LMFDB - Embedded newform 1008.2.df.e.689.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.20
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.e.929.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45594 + 0.938214i) q^{3} -1.81173 q^{5} +(-1.69266 + 2.03345i) q^{7} +(1.23951 + 2.73196i) q^{9} +O(q^{10})$	\(q+(1.45594 + 0.938214i) q^{3} -1.81173 q^{5} +(-1.69266 + 2.03345i) q^{7} +(1.23951 + 2.73196i) q^{9} -0.255864i q^{11} +(-5.77765 - 3.33573i) q^{13} +(-2.63777 - 1.69979i) q^{15} +(-1.99857 + 3.46163i) q^{17} +(-1.24687 + 0.719882i) q^{19} +(-4.37221 + 1.37250i) q^{21} -5.66665i q^{23} -1.71762 q^{25} +(-0.758514 + 5.14049i) q^{27} +(-4.18486 + 2.41613i) q^{29} +(8.80648 - 5.08442i) q^{31} +(0.240055 - 0.372522i) q^{33} +(3.06665 - 3.68407i) q^{35} +(-1.65567 - 2.86771i) q^{37} +(-5.28228 - 10.2773i) q^{39} +(-5.10089 + 8.83499i) q^{41} +(-1.12248 - 1.94419i) q^{43} +(-2.24566 - 4.94959i) q^{45} +(-5.97092 + 10.3419i) q^{47} +(-1.26982 - 6.88386i) q^{49} +(-6.15755 + 3.16483i) q^{51} +(-3.97466 - 2.29477i) q^{53} +0.463558i q^{55} +(-2.49077 - 0.121729i) q^{57} +(2.55575 + 4.42670i) q^{59} +(8.60220 + 4.96648i) q^{61} +(-7.65337 - 2.10380i) q^{63} +(10.4676 + 6.04346i) q^{65} +(0.962135 + 1.66647i) q^{67} +(5.31652 - 8.25028i) q^{69} +7.31241i q^{71} +(-2.47807 - 1.43071i) q^{73} +(-2.50074 - 1.61149i) q^{75} +(0.520286 + 0.433090i) q^{77} +(-1.83153 + 3.17231i) q^{79} +(-5.92723 + 6.77259i) q^{81} +(-2.68261 - 4.64642i) q^{83} +(3.62089 - 6.27156i) q^{85} +(-8.35975 - 0.408558i) q^{87} +(-0.378446 - 0.655488i) q^{89} +(16.5626 - 6.10230i) q^{91} +(17.5920 + 0.859756i) q^{93} +(2.25900 - 1.30424i) q^{95} +(4.21765 - 2.43506i) q^{97} +(0.699011 - 0.317146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} + 32 q^{63} - 36 q^{65} - 12 q^{77} - 6 q^{79} + 6 q^{81} + 54 q^{87} - 18 q^{89} - 6 q^{91} + 4 q^{93} + 54 q^{95} + 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.45594	+	0.938214i	0.840586	+	0.541678i
$3$	1.45594	+	0.938214i	0.840586	+	0.541678i
$4$		0			0
$5$	−1.81173			−0.810232			−0.405116	−	0.914265i	$-0.632769\pi$
$5$	−1.81173			−0.810232			−0.405116	+	0.914265i	$0.632769\pi$
$6$		0			0
$7$	−1.69266	+	2.03345i	−0.639765	+	0.768571i
$7$	−1.69266	+	2.03345i	−0.639765	+	0.768571i
$8$		0			0
$9$	1.23951	+	2.73196i	0.413170	+	0.910654i
$10$		0			0
$11$		−	0.255864i		−	0.0771459i	−0.999256	−	0.0385730i	$-0.987719\pi$
$11$		−	0.255864i		−	0.0771459i	0.999256	−	0.0385730i	$-0.0122812\pi$
$12$		0			0
$13$	−5.77765	−	3.33573i	−1.60243	−	0.925165i	−0.990999	−	0.133869i	$-0.957260\pi$
$13$	−5.77765	−	3.33573i	−1.60243	−	0.925165i	−0.611433	−	0.791296i	$-0.709407\pi$
$14$		0			0
$15$	−2.63777	−	1.69979i	−0.681070	−	0.438885i
$16$		0			0
$17$	−1.99857	+	3.46163i	−0.484725	+	0.839569i	−0.999846	−	0.0175487i	$-0.994414\pi$
$17$	−1.99857	+	3.46163i	−0.484725	+	0.839569i	0.515121	+	0.857118i	$0.327747\pi$
$18$		0			0
$19$	−1.24687	+	0.719882i	−0.286052	+	0.165152i	−0.636160	−	0.771557i	$-0.719478\pi$
$19$	−1.24687	+	0.719882i	−0.286052	+	0.165152i	0.350108	+	0.936709i	$0.386145\pi$
$20$		0			0
$21$	−4.37221	+	1.37250i	−0.954095	+	0.299504i
$22$		0			0
$23$		−	5.66665i		−	1.18158i	−0.806826	−	0.590789i	$-0.798817\pi$
$23$		−	5.66665i		−	1.18158i	0.806826	−	0.590789i	$-0.201183\pi$
$24$		0			0
$25$	−1.71762			−0.343523
$26$		0			0
$27$	−0.758514	+	5.14049i	−0.145976	+	0.989288i
$28$		0			0
$29$	−4.18486	+	2.41613i	−0.777110	+	0.448665i	−0.835405	−	0.549635i	$-0.814767\pi$
$29$	−4.18486	+	2.41613i	−0.777110	+	0.448665i	0.0582952	+	0.998299i	$0.481434\pi$
$30$		0			0
$31$	8.80648	−	5.08442i	1.58169	−	0.913189i	0.587077	−	0.809531i	$-0.300278\pi$
$31$	8.80648	−	5.08442i	1.58169	−	0.913189i	0.994613	−	0.103658i	$-0.0330549\pi$
$32$		0			0
$33$	0.240055	−	0.372522i	0.0417882	−	0.0648478i
$34$		0			0
$35$	3.06665	−	3.68407i	0.518358	−	0.622721i
$36$		0			0
$37$	−1.65567	−	2.86771i	−0.272191	−	0.471448i	0.697232	−	0.716846i	$-0.254415\pi$
$37$	−1.65567	−	2.86771i	−0.272191	−	0.471448i	−0.969423	+	0.245398i	$0.921082\pi$
$38$		0			0
$39$	−5.28228	−	10.2773i	−0.845841	−	1.64568i
$40$		0			0
$41$	−5.10089	+	8.83499i	−0.796624	+	1.37979i	0.125178	+	0.992134i	$0.460050\pi$
$41$	−5.10089	+	8.83499i	−0.796624	+	1.37979i	−0.921803	+	0.387660i	$0.873284\pi$
$42$		0			0
$43$	−1.12248	−	1.94419i	−0.171176	−	0.296486i	0.767655	−	0.640863i	$-0.221423\pi$
$43$	−1.12248	−	1.94419i	−0.171176	−	0.296486i	−0.938831	+	0.344377i	$0.888090\pi$
$44$		0			0
$45$	−2.24566	−	4.94959i	−0.334764	−	0.737841i
$46$		0			0
$47$	−5.97092	+	10.3419i	−0.870948	+	1.50853i	−0.00993133	+	0.999951i	$0.503161\pi$
$47$	−5.97092	+	10.3419i	−0.870948	+	1.50853i	−0.861017	+	0.508576i	$0.830172\pi$
$48$		0			0
$49$	−1.26982	−	6.88386i	−0.181403	−	0.983409i
$50$		0			0
$51$	−6.15755	+	3.16483i	−0.862229	+	0.443165i
$52$		0			0
$53$	−3.97466	−	2.29477i	−0.545962	−	0.315211i	0.201530	−	0.979482i	$-0.435409\pi$
$53$	−3.97466	−	2.29477i	−0.545962	−	0.315211i	−0.747492	+	0.664271i	$0.768742\pi$
$54$		0			0
$55$			0.463558i			0.0625061i
$56$		0			0
$57$	−2.49077	−	0.121729i	−0.329911	−	0.0161234i
$58$		0			0
$59$	2.55575	+	4.42670i	0.332731	+	0.576307i	0.983046	−	0.183358i	$-0.0586966\pi$
$59$	2.55575	+	4.42670i	0.332731	+	0.576307i	−0.650316	+	0.759664i	$0.725363\pi$
$60$		0			0
$61$	8.60220	+	4.96648i	1.10140	+	0.635893i	0.936588	−	0.350432i	$-0.113965\pi$
$61$	8.60220	+	4.96648i	1.10140	+	0.635893i	0.164811	+	0.986325i	$0.447299\pi$
$62$		0			0
$63$	−7.65337	−	2.10380i	−0.964234	−	0.265054i
$64$		0			0
$65$	10.4676	+	6.04346i	1.29834	+	0.749598i
$66$		0			0
$67$	0.962135	+	1.66647i	0.117544	+	0.203591i	0.918794	−	0.394738i	$-0.129165\pi$
$67$	0.962135	+	1.66647i	0.117544	+	0.203591i	−0.801250	+	0.598330i	$0.795831\pi$
$68$		0			0
$69$	5.31652	−	8.25028i	0.640034	−	0.993217i
$70$		0			0
$71$			7.31241i			0.867823i	0.900955	+	0.433912i	$0.142867\pi$
$71$			7.31241i			0.867823i	−0.900955	+	0.433912i	$0.857133\pi$
$72$		0			0
$73$	−2.47807	−	1.43071i	−0.290036	−	0.167452i	0.347922	−	0.937523i	$-0.386887\pi$
$73$	−2.47807	−	1.43071i	−0.290036	−	0.167452i	−0.637958	+	0.770071i	$0.720221\pi$
$74$		0			0
$75$	−2.50074	−	1.61149i	−0.288761	−	0.186079i
$76$		0			0
$77$	0.520286	+	0.433090i	0.0592921	+	0.0493552i
$78$		0			0
$79$	−1.83153	+	3.17231i	−0.206063	+	0.356912i	−0.950471	−	0.310813i	$-0.899399\pi$
$79$	−1.83153	+	3.17231i	−0.206063	+	0.356912i	0.744408	+	0.667725i	$0.232732\pi$
$80$		0			0
$81$	−5.92723	+	6.77259i	−0.658581	+	0.752510i
$82$		0			0
$83$	−2.68261	−	4.64642i	−0.294455	−	0.510011i	0.680403	−	0.732838i	$-0.261805\pi$
$83$	−2.68261	−	4.64642i	−0.294455	−	0.510011i	−0.974858	+	0.222827i	$0.928471\pi$
$84$		0			0
$85$	3.62089	−	6.27156i	0.392740	−	0.680246i
$86$		0			0
$87$	−8.35975	−	0.408558i	−0.896259	−	0.0438021i
$88$		0			0
$89$	−0.378446	−	0.655488i	−0.0401152	−	0.0694815i	0.845271	−	0.534338i	$-0.179439\pi$
$89$	−0.378446	−	0.655488i	−0.0401152	−	0.0694815i	−0.885386	+	0.464857i	$0.846106\pi$
$90$		0			0
$91$	16.5626	−	6.10230i	1.73623	−	0.639695i
$92$		0			0
$93$	17.5920	+	0.859756i	1.82420	+	0.0891525i
$94$		0			0
$95$	2.25900	−	1.30424i	0.231769	−	0.133812i
$96$		0			0
$97$	4.21765	−	2.43506i	0.428237	−	0.247243i	−0.270358	−	0.962760i	$-0.587142\pi$
$97$	4.21765	−	2.43506i	0.428237	−	0.247243i	0.698595	+	0.715517i	$0.253809\pi$
$98$		0			0
$99$	0.699011	−	0.317146i	0.0702532	−	0.0318744i
$100$		0			0
$101$	−16.4145			−1.63330			−0.816652	−	0.577131i	$-0.804172\pi$
$101$	−16.4145			−1.63330			−0.816652	+	0.577131i	$0.804172\pi$
$102$		0			0
$103$			19.3989i			1.91143i	0.294291	+	0.955716i	$0.404916\pi$
$103$			19.3989i			1.91143i	−0.294291	+	0.955716i	$0.595084\pi$
$104$		0			0
$105$	7.92129	−	2.48660i	0.773039	−	0.242668i
$106$		0			0
$107$	6.47695	−	3.73947i	0.626150	−	0.361508i	−0.153109	−	0.988209i	$-0.548929\pi$
$107$	6.47695	−	3.73947i	0.626150	−	0.361508i	0.779260	+	0.626701i	$0.215595\pi$
$108$		0			0
$109$	4.26712	−	7.39087i	0.408716	−	0.707917i	−0.586030	−	0.810289i	$-0.699310\pi$
$109$	4.26712	−	7.39087i	0.408716	−	0.707917i	0.994746	+	0.102372i	$0.0326432\pi$
$110$		0			0
$111$	0.279968	−	5.72858i	0.0265733	−	0.543733i
$112$		0			0
$113$	1.22966	+	0.709943i	0.115676	+	0.0667858i	0.556722	−	0.830699i	$-0.312059\pi$
$113$	1.22966	+	0.709943i	0.115676	+	0.0667858i	−0.441045	+	0.897485i	$0.645392\pi$
$114$		0			0
$115$			10.2665i			0.957352i
$116$		0			0
$117$	1.95163	−	19.9190i	0.180428	−	1.84151i
$118$		0			0
$119$	−3.65614	−	9.92335i	−0.335158	−	0.909672i
$120$		0			0
$121$	10.9345			0.994049
$122$		0			0
$123$	−15.7157	+	8.07748i	−1.41704	+	0.728322i
$124$		0			0
$125$	12.1705			1.08857
$126$		0			0
$127$	5.17294			0.459024			0.229512	−	0.973306i	$-0.426287\pi$
$127$	5.17294			0.459024			0.229512	+	0.973306i	$0.426287\pi$
$128$		0			0
$129$	0.189806	−	3.88374i	0.0167115	−	0.341944i
$130$		0			0
$131$	6.36524			0.556133			0.278067	−	0.960562i	$-0.410306\pi$
$131$	6.36524			0.556133			0.278067	+	0.960562i	$0.410306\pi$
$132$		0			0
$133$	0.646686	−	3.75397i	0.0560748	−	0.325510i
$134$		0			0
$135$	1.37423	−	9.31321i	0.118275	−	0.801553i
$136$		0			0
$137$			0.0486198i			0.00415387i	0.999998	+	0.00207693i	$0.000661109\pi$
$137$			0.0486198i			0.00415387i	−0.999998	+	0.00207693i	$0.999339\pi$
$138$		0			0
$139$	−2.95962	−	1.70874i	−0.251032	−	0.144933i	0.369205	−	0.929348i	$-0.379630\pi$
$139$	−2.95962	−	1.70874i	−0.251032	−	0.144933i	−0.620237	+	0.784415i	$0.712963\pi$
$140$		0			0
$141$	−18.3962	+	9.45522i	−1.54924	+	0.796273i
$142$		0			0
$143$	−0.853493	+	1.47829i	−0.0713727	+	0.123621i
$144$		0			0
$145$	7.58186	−	4.37739i	0.629640	−	0.363523i
$146$		0			0
$147$	4.60976	−	11.2138i	0.380206	−	0.924902i
$148$		0			0
$149$			9.89196i			0.810381i	0.914232	+	0.405190i	$0.132795\pi$
$149$			9.89196i			0.810381i	−0.914232	+	0.405190i	$0.867205\pi$
$150$		0			0
$151$	−8.48564			−0.690552			−0.345276	−	0.938501i	$-0.612215\pi$
$151$	−8.48564			−0.690552			−0.345276	+	0.938501i	$0.612215\pi$
$152$		0			0
$153$	−11.9343	−	1.16930i	−0.964831	−	0.0945323i
$154$		0			0
$155$	−15.9550	+	9.21163i	−1.28154	+	0.739896i
$156$		0			0
$157$	−16.0079	+	9.24219i	−1.27757	+	0.737607i	−0.976402	−	0.215963i	$-0.930711\pi$
$157$	−16.0079	+	9.24219i	−1.27757	+	0.737607i	−0.301171	+	0.953570i	$0.597378\pi$
$158$		0			0
$159$	−3.63388	−	7.07013i	−0.288185	−	0.560698i
$160$		0			0
$161$	11.5228	+	9.59169i	0.908126	+	0.755931i
$162$		0			0
$163$	−3.81360	−	6.60534i	−0.298704	−	0.517370i	0.677136	−	0.735858i	$-0.263221\pi$
$163$	−3.81360	−	6.60534i	−0.298704	−	0.517370i	−0.975840	+	0.218488i	$0.929888\pi$
$164$		0			0
$165$	−0.434916	+	0.674911i	−0.0338582	+	0.0525418i
$166$		0			0
$167$	−8.86874	+	15.3611i	−0.686284	+	1.18868i	0.286748	+	0.958006i	$0.407426\pi$
$167$	−8.86874	+	15.3611i	−0.686284	+	1.18868i	−0.973032	+	0.230672i	$0.925908\pi$
$168$		0			0
$169$	15.7542	+	27.2870i	1.21186	+	2.09900i
$170$		0			0
$171$	−3.51220	−	2.51411i	−0.268585	−	0.192259i
$172$		0			0
$173$	−7.01266	+	12.1463i	−0.533163	+	0.923465i	0.466087	+	0.884739i	$0.345663\pi$
$173$	−7.01266	+	12.1463i	−0.533163	+	0.923465i	−0.999250	+	0.0387263i	$0.987670\pi$
$174$		0			0
$175$	2.90734	−	3.49268i	0.219774	−	0.264022i
$176$		0			0
$177$	−0.432168	+	8.84284i	−0.0324837	+	0.664668i
$178$		0			0
$179$	8.29501	+	4.78913i	0.619998	+	0.357956i	0.776868	−	0.629663i	$-0.216807\pi$
$179$	8.29501	+	4.78913i	0.619998	+	0.357956i	−0.156870	+	0.987619i	$0.550140\pi$
$180$		0			0
$181$			1.57861i			0.117337i	0.998278	+	0.0586687i	$0.0186856\pi$
$181$			1.57861i			0.117337i	−0.998278	+	0.0586687i	$0.981314\pi$
$182$		0			0
$183$	7.86465	+	15.3016i	0.581372	+	1.13113i
$184$		0			0
$185$	2.99964	+	5.19553i	0.220538	+	0.381983i
$186$		0			0
$187$	0.885707	+	0.511363i	0.0647693	+	0.0373946i
$188$		0			0
$189$	−9.16902	−	10.2435i	−0.666948	−	0.745105i
$190$		0			0
$191$	15.1037	+	8.72014i	1.09287	+	0.630967i	0.934338	−	0.356387i	$-0.115992\pi$
$191$	15.1037	+	8.72014i	1.09287	+	0.630967i	0.158529	+	0.987354i	$0.449325\pi$
$192$		0			0
$193$	−11.9263	−	20.6569i	−0.858472	−	1.48692i	−0.873386	−	0.487029i	$-0.838081\pi$
$193$	−11.9263	−	20.6569i	−0.858472	−	1.48692i	0.0149136	−	0.999889i	$-0.495253\pi$
$194$		0			0
$195$	9.57008	+	18.6197i	0.685328	+	1.33339i
$196$		0			0
$197$		−	19.1271i		−	1.36275i	−0.731935	−	0.681374i	$-0.761383\pi$
$197$		−	19.1271i		−	1.36275i	0.731935	−	0.681374i	$-0.238617\pi$
$198$		0			0
$199$	−5.15196	−	2.97449i	−0.365213	−	0.210856i	0.306152	−	0.951983i	$-0.400958\pi$
$199$	−5.15196	−	2.97449i	−0.365213	−	0.210856i	−0.671365	+	0.741127i	$0.734292\pi$
$200$		0			0
$201$	−0.162693	+	3.32896i	−0.0114755	+	0.234807i
$202$		0			0
$203$	2.17047	−	12.5994i	0.152337	−	0.884304i
$204$		0			0
$205$	9.24145	−	16.0067i	0.645451	−	1.11795i
$206$		0			0
$207$	15.4811	−	7.02386i	1.07601	−	0.488192i
$208$		0			0
$209$	0.184192	+	0.319030i	0.0127408	+	0.0220678i
$210$		0			0
$211$	5.86415	−	10.1570i	0.403704	−	0.699237i	−0.590465	−	0.807063i	$-0.701056\pi$
$211$	5.86415	−	10.1570i	0.403704	−	0.699237i	0.994170	+	0.107826i	$0.0343891\pi$
$212$		0			0
$213$	−6.86060	+	10.6464i	−0.470081	+	0.729480i
$214$		0			0
$215$	2.03363	+	3.52235i	0.138692	+	0.240222i
$216$		0			0
$217$	−4.56745	+	26.5137i	−0.310059	+	1.79987i
$218$		0			0
$219$	−2.26560	−	4.40799i	−0.153095	−	0.297864i
$220$		0			0
$221$	23.0941	−	13.3334i	1.55348	−	0.896902i
$222$		0			0
$223$	16.0209	−	9.24969i	1.07284	−	0.619405i	0.143885	−	0.989594i	$-0.454040\pi$
$223$	16.0209	−	9.24969i	1.07284	−	0.619405i	0.928956	+	0.370189i	$0.120707\pi$
$224$		0			0
$225$	−2.12900	−	4.69246i	−0.141934	−	0.312831i
$226$		0			0
$227$	0.677545			0.0449702			0.0224851	−	0.999747i	$-0.492842\pi$
$227$	0.677545			0.0449702			0.0224851	+	0.999747i	$0.492842\pi$
$228$		0			0
$229$		−	0.386469i		−	0.0255386i	−0.999918	−	0.0127693i	$-0.995935\pi$
$229$		−	0.386469i		−	0.0255386i	0.999918	−	0.0127693i	$-0.00406470\pi$
$230$		0			0
$231$	0.351173	+	1.11869i	0.0231055	+	0.0736046i
$232$		0			0
$233$	−3.35520	+	1.93712i	−0.219806	+	0.126905i	−0.605861	−	0.795571i	$-0.707171\pi$
$233$	−3.35520	+	1.93712i	−0.219806	+	0.126905i	0.386054	+	0.922476i	$0.373838\pi$
$234$		0			0
$235$	10.8177	−	18.7368i	0.705671	−	1.22226i
$236$		0			0
$237$	−5.64290	+	2.90031i	−0.366546	+	0.188395i
$238$		0			0
$239$	9.97301	+	5.75792i	0.645100	+	0.372449i	0.786576	−	0.617493i	$-0.211852\pi$
$239$	9.97301	+	5.75792i	0.645100	+	0.372449i	−0.141476	+	0.989942i	$0.545185\pi$
$240$		0			0
$241$		−	11.7943i		−	0.759739i	−0.925040	−	0.379869i	$-0.875969\pi$
$241$		−	11.7943i		−	0.759739i	0.925040	−	0.379869i	$-0.124031\pi$
$242$		0			0
$243$	−14.9838	+	4.29946i	−0.961212	+	0.275810i
$244$		0			0
$245$	2.30057	+	12.4717i	0.146978	+	0.796790i
$246$		0			0
$247$	9.60533			0.611173
$248$		0			0
$249$	0.453619	−	9.28176i	0.0287469	−	0.588208i
$250$		0			0
$251$	9.76523			0.616376			0.308188	−	0.951326i	$-0.400277\pi$
$251$	9.76523			0.616376			0.308188	+	0.951326i	$0.400277\pi$
$252$		0			0
$253$	−1.44989			−0.0911539
$254$		0			0
$255$	11.1558	−	5.73383i	0.698606	−	0.359067i
$256$		0			0
$257$	14.1561			0.883034			0.441517	−	0.897253i	$-0.354440\pi$
$257$	14.1561			0.883034			0.441517	+	0.897253i	$0.354440\pi$
$258$		0			0
$259$	8.63382	+	1.48733i	0.536479	+	0.0924180i
$260$		0			0
$261$	−11.7880	−	8.43807i	−0.729657	−	0.522303i
$262$		0			0
$263$			10.2979i			0.634998i	0.948259	+	0.317499i	$0.102843\pi$
$263$			10.2979i			0.634998i	−0.948259	+	0.317499i	$0.897157\pi$
$264$		0			0
$265$	7.20104	+	4.15752i	0.442356	+	0.255395i
$266$		0			0
$267$	0.0639937	−	1.30941i	0.00391635	−	0.0801347i
$268$		0			0
$269$	−3.95947	+	6.85801i	−0.241413	+	0.418140i	−0.961117	−	0.276141i	$-0.910944\pi$
$269$	−3.95947	+	6.85801i	−0.241413	+	0.418140i	0.719704	+	0.694281i	$0.244278\pi$
$270$		0			0
$271$	9.45707	−	5.46004i	0.574476	−	0.331674i	−0.184459	−	0.982840i	$-0.559053\pi$
$271$	9.45707	−	5.46004i	0.574476	−	0.331674i	0.758935	+	0.651166i	$0.225720\pi$
$272$		0			0
$273$	29.8394	+	6.65470i	1.80596	+	0.402761i
$274$		0			0
$275$			0.439477i			0.0265014i
$276$		0			0
$277$	12.8204			0.770304			0.385152	−	0.922853i	$-0.374149\pi$
$277$	12.8204			0.770304			0.385152	+	0.922853i	$0.374149\pi$
$278$		0			0
$279$	24.8062	+	17.7568i	1.48511	+	1.06307i
$280$		0			0
$281$	−18.3380	+	10.5874i	−1.09395	+	0.631593i	−0.934626	−	0.355633i	$-0.884265\pi$
$281$	−18.3380	+	10.5874i	−1.09395	+	0.631593i	−0.159326	+	0.987226i	$0.550932\pi$
$282$		0			0
$283$	−22.2420	+	12.8415i	−1.32215	+	0.763345i	−0.984072	−	0.177772i	$-0.943111\pi$
$283$	−22.2420	+	12.8415i	−1.32215	+	0.763345i	−0.338081	+	0.941117i	$0.609778\pi$
$284$		0			0
$285$	4.51262	+	0.220541i	0.267305	+	0.0130637i
$286$		0			0
$287$	−9.33144	−	25.3270i	−0.550818	−	1.49501i
$288$		0			0
$289$	0.511404	+	0.885777i	0.0300826	+	0.0521046i
$290$		0			0
$291$	8.42524	+	0.411759i	0.493897	+	0.0241377i
$292$		0			0
$293$	14.4817	−	25.0831i	0.846031	−	1.46537i	−0.0386925	−	0.999251i	$-0.512319\pi$
$293$	14.4817	−	25.0831i	0.846031	−	1.46537i	0.884723	−	0.466117i	$-0.154347\pi$
$294$		0			0
$295$	−4.63035	−	8.02000i	−0.269589	−	0.466942i
$296$		0			0
$297$	1.31527	+	0.194077i	0.0763195	+	0.0112615i
$298$		0			0
$299$	−18.9024	+	32.7399i	−1.09315	+	1.89340i
$300$		0			0
$301$	5.85337	+	1.00834i	0.337382	+	0.0581200i
$302$		0			0
$303$	−23.8985	−	15.4003i	−1.37293	−	0.884724i
$304$		0			0
$305$	−15.5849	−	8.99795i	−0.892389	−	0.515221i
$306$		0			0
$307$		−	28.0634i		−	1.60167i	−0.598888	−	0.800833i	$-0.704391\pi$
$307$		−	28.0634i		−	1.60167i	0.598888	−	0.800833i	$-0.295609\pi$
$308$		0			0
$309$	−18.2003	+	28.2436i	−1.03538	+	1.60672i
$310$		0			0
$311$	3.95974	+	6.85847i	0.224536	+	0.388908i	0.956180	−	0.292779i	$-0.0945800\pi$
$311$	3.95974	+	6.85847i	0.224536	+	0.388908i	−0.731644	+	0.681687i	$0.761247\pi$
$312$		0			0
$313$	10.2043	+	5.89145i	0.576780	+	0.333004i	0.759853	−	0.650095i	$-0.225271\pi$
$313$	10.2043	+	5.89145i	0.576780	+	0.333004i	−0.183073	+	0.983099i	$0.558604\pi$
$314$		0			0
$315$	13.8659	+	3.81152i	0.781253	+	0.214755i
$316$		0			0
$317$	−14.3671	−	8.29484i	−0.806936	−	0.465884i	0.0389550	−	0.999241i	$-0.487597\pi$
$317$	−14.3671	−	8.29484i	−0.806936	−	0.465884i	−0.845891	+	0.533356i	$0.820930\pi$
$318$		0			0
$319$	0.618202	+	1.07076i	0.0346126	+	0.0599509i
$320$		0			0
$321$	12.9385	+	0.632329i	0.722154	+	0.0352932i
$322$		0			0
$323$		−	5.75495i		−	0.320214i
$324$		0			0
$325$	9.92379	+	5.72950i	0.550473	+	0.317816i
$326$		0			0
$327$	13.1469	−	6.75718i	0.727024	−	0.373673i
$328$		0			0
$329$	−10.9231	−	29.6469i	−0.602208	−	1.63449i
$330$		0			0
$331$	2.35856	−	4.08515i	0.129638	−	0.224540i	−0.793898	−	0.608051i	$-0.791952\pi$
$331$	2.35856	−	4.08515i	0.129638	−	0.224540i	0.923536	+	0.383511i	$0.125285\pi$
$332$		0			0
$333$	5.78225	−	8.07779i	0.316865	−	0.442660i
$334$		0			0
$335$	−1.74313	−	3.01920i	−0.0952376	−	0.164956i
$336$		0			0
$337$	1.79195	−	3.10375i	0.0976138	−	0.169072i	−0.813083	−	0.582148i	$-0.802212\pi$
$337$	1.79195	−	3.10375i	0.0976138	−	0.169072i	0.910697	+	0.413076i	$0.135546\pi$
$338$		0			0
$339$	1.12423	+	2.18731i	0.0610596	+	0.118799i
$340$		0			0
$341$	−1.30092	−	2.25326i	−0.0704488	−	0.122021i
$342$		0			0
$343$	16.1473	+	9.06992i	0.871874	+	0.489729i
$344$		0			0
$345$	−9.63213	+	14.9473i	−0.518577	+	0.804737i
$346$		0			0
$347$	15.7201	−	9.07599i	0.843898	−	0.487225i	−0.0146894	−	0.999892i	$-0.504676\pi$
$347$	15.7201	−	9.07599i	0.843898	−	0.487225i	0.858587	+	0.512667i	$0.171343\pi$
$348$		0			0
$349$	−28.1608	+	16.2586i	−1.50741	+	0.870304i	−0.507448	+	0.861683i	$0.669411\pi$
$349$	−28.1608	+	16.2586i	−1.50741	+	0.870304i	−0.999963	+	0.00862123i	$0.997256\pi$
$350$		0			0
$351$	21.5297	−	27.1698i	1.14917	−	1.45022i
$352$		0			0
$353$	0.212061			0.0112869			0.00564343	−	0.999984i	$-0.498204\pi$
$353$	0.212061			0.0112869			0.00564343	+	0.999984i	$0.498204\pi$
$354$		0			0
$355$		−	13.2481i		−	0.703138i
$356$		0			0
$357$	3.98711	−	17.8780i	0.211020	−	0.946206i
$358$		0			0
$359$	−28.7469	+	16.5970i	−1.51720	+	0.875958i	−0.517408	+	0.855739i	$0.673103\pi$
$359$	−28.7469	+	16.5970i	−1.51720	+	0.875958i	−0.999796	+	0.0202187i	$0.993564\pi$
$360$		0			0
$361$	−8.46354	+	14.6593i	−0.445449	+	0.771541i
$362$		0			0
$363$	15.9200	+	10.2589i	0.835583	+	0.538454i
$364$		0			0
$365$	4.48961	+	2.59208i	0.234997	+	0.135675i
$366$		0			0
$367$		−	0.231688i		−	0.0120940i	−0.999982	−	0.00604701i	$-0.998075\pi$
$367$		−	0.231688i		−	0.0120940i	0.999982	−	0.00604701i	$-0.00192484\pi$
$368$		0			0
$369$	−30.4595	−	2.98436i	−1.58566	−	0.155360i
$370$		0			0
$371$	11.3941	−	4.19801i	0.591550	−	0.217950i
$372$		0			0
$373$	17.6955			0.916239			0.458119	−	0.888891i	$-0.348523\pi$
$373$	17.6955			0.916239			0.458119	+	0.888891i	$0.348523\pi$
$374$		0			0
$375$	17.7196	+	11.4186i	0.915034	+	0.589652i
$376$		0			0
$377$	32.2383			1.66035
$378$		0			0
$379$	−28.9131			−1.48516			−0.742582	−	0.669755i	$-0.766399\pi$
$379$	−28.9131			−1.48516			−0.742582	+	0.669755i	$0.766399\pi$
$380$		0			0
$381$	7.53148	+	4.85332i	0.385849	+	0.248643i
$382$		0			0
$383$	2.35585			0.120378			0.0601891	−	0.998187i	$-0.480830\pi$
$383$	2.35585			0.120378			0.0601891	+	0.998187i	$0.480830\pi$
$384$		0			0
$385$	−0.942621	−	0.784645i	−0.0480404	−	0.0399892i
$386$		0			0
$387$	3.92012	−	5.47640i	0.199271	−	0.278381i
$388$		0			0
$389$		−	11.1007i		−	0.562827i	−0.959587	−	0.281413i	$-0.909197\pi$
$389$		−	11.1007i		−	0.562827i	0.959587	−	0.281413i	$-0.0908032\pi$
$390$		0			0
$391$	19.6158	+	11.3252i	0.992016	+	0.572740i
$392$		0			0
$393$	9.26739	+	5.97195i	0.467478	+	0.301245i
$394$		0			0
$395$	3.31825	−	5.74738i	0.166959	−	0.289182i
$396$		0			0
$397$	−4.59168	+	2.65101i	−0.230450	+	0.133050i	−0.610780	−	0.791801i	$-0.709144\pi$
$397$	−4.59168	+	2.65101i	−0.230450	+	0.133050i	0.380330	+	0.924851i	$0.375810\pi$
$398$		0			0
$399$	4.46356	−	4.85881i	0.223457	−	0.243245i
$400$		0			0
$401$			32.8070i			1.63830i	0.573578	+	0.819151i	$0.305555\pi$
$401$			32.8070i			1.63830i	−0.573578	+	0.819151i	$0.694445\pi$
$402$		0			0
$403$	−67.8410			−3.37940
$404$		0			0
$405$	10.7386	−	12.2701i	0.533604	−	0.609708i
$406$		0			0
$407$	−0.733744	+	0.423627i	−0.0363703	+	0.0209984i
$408$		0			0
$409$	−13.1858	+	7.61284i	−0.651997	+	0.376431i	−0.789221	−	0.614109i	$-0.789515\pi$
$409$	−13.1858	+	7.61284i	−0.651997	+	0.376431i	0.137224	+	0.990540i	$0.456182\pi$
$410$		0			0
$411$	−0.0456158	+	0.0707874i	−0.00225006	+	0.00349168i
$412$		0			0
$413$	−13.3275	−	2.29589i	−0.655802	−	0.112973i
$414$		0			0
$415$	4.86018	+	8.41808i	0.238577	+	0.413227i
$416$		0			0
$417$	−2.70587	−	5.26458i	−0.132507	−	0.257808i
$418$		0			0
$419$	−6.32224	+	10.9504i	−0.308861	+	0.534964i	−0.978114	−	0.208072i	$-0.933281\pi$
$419$	−6.32224	+	10.9504i	−0.308861	+	0.534964i	0.669252	+	0.743035i	$0.266615\pi$
$420$		0			0
$421$	−14.4841	−	25.0872i	−0.705911	−	1.22267i	−0.966362	−	0.257187i	$-0.917204\pi$
$421$	−14.4841	−	25.0872i	−0.705911	−	1.22267i	0.260451	−	0.965487i	$-0.416129\pi$
$422$		0			0
$423$	−35.6548	−	3.49339i	−1.73360	−	0.169855i
$424$		0			0
$425$	3.43279	−	5.94576i	0.166515	−	0.288412i
$426$		0			0
$427$	−24.6597	+	9.08557i	−1.19337	+	0.439682i
$428$		0			0
$429$	−2.62959	+	1.35154i	−0.126958	+	0.0652532i
$430$		0			0
$431$	−31.6662	−	18.2825i	−1.52531	−	0.880638i	−0.999550	−	0.0300048i	$-0.990448\pi$
$431$	−31.6662	−	18.2825i	−1.52531	−	0.880638i	−0.525760	−	0.850633i	$-0.676219\pi$
$432$		0			0
$433$			29.3243i			1.40924i	0.709586	+	0.704619i	$0.248882\pi$
$433$			29.3243i			1.40924i	−0.709586	+	0.704619i	$0.751118\pi$
$434$		0			0
$435$	15.1457	+	0.740199i	0.726178	+	0.0354898i
$436$		0			0
$437$	4.07932	+	7.06559i	0.195140	+	0.337993i
$438$		0			0
$439$	14.3630	+	8.29248i	0.685508	+	0.395778i	0.801927	−	0.597422i	$-0.203808\pi$
$439$	14.3630	+	8.29248i	0.685508	+	0.395778i	−0.116419	+	0.993200i	$0.537141\pi$
$440$		0			0
$441$	17.2325	−	12.0017i	0.820595	−	0.571510i
$442$		0			0
$443$	13.2842	+	7.66961i	0.631149	+	0.364394i	0.781197	−	0.624285i	$-0.214609\pi$
$443$	13.2842	+	7.66961i	0.631149	+	0.364394i	−0.150048	+	0.988679i	$0.547943\pi$
$444$		0			0
$445$	0.685644	+	1.18757i	0.0325026	+	0.0562962i
$446$		0			0
$447$	−9.28077	+	14.4021i	−0.438965	+	0.681195i
$448$		0			0
$449$		−	22.9580i		−	1.08346i	−0.840554	−	0.541728i	$-0.817770\pi$
$449$		−	22.9580i		−	1.08346i	0.840554	−	0.541728i	$-0.182230\pi$
$450$		0			0
$451$	2.26056	+	1.30513i	0.106445	+	0.0614563i
$452$		0			0
$453$	−12.3546	−	7.96135i	−0.580468	−	0.374057i
$454$		0			0
$455$	−30.0071	+	11.0558i	−1.40675	+	0.518302i
$456$		0			0
$457$	10.9126	−	18.9011i	0.510468	−	0.884156i	−0.489459	−	0.872026i	$-0.662806\pi$
$457$	10.9126	−	18.9011i	0.510468	−	0.884156i	0.999926	−	0.0121294i	$-0.00386099\pi$
$458$		0			0
$459$	−16.2785	−	12.8994i	−0.759817	−	0.602090i
$460$		0			0
$461$	16.9154	+	29.2984i	0.787830	+	1.36456i	0.927294	+	0.374335i	$0.122129\pi$
$461$	16.9154	+	29.2984i	0.787830	+	1.36456i	−0.139463	+	0.990227i	$0.544538\pi$
$462$		0			0
$463$	1.82082	−	3.15375i	0.0846206	−	0.146567i	−0.820609	−	0.571490i	$-0.806366\pi$
$463$	1.82082	−	3.15375i	0.0846206	−	0.146567i	0.905229	+	0.424923i	$0.139699\pi$
$464$		0			0
$465$	−31.8720	−	1.55765i	−1.47803	−	0.0722342i
$466$		0			0
$467$	−12.1438	−	21.0337i	−0.561948	−	0.973322i	−0.997326	−	0.0730749i	$-0.976719\pi$
$467$	−12.1438	−	21.0337i	−0.561948	−	0.973322i	0.435378	−	0.900248i	$-0.356615\pi$
$468$		0			0
$469$	−5.01724	−	0.864307i	−0.231675	−	0.0399100i
$470$		0			0
$471$	−31.9777	−	1.56282i	−1.47346	−	0.0720108i
$472$		0			0
$473$	−0.497447	+	0.287201i	−0.0228727	+	0.0132055i
$474$		0			0
$475$	2.14165	−	1.23648i	0.0982657	−	0.0567337i
$476$		0			0
$477$	1.34260	−	13.7030i	0.0614733	−	0.627419i
$478$		0			0
$479$	−30.2200			−1.38079			−0.690393	−	0.723434i	$-0.742563\pi$
$479$	−30.2200			−1.38079			−0.690393	+	0.723434i	$0.742563\pi$
$480$		0			0
$481$			22.0915i			1.00729i
$482$		0			0
$483$	7.77746	+	24.7758i	0.353887	+	1.12734i
$484$		0			0
$485$	−7.64126	+	4.41169i	−0.346972	+	0.200324i
$486$		0			0
$487$	−2.84999	+	4.93634i	−0.129146	+	0.223687i	−0.923346	−	0.383969i	$-0.874557\pi$
$487$	−2.84999	+	4.93634i	−0.129146	+	0.223687i	0.794200	+	0.607656i	$0.207890\pi$
$488$		0			0
$489$	0.644864	−	13.1949i	0.0291618	−	0.596696i
$490$		0			0
$491$	28.3275	+	16.3549i	1.27840	+	0.738086i	0.976555	−	0.215270i	$-0.0690631\pi$
$491$	28.3275	+	16.3549i	1.27840	+	0.738086i	0.301848	+	0.953356i	$0.402396\pi$
$492$		0			0
$493$		−	19.3153i		−	0.869916i
$494$		0			0
$495$	−1.26642	+	0.574585i	−0.0569215	+	0.0258257i
$496$		0			0
$497$	−14.8694	−	12.3774i	−0.666984	−	0.555202i
$498$		0			0
$499$	−7.47286			−0.334531			−0.167266	−	0.985912i	$-0.553494\pi$
$499$	−7.47286			−0.334531			−0.167266	+	0.985912i	$0.553494\pi$
$500$		0			0
$501$	−27.3243	+	14.0440i	−1.22076	+	0.627442i
$502$		0			0
$503$	−29.2765			−1.30537			−0.652686	−	0.757628i	$-0.726358\pi$
$503$	−29.2765			−1.30537			−0.652686	+	0.757628i	$0.726358\pi$
$504$		0			0
$505$	29.7387			1.32336
$506$		0			0
$507$	−2.66397	+	54.5090i	−0.118311	+	2.42083i
$508$		0			0
$509$	−19.1385			−0.848299			−0.424150	−	0.905592i	$-0.639427\pi$
$509$	−19.1385			−0.848299			−0.424150	+	0.905592i	$0.639427\pi$
$510$		0			0
$511$	7.10381	−	2.61732i	0.314254	−	0.115783i
$512$		0			0
$513$	−2.75478	−	6.95558i	−0.121626	−	0.307096i
$514$		0			0
$515$		−	35.1457i		−	1.54870i
$516$		0			0
$517$	2.64613	+	1.52774i	0.116377	+	0.0671901i
$518$		0			0
$519$	−21.6058	+	11.1049i	−0.948390	+	0.487449i
$520$		0			0
$521$	12.0228	−	20.8241i	0.526727	−	0.912318i	−0.472788	−	0.881176i	$-0.656752\pi$
$521$	12.0228	−	20.8241i	0.526727	−	0.912318i	0.999515	−	0.0311420i	$-0.00991442\pi$
$522$		0			0
$523$	−22.2119	+	12.8241i	−0.971259	+	0.560757i	−0.899620	−	0.436674i	$-0.856156\pi$
$523$	−22.2119	+	12.8241i	−0.971259	+	0.560757i	−0.0716394	+	0.997431i	$0.522823\pi$
$524$		0			0
$525$	7.50979	−	2.35743i	0.327754	−	0.102887i
$526$		0			0
$527$			40.6464i			1.77058i
$528$		0			0
$529$	−9.11087			−0.396125
$530$		0			0
$531$	−8.92568	+	12.4692i	−0.387341	+	0.541115i
$532$		0			0
$533$	58.9423	−	34.0303i	2.55307	−	1.47402i
$534$		0			0
$535$	−11.7345	+	6.77493i	−0.507327	+	0.292906i
$536$		0			0
$537$	7.58380	+	14.7552i	0.327265	+	0.636732i
$538$		0			0
$539$	−1.76133	+	0.324901i	−0.0758660	+	0.0139945i
$540$		0			0
$541$	−10.4700	−	18.1346i	−0.450141	−	0.779667i	0.548254	−	0.836312i	$-0.315293\pi$
$541$	−10.4700	−	18.1346i	−0.450141	−	0.779667i	−0.998394	+	0.0566455i	$0.981960\pi$
$542$		0			0
$543$	−1.48108	+	2.29836i	−0.0635591	+	0.0986322i
$544$		0			0
$545$	−7.73089	+	13.3903i	−0.331155	+	0.573578i
$546$		0			0
$547$	−6.53210	−	11.3139i	−0.279292	−	0.483748i	0.691917	−	0.721977i	$-0.256766\pi$
$547$	−6.53210	−	11.3139i	−0.279292	−	0.483748i	−0.971209	+	0.238229i	$0.923433\pi$
$548$		0			0
$549$	−2.90573	+	29.6569i	−0.124013	+	1.26573i
$550$		0			0
$551$	3.47866	−	6.02522i	0.148196	−	0.256683i
$552$		0			0
$553$	−3.35056	−	9.09395i	−0.142480	−	0.386714i
$554$		0			0
$555$	−0.507227	+	10.3787i	−0.0215306	+	0.440550i
$556$		0			0
$557$	−32.5390	−	18.7864i	−1.37872	−	0.796006i	−0.386717	−	0.922198i	$-0.626391\pi$
$557$	−32.5390	−	18.7864i	−1.37872	−	0.796006i	−0.992006	+	0.126193i	$0.959724\pi$
$558$		0			0
$559$			14.9771i			0.633464i
$560$		0			0
$561$	0.809767	+	1.57550i	0.0341884	+	0.0665175i
$562$		0			0
$563$	−5.53671	−	9.58986i	−0.233344	−	0.404164i	0.725446	−	0.688279i	$-0.241634\pi$
$563$	−5.53671	−	9.58986i	−0.233344	−	0.404164i	−0.958790	+	0.284115i	$0.908300\pi$
$564$		0			0
$565$	−2.22781	−	1.28623i	−0.0937248	−	0.0541120i
$566$		0			0
$567$	−3.73893	−	23.5164i	−0.157020	−	0.987595i
$568$		0			0
$569$	−18.5956	−	10.7362i	−0.779570	−	0.450085i	0.0567078	−	0.998391i	$-0.481940\pi$
$569$	−18.5956	−	10.7362i	−0.779570	−	0.450085i	−0.836278	+	0.548306i	$0.815273\pi$
$570$		0			0
$571$	−7.45689	−	12.9157i	−0.312061	−	0.540506i	0.666747	−	0.745284i	$-0.267686\pi$
$571$	−7.45689	−	12.9157i	−0.312061	−	0.540506i	−0.978808	+	0.204778i	$0.934353\pi$
$572$		0			0
$573$	13.8087	+	26.8665i	0.576868	+	1.12236i
$574$		0			0
$575$			9.73313i			0.405899i
$576$		0			0
$577$	−28.0634	−	16.2024i	−1.16829	−	0.674515i	−0.215017	−	0.976610i	$-0.568981\pi$
$577$	−28.0634	−	16.2024i	−1.16829	−	0.674515i	−0.953278	+	0.302095i	$0.902314\pi$
$578$		0			0
$579$	2.01669	−	41.2646i	0.0838106	−	1.71490i
$580$		0			0
$581$	13.9890	+	2.40985i	0.580362	+	0.0999774i
$582$		0			0
$583$	−0.587150	+	1.01697i	−0.0243173	+	0.0421188i
$584$		0			0
$585$	−3.53583	+	36.0879i	−0.146189	+	1.49205i
$586$		0			0
$587$	−9.88731	−	17.1253i	−0.408093	−	0.706838i	0.586583	−	0.809889i	$-0.300473\pi$
$587$	−9.88731	−	17.1253i	−0.408093	−	0.706838i	−0.994676	+	0.103051i	$0.967139\pi$
$588$		0			0
$589$	−7.32037	+	12.6793i	−0.301631	+	0.522440i
$590$		0			0
$591$	17.9453	−	27.8478i	0.738170	−	1.14551i
$592$		0			0
$593$	−4.41904	−	7.65401i	−0.181468	−	0.314312i	0.760912	−	0.648855i	$-0.224752\pi$
$593$	−4.41904	−	7.65401i	−0.181468	−	0.314312i	−0.942381	+	0.334542i	$0.891418\pi$
$594$		0			0
$595$	6.62396	+	17.9785i	0.271556	+	0.737046i
$596$		0			0
$597$	−4.71023	−	9.16431i	−0.192777	−	0.375070i
$598$		0			0
$599$	32.7862	−	18.9291i	1.33961	−	0.773423i	0.352859	−	0.935676i	$-0.385209\pi$
$599$	32.7862	−	18.9291i	1.33961	−	0.773423i	0.986749	+	0.162253i	$0.0518761\pi$
$600$		0			0
$601$	−30.5662	+	17.6474i	−1.24682	+	0.719853i	−0.970474	−	0.241205i	$-0.922457\pi$
$601$	−30.5662	+	17.6474i	−1.24682	+	0.719853i	−0.276347	+	0.961058i	$0.589124\pi$
$602$		0			0
$603$	−3.36015	+	4.69412i	−0.136836	+	0.191159i
$604$		0			0
$605$	−19.8105			−0.805410
$606$		0			0
$607$			7.36587i			0.298971i	0.988764	+	0.149486i	$0.0477618\pi$
$607$			7.36587i			0.298971i	−0.988764	+	0.149486i	$0.952238\pi$
$608$		0			0
$609$	14.9810	−	16.3076i	0.607060	−	0.660816i
$610$		0			0
$611$	68.9958	−	39.8347i	2.79127	−	1.61154i
$612$		0			0
$613$	−9.39378	+	16.2705i	−0.379411	+	0.657159i	−0.990977	−	0.134034i	$-0.957207\pi$
$613$	−9.39378	+	16.2705i	−0.379411	+	0.657159i	0.611566	+	0.791194i	$0.290540\pi$
$614$		0			0
$615$	28.4727	−	14.6343i	1.14813	−	0.590110i
$616$		0			0
$617$	3.17209	+	1.83141i	0.127703	+	0.0737296i	0.562491	−	0.826804i	$-0.309843\pi$
$617$	3.17209	+	1.83141i	0.127703	+	0.0737296i	−0.434787	+	0.900533i	$0.643176\pi$
$618$		0			0
$619$			4.61969i			0.185681i	0.995681	+	0.0928405i	$0.0295947\pi$
$619$			4.61969i			0.185681i	−0.995681	+	0.0928405i	$0.970405\pi$
$620$		0			0
$621$	29.1293	+	4.29823i	1.16892	+	0.172482i
$622$		0			0
$623$	1.97348	+	0.339966i	0.0790658	+	0.0136205i
$624$		0			0
$625$	−13.4617			−0.538468
$626$		0			0
$627$	−0.0311461	+	0.637299i	−0.00124386	+	0.0254513i
$628$		0			0
$629$	13.2359			0.527751
$630$		0			0
$631$	−40.5302			−1.61348			−0.806740	−	0.590906i	$-0.798770\pi$
$631$	−40.5302			−1.61348			−0.806740	+	0.590906i	$0.798770\pi$
$632$		0			0
$633$	18.0673	−	9.28614i	0.718109	−	0.369091i
$634$		0			0
$635$	−9.37200			−0.371916
$636$		0			0
$637$	−15.6261	+	44.0083i	−0.619130	+	1.74367i
$638$		0			0
$639$	−19.9772	+	9.06380i	−0.790286	+	0.358558i
$640$		0			0
$641$		−	15.6234i		−	0.617088i	−0.951210	−	0.308544i	$-0.900158\pi$
$641$		−	15.6234i		−	0.617088i	0.951210	−	0.308544i	$-0.0998416\pi$
$642$		0			0
$643$	−13.9719	−	8.06670i	−0.550999	−	0.318120i	0.198526	−	0.980096i	$-0.436385\pi$
$643$	−13.9719	−	8.06670i	−0.550999	−	0.318120i	−0.749525	+	0.661976i	$0.769718\pi$
$644$		0			0
$645$	−0.343879	+	7.03630i	−0.0135402	+	0.277054i
$646$		0			0
$647$	17.2365	−	29.8545i	0.677637	−	1.17370i	−0.298054	−	0.954549i	$-0.596337\pi$
$647$	17.2365	−	29.8545i	0.677637	−	1.17370i	0.975691	−	0.219152i	$-0.0703292\pi$
$648$		0			0
$649$	1.13263	−	0.653926i	0.0444597	−	0.0256688i
$650$		0			0
$651$	−31.5254	+	34.3171i	−1.23558	+	1.34499i
$652$		0			0
$653$			12.8990i			0.504777i	0.967626	+	0.252388i	$0.0812161\pi$
$653$			12.8990i			0.504777i	−0.967626	+	0.252388i	$0.918784\pi$
$654$		0			0
$655$	−11.5321			−0.450597
$656$		0			0
$657$	0.837064	−	8.54338i	0.0326570	−	0.333309i
$658$		0			0
$659$	9.60396	−	5.54485i	0.374117	−	0.215997i	−0.301138	−	0.953580i	$-0.597367\pi$
$659$	9.60396	−	5.54485i	0.374117	−	0.215997i	0.675256	+	0.737584i	$0.264033\pi$
$660$		0			0
$661$	4.35683	−	2.51541i	0.169461	−	0.0978383i	−0.412871	−	0.910790i	$-0.635474\pi$
$661$	4.35683	−	2.51541i	0.169461	−	0.0978383i	0.582332	+	0.812951i	$0.302141\pi$
$662$		0			0
$663$	46.1332	+	2.25462i	1.79166	+	0.0875624i
$664$		0			0
$665$	−1.17162	+	6.80119i	−0.0454336	+	0.263739i
$666$		0			0
$667$	13.6914	+	23.7141i	0.530132	+	0.918215i
$668$		0			0
$669$	32.0037	+	1.56409i	1.23733	+	0.0604711i
$670$		0			0
$671$	1.27074	−	2.20099i	0.0490566	−	0.0849685i
$672$		0			0
$673$	−2.50713	−	4.34248i	−0.0966428	−	0.167390i	0.813650	−	0.581355i	$-0.197477\pi$
$673$	−2.50713	−	4.34248i	−0.0966428	−	0.167390i	−0.910293	+	0.413964i	$0.864144\pi$
$674$		0			0
$675$	1.30284	−	8.82940i	0.0501462	−	0.339844i
$676$		0			0
$677$	−18.7728	+	32.5155i	−0.721498	+	1.24967i	0.238902	+	0.971044i	$0.423213\pi$
$677$	−18.7728	+	32.5155i	−0.721498	+	1.24967i	−0.960399	+	0.278627i	$0.910121\pi$
$678$		0			0
$679$	−2.18747	+	12.6981i	−0.0839474	+	0.487308i
$680$		0			0
$681$	0.986463	+	0.635682i	0.0378014	+	0.0243594i
$682$		0			0
$683$	20.4810	+	11.8247i	0.783684	+	0.452460i	0.837734	−	0.546078i	$-0.183880\pi$
$683$	20.4810	+	11.8247i	0.783684	+	0.452460i	−0.0540503	+	0.998538i	$0.517213\pi$
$684$		0			0
$685$		−	0.0880862i		−	0.00336560i
$686$		0			0
$687$	0.362590	−	0.562675i	0.0138337	−	0.0214674i
$688$		0			0
$689$	15.3095	+	26.5168i	0.583245	+	1.01021i
$690$		0			0
$691$	20.8588	+	12.0429i	0.793508	+	0.458132i	0.841196	−	0.540730i	$-0.181852\pi$
$691$	20.8588	+	12.0429i	0.793508	+	0.458132i	−0.0476881	+	0.998862i	$0.515185\pi$
$692$		0			0
$693$	−0.538286	+	1.95822i	−0.0204478	+	0.0743867i
$694$		0			0
$695$	5.36205	+	3.09578i	0.203394	+	0.117430i
$696$		0			0
$697$	−20.3890	−	35.3148i	−0.772288	−	1.33764i
$698$		0			0
$699$	−6.70239	−	0.327560i	−0.253508	−	0.0123894i
$700$		0			0
$701$		−	15.6261i		−	0.590190i	−0.955468	−	0.295095i	$-0.904649\pi$
$701$		−	15.6261i		−	0.590190i	0.955468	−	0.295095i	$-0.0953513\pi$
$702$		0			0
$703$	4.12883	+	2.38378i	0.155722	+	0.0899059i
$704$		0			0
$705$	33.3291	−	17.1304i	1.25525	−	0.645166i
$706$		0			0
$707$	27.7841	−	33.3780i	1.04493	−	1.25531i
$708$		0			0
$709$	−7.20504	+	12.4795i	−0.270591	+	0.468678i	−0.969013	−	0.247008i	$-0.920552\pi$
$709$	−7.20504	+	12.4795i	−0.270591	+	0.468678i	0.698422	+	0.715686i	$0.253886\pi$
$710$		0			0
$711$	−10.9368	−	1.07157i	−0.410163	−	0.0401870i
$712$		0			0
$713$	−28.8116	−	49.9032i	−1.07900	−	1.86889i
$714$		0			0
$715$	1.54630	−	2.67828i	0.0578285	−	0.100162i
$716$		0			0
$717$	9.11792	+	17.7400i	0.340515	+	0.662512i
$718$		0			0
$719$	−7.49770	−	12.9864i	−0.279617	−	0.484311i	0.691673	−	0.722211i	$-0.256874\pi$
$719$	−7.49770	−	12.9864i	−0.279617	−	0.484311i	−0.971290	+	0.237900i	$0.923541\pi$
$720$		0			0
$721$	−39.4467	−	32.8357i	−1.46907	−	1.22287i
$722$		0			0
$723$	11.0656	−	17.1718i	0.411534	−	0.638626i
$724$		0			0
$725$	7.18800	−	4.14999i	0.266955	−	0.154127i
$726$		0			0
$727$	17.9806	−	10.3811i	0.666862	−	0.385013i	−0.128025	−	0.991771i	$-0.540864\pi$
$727$	17.9806	−	10.3811i	0.666862	−	0.385013i	0.794887	+	0.606758i	$0.207530\pi$
$728$		0			0
$729$	−25.8493	−	7.79827i	−0.957382	−	0.288825i
$730$		0			0
$731$	8.97341			0.331893
$732$		0			0
$733$			24.4072i			0.901502i	0.892650	+	0.450751i	$0.148844\pi$
$733$			24.4072i			0.901502i	−0.892650	+	0.450751i	$0.851156\pi$
$734$		0			0
$735$	−8.35166	+	20.3165i	−0.308056	+	0.749385i
$736$		0			0
$737$	0.426389	−	0.246176i	0.0157062	−	0.00906800i
$738$		0			0
$739$	−0.295124	+	0.511169i	−0.0108563	+	0.0188037i	−0.871403	−	0.490569i	$-0.836789\pi$
$739$	−0.295124	+	0.511169i	−0.0108563	+	0.0188037i	0.860546	+	0.509372i	$0.170122\pi$
$740$		0			0
$741$	13.9848	+	9.01185i	0.513743	+	0.331059i
$742$		0			0
$743$	−33.2573	−	19.2011i	−1.22009	−	0.704421i	−0.255155	−	0.966900i	$-0.582127\pi$
$743$	−33.2573	−	19.2011i	−1.22009	−	0.704421i	−0.964938	+	0.262479i	$0.915460\pi$
$744$		0			0
$745$		−	17.9216i		−	0.656597i
$746$		0			0
$747$	9.36872	−	13.0881i	0.342784	−	0.478868i
$748$		0			0
$749$	−3.35925	+	19.5002i	−0.122744	+	0.712521i
$750$		0			0
$751$	45.7173			1.66825			0.834124	−	0.551577i	$-0.185974\pi$
$751$	45.7173			1.66825			0.834124	+	0.551577i	$0.185974\pi$
$752$		0			0
$753$	14.2176	+	9.16187i	0.518117	+	0.333877i
$754$		0			0
$755$	15.3737			0.559507
$756$		0			0
$757$	−7.42071			−0.269710			−0.134855	−	0.990865i	$-0.543057\pi$
$757$	−7.42071			−0.269710			−0.134855	+	0.990865i	$0.543057\pi$
$758$		0			0
$759$	−2.11095	−	1.36031i	−0.0766227	−	0.0493760i
$760$		0			0
$761$	−47.3041			−1.71477			−0.857387	−	0.514672i	$-0.827914\pi$
$761$	−47.3041			−1.71477			−0.857387	+	0.514672i	$0.827914\pi$
$762$		0			0
$763$	7.80617	+	21.1872i	0.282602	+	0.767028i
$764$		0			0
$765$	21.6218	+	2.11846i	0.781737	+	0.0765932i
$766$		0			0
$767$		−	34.1012i		−	1.23132i
$768$		0			0
$769$	42.3251	+	24.4364i	1.52628	+	0.881199i	0.999513	+	0.0311905i	$0.00992986\pi$
$769$	42.3251	+	24.4364i	1.52628	+	0.881199i	0.526769	+	0.850009i	$0.323403\pi$
$770$		0			0
$771$	20.6104	+	13.2815i	0.742266	+	0.478320i
$772$		0			0
$773$	−11.4374	+	19.8101i	−0.411374	+	0.712521i	−0.995040	−	0.0994731i	$-0.968284\pi$
$773$	−11.4374	+	19.8101i	−0.411374	+	0.712521i	0.583666	+	0.811994i	$0.301618\pi$
$774$		0			0
$775$	−15.1262	+	8.73309i	−0.543348	+	0.313702i
$776$		0			0
$777$	11.1749	+	10.2658i	0.400896	+	0.368284i
$778$		0			0
$779$		−	14.6882i		−	0.526258i
$780$		0			0
$781$	1.87098			0.0669490
$782$		0			0
$783$	−9.24583	−	23.3449i	−0.330419	−	0.834280i
$784$		0			0
$785$	29.0021	−	16.7444i	1.03513	−	0.597633i
$786$		0			0
$787$	22.8346	−	13.1836i	0.813966	−	0.469943i	−0.0343656	−	0.999409i	$-0.510941\pi$
$787$	22.8346	−	13.1836i	0.813966	−	0.469943i	0.848331	+	0.529466i	$0.177608\pi$
$788$		0			0
$789$	−9.66167	+	14.9932i	−0.343965	+	0.533771i
$790$		0			0
$791$	−3.52502	+	1.29875i	−0.125335	+	0.0461783i
$792$		0			0
$793$	−33.1337	−	57.3892i	−1.17661	−	2.03795i
$794$		0			0
$795$	6.58362	+	12.8092i	0.233497	+	0.454296i
$796$		0			0
$797$	−8.16906	+	14.1492i	−0.289363	+	0.501191i	−0.973658	−	0.228014i	$-0.926777\pi$
$797$	−8.16906	+	14.1492i	−0.289363	+	0.501191i	0.684295	+	0.729205i	$0.260110\pi$
$798$		0			0
$799$	−23.8667	−	41.3383i	−0.844342	−	1.46244i
$800$		0			0
$801$	1.32168	−	1.84638i	0.0466992	−	0.0652387i
$802$		0			0
$803$	−0.366068	+	0.634049i	−0.0129183	+	0.0223751i
$804$		0			0
$805$	−20.8763	−	17.3776i	−0.735793	−	0.612480i
$806$		0			0
$807$	−12.1990	+	6.27000i	−0.429426	+	0.220714i
$808$		0			0
$809$	11.1321	+	6.42711i	0.391383	+	0.225965i	0.682759	−	0.730643i	$-0.260780\pi$
$809$	11.1321	+	6.42711i	0.391383	+	0.225965i	−0.291376	+	0.956609i	$0.594113\pi$
$810$		0			0
$811$			38.3887i			1.34801i	0.738727	+	0.674005i	$0.235427\pi$
$811$			38.3887i			1.34801i	−0.738727	+	0.674005i	$0.764573\pi$
$812$		0			0
$813$	18.8916	+	0.923271i	0.662557	+	0.0323805i
$814$		0			0
$815$	6.90922	+	11.9671i	0.242020	+	0.419190i
$816$		0			0
$817$	2.79917	+	1.61610i	0.0979306	+	0.0565402i
$818$		0			0
$819$	37.2008	+	37.6846i	1.29990	+	1.31681i
$820$		0			0
$821$	19.2629	+	11.1215i	0.672282	+	0.388142i	0.796941	−	0.604058i	$-0.206450\pi$
$821$	19.2629	+	11.1215i	0.672282	+	0.388142i	−0.124659	+	0.992200i	$0.539784\pi$
$822$		0			0
$823$	17.5785	+	30.4469i	0.612748	+	1.06131i	0.990775	+	0.135516i	$0.0432694\pi$
$823$	17.5785	+	30.4469i	0.612748	+	1.06131i	−0.378027	+	0.925795i	$0.623397\pi$
$824$		0			0
$825$	−0.412323	+	0.639851i	−0.0143552	+	0.0222767i
$826$		0			0
$827$			42.3779i			1.47362i	0.676098	+	0.736812i	$0.263670\pi$
$827$			42.3779i			1.47362i	−0.676098	+	0.736812i	$0.736330\pi$
$828$		0			0
$829$	46.8574	+	27.0531i	1.62742	+	0.939593i	0.984858	+	0.173362i	$0.0554630\pi$
$829$	46.8574	+	27.0531i	1.62742	+	0.939593i	0.642565	+	0.766231i	$0.277870\pi$
$830$		0			0
$831$	18.6657	+	12.0283i	0.647507	+	0.417257i
$832$		0			0
$833$	26.3672	+	9.36227i	0.913570	+	0.324383i
$834$		0			0
$835$	16.0678	−	27.8303i	0.556049	−	0.963106i
$836$		0			0
$837$	19.4566	+	49.1262i	0.672518	+	1.69805i
$838$		0			0
$839$	−20.1561	−	34.9114i	−0.695866	−	1.20528i	−0.969888	−	0.243552i	$-0.921687\pi$
$839$	−20.1561	−	34.9114i	−0.695866	−	1.20528i	0.274022	−	0.961724i	$-0.411646\pi$
$840$		0			0
$841$	−2.82461	+	4.89236i	−0.0974002	+	0.168702i
$842$		0			0
$843$	−36.6322	−	1.79029i	−1.26168	−	0.0616610i
$844$		0			0
$845$	−28.5424	−	49.4369i	−0.981888	−	1.70068i
$846$		0			0
$847$	−18.5084	+	22.2348i	−0.635957	+	0.763997i
$848$		0			0
$849$	−44.4311	−	2.17144i	−1.52487	−	0.0745236i
$850$		0			0
$851$	−16.2503	+	9.38211i	−0.557053	+	0.321614i
$852$		0			0
$853$	−8.81155	+	5.08735i	−0.301702	+	0.174188i	−0.643207	−	0.765692i	$-0.722397\pi$
$853$	−8.81155	+	5.08735i	−0.301702	+	0.174188i	0.341505	+	0.939880i	$0.389063\pi$
$854$		0			0
$855$	6.36318	+	4.55490i	0.217616	+	0.155774i
$856$		0			0
$857$	14.4428			0.493357			0.246679	−	0.969097i	$-0.420661\pi$
$857$	14.4428			0.493357			0.246679	+	0.969097i	$0.420661\pi$
$858$		0			0
$859$		−	17.3135i		−	0.590728i	−0.955385	−	0.295364i	$-0.904559\pi$
$859$		−	17.3135i		−	0.590728i	0.955385	−	0.295364i	$-0.0954409\pi$
$860$		0			0
$861$	10.1761	−	45.6294i	0.346802	−	1.55505i
$862$		0			0
$863$	24.1380	−	13.9361i	0.821667	−	0.474390i	−0.0293239	−	0.999570i	$-0.509335\pi$
$863$	24.1380	−	13.9361i	0.821667	−	0.474390i	0.850991	+	0.525180i	$0.176002\pi$
$864$		0			0
$865$	12.7051	−	22.0059i	0.431986	−	0.748221i
$866$		0			0
$867$	−0.0864763	+	1.76944i	−0.00293689	+	0.0600934i
$868$		0			0
$869$	0.811679	+	0.468623i	0.0275343	+	0.0158970i
$870$		0			0
$871$		−	12.8377i		−	0.434988i
$872$		0			0
$873$	11.8803	+	8.50418i	0.402088	+	0.287823i
$874$		0			0
$875$	−20.6006	+	24.7482i	−0.696426	+	0.836640i
$876$		0			0
$877$	10.3087			0.348099			0.174049	−	0.984737i	$-0.444315\pi$
$877$	10.3087			0.348099			0.174049	+	0.984737i	$0.444315\pi$
$878$		0			0
$879$	44.6177	−	22.9324i	1.50492	−	0.773492i
$880$		0			0
$881$	−2.48707			−0.0837914			−0.0418957	−	0.999122i	$-0.513340\pi$
$881$	−2.48707			−0.0837914			−0.0418957	+	0.999122i	$0.513340\pi$
$882$		0			0
$883$	−7.98895			−0.268850			−0.134425	−	0.990924i	$-0.542919\pi$
$883$	−7.98895			−0.268850			−0.134425	+	0.990924i	$0.542919\pi$
$884$		0			0
$885$	0.782973	−	16.0209i	0.0263194	−	0.538536i
$886$		0			0
$887$	1.61445			0.0542078			0.0271039	−	0.999633i	$-0.491371\pi$
$887$	1.61445			0.0542078			0.0271039	+	0.999633i	$0.491371\pi$
$888$		0			0
$889$	−8.75602	+	10.5189i	−0.293668	+	0.352793i
$890$		0			0
$891$	1.73286	+	1.51657i	0.0580531	+	0.0508068i
$892$		0			0
$893$		−	17.1934i		−	0.575357i
$894$		0			0
$895$	−15.0284	−	8.67663i	−0.502343	−	0.290028i
$896$		0			0
$897$	−58.2377	+	29.9328i	−1.94450	+	0.999426i
$898$		0			0
$899$	−24.5693	+	42.5552i	−0.819431	+	1.41930i
$900$		0			0
$901$	15.8873	−	9.17255i	0.529283	−	0.305582i
$902$		0			0
$903$	7.57610	+	6.95980i	0.252117	+	0.231608i
$904$		0			0
$905$		−	2.86003i		−	0.0950706i
$906$		0			0
$907$	−1.61913			−0.0537623			−0.0268812	−	0.999639i	$-0.508558\pi$
$907$	−1.61913			−0.0537623			−0.0268812	+	0.999639i	$0.508558\pi$
$908$		0			0
$909$	−20.3459	−	44.8438i	−0.674832	−	1.48737i
$910$		0			0
$911$	20.1759	−	11.6485i	0.668456	−	0.385933i	−0.127035	−	0.991898i	$-0.540546\pi$
$911$	20.1759	−	11.6485i	0.668456	−	0.385933i	0.795492	+	0.605965i	$0.207213\pi$
$912$		0			0
$913$	−1.18885	+	0.686384i	−0.0393453	+	0.0227160i
$914$		0			0
$915$	−14.2487	−	27.7224i	−0.471046	−	0.916475i
$916$		0			0
$917$	−10.7742	+	12.9434i	−0.355794	+	0.427428i
$918$		0			0
$919$	0.928631	+	1.60844i	0.0306327	+	0.0530574i	0.880935	−	0.473237i	$-0.156914\pi$
$919$	0.928631	+	1.60844i	0.0306327	+	0.0530574i	−0.850303	+	0.526294i	$0.823581\pi$
$920$		0			0
$921$	26.3295	−	40.8586i	0.867587	−	1.34634i
$922$		0			0
$923$	24.3922	−	42.2485i	0.802879	−	1.39063i
$924$		0			0
$925$	2.84381	+	4.92562i	0.0935039	+	0.161954i
$926$		0			0
$927$	−52.9971	+	24.0451i	−1.74065	+	0.789746i
$928$		0			0
$929$	−23.0332	+	39.8947i	−0.755695	+	1.30890i	0.189332	+	0.981913i	$0.439368\pi$
$929$	−23.0332	+	39.8947i	−0.755695	+	1.30890i	−0.945028	+	0.326990i	$0.893966\pi$
$930$		0			0
$931$	6.53887	+	7.66918i	0.214303	+	0.251347i
$932$		0			0
$933$	−0.669576	+	13.7006i	−0.0219209	+	0.448537i
$934$		0			0
$935$	−1.60467	−	0.926455i	−0.0524782	−	0.0302983i
$936$		0			0
$937$		−	19.2806i		−	0.629871i	−0.949113	−	0.314935i	$-0.898017\pi$
$937$		−	19.2806i		−	0.629871i	0.949113	−	0.314935i	$-0.101983\pi$
$938$		0			0
$939$	9.32937	+	18.1514i	0.304452	+	0.592348i
$940$		0			0
$941$	8.31298	+	14.3985i	0.270995	+	0.469378i	0.969117	−	0.246601i	$-0.0793139\pi$
$941$	8.31298	+	14.3985i	0.270995	+	0.469378i	−0.698122	+	0.715979i	$0.745981\pi$
$942$		0			0
$943$	50.0648	+	28.9049i	1.63033	+	0.941273i
$944$		0			0
$945$	16.6118	+	18.5585i	0.540383	+	0.603708i
$946$		0			0
$947$	10.8861	+	6.28511i	0.353751	+	0.204238i	0.666336	−	0.745651i	$-0.267862\pi$
$947$	10.8861	+	6.28511i	0.353751	+	0.204238i	−0.312585	+	0.949890i	$0.601195\pi$
$948$		0			0
$949$	9.54495	+	16.5323i	0.309842	+	0.536662i
$950$		0			0
$951$	−13.1352	−	25.5562i	−0.425940	−	0.828715i
$952$		0			0
$953$			47.3870i			1.53502i	0.641040	+	0.767508i	$0.278503\pi$
$953$			47.3870i			1.53502i	−0.641040	+	0.767508i	$0.721497\pi$
$954$		0			0
$955$	−27.3639	−	15.7986i	−0.885476	−	0.511230i
$956$		0			0
$957$	−0.104535	+	2.13896i	−0.00337915	+	0.0691428i
$958$		0			0
$959$	−0.0988658	−	0.0822967i	−0.00319254	−	0.00265750i
$960$		0			0
$961$	36.2027	−	62.7049i	1.16783	−	2.02274i
$962$		0			0
$963$	18.2443	+	13.0597i	0.587915	+	0.420842i
$964$		0			0
$965$	21.6073	+	37.4249i	0.695562	+	1.20475i
$966$		0			0
$967$	11.6171	−	20.1215i	0.373582	−	0.647063i	−0.616532	−	0.787330i	$-0.711463\pi$
$967$	11.6171	−	20.1215i	0.373582	−	0.647063i	0.990114	+	0.140267i	$0.0447961\pi$
$968$		0			0
$969$	5.39938	−	8.37885i	0.173453	−	0.269168i
$970$		0			0
$971$	−21.1024	−	36.5504i	−0.677208	−	1.17296i	−0.975818	−	0.218583i	$-0.929856\pi$
$971$	−21.1024	−	36.5504i	−0.677208	−	1.17296i	0.298610	−	0.954375i	$-0.403477\pi$
$972$		0			0
$973$	8.48426	−	3.12593i	0.271993	−	0.100213i
$974$		0			0
$975$	9.07293	+	17.6524i	0.290566	+	0.565331i
$976$		0			0
$977$	−25.7568	+	14.8707i	−0.824031	+	0.475755i	−0.851805	−	0.523859i	$-0.824492\pi$
$977$	−25.7568	+	14.8707i	−0.824031	+	0.475755i	0.0277732	+	0.999614i	$0.491158\pi$
$978$		0			0
$979$	−0.167716	+	0.0968307i	−0.00536022	+	0.00309472i
$980$		0			0
$981$	25.4807	+	2.49655i	0.813537	+	0.0797089i
$982$		0			0
$983$	17.5969			0.561253			0.280626	−	0.959817i	$-0.409458\pi$
$983$	17.5969			0.561253			0.280626	+	0.959817i	$0.409458\pi$
$984$		0			0
$985$			34.6532i			1.10414i
$986$		0			0
$987$	11.9118	−	53.4122i	0.379158	−	1.70013i
$988$		0			0
$989$	−11.0170	+	6.36067i	−0.350321	+	0.202258i
$990$		0			0
$991$	−8.84717	+	15.3238i	−0.281040	+	0.486775i	−0.971641	−	0.236461i	$-0.924013\pi$
$991$	−8.84717	+	15.3238i	−0.281040	+	0.486775i	0.690601	+	0.723236i	$0.257346\pi$
$992$		0			0
$993$	7.26666	−	3.73489i	0.230601	−	0.118523i
$994$		0			0
$995$	9.33399	+	5.38898i	0.295907	+	0.170842i
$996$		0			0
$997$		−	36.4807i		−	1.15535i	−0.816265	−	0.577677i	$-0.803959\pi$
$997$		−	36.4807i		−	1.15535i	0.816265	−	0.577677i	$-0.196041\pi$
$998$		0			0
$999$	15.9973	−	6.33577i	0.506132	−	0.200455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.e.689.20		48
3.2	odd	2		3024.2.df.e.17.19		48
4.3	odd	2		504.2.cx.a.185.5	yes	48
7.5	odd	6		1008.2.ca.e.257.21		48
9.2	odd	6		1008.2.ca.e.353.21		48
9.7	even	3		3024.2.ca.e.2033.19		48
12.11	even	2		1512.2.cx.a.17.19		48
21.5	even	6		3024.2.ca.e.2609.19		48
28.19	even	6		504.2.bs.a.257.4	✓	48
36.7	odd	6		1512.2.bs.a.521.19		48
36.11	even	6		504.2.bs.a.353.4	yes	48
63.47	even	6	inner	1008.2.df.e.929.20		48
63.61	odd	6		3024.2.df.e.1601.19		48
84.47	odd	6		1512.2.bs.a.1097.19		48
252.47	odd	6		504.2.cx.a.425.5	yes	48
252.187	even	6		1512.2.cx.a.89.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.4	✓	48	28.19	even	6
504.2.bs.a.353.4	yes	48	36.11	even	6
504.2.cx.a.185.5	yes	48	4.3	odd	2
504.2.cx.a.425.5	yes	48	252.47	odd	6
1008.2.ca.e.257.21		48	7.5	odd	6
1008.2.ca.e.353.21		48	9.2	odd	6
1008.2.df.e.689.20		48	1.1	even	1	trivial
1008.2.df.e.929.20		48	63.47	even	6	inner
1512.2.bs.a.521.19		48	36.7	odd	6
1512.2.bs.a.1097.19		48	84.47	odd	6
1512.2.cx.a.17.19		48	12.11	even	2
1512.2.cx.a.89.19		48	252.187	even	6
3024.2.ca.e.2033.19		48	9.7	even	3
3024.2.ca.e.2609.19		48	21.5	even	6
3024.2.df.e.17.19		48	3.2	odd	2
3024.2.df.e.1601.19		48	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45594 + 0.938214i) q^{3} -1.81173 q^{5} +(-1.69266 + 2.03345i) q^{7} +(1.23951 + 2.73196i) q^{9} +O(q^{10})\)	\(q+(1.45594 + 0.938214i) q^{3} -1.81173 q^{5} +(-1.69266 + 2.03345i) q^{7} +(1.23951 + 2.73196i) q^{9} -0.255864i q^{11} +(-5.77765 - 3.33573i) q^{13} +(-2.63777 - 1.69979i) q^{15} +(-1.99857 + 3.46163i) q^{17} +(-1.24687 + 0.719882i) q^{19} +(-4.37221 + 1.37250i) q^{21} -5.66665i q^{23} -1.71762 q^{25} +(-0.758514 + 5.14049i) q^{27} +(-4.18486 + 2.41613i) q^{29} +(8.80648 - 5.08442i) q^{31} +(0.240055 - 0.372522i) q^{33} +(3.06665 - 3.68407i) q^{35} +(-1.65567 - 2.86771i) q^{37} +(-5.28228 - 10.2773i) q^{39} +(-5.10089 + 8.83499i) q^{41} +(-1.12248 - 1.94419i) q^{43} +(-2.24566 - 4.94959i) q^{45} +(-5.97092 + 10.3419i) q^{47} +(-1.26982 - 6.88386i) q^{49} +(-6.15755 + 3.16483i) q^{51} +(-3.97466 - 2.29477i) q^{53} +0.463558i q^{55} +(-2.49077 - 0.121729i) q^{57} +(2.55575 + 4.42670i) q^{59} +(8.60220 + 4.96648i) q^{61} +(-7.65337 - 2.10380i) q^{63} +(10.4676 + 6.04346i) q^{65} +(0.962135 + 1.66647i) q^{67} +(5.31652 - 8.25028i) q^{69} +7.31241i q^{71} +(-2.47807 - 1.43071i) q^{73} +(-2.50074 - 1.61149i) q^{75} +(0.520286 + 0.433090i) q^{77} +(-1.83153 + 3.17231i) q^{79} +(-5.92723 + 6.77259i) q^{81} +(-2.68261 - 4.64642i) q^{83} +(3.62089 - 6.27156i) q^{85} +(-8.35975 - 0.408558i) q^{87} +(-0.378446 - 0.655488i) q^{89} +(16.5626 - 6.10230i) q^{91} +(17.5920 + 0.859756i) q^{93} +(2.25900 - 1.30424i) q^{95} +(4.21765 - 2.43506i) q^{97} +(0.699011 - 0.317146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} + 32 q^{63} - 36 q^{65} - 12 q^{77} - 6 q^{79} + 6 q^{81} + 54 q^{87} - 18 q^{89} - 6 q^{91} + 4 q^{93} + 54 q^{95} + 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

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