-3.79815 - 2.75952i) q^{29} +(2.52450 - 7.76962i) q^{31} +(-0.203550 - 0.619293i) q^{33} +(7.19476 - 1.09115i) q^{35} +(-1.76715 - 11.1573i) q^{37} +(0.323642 + 0.996068i) q^{39} +(5.80437 + 7.98904i) q^{41} +(-5.17742 - 5.17742i) q^{43} +(-6.28415 - 2.08757i) q^{45} +(0.662035 + 0.104856i) q^{47} +(3.41527 - 1.10969i) q^{49} +(0.463472 - 0.637915i) q^{51} +(-2.88788 - 5.66778i) q^{53} +(6.61852 - 3.34592i) q^{55} +(0.489295 + 0.960296i) q^{57} +(4.44597 - 6.11936i) q^{59} +(-7.85138 + 2.55107i) q^{61} +(-9.51878 - 1.50763i) q^{63} +(-10.6516 + 5.33943i) q^{65} +(7.99503 + 7.99503i) q^{67} +(0.425284 + 0.585353i) q^{69} +(3.11574 + 9.58925i) q^{71} +(0.177831 + 1.12278i) q^{73} +(-0.166473 + 0.968554i) q^{75} +(8.71058 - 6.37394i) q^{77} +(1.14340 - 3.51903i) q^{79} +(7.00107 + 5.08658i) q^{81} +(0.851148 - 1.67047i) q^{83} +(7.96581 + 4.12490i) q^{85} +(0.652493 - 0.652493i) q^{87} +1.02792i q^{89} +(-14.0292 + 10.1928i) q^{91} +(1.43071 + 0.728981i) q^{93} +(-9.96665 + 7.14166i) q^{95} +(-3.00091 + 1.52904i) q^{97} +(-9.69555 + 1.56941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	−0.0307474	+	0.194131i	−0.0177520	+	0.112082i	−0.994973	−	0.100142i	$-0.968070\pi$
$3$	−0.0307474	+	0.194131i	−0.0177520	+	0.112082i	0.977221	+	0.212223i	$0.0680704\pi$
$4$		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	−0.730799	−	0.682592i	$-0.760852\pi$
$7$	−3.21432	+	0.509098i	−1.21490	+	0.192421i	−0.484099	+	0.875013i	$0.660852\pi$
$8$		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	0.0519075	−	0.998652i	$-0.483470\pi$
$19$	4.43615	−	3.22305i	1.01772	−	0.739418i	0.965815	+	0.259233i	$0.0834699\pi$
$20$		0			0
$21$		−	0.639653i		−	0.139584i
$22$		0			0
$23$	2.60297	−	2.60297i	0.542757	−	0.542757i	−0.381579	−	0.924336i	$-0.624620\pi$
$23$	2.60297	−	2.60297i	0.542757	−	0.542757i	0.924336	+	0.381579i	$0.124620\pi$
$24$		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	$-0.637820\pi$
$31$	2.52450	−	7.76962i	0.453414	−	1.39547i	0.872987	−	0.487744i	$-0.162180\pi$
$32$		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	0.191871	−	0.981420i	$-0.438544\pi$
$43$	−5.17742	−	5.17742i	−0.789549	−	0.789549i	−0.981420	+	0.191871i	$0.938544\pi$
$44$		0			0
$45$	−6.28415	−	2.08757i	−0.936786	−	0.311197i
$46$		0			0
$47$	0.662035	+	0.104856i	0.0965678	+	0.0152948i	0.204531	−	0.978860i	$-0.434433\pi$
$47$	0.662035	+	0.104856i	0.0965678	+	0.0152948i	−0.107964	+	0.994155i	$0.534433\pi$
$48$		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	−0.414748	−	0.909936i	$-0.636130\pi$
$59$	4.44597	−	6.11936i	0.578817	−	0.796673i	0.993565	+	0.113263i	$0.0361304\pi$
$60$		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	0.999736	−	0.0229875i	$-0.00731778\pi$
$67$	7.99503	+	7.99503i	0.976748	+	0.976748i	−0.0229875	+	0.999736i	$0.507318\pi$
$68$		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	$0.104157\pi$
$71$	3.11574	+	9.58925i	0.369770	+	1.13803i	−0.577170	+	0.816624i	$0.695843\pi$
$72$		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	−0.865904	−	0.500210i	$-0.833256\pi$
$79$	1.14340	−	3.51903i	0.128643	−	0.395922i	0.994547	+	0.104288i	$0.0332563\pi$
$80$		0			0
$81$	7.00107	+	5.08658i	0.777897	+	0.565175i
$82$		0			0
$83$	0.851148	−	1.67047i	0.0934256	−	0.183358i	−0.839565	−	0.543260i	$-0.817190\pi$
$83$	0.851148	−	1.67047i	0.0934256	−	0.183358i	0.932990	+	0.359902i	$0.117190\pi$
$84$		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	−0.161446	−	0.986882i	$-0.551616\pi$
$103$	−0.101767	+	0.0161183i	−0.0100274	+	0.00158818i	0.151419	+	0.988470i	$0.451616\pi$
$104$		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	$-0.669708\pi$
$107$	2.49553	−	15.7562i	0.241252	−	1.52321i	0.749505	−	0.661999i	$-0.230292\pi$
$108$		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	0.283948	−	0.958840i	$-0.408356\pi$
$127$	−3.66110	−	1.86542i	−0.324870	−	0.165529i	−0.608817	+	0.793310i	$0.708356\pi$
$128$		0			0
$129$	1.16429	−	0.845907i	0.102510	−	0.0744780i
$130$		0			0
$131$		−	8.42076i		−	0.735725i	−0.929880	−	0.367863i	$-0.880090\pi$
$131$		−	8.42076i		−	0.735725i	0.929880	−	0.367863i	$-0.119910\pi$
$132$		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	0.699862	−	0.714279i	$-0.253245\pi$
$139$	2.79197	+	2.02848i	0.236811	+	0.172054i	−0.463050	+	0.886332i	$0.653245\pi$
$140$		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	0.687231	−	0.726439i	$-0.258826\pi$
$151$	−2.65450	−	3.65361i	−0.216020	−	0.297326i	−0.903251	+	0.429113i	$0.858826\pi$
$152$		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	$-0.988006\pi$
$163$	−5.64816	−	11.0851i	−0.442398	−	0.868255i	0.556892	−	0.830585i	$-0.311994\pi$
$164$		0			0
$165$	0.446046	+	1.38774i	0.0347246	+	0.108035i
$166$		0			0
$167$	2.85138	+	5.59615i	0.220646	+	0.433043i	0.974621	−	0.223861i	$-0.0718660\pi$
$167$	2.85138	+	5.59615i	0.220646	+	0.433043i	−0.753975	+	0.656903i	$0.771866\pi$
$168$		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	0.620831	−	0.783944i	$-0.286795\pi$
$179$	−4.23571	−	5.82995i	−0.316592	−	0.435751i	−0.937423	+	0.348193i	$0.886795\pi$
$180$		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	0.949787	−	0.312898i	$-0.101300\pi$
$191$	13.0699	+	9.49582i	0.945703	+	0.687094i	−0.00408349	+	0.999992i	$0.501300\pi$
$192$		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	$0.0912514\pi$
$199$			7.97776i			0.565529i	−0.959189	+	0.282764i	$0.908749\pi$
$200$		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	0.136737	−	0.990607i	$-0.456339\pi$
$211$	−4.86478	−	1.58066i	−0.334905	−	0.108817i	−0.471642	+	0.881790i	$0.656339\pi$
$212$		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	$-0.845039\pi$
$223$	1.51284	−	9.55172i	0.101308	−	0.639631i	0.985130	−	0.171809i	$-0.0549611\pi$
$224$		0			0
$225$	14.0208	+	4.76014i	0.934722	+	0.317342i
$226$		0			0
$227$	−12.0925	+	1.91526i	−0.802607	+	0.127120i	−0.544243	−	0.838927i	$-0.683183\pi$
$227$	−12.0925	+	1.91526i	−0.802607	+	0.127120i	−0.258363	+	0.966048i	$0.583183\pi$
$228$		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	$0.653448\pi$
$239$	−22.4095	+	16.2815i	−1.44955	+	1.05316i	−0.985936	+	0.167125i	$0.946552\pi$
$240$		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	$0.370979\pi$
$251$	−7.36460	+	22.6659i	−0.464849	+	1.43066i	−0.859172	+	0.511687i	$0.829021\pi$
$252$		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	0.200294	−	0.979736i	$-0.435810\pi$
$263$	−12.6404	−	12.6404i	−0.779442	−	0.779442i	−0.979736	+	0.200294i	$0.935810\pi$
$264$		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	−0.682499	−	0.730887i	$-0.739107\pi$
$271$	3.67960	−	5.06454i	0.223520	−	0.307649i	0.906018	+	0.423238i	$0.139107\pi$
$272$		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	0.530564	−	0.847645i	$-0.321980\pi$
$283$	13.0076	+	2.06021i	0.773225	+	0.122467i	0.242660	+	0.970111i	$0.421980\pi$
$284$		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	−0.870996	−	0.491289i	$-0.836526\pi$
$307$	−6.65300	+	6.65300i	−0.379707	+	0.379707i	0.491289	+	0.870996i	$0.336526\pi$
$308$		0			0
$309$		−	0.0202518i		−	0.00115208i
$310$		0			0
$311$	−6.20361	+	4.50719i	−0.351774	+	0.255579i	−0.749613	−	0.661876i	$-0.769760\pi$
$311$	−6.20361	+	4.50719i	−0.351774	+	0.255579i	0.397839	+	0.917455i	$0.369760\pi$
$312$		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	$-0.346087\pi$
$331$	16.9166			0.929820			0.464910	+	0.885358i	$0.346087\pi$
$332$		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	−0.265461	−	0.964122i	$-0.585524\pi$
$347$	−22.3812	−	11.4038i	−1.20149	−	0.612187i	−0.936025	+	0.351934i	$0.885524\pi$
$348$		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	0.367237	−	0.930127i	$-0.380304\pi$
$359$	−7.65250	−	5.55987i	−0.403883	−	0.293439i	−0.771121	+	0.636689i	$0.780304\pi$
$360$		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	$0.101647\pi$
$367$	2.74867	+	17.3544i	0.143480	+	0.905895i	−0.805966	+	0.591962i	$0.798353\pi$
$368$		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	−0.319817	−	0.947479i	$-0.603621\pi$
$379$	−0.421294	+	0.136887i	−0.0216404	+	0.00703139i	0.298177	+	0.954511i	$0.403621\pi$
$380$		0			0
$381$	0.474706	−	0.653377i	0.0243199	−	0.0334735i
$382$		0			0
$383$	6.26658	+	12.2989i	0.320207	+	0.628442i	0.993865	−	0.110602i	$-0.0352778\pi$
$383$	6.26658	+	12.2989i	0.320207	+	0.628442i	−0.673658	+	0.739044i	$0.735278\pi$
$384$		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	$0.148692\pi$
$419$			18.4358i			0.900648i	−0.892865	+	0.450324i	$0.851308\pi$
$420$		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	0.106018	−	0.994364i	$-0.466190\pi$
$431$	−8.15236	−	2.64886i	−0.392685	−	0.127591i	−0.498703	+	0.866773i	$0.666190\pi$
$432$		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	$-0.405964\pi$
$439$	12.2003			0.582288			0.291144	+	0.956679i	$0.405964\pi$
$440$		0			0
$441$	10.6343			0.506397
$442$		0			0
$443$	1.73420	−	10.9493i	0.0823944	−	0.520218i	−0.911626	−	0.411021i	$-0.865172\pi$
$443$	1.73420	−	10.9493i	0.0823944	−	0.520218i	0.994020	−	0.109197i	$-0.0348278\pi$
$444$		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	−0.714830	−	0.699298i	$-0.753496\pi$
$463$	−0.334220	+	0.334220i	−0.0155325	+	0.0155325i	0.699298	+	0.714830i	$0.253496\pi$
$464$		0			0
$465$	−3.18838	−	1.65103i	−0.147858	−	0.0765645i
$466$		0			0
$467$	−0.468732	+	0.919938i	−0.0216903	+	0.0425697i	−0.901597	−	0.432576i	$-0.857605\pi$
$467$	−0.468732	+	0.919938i	−0.0216903	+	0.0425697i	0.879907	+	0.475146i	$0.157605\pi$
$468$		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	$-0.740980\pi$
$479$	−12.2212	−	37.6130i	−0.558401	−	1.71858i	0.128388	−	0.991724i	$-0.459020\pi$
$480$		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	0.907802	−	0.419400i	$-0.137759\pi$
$487$	36.2263	+	5.73768i	1.64157	+	0.259999i	0.733769	+	0.679399i	$0.237759\pi$
$488$		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	$-0.406763\pi$
$491$	24.5974	−	33.8554i	1.11006	−	1.52787i	0.821322	−	0.570465i	$-0.193237\pi$
$492$		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	$-0.354079\pi$
$499$	25.8822	−	35.6238i	1.15865	−	1.59474i	0.716109	−	0.697989i	$-0.245921\pi$
$500$		0			0
$501$	−1.17406	+	0.381475i	−0.0524531	+	0.0170431i
$502$		0			0
$503$	19.3133	+	3.05893i	0.861137	+	0.136391i	0.571356	−	0.820702i	$-0.306417\pi$
$503$	19.3133	+	3.05893i	0.861137	+	0.136391i	0.289781	+	0.957093i	$0.406417\pi$
$504$		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	$0.375380\pi$
$523$	−13.5045	+	26.5041i	−0.590511	+	1.15894i	−0.972090	+	0.234607i	$0.924620\pi$
$524$		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	$0.366667\pi$
$547$	−6.13688	+	38.7467i	−0.262394	+	1.65669i	−0.669131	+	0.743144i	$0.733333\pi$
$548$		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	−0.909153	−	0.416462i	$-0.863270\pi$
$563$	−26.2573	+	13.3788i	−1.10661	+	0.563848i	−0.197462	+	0.980311i	$0.563270\pi$
$564$		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	$-0.995588\pi$
$571$		−	0.662428i		−	0.0277217i	0.999904	−	0.0138609i	$-0.00441219\pi$
$572$		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	0.994226	−	0.107302i	$-0.0342212\pi$
$587$	0.375602	+	2.37146i	0.0155027	+	0.0978805i	−0.978724	+	0.205183i	$0.934221\pi$
$588$		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	0.0160087	−	0.999872i	$-0.494904\pi$
$599$	15.0927	−	4.90391i	0.616670	−	0.200368i	0.600661	+	0.799504i	$0.294904\pi$
$600$		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	0.994933	−	0.100536i	$-0.0320557\pi$
$607$	8.10055	+	15.8982i	0.328791	+	0.645289i	−0.666142	+	0.745825i	$0.732056\pi$
$608$		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	0.740931	−	0.671582i	$-0.234385\pi$
$619$	−3.15329	−	4.34013i	−0.126741	−	0.174445i	−0.867672	+	0.497137i	$0.834385\pi$
$620$		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	−0.134511	−	0.990912i	$-0.542946\pi$
$631$	−28.0962	−	20.4131i	−1.11849	−	0.812631i	−0.983980	+	0.178281i	$0.942946\pi$
$632$		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	0.856344	−	0.516405i	$-0.172730\pi$
$643$	23.8844	+	12.1697i	0.941911	+	0.479927i	0.0855661	+	0.996332i	$0.472730\pi$
$644$		0			0
$645$	−2.61580	+	1.87437i	−0.102997	+	0.0738031i
$646$		0			0
$647$	−7.02618	+	3.58002i	−0.276228	+	0.140745i	−0.586617	−	0.809865i	$-0.699541\pi$
$647$	−7.02618	+	3.58002i	−0.276228	+	0.140745i	0.310389	+	0.950610i	$0.399541\pi$
$648$		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	$-0.808056\pi$
$659$	−42.2869			−1.64726			−0.823632	+	0.567125i	$0.808056\pi$
$660$		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	−0.556140	−	0.831089i	$-0.687718\pi$
$683$	7.18559	−	7.18559i	0.274949	−	0.274949i	0.831089	+	0.556140i	$0.187718\pi$
$684$		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	$0.212407\pi$
$691$	−5.61862	+	17.2923i	−0.213742	+	0.657831i	−0.999240	+	0.0389674i	$0.987593\pi$
$692$		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	−0.987156	−	0.159758i	$-0.948928\pi$
$719$	−14.2160	+	19.5667i	−0.530169	+	0.729715i	0.456987	+	0.889473i	$0.348928\pi$
$720$		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	0.713539	−	0.700616i	$-0.247091\pi$
$727$	0.348445	+	0.348445i	0.0129231	+	0.0129231i	−0.700616	+	0.713539i	$0.747091\pi$
$728$		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	−0.991418	−	0.130731i	$-0.958268\pi$
$739$	−3.05832	+	9.41255i	−0.112502	+	0.346246i	0.878916	+	0.476977i	$0.158268\pi$
$740$		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	$0.315264\pi$
$743$	−12.2803	+	24.1015i	−0.450521	+	0.884198i	−0.998850	+	0.0479352i	$0.984736\pi$
$744$		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	−0.670192	−	0.742187i	$-0.733788\pi$
$751$	−4.69796	+	3.41327i	−0.171431	+	0.124552i	0.498761	+	0.866739i	$0.333788\pi$
$752$		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	0.957301	−	0.289094i	$-0.0933539\pi$
$787$	36.0798	+	18.3836i	1.28611	+	0.655304i	0.328806	+	0.944398i	$0.393354\pi$
$788$		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	0.893610	−	0.448845i	$-0.148164\pi$
$811$	5.42770	+	7.47059i	0.190592	+	0.262328i	−0.703017	+	0.711173i	$0.748164\pi$
$812$		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	0.657690	−	0.753288i	$-0.271534\pi$
$823$	−9.70553	−	19.0482i	−0.338313	−	0.663977i	−0.996004	+	0.0893109i	$0.971534\pi$
$824$		0			0
$825$	−0.976988	−	3.10957i	−0.0340144	−	0.108261i
$826$		0			0
$827$	−1.76115	−	3.45645i	−0.0612412	−	0.120193i	0.858357	−	0.513053i	$-0.171486\pi$
$827$	−1.76115	−	3.45645i	−0.0612412	−	0.120193i	−0.919598	+	0.392860i	$0.871486\pi$
$828$		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	0.999972	−	0.00749608i	$-0.00238610\pi$
$839$	19.8076	+	27.2628i	0.683834	+	0.941217i	−0.316138	+	0.948713i	$0.602386\pi$
$840$		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	$-0.966022\pi$
$859$		−	6.24532i		−	0.213088i	0.994308	−	0.106544i	$-0.0339784\pi$
$860$		0			0
$861$	5.11021	−	3.71279i	0.174156	−	0.126531i
$862$		0			0
$863$	15.6521	+	7.97514i	0.532804	+	0.271477i	0.699625	−	0.714510i	$-0.253350\pi$
$863$	15.6521	+	7.97514i	0.532804	+	0.271477i	−0.166822	+	0.985987i	$0.553350\pi$
$864$		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	$0.272826\pi$
$883$	−5.98949	+	37.8161i	−0.201562	+	1.27261i	−0.856189	+	0.516662i	$0.827174\pi$
$884$		0			0
$885$	−2.33519	−	2.36607i	−0.0784967	−	0.0795346i
$886$		0			0
$887$	−43.4632	+	6.88389i	−1.45935	+	0.231138i	−0.835105	−	0.550090i	$-0.814593\pi$
$887$	−43.4632	+	6.88389i	−1.45935	+	0.231138i	−0.624245	+	0.781228i	$0.714593\pi$
$888$		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	−0.957756	−	0.287582i	$-0.907149\pi$
$907$	−4.88315	+	9.58372i	−0.162142	+	0.318222i	0.795614	+	0.605804i	$0.207149\pi$
$908$		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	$-0.798741\pi$
$911$	5.83452	−	17.9568i	0.193306	−	0.594936i	0.999992	−	0.00395526i	$-0.00125900\pi$
$912$		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	0.999464	−	0.0327436i	$-0.0104245\pi$
$919$	5.20310	+	16.0135i	0.171634	+	0.528236i	−0.827829	+	0.560980i	$0.810424\pi$
$920$		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	0.973585	−	0.228324i	$-0.0733246\pi$
$947$	22.9342	+	22.9342i	0.745261	+	0.745261i	−0.228324	+	0.973585i	$0.573325\pi$
$948$		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	−0.283669	−	0.958922i	$-0.591552\pi$
$967$	20.9981	−	20.9981i	0.675253	−	0.675253i	0.958922	+	0.283669i	$0.0915518\pi$
$968$		0			0
$969$		−	4.32368i		−	0.138897i
$970$		0			0
$971$	−0.106113	+	0.0770954i	−0.00340532	+	0.00247411i	−0.589487	−	0.807778i	$-0.700670\pi$
$971$	−0.106113	+	0.0770954i	−0.00340532	+	0.00247411i	0.586081	+	0.810252i	$0.300670\pi$
$972$		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	0.520376	−	0.853937i	$-0.325792\pi$
$983$	40.1054	−	6.35207i	1.27916	−	0.202600i	0.758788	+	0.651338i	$0.225792\pi$
$984$		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	$-0.622272\pi$
$991$	−23.5944			−0.749502			−0.374751	+	0.927126i	$0.622272\pi$
$992$		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	880.2.cm.b.497.3		48
4.3	odd	2		220.2.u.a.57.4	yes	48
5.3	odd	4	inner	880.2.cm.b.673.3		48
11.6	odd	10	inner	880.2.cm.b.17.3		48
20.3	even	4		220.2.u.a.13.4	✓	48
44.39	even	10		220.2.u.a.17.4	yes	48
55.28	even	20	inner	880.2.cm.b.193.3		48
220.83	odd	20		220.2.u.a.193.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.13.4	✓	48	20.3	even	4
220.2.u.a.17.4	yes	48	44.39	even	10
220.2.u.a.57.4	yes	48	4.3	odd	2
220.2.u.a.193.4	yes	48	220.83	odd	20
880.2.cm.b.17.3		48	11.6	odd	10	inner
880.2.cm.b.193.3		48	55.28	even	20	inner
880.2.cm.b.497.3		48	1.1	even	1	trivial
880.2.cm.b.673.3		48	5.3	odd	4	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not 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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