LMFDB - Embedded newform 1008.2.r.h.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.h.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.592396 - 1.62760i) q^{3} +(-0.673648 + 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})$	\(q+(0.592396 - 1.62760i) q^{3} +(-0.673648 + 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +(0.826352 + 1.43128i) q^{11} +(1.68479 - 2.91815i) q^{13} +(1.50000 + 1.78763i) q^{15} +0.467911 q^{17} +3.22668 q^{19} +(1.70574 - 0.300767i) q^{21} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(4.61721 - 7.99724i) q^{31} +(2.81908 - 0.497079i) q^{33} -1.34730 q^{35} +9.23442 q^{37} +(-3.75150 - 4.47086i) q^{39} +(-1.70574 + 2.95442i) q^{41} +(-2.20574 - 3.82045i) q^{43} +(3.79813 - 1.38241i) q^{45} +(4.67752 + 8.10170i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.277189 - 0.761570i) q^{51} -0.573978 q^{53} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +(0.520945 - 2.95442i) q^{63} +(2.26991 + 3.93161i) q^{65} +(0.298133 - 0.516382i) q^{67} +(-9.95723 - 11.8666i) q^{69} +0.554378 q^{71} +2.04963 q^{73} +(5.43242 - 0.957882i) q^{75} +(-0.826352 + 1.43128i) q^{77} +(-1.20187 - 2.08169i) q^{79} +(1.56283 + 8.86327i) q^{81} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(-10.6925 + 1.88538i) q^{87} +9.08647 q^{89} +3.36959 q^{91} +(-10.2811 - 12.2525i) q^{93} +(-2.17365 + 3.76487i) q^{95} +(0.949493 + 1.64457i) q^{97} +(0.860967 - 4.88279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 + 3 * q^7	$ 6 q - 3 q^{5} + 3 q^{7} + 6 q^{11} + 3 q^{13} + 9 q^{15} + 12 q^{17} + 6 q^{19} + 12 q^{23} + 6 q^{25} - 27 q^{27} - 9 q^{29} - 3 q^{31} - 6 q^{35} - 6 q^{37} + 18 q^{39} - 3 q^{43} + 9 q^{45} + 3 q^{47} - 3 q^{49} - 9 q^{51} + 12 q^{53} - 9 q^{57} - 3 q^{59} - 6 q^{61} - 15 q^{65} - 12 q^{67} - 9 q^{69} - 18 q^{71} - 42 q^{73} + 9 q^{75} - 6 q^{77} - 21 q^{79} - 18 q^{83} - 9 q^{85} - 9 q^{87} + 24 q^{89} + 6 q^{91} - 27 q^{93} - 12 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 + 3 * q^7 + 6 * q^11 + 3 * q^13 + 9 * q^15 + 12 * q^17 + 6 * q^19 + 12 * q^23 + 6 * q^25 - 27 * q^27 - 9 * q^29 - 3 * q^31 - 6 * q^35 - 6 * q^37 + 18 * q^39 - 3 * q^43 + 9 * q^45 + 3 * q^47 - 3 * q^49 - 9 * q^51 + 12 * q^53 - 9 * q^57 - 3 * q^59 - 6 * q^61 - 15 * q^65 - 12 * q^67 - 9 * q^69 - 18 * q^71 - 42 * q^73 + 9 * q^75 - 6 * q^77 - 21 * q^79 - 18 * q^83 - 9 * q^85 - 9 * q^87 + 24 * q^89 + 6 * q^91 - 27 * q^93 - 12 * q^95 + 3 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.592396	−	1.62760i	0.342020	−	0.939693i
$3$	0.592396	−	1.62760i	0.342020	−	0.939693i
$4$		0			0
$5$	−0.673648	+	1.16679i	−0.301265	+	0.521806i	−0.976423	−	0.215867i	$-0.930742\pi$
$5$	−0.673648	+	1.16679i	−0.301265	+	0.521806i	0.675158	+	0.737673i	$0.264075\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	−2.29813	−	1.92836i	−0.766044	−	0.642788i
$10$		0			0
$11$	0.826352	+	1.43128i	0.249154	+	0.431548i	0.963291	−	0.268458i	$-0.0865140\pi$
$11$	0.826352	+	1.43128i	0.249154	+	0.431548i	−0.714137	+	0.700006i	$0.753181\pi$
$12$		0			0
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	−0.532024	−	0.846729i	$-0.678568\pi$
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	0.999301	+	0.0373813i	$0.0119016\pi$
$14$		0			0
$15$	1.50000	+	1.78763i	0.387298	+	0.461564i
$16$		0			0
$17$	0.467911			0.113485			0.0567426	−	0.998389i	$-0.481929\pi$
$17$	0.467911			0.113485			0.0567426	+	0.998389i	$0.481929\pi$
$18$		0			0
$19$	3.22668			0.740252			0.370126	−	0.928982i	$-0.379315\pi$
$19$	3.22668			0.740252			0.370126	+	0.928982i	$0.379315\pi$
$20$		0			0
$21$	1.70574	−	0.300767i	0.372222	−	0.0656328i
$22$		0			0
$23$	4.47178	−	7.74535i	0.932431	−	1.61502i	0.153279	−	0.988183i	$-0.451017\pi$
$23$	4.47178	−	7.74535i	0.932431	−	1.61502i	0.779152	−	0.626835i	$-0.215650\pi$
$24$		0			0
$25$	1.59240	+	2.75811i	0.318479	+	0.551622i
$26$		0			0
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	−0.995239	−	0.0974595i	$-0.968928\pi$
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	0.413217	−	0.910632i	$-0.364405\pi$
$30$		0			0
$31$	4.61721	−	7.99724i	0.829276	−	1.43635i	−0.0693317	−	0.997594i	$-0.522087\pi$
$31$	4.61721	−	7.99724i	0.829276	−	1.43635i	0.898607	−	0.438754i	$-0.144580\pi$
$32$		0			0
$33$	2.81908	−	0.497079i	0.490738	−	0.0865304i
$34$		0			0
$35$	−1.34730			−0.227735
$36$		0			0
$37$	9.23442			1.51813			0.759065	−	0.651015i	$-0.225657\pi$
$37$	9.23442			1.51813			0.759065	+	0.651015i	$0.225657\pi$
$38$		0			0
$39$	−3.75150	−	4.47086i	−0.600720	−	0.715910i
$40$		0			0
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	−0.967927	−	0.251231i	$-0.919165\pi$
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	0.701536	+	0.712634i	$0.252498\pi$
$42$		0			0
$43$	−2.20574	−	3.82045i	−0.336372	−	0.582613i	0.647376	−	0.762171i	$-0.275867\pi$
$43$	−2.20574	−	3.82045i	−0.336372	−	0.582613i	−0.983747	+	0.179558i	$0.942533\pi$
$44$		0			0
$45$	3.79813	−	1.38241i	0.566192	−	0.206077i
$46$		0			0
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	0.974281	+	0.225335i	$0.0723475\pi$
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	−0.291995	+	0.956420i	$0.594319\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	0.277189	−	0.761570i	0.0388142	−	0.106641i
$52$		0			0
$53$	−0.573978			−0.0788419			−0.0394210	−	0.999223i	$-0.512551\pi$
$53$	−0.573978			−0.0788419			−0.0394210	+	0.999223i	$0.512551\pi$
$54$		0			0
$55$	−2.22668			−0.300246
$56$		0			0
$57$	1.91147	−	5.25173i	0.253181	−	0.695609i
$58$		0			0
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	0.299162	+	0.954202i	$0.403293\pi$
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	−0.975945	+	0.218019i	$0.930041\pi$
$60$		0			0
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	0.510937	−	0.859618i	$-0.329299\pi$
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	−0.999920	+	0.0126752i	$0.995965\pi$
$62$		0			0
$63$	0.520945	−	2.95442i	0.0656328	−	0.372222i
$64$		0			0
$65$	2.26991	+	3.93161i	0.281548	+	0.487656i
$66$		0			0
$67$	0.298133	−	0.516382i	0.0364228	−	0.0630861i	−0.847239	−	0.531211i	$-0.821737\pi$
$67$	0.298133	−	0.516382i	0.0364228	−	0.0630861i	0.883662	+	0.468125i	$0.155070\pi$
$68$		0			0
$69$	−9.95723	−	11.8666i	−1.19871	−	1.42857i
$70$		0			0
$71$	0.554378			0.0657925			0.0328963	−	0.999459i	$-0.489527\pi$
$71$	0.554378			0.0657925			0.0328963	+	0.999459i	$0.489527\pi$
$72$		0			0
$73$	2.04963			0.239891			0.119946	−	0.992780i	$-0.461728\pi$
$73$	2.04963			0.239891			0.119946	+	0.992780i	$0.461728\pi$
$74$		0			0
$75$	5.43242	−	0.957882i	0.627282	−	0.110607i
$76$		0			0
$77$	−0.826352	+	1.43128i	−0.0941715	+	0.163110i
$78$		0			0
$79$	−1.20187	−	2.08169i	−0.135221	−	0.234209i	0.790461	−	0.612512i	$-0.209841\pi$
$79$	−1.20187	−	2.08169i	−0.135221	−	0.234209i	−0.925682	+	0.378303i	$0.876508\pi$
$80$		0			0
$81$	1.56283	+	8.86327i	0.173648	+	0.984808i
$82$		0			0
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	−0.901187	−	0.433431i	$-0.857303\pi$
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	0.0752309	−	0.997166i	$-0.476031\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$		0			0
$87$	−10.6925	+	1.88538i	−1.14636	+	0.202134i
$88$		0			0
$89$	9.08647			0.963164			0.481582	−	0.876401i	$-0.340062\pi$
$89$	9.08647			0.963164			0.481582	+	0.876401i	$0.340062\pi$
$90$		0			0
$91$	3.36959			0.353228
$92$		0			0
$93$	−10.2811	−	12.2525i	−1.06610	−	1.27052i
$94$		0			0
$95$	−2.17365	+	3.76487i	−0.223012	+	0.386267i
$96$		0			0
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	0.910195	−	0.414181i	$-0.135932\pi$
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	−0.813788	+	0.581161i	$0.802598\pi$
$98$		0			0
$99$	0.860967	−	4.88279i	0.0865304	−	0.490738i
$100$		0			0
$101$	0.854570	+	1.48016i	0.0850329	+	0.147281i	0.905405	−	0.424548i	$-0.139567\pi$
$101$	0.854570	+	1.48016i	0.0850329	+	0.147281i	−0.820372	+	0.571830i	$0.806234\pi$
$102$		0			0
$103$	−1.81908	+	3.15074i	−0.179239	+	0.310451i	−0.941620	−	0.336677i	$-0.890697\pi$
$103$	−1.81908	+	3.15074i	−0.179239	+	0.310451i	0.762381	+	0.647128i	$0.224030\pi$
$104$		0			0
$105$	−0.798133	+	2.19285i	−0.0778898	+	0.214001i
$106$		0			0
$107$	−7.12836			−0.689124			−0.344562	−	0.938764i	$-0.611973\pi$
$107$	−7.12836			−0.689124			−0.344562	+	0.938764i	$0.611973\pi$
$108$		0			0
$109$	0.403733			0.0386706			0.0193353	−	0.999813i	$-0.493845\pi$
$109$	0.403733			0.0386706			0.0193353	+	0.999813i	$0.493845\pi$
$110$		0			0
$111$	5.47044	−	15.0299i	0.519231	−	1.42658i
$112$		0			0
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	0.300320	+	0.953839i	$0.402907\pi$
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	−0.976208	+	0.216835i	$0.930427\pi$
$114$		0			0
$115$	6.02481	+	10.4353i	0.561817	+	0.973095i
$116$		0			0
$117$	−9.49912	+	3.45740i	−0.878194	+	0.319637i
$118$		0			0
$119$	0.233956	+	0.405223i	0.0214467	+	0.0371467i
$120$		0			0
$121$	4.13429	−	7.16079i	0.375844	−	0.650981i
$122$		0			0
$123$	3.79813	+	4.52644i	0.342466	+	0.408135i
$124$		0			0
$125$	−11.0273			−0.986315
$126$		0			0
$127$	20.7716			1.84318			0.921589	−	0.388167i	$-0.126892\pi$
$127$	20.7716			1.84318			0.921589	+	0.388167i	$0.126892\pi$
$128$		0			0
$129$	−7.52481	+	1.32683i	−0.662523	+	0.116821i
$130$		0			0
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	−0.979013	−	0.203797i	$-0.934672\pi$
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	0.666000	+	0.745952i	$0.268005\pi$
$132$		0			0
$133$	1.61334	+	2.79439i	0.139894	+	0.242304i
$134$		0			0
$135$		−	7.00076i		−	0.602529i
$136$		0			0
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	0.805925	−	0.592017i	$-0.201668\pi$
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	−0.915665	+	0.401943i	$0.868335\pi$
$138$		0			0
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	−0.966272	−	0.257523i	$-0.917094\pi$
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	0.706158	+	0.708055i	$0.250427\pi$
$140$		0			0
$141$	15.9572	−	2.81369i	1.34384	−	0.236956i
$142$		0			0
$143$	5.56893			0.465697
$144$		0			0
$145$	8.44562			0.701371
$146$		0			0
$147$	1.11334	+	1.32683i	0.0918268	+	0.109435i
$148$		0			0
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	−0.874719	−	0.484630i	$-0.838954\pi$
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	0.857062	+	0.515214i	$0.172288\pi$
$150$		0			0
$151$	−1.23530	−	2.13960i	−0.100527	−	0.174118i	0.811375	−	0.584526i	$-0.198720\pi$
$151$	−1.23530	−	2.13960i	−0.100527	−	0.174118i	−0.911902	+	0.410408i	$0.865386\pi$
$152$		0			0
$153$	−1.07532	−	0.902302i	−0.0869346	−	0.0729468i
$154$		0			0
$155$	6.22075	+	10.7747i	0.499663	+	0.865441i
$156$		0			0
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	−0.994248	−	0.107106i	$-0.965841\pi$
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	0.589881	+	0.807491i	$0.299175\pi$
$158$		0			0
$159$	−0.340022	+	0.934204i	−0.0269655	+	0.0740872i
$160$		0			0
$161$	8.94356			0.704852
$162$		0			0
$163$	2.59627			0.203355			0.101678	−	0.994817i	$-0.467579\pi$
$163$	2.59627			0.203355			0.101678	+	0.994817i	$0.467579\pi$
$164$		0			0
$165$	−1.31908	+	3.62414i	−0.102690	+	0.282139i
$166$		0			0
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.0656422	+	0.997843i	$0.520910\pi$
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.831337	+	0.555769i	$0.812424\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$		0			0
$171$	−7.41534	−	6.22221i	−0.567066	−	0.475825i
$172$		0			0
$173$	2.37598	+	4.11532i	0.180643	+	0.312882i	0.942100	−	0.335333i	$-0.108849\pi$
$173$	2.37598	+	4.11532i	0.180643	+	0.312882i	−0.761457	+	0.648215i	$0.775516\pi$
$174$		0			0
$175$	−1.59240	+	2.75811i	−0.120374	+	0.208494i
$176$		0			0
$177$	11.5753	+	13.7949i	0.870054	+	1.03689i
$178$		0			0
$179$	8.53209			0.637718			0.318859	−	0.947802i	$-0.396700\pi$
$179$	8.53209			0.637718			0.318859	+	0.947802i	$0.396700\pi$
$180$		0			0
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$		0			0
$183$	−13.0287	+	2.29731i	−0.963108	+	0.169822i
$184$		0			0
$185$	−6.22075	+	10.7747i	−0.457359	+	0.792169i
$186$		0			0
$187$	0.386659	+	0.669713i	0.0282753	+	0.0489743i
$188$		0			0
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$		0			0
$191$	6.45471	+	11.1799i	0.467046	+	0.808948i	0.999291	−	0.0376425i	$-0.0119848\pi$
$191$	6.45471	+	11.1799i	0.467046	+	0.808948i	−0.532245	+	0.846590i	$0.678651\pi$
$192$		0			0
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	−0.854313	−	0.519759i	$-0.826022\pi$
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	0.877281	+	0.479977i	$0.159355\pi$
$194$		0			0
$195$	7.74376	−	1.36543i	0.554542	−	0.0977807i
$196$		0			0
$197$	11.4456			0.815467			0.407733	−	0.913101i	$-0.366319\pi$
$197$	11.4456			0.815467			0.407733	+	0.913101i	$0.366319\pi$
$198$		0			0
$199$	3.63816			0.257902			0.128951	−	0.991651i	$-0.458839\pi$
$199$	3.63816			0.257902			0.128951	+	0.991651i	$0.458839\pi$
$200$		0			0
$201$	−0.663848	−	0.791143i	−0.0468242	−	0.0558029i
$202$		0			0
$203$	3.13429	−	5.42874i	0.219984	−	0.381023i
$204$		0			0
$205$	−2.29813	−	3.98048i	−0.160509	−	0.278009i
$206$		0			0
$207$	−25.2126	+	9.17664i	−1.75240	+	0.637820i
$208$		0			0
$209$	2.66637	+	4.61830i	0.184437	+	0.319454i
$210$		0			0
$211$	2.91147	−	5.04282i	0.200434	−	0.347162i	−0.748234	−	0.663435i	$-0.769098\pi$
$211$	2.91147	−	5.04282i	0.200434	−	0.347162i	0.948668	+	0.316273i	$0.102431\pi$
$212$		0			0
$213$	0.328411	−	0.902302i	0.0225024	−	0.0618247i
$214$		0			0
$215$	5.94356			0.405348
$216$		0			0
$217$	9.23442			0.626873
$218$		0			0
$219$	1.21419	−	3.33597i	0.0820476	−	0.225424i
$220$		0			0
$221$	0.788333	−	1.36543i	0.0530290	−	0.0918490i
$222$		0			0
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	0.959905	−	0.280327i	$-0.0904428\pi$
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	−0.722722	+	0.691139i	$0.757109\pi$
$224$		0			0
$225$	1.65910	−	9.40923i	0.110607	−	0.627282i
$226$		0			0
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	0.596913	−	0.802306i	$-0.296394\pi$
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	−0.993274	+	0.115789i	$0.963060\pi$
$228$		0			0
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636403\pi$
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	0.995484	−	0.0949315i	$-0.0302632\pi$
$230$		0			0
$231$	1.84002	+	2.19285i	0.121065	+	0.144279i
$232$		0			0
$233$	16.2540			1.06484			0.532418	−	0.846481i	$-0.321283\pi$
$233$	16.2540			1.06484			0.532418	+	0.846481i	$0.321283\pi$
$234$		0			0
$235$	−12.6040			−0.822195
$236$		0			0
$237$	−4.10014	+	0.722965i	−0.266333	+	0.0469616i
$238$		0			0
$239$	−7.54963	+	13.0763i	−0.488345	+	0.845838i	−0.999910	−	0.0134062i	$-0.995733\pi$
$239$	−7.54963	+	13.0763i	−0.488345	+	0.845838i	0.511565	+	0.859244i	$0.329066\pi$
$240$		0			0
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	0.999991	+	0.00424420i	$0.00135097\pi$
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$242$		0			0
$243$	15.3516	+	2.70691i	0.984808	+	0.173648i
$244$		0			0
$245$	−0.673648	−	1.16679i	−0.0430378	−	0.0745437i
$246$		0			0
$247$	5.43629	−	9.41593i	0.345903	−	0.599121i
$248$		0			0
$249$	−25.6707	+	4.52644i	−1.62682	+	0.286851i
$250$		0			0
$251$	−19.0651			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$		0			0
$255$	0.701867	+	0.836452i	0.0439526	+	0.0523807i
$256$		0			0
$257$	−13.2909	+	23.0204i	−0.829061	+	1.43598i	0.0697146	+	0.997567i	$0.477791\pi$
$257$	−13.2909	+	23.0204i	−0.829061	+	1.43598i	−0.898776	+	0.438409i	$0.855542\pi$
$258$		0			0
$259$	4.61721	+	7.99724i	0.286900	+	0.496925i
$260$		0			0
$261$	−3.26558	+	18.5200i	−0.202134	+	1.14636i
$262$		0			0
$263$	−0.367059	−	0.635765i	−0.0226338	−	0.0392029i	0.854487	−	0.519473i	$-0.173872\pi$
$263$	−0.367059	−	0.635765i	−0.0226338	−	0.0392029i	−0.877120	+	0.480270i	$0.840539\pi$
$264$		0			0
$265$	0.386659	−	0.669713i	0.0237523	−	0.0411402i
$266$		0			0
$267$	5.38279	−	14.7891i	0.329421	−	0.905078i
$268$		0			0
$269$	−20.8503			−1.27126			−0.635632	−	0.771992i	$-0.719261\pi$
$269$	−20.8503			−1.27126			−0.635632	+	0.771992i	$0.719261\pi$
$270$		0			0
$271$	−6.95811			−0.422675			−0.211338	−	0.977413i	$-0.567782\pi$
$271$	−6.95811			−0.422675			−0.211338	+	0.977413i	$0.567782\pi$
$272$		0			0
$273$	1.99613	−	5.48432i	0.120811	−	0.331926i
$274$		0			0
$275$	−2.63176	+	4.55834i	−0.158701	+	0.274878i
$276$		0			0
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$		0			0
$279$	−26.0326	+	9.47508i	−1.55853	+	0.567258i
$280$		0			0
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	−0.979159	−	0.203095i	$-0.934900\pi$
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	0.313694	−	0.949524i	$-0.398433\pi$
$282$		0			0
$283$	−9.29726	+	16.1033i	−0.552665	+	0.957243i	0.445417	+	0.895323i	$0.353056\pi$
$283$	−9.29726	+	16.1033i	−0.552665	+	0.957243i	−0.998081	+	0.0619196i	$0.980278\pi$
$284$		0			0
$285$	4.84002	+	5.76811i	0.286698	+	0.341674i
$286$		0			0
$287$	−3.41147			−0.201373
$288$		0			0
$289$	−16.7811			−0.987121
$290$		0			0
$291$	3.23917	−	0.571153i	0.189884	−	0.0334816i
$292$		0			0
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	−0.991406	−	0.130822i	$-0.958238\pi$
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	0.608998	+	0.793171i	$0.291572\pi$
$294$		0			0
$295$	−7.00387	−	12.1311i	−0.407781	−	0.706298i
$296$		0			0
$297$	−7.43717	−	4.29385i	−0.431548	−	0.249154i
$298$		0			0
$299$	−15.0680	−	26.0986i	−0.871408	−	1.50932i
$300$		0			0
$301$	2.20574	−	3.82045i	0.127137	−	0.220207i
$302$		0			0
$303$	2.91534	−	0.514054i	0.167482	−	0.0295316i
$304$		0			0
$305$	10.2909			0.589253
$306$		0			0
$307$	−6.31046			−0.360157			−0.180078	−	0.983652i	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$	4.05051	+	4.82721i	0.230425	+	0.274610i
$310$		0			0
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	−0.968871	−	0.247565i	$-0.920370\pi$
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	0.698833	+	0.715285i	$0.253703\pi$
$312$		0			0
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	0.999998	−	0.00205946i	$-0.000655547\pi$
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	−0.501782	+	0.864994i	$0.667322\pi$
$314$		0			0
$315$	3.09627	+	2.59808i	0.174455	+	0.146385i
$316$		0			0
$317$	−4.03849	−	6.99486i	−0.226824	−	0.392871i	0.730041	−	0.683403i	$-0.239501\pi$
$317$	−4.03849	−	6.99486i	−0.226824	−	0.392871i	−0.956865	+	0.290533i	$0.906168\pi$
$318$		0			0
$319$	5.18004	−	8.97210i	0.290027	−	0.502341i
$320$		0			0
$321$	−4.22281	+	11.6021i	−0.235694	+	0.647565i
$322$		0			0
$323$	1.50980			0.0840075
$324$		0			0
$325$	10.7314			0.595273
$326$		0			0
$327$	0.239170	−	0.657115i	0.0132261	−	0.0363385i
$328$		0			0
$329$	−4.67752	+	8.10170i	−0.257880	+	0.446661i
$330$		0			0
$331$	11.5248	+	19.9616i	0.633461	+	1.09719i	0.986839	+	0.161706i	$0.0516997\pi$
$331$	11.5248	+	19.9616i	0.633461	+	1.09719i	−0.353378	+	0.935481i	$0.614967\pi$
$332$		0			0
$333$	−21.2219	−	17.8073i	−1.16295	−	0.975835i
$334$		0			0
$335$	0.401674	+	0.695720i	0.0219458	+	0.0380112i
$336$		0			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$		0			0
$339$	15.9982	+	19.0660i	0.868905	+	1.03552i
$340$		0			0
$341$	15.2618			0.826471
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	20.5535	−	3.62414i	1.10656	−	0.195117i
$346$		0			0
$347$	6.47313	−	11.2118i	0.347496	−	0.601880i	−0.638308	−	0.769781i	$-0.720365\pi$
$347$	6.47313	−	11.2118i	0.347496	−	0.601880i	0.985804	+	0.167901i	$0.0536988\pi$
$348$		0			0
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	0.845785	−	0.533524i	$-0.179132\pi$
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	−0.884938	+	0.465710i	$0.845799\pi$
$350$		0			0
$351$			17.5089i			0.934555i
$352$		0			0
$353$	−7.16637	−	12.4125i	−0.381428	−	0.660652i	0.609839	−	0.792525i	$-0.291234\pi$
$353$	−7.16637	−	12.4125i	−0.381428	−	0.660652i	−0.991267	+	0.131873i	$0.957901\pi$
$354$		0			0
$355$	−0.373455	+	0.646844i	−0.0198210	+	0.0343309i
$356$		0			0
$357$	0.798133	−	0.140732i	0.0422417	−	0.00744835i
$358$		0			0
$359$	20.9368			1.10500			0.552500	−	0.833513i	$-0.313674\pi$
$359$	20.9368			1.10500			0.552500	+	0.833513i	$0.313674\pi$
$360$		0			0
$361$	−8.58853			−0.452028
$362$		0			0
$363$	−9.20574	−	10.9710i	−0.483176	−	0.575827i
$364$		0			0
$365$	−1.38073	+	2.39149i	−0.0722707	+	0.125176i
$366$		0			0
$367$	−6.02869	−	10.4420i	−0.314695	−	0.545067i	0.664678	−	0.747130i	$-0.268569\pi$
$367$	−6.02869	−	10.4420i	−0.314695	−	0.545067i	−0.979373	+	0.202063i	$0.935236\pi$
$368$		0			0
$369$	9.61721	−	3.50038i	0.500652	−	0.182222i
$370$		0			0
$371$	−0.286989	−	0.497079i	−0.0148997	−	0.0258071i
$372$		0			0
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$		0			0
$375$	−6.53256	+	17.9480i	−0.337340	+	0.926833i
$376$		0			0
$377$	−21.1225			−1.08786
$378$		0			0
$379$	6.92396			0.355660			0.177830	−	0.984061i	$-0.443092\pi$
$379$	6.92396			0.355660			0.177830	+	0.984061i	$0.443092\pi$
$380$		0			0
$381$	12.3050	−	33.8077i	0.630404	−	1.73202i
$382$		0			0
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	−0.750182	−	0.661232i	$-0.770034\pi$
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	0.947734	+	0.319061i	$0.103367\pi$
$384$		0			0
$385$	−1.11334	−	1.92836i	−0.0567411	−	0.0982785i
$386$		0			0
$387$	−2.29813	+	13.0334i	−0.116821	+	0.662523i
$388$		0			0
$389$	−2.69981	−	4.67620i	−0.136886	−	0.237093i	0.789431	−	0.613840i	$-0.210376\pi$
$389$	−2.69981	−	4.67620i	−0.136886	−	0.237093i	−0.926316	+	0.376747i	$0.877043\pi$
$390$		0			0
$391$	2.09240	−	3.62414i	0.105817	−	0.183280i
$392$		0			0
$393$	7.97730	+	9.50698i	0.402402	+	0.479564i
$394$		0			0
$395$	3.23854			0.162949
$396$		0			0
$397$	−29.2344			−1.46723			−0.733617	−	0.679563i	$-0.762169\pi$
$397$	−29.2344			−1.46723			−0.733617	+	0.679563i	$0.762169\pi$
$398$		0			0
$399$	5.50387	−	0.970481i	0.275538	−	0.0485848i
$400$		0			0
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	−0.289629	−	0.957139i	$-0.593532\pi$
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	0.973721	−	0.227743i	$-0.0731346\pi$
$402$		0			0
$403$	−15.5581	−	26.9474i	−0.775003	−	1.34235i
$404$		0			0
$405$	−11.3944	−	4.14722i	−0.566192	−	0.206077i
$406$		0			0
$407$	7.63088	+	13.2171i	0.378249	+	0.655146i
$408$		0			0
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	−0.732628	−	0.680629i	$-0.761706\pi$
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	0.955756	+	0.294160i	$0.0950398\pi$
$410$		0			0
$411$	−4.38191	+	0.772649i	−0.216144	+	0.0381120i
$412$		0			0
$413$	−10.3969			−0.511599
$414$		0			0
$415$	20.2763			0.995325
$416$		0			0
$417$	6.82857	+	8.13798i	0.334397	+	0.398518i
$418$		0			0
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	−0.863877	−	0.503704i	$-0.831970\pi$
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	0.868158	+	0.496287i	$0.165304\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$		0			0
$423$	4.87346	−	27.6387i	0.236956	−	1.34384i
$424$		0			0
$425$	0.745100	+	1.29055i	0.0361427	+	0.0626009i
$426$		0			0
$427$	3.81908	−	6.61484i	0.184818	−	0.320114i
$428$		0			0
$429$	3.29901	−	9.06396i	0.159278	−	0.437612i
$430$		0			0
$431$	29.3191			1.41225			0.706126	−	0.708086i	$-0.250441\pi$
$431$	29.3191			1.41225			0.706126	+	0.708086i	$0.250441\pi$
$432$		0			0
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$		0			0
$435$	5.00316	−	13.7461i	0.239883	−	0.659073i
$436$		0			0
$437$	14.4290	−	24.9918i	0.690233	−	1.19552i
$438$		0			0
$439$	−10.9650	−	18.9919i	−0.523330	−	0.906434i	−0.999631	−	0.0271516i	$-0.991356\pi$
$439$	−10.9650	−	18.9919i	−0.523330	−	0.906434i	0.476302	−	0.879282i	$-0.341977\pi$
$440$		0			0
$441$	2.81908	−	1.02606i	0.134242	−	0.0488600i
$442$		0			0
$443$	−9.35504	−	16.2034i	−0.444471	−	0.769847i	0.553544	−	0.832820i	$-0.313275\pi$
$443$	−9.35504	−	16.2034i	−0.444471	−	0.769847i	−0.998015	+	0.0629732i	$0.979942\pi$
$444$		0			0
$445$	−6.12108	+	10.6020i	−0.290167	+	0.502584i
$446$		0			0
$447$	0.479933	+	0.571962i	0.0227000	+	0.0270529i
$448$		0			0
$449$	6.68004			0.315251			0.157625	−	0.987499i	$-0.449616\pi$
$449$	6.68004			0.315251			0.157625	+	0.987499i	$0.449616\pi$
$450$		0			0
$451$	−5.63816			−0.265490
$452$		0			0
$453$	−4.21419	+	0.743076i	−0.198000	+	0.0349128i
$454$		0			0
$455$	−2.26991	+	3.93161i	−0.106415	+	0.184317i
$456$		0			0
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	0.998655	−	0.0518563i	$-0.0165138\pi$
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	−0.544236	+	0.838932i	$0.683180\pi$
$458$		0			0
$459$	−2.10560	+	1.21567i	−0.0982810	+	0.0567426i
$460$		0			0
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	0.877052	−	0.480395i	$-0.159507\pi$
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	−0.854560	+	0.519352i	$0.826173\pi$
$462$		0			0
$463$	−0.222811	+	0.385920i	−0.0103549	+	0.0179352i	−0.871156	−	0.491006i	$-0.836629\pi$
$463$	−0.222811	+	0.385920i	−0.0103549	+	0.0179352i	0.860802	+	0.508941i	$0.169963\pi$
$464$		0			0
$465$	21.2219	−	3.74200i	0.984144	−	0.173531i
$466$		0			0
$467$	34.2148			1.58327			0.791637	−	0.610992i	$-0.209229\pi$
$467$	34.2148			1.58327			0.791637	+	0.610992i	$0.209229\pi$
$468$		0			0
$469$	0.596267			0.0275330
$470$		0			0
$471$	11.2819	+	13.4453i	0.519844	+	0.619526i
$472$		0			0
$473$	3.64543	−	6.31407i	0.167617	−	0.290321i
$474$		0			0
$475$	5.13816	+	8.89955i	0.235755	+	0.408339i
$476$		0			0
$477$	1.31908	+	1.10684i	0.0603964	+	0.0506786i
$478$		0			0
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	0.502125	−	0.864795i	$-0.332552\pi$
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	−0.999997	+	0.00245553i	$0.999218\pi$
$480$		0			0
$481$	15.5581	−	26.9474i	0.709388	−	1.22870i
$482$		0			0
$483$	5.29813	−	14.5565i	0.241073	−	0.662344i
$484$		0			0
$485$	−2.55850			−0.116175
$486$		0			0
$487$	−19.3928			−0.878772			−0.439386	−	0.898298i	$-0.644804\pi$
$487$	−19.3928			−0.878772			−0.439386	+	0.898298i	$0.644804\pi$
$488$		0			0
$489$	1.53802	−	4.22567i	0.0695516	−	0.191091i
$490$		0			0
$491$	13.0783	−	22.6523i	0.590216	−	1.02228i	−0.403987	−	0.914765i	$-0.632376\pi$
$491$	13.0783	−	22.6523i	0.590216	−	1.02228i	0.994203	−	0.107519i	$-0.0342908\pi$
$492$		0			0
$493$	−1.46657	−	2.54017i	−0.0660509	−	0.114403i
$494$		0			0
$495$	5.11721	+	4.29385i	0.230002	+	0.192994i
$496$		0			0
$497$	0.277189	+	0.480105i	0.0124336	+	0.0215357i
$498$		0			0
$499$	−7.15064	+	12.3853i	−0.320107	+	0.554441i	−0.980510	−	0.196470i	$-0.937052\pi$
$499$	−7.15064	+	12.3853i	−0.320107	+	0.554441i	0.660403	+	0.750911i	$0.270385\pi$
$500$		0			0
$501$	25.8106	+	30.7599i	1.15313	+	1.37425i
$502$		0			0
$503$	−18.7033			−0.833937			−0.416969	−	0.908921i	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$		0			0
$507$	2.80747	−	0.495032i	0.124684	−	0.0219851i
$508$		0			0
$509$	12.8045	−	22.1781i	0.567551	−	0.983027i	−0.429257	−	0.903183i	$-0.641224\pi$
$509$	12.8045	−	22.1781i	0.567551	−	0.983027i	0.996807	−	0.0798442i	$-0.0254423\pi$
$510$		0			0
$511$	1.02481	+	1.77503i	0.0453351	+	0.0785228i
$512$		0			0
$513$	−14.5201	+	8.38316i	−0.641077	+	0.370126i
$514$		0			0
$515$	−2.45084	−	4.24497i	−0.107997	−	0.187056i
$516$		0			0
$517$	−7.73055	+	13.3897i	−0.339989	+	0.588879i
$518$		0			0
$519$	8.10560	−	1.42924i	0.355796	−	0.0627365i
$520$		0			0
$521$	−21.2121			−0.929320			−0.464660	−	0.885489i	$-0.653824\pi$
$521$	−21.2121			−0.929320			−0.464660	+	0.885489i	$0.653824\pi$
$522$		0			0
$523$	−20.8057			−0.909770			−0.454885	−	0.890550i	$-0.650320\pi$
$523$	−20.8057			−0.909770			−0.454885	+	0.890550i	$0.650320\pi$
$524$		0			0
$525$	3.54576	+	4.22567i	0.154750	+	0.184423i
$526$		0			0
$527$	2.16044	−	3.74200i	0.0941104	−	0.163004i
$528$		0			0
$529$	−28.4937	−	49.3525i	−1.23885	−	2.14576i
$530$		0			0
$531$	29.3097	−	10.6679i	1.27193	−	0.462946i
$532$		0			0
$533$	5.74763	+	9.95518i	0.248957	+	0.431207i
$534$		0			0
$535$	4.80200	−	8.31731i	0.207609	−	0.359589i
$536$		0			0
$537$	5.05438	−	13.8868i	0.218112	−	0.599259i
$538$		0			0
$539$	−1.65270			−0.0711870
$540$		0			0
$541$	26.7297			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$541$	26.7297			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$542$		0			0
$543$	−10.2096	+	28.0507i	−0.438136	+	1.20377i
$544$		0			0
$545$	−0.271974	+	0.471073i	−0.0116501	+	0.0201786i
$546$		0			0
$547$	18.3812	+	31.8372i	0.785923	+	1.36126i	0.928446	+	0.371467i	$0.121145\pi$
$547$	18.3812	+	31.8372i	0.785923	+	1.36126i	−0.142523	+	0.989792i	$0.545521\pi$
$548$		0			0
$549$	−3.97906	+	22.5663i	−0.169822	+	0.963108i
$550$		0			0
$551$	−10.1133	−	17.5168i	−0.430843	−	0.746242i
$552$		0			0
$553$	1.20187	−	2.08169i	0.0511086	−	0.0885226i
$554$		0			0
$555$	13.8516	+	16.5077i	0.587969	+	0.700714i
$556$		0			0
$557$	32.3387			1.37024			0.685118	−	0.728432i	$-0.259751\pi$
$557$	32.3387			1.37024			0.685118	+	0.728432i	$0.259751\pi$
$558$		0			0
$559$	−14.8648			−0.628716
$560$		0			0
$561$	1.31908	−	0.232589i	0.0556915	−	0.00981992i
$562$		0			0
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	−0.990156	−	0.139965i	$-0.955301\pi$
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	0.616291	+	0.787518i	$0.288634\pi$
$564$		0			0
$565$	−9.68004	−	16.7663i	−0.407243	−	0.705365i
$566$		0			0
$567$	−6.89440	+	5.78509i	−0.289538	+	0.242951i
$568$		0			0
$569$	13.3007	+	23.0374i	0.557593	+	0.965779i	0.997697	+	0.0678320i	$0.0216082\pi$
$569$	13.3007	+	23.0374i	0.557593	+	0.965779i	−0.440104	+	0.897947i	$0.645058\pi$
$570$		0			0
$571$	−5.00862	+	8.67518i	−0.209604	+	0.363045i	−0.951590	−	0.307371i	$-0.900551\pi$
$571$	−5.00862	+	8.67518i	−0.209604	+	0.363045i	0.741986	+	0.670416i	$0.233884\pi$
$572$		0			0
$573$	22.0201	−	3.88273i	0.919902	−	0.162203i
$574$		0			0
$575$	28.4834			1.18784
$576$		0			0
$577$	−32.9145			−1.37025			−0.685124	−	0.728427i	$-0.740252\pi$
$577$	−32.9145			−1.37025			−0.685124	+	0.728427i	$0.740252\pi$
$578$		0			0
$579$	−0.710485	−	0.846723i	−0.0295267	−	0.0351886i
$580$		0			0
$581$	7.52481	−	13.0334i	0.312182	−	0.540715i
$582$		0			0
$583$	−0.474308	−	0.821525i	−0.0196438	−	0.0340241i
$584$		0			0
$585$	2.36500	−	13.4126i	0.0977807	−	0.554542i
$586$		0			0
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	0.667531	−	0.744582i	$-0.267351\pi$
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	−0.978592	+	0.205808i	$0.934018\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$		0			0
$591$	6.78034	−	18.6288i	0.278906	−	0.766288i
$592$		0			0
$593$	41.0009			1.68371			0.841853	−	0.539706i	$-0.181465\pi$
$593$	41.0009			1.68371			0.841853	+	0.539706i	$0.181465\pi$
$594$		0			0
$595$	−0.630415			−0.0258445
$596$		0			0
$597$	2.15523	−	5.92145i	0.0882077	−	0.242349i
$598$		0			0
$599$	3.03684	−	5.25996i	0.124082	−	0.214916i	−0.797292	−	0.603594i	$-0.793735\pi$
$599$	3.03684	−	5.25996i	0.124082	−	0.214916i	0.921374	+	0.388678i	$0.127068\pi$
$600$		0			0
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	0.973402	−	0.229102i	$-0.0735791\pi$
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	−0.685110	+	0.728440i	$0.740246\pi$
$602$		0			0
$603$	−1.68092	+	0.611806i	−0.0684524	+	0.0249147i
$604$		0			0
$605$	5.57011	+	9.64771i	0.226457	+	0.392235i
$606$		0			0
$607$	23.0449	−	39.9149i	0.935363	−	1.62010i	0.161377	−	0.986893i	$-0.448406\pi$
$607$	23.0449	−	39.9149i	0.935363	−	1.62010i	0.773986	−	0.633203i	$-0.218260\pi$
$608$		0			0
$609$	−6.97906	−	8.31731i	−0.282806	−	0.337035i
$610$		0			0
$611$	31.5226			1.27527
$612$		0			0
$613$	−26.4938			−1.07008			−0.535038	−	0.844828i	$-0.679703\pi$
$613$	−26.4938			−1.07008			−0.535038	+	0.844828i	$0.679703\pi$
$614$		0			0
$615$	−7.84002	+	1.38241i	−0.316140	+	0.0557440i
$616$		0			0
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	−0.842492	−	0.538708i	$-0.818913\pi$
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	0.887781	+	0.460266i	$0.152246\pi$
$618$		0			0
$619$	3.09539	+	5.36137i	0.124414	+	0.215492i	0.921504	−	0.388369i	$-0.126962\pi$
$619$	3.09539	+	5.36137i	0.124414	+	0.215492i	−0.797090	+	0.603861i	$0.793628\pi$
$620$		0			0
$621$			46.4721i			1.86486i
$622$		0			0
$623$	4.54323	+	7.86911i	0.182021	+	0.315269i
$624$		0			0
$625$	−0.533433	+	0.923933i	−0.0213373	+	0.0369573i
$626$		0			0
$627$	9.09627	−	1.60392i	0.363270	−	0.0640543i
$628$		0			0
$629$	4.32089			0.172285
$630$		0			0
$631$	−26.1661			−1.04166			−0.520829	−	0.853661i	$-0.674377\pi$
$631$	−26.1661			−1.04166			−0.520829	+	0.853661i	$0.674377\pi$
$632$		0			0
$633$	−6.48293	−	7.72605i	−0.257673	−	0.307083i
$634$		0			0
$635$	−13.9927	+	24.2361i	−0.555284	+	0.961781i
$636$		0			0
$637$	1.68479	+	2.91815i	0.0667539	+	0.115621i
$638$		0			0
$639$	−1.27403	−	1.06904i	−0.0504000	−	0.0422906i
$640$		0			0
$641$	−2.44444	−	4.23389i	−0.0965496	−	0.167229i	0.813705	−	0.581278i	$-0.197447\pi$
$641$	−2.44444	−	4.23389i	−0.0965496	−	0.167229i	−0.910254	+	0.414050i	$0.864114\pi$
$642$		0			0
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	0.126242	+	0.992000i	$0.459709\pi$
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	−0.922218	+	0.386671i	$0.873625\pi$
$644$		0			0
$645$	3.52094	−	9.67372i	0.138637	−	0.380902i
$646$		0			0
$647$	2.28075			0.0896657			0.0448329	−	0.998995i	$-0.485724\pi$
$647$	2.28075			0.0896657			0.0448329	+	0.998995i	$0.485724\pi$
$648$		0			0
$649$	−17.1830			−0.674493
$650$		0			0
$651$	5.47044	−	15.0299i	0.214403	−	0.589068i
$652$		0			0
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	−0.998930	−	0.0462542i	$-0.985272\pi$
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	0.539522	+	0.841971i	$0.318605\pi$
$654$		0			0
$655$	−4.82682	−	8.36030i	−0.188599	−	0.326664i
$656$		0			0
$657$	−4.71032	−	3.95243i	−0.183767	−	0.154199i
$658$		0			0
$659$	−23.9812	−	41.5366i	−0.934174	−	1.61804i	−0.776101	−	0.630609i	$-0.782805\pi$
$659$	−23.9812	−	41.5366i	−0.934174	−	1.61804i	−0.158073	−	0.987427i	$-0.550528\pi$
$660$		0			0
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	0.426571	+	0.904454i	$0.359721\pi$
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	−0.996566	+	0.0828055i	$0.973612\pi$
$662$		0			0
$663$	−1.75537	−	2.09196i	−0.0681728	−	0.0812452i
$664$		0			0
$665$	−4.34730			−0.168581
$666$		0			0
$667$	−56.0634			−2.17078
$668$		0			0
$669$	12.0831	−	2.13057i	0.467158	−	0.0823726i
$670$		0			0
$671$	6.31180	−	10.9324i	0.243664	−	0.422039i
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$		0			0
$675$	−14.3316	−	8.27433i	−0.551622	−	0.318479i
$676$		0			0
$677$	−17.9454	−	31.0823i	−0.689697	−	1.19459i	−0.971936	−	0.235246i	$-0.924411\pi$
$677$	−17.9454	−	31.0823i	−0.689697	−	1.19459i	0.282239	−	0.959344i	$-0.408923\pi$
$678$		0			0
$679$	−0.949493	+	1.64457i	−0.0364382	+	0.0631128i
$680$		0			0
$681$	−20.3726	+	3.59224i	−0.780679	+	0.137655i
$682$		0			0
$683$	−35.0642			−1.34169			−0.670847	−	0.741596i	$-0.734069\pi$
$683$	−35.0642			−1.34169			−0.670847	+	0.741596i	$0.734069\pi$
$684$		0			0
$685$	3.46110			0.132242
$686$		0			0
$687$	−19.5421	−	23.2893i	−0.745576	−	0.888543i
$688$		0			0
$689$	−0.967034	+	1.67495i	−0.0368411	+	0.0638106i
$690$		0			0
$691$	1.03343	+	1.78996i	0.0393136	+	0.0680932i	0.885013	−	0.465567i	$-0.154150\pi$
$691$	1.03343	+	1.78996i	0.0393136	+	0.0680932i	−0.845699	+	0.533660i	$0.820816\pi$
$692$		0			0
$693$	4.65910	−	1.69577i	0.176985	−	0.0644171i
$694$		0			0
$695$	−4.13176	−	7.15642i	−0.156727	−	0.271458i
$696$		0			0
$697$	−0.798133	+	1.38241i	−0.0302315	+	0.0523624i
$698$		0			0
$699$	9.62882	−	26.4550i	0.364196	−	1.00062i
$700$		0			0
$701$	−7.36009			−0.277987			−0.138993	−	0.990293i	$-0.544387\pi$
$701$	−7.36009			−0.277987			−0.138993	+	0.990293i	$0.544387\pi$
$702$		0			0
$703$	29.7965			1.12380
$704$		0			0
$705$	−7.46657	+	20.5142i	−0.281207	+	0.772610i
$706$		0			0
$707$	−0.854570	+	1.48016i	−0.0321394	+	0.0556671i
$708$		0			0
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	0.767742	−	0.640760i	$-0.221380\pi$
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	−0.938785	+	0.344504i	$0.888047\pi$
$710$		0			0
$711$	−1.25221	+	7.10165i	−0.0469616	+	0.266333i
$712$		0			0
$713$	−41.2943	−	71.5239i	−1.54648	−	2.67859i
$714$		0			0
$715$	−3.75150	+	6.49778i	−0.140298	+	0.243003i
$716$		0			0
$717$	16.8106	+	20.0341i	0.627804	+	0.748188i
$718$		0			0
$719$	25.9537			0.967908			0.483954	−	0.875093i	$-0.339200\pi$
$719$	25.9537			0.967908			0.483954	+	0.875093i	$0.339200\pi$
$720$		0			0
$721$	−3.63816			−0.135492
$722$		0			0
$723$	26.6746	−	4.70345i	0.992038	−	0.174923i
$724$		0			0
$725$	9.98205	−	17.2894i	0.370724	−	0.642113i
$726$		0			0
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	0.756311	−	0.654213i	$-0.227000\pi$
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	−0.944720	+	0.327878i	$0.893667\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$		0			0
$731$	−1.03209	−	1.78763i	−0.0381732	−	0.0661179i
$732$		0			0
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	0.196441	+	0.980516i	$0.437062\pi$
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	−0.947372	+	0.320135i	$0.896272\pi$
$734$		0			0
$735$	−2.29813	+	0.405223i	−0.0847679	+	0.0149469i
$736$		0			0
$737$	0.985452			0.0362996
$738$		0			0
$739$	25.3618			0.932951			0.466475	−	0.884534i	$-0.345524\pi$
$739$	25.3618			0.932951			0.466475	+	0.884534i	$0.345524\pi$
$740$		0			0
$741$	−12.1049	−	14.4260i	−0.444684	−	0.529954i
$742$		0			0
$743$	−11.2221	+	19.4372i	−0.411699	+	0.713083i	−0.995076	−	0.0991184i	$-0.968398\pi$
$743$	−11.2221	+	19.4372i	−0.411699	+	0.713083i	0.583377	+	0.812202i	$0.301731\pi$
$744$		0			0
$745$	−0.290393	−	0.502975i	−0.0106392	−	0.0184276i
$746$		0			0
$747$	−7.84002	+	44.4630i	−0.286851	+	1.62682i
$748$		0			0
$749$	−3.56418	−	6.17334i	−0.130232	−	0.225569i
$750$		0			0
$751$	12.1086	−	20.9727i	0.441849	−	0.765305i	−0.555978	−	0.831197i	$-0.687656\pi$
$751$	12.1086	−	20.9727i	0.441849	−	0.765305i	0.997827	+	0.0658924i	$0.0209894\pi$
$752$		0			0
$753$	−11.2941	+	31.0303i	−0.411580	+	1.13081i
$754$		0			0
$755$	3.32863			0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$		0			0
$759$	8.75624	−	24.0576i	0.317832	−	0.873235i
$760$		0			0
$761$	9.13610	−	15.8242i	0.331183	−	0.573626i	−0.651561	−	0.758596i	$-0.725886\pi$
$761$	9.13610	−	15.8242i	0.331183	−	0.573626i	0.982744	+	0.184970i	$0.0592188\pi$
$762$		0			0
$763$	0.201867	+	0.349643i	0.00730806	+	0.0126579i
$764$		0			0
$765$	1.77719	−	0.646844i	0.0642544	−	0.0233867i
$766$		0			0
$767$	17.5167	+	30.3398i	0.632490	+	1.09550i
$768$		0			0
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	−0.983310	−	0.181936i	$-0.941764\pi$
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	0.649217	+	0.760604i	$0.275097\pi$
$770$		0			0
$771$	29.5945	+	35.2694i	1.06582	+	1.27020i
$772$		0			0
$773$	−2.96080			−0.106493			−0.0532463	−	0.998581i	$-0.516957\pi$
$773$	−2.96080			−0.106493			−0.0532463	+	0.998581i	$0.516957\pi$
$774$		0			0
$775$	29.4097			1.05643
$776$		0			0
$777$	15.7515	−	2.77741i	0.565082	−	0.0996392i
$778$		0			0
$779$	−5.50387	+	9.53298i	−0.197197	+	0.341555i
$780$		0			0
$781$	0.458111	+	0.793471i	0.0163925	+	0.0283926i
$782$		0			0
$783$	28.2086	+	16.2862i	1.00809	+	0.582022i
$784$		0			0
$785$	−6.82635	−	11.8236i	−0.243643	−	0.422002i
$786$		0			0
$787$	−16.7010	+	28.9270i	−0.595326	+	1.03113i	0.398175	+	0.917310i	$0.369644\pi$
$787$	−16.7010	+	28.9270i	−0.595326	+	1.03113i	−0.993501	+	0.113825i	$0.963690\pi$
$788$		0			0
$789$	−1.25221	+	0.220799i	−0.0445799	+	0.00786064i
$790$		0			0
$791$	−14.3696			−0.510924
$792$		0			0
$793$	−25.7374			−0.913962
$794$		0			0
$795$	−0.860967	−	1.02606i	−0.0305354	−	0.0363906i
$796$		0			0
$797$	−24.6755	+	42.7391i	−0.874050	+	1.51390i	−0.0162779	+	0.999868i	$0.505182\pi$
$797$	−24.6755	+	42.7391i	−0.874050	+	1.51390i	−0.857772	+	0.514031i	$0.828152\pi$
$798$		0			0
$799$	2.18866	+	3.79088i	0.0774293	+	0.134112i
$800$		0			0
$801$	−20.8819	−	17.5220i	−0.737826	−	0.619110i
$802$		0			0
$803$	1.69372	+	2.93360i	0.0597699	+	0.103525i
$804$		0			0
$805$	−6.02481	+	10.4353i	−0.212347	+	0.367795i
$806$		0			0
$807$	−12.3516	+	33.9358i	−0.434798	+	1.19460i
$808$		0			0
$809$	19.8280			0.697115			0.348558	−	0.937287i	$-0.386672\pi$
$809$	19.8280			0.697115			0.348558	+	0.937287i	$0.386672\pi$
$810$		0			0
$811$	23.8557			0.837686			0.418843	−	0.908059i	$-0.362436\pi$
$811$	23.8557			0.837686			0.418843	+	0.908059i	$0.362436\pi$
$812$		0			0
$813$	−4.12196	+	11.3250i	−0.144563	+	0.397185i
$814$		0			0
$815$	−1.74897	+	3.02931i	−0.0612638	+	0.106112i
$816$		0			0
$817$	−7.11721	−	12.3274i	−0.249000	−	0.431280i
$818$		0			0
$819$	−7.74376	−	6.49778i	−0.270589	−	0.227051i
$820$		0			0
$821$	25.4714	+	44.1177i	0.888957	+	1.53972i	0.841110	+	0.540864i	$0.181903\pi$
$821$	25.4714	+	44.1177i	0.888957	+	1.53972i	0.0478469	+	0.998855i	$0.484764\pi$
$822$		0			0
$823$	6.80747	−	11.7909i	0.237293	−	0.411004i	−0.722643	−	0.691221i	$-0.757073\pi$
$823$	6.80747	−	11.7909i	0.237293	−	0.411004i	0.959937	+	0.280217i	$0.0904064\pi$
$824$		0			0
$825$	5.86009	+	6.98378i	0.204022	+	0.243144i
$826$		0			0
$827$	−36.2158			−1.25935			−0.629673	−	0.776861i	$-0.716811\pi$
$827$	−36.2158			−1.25935			−0.629673	+	0.776861i	$0.716811\pi$
$828$		0			0
$829$	25.3259			0.879606			0.439803	−	0.898094i	$-0.355048\pi$
$829$	25.3259			0.879606			0.439803	+	0.898094i	$0.355048\pi$
$830$		0			0
$831$	−30.4859	+	5.37549i	−1.05754	+	0.186474i
$832$		0			0
$833$	−0.233956	+	0.405223i	−0.00810608	+	0.0140401i
$834$		0			0
$835$	−15.6172	−	27.0498i	−0.540456	−	0.936097i
$836$		0			0
$837$			47.9835i			1.65855i
$838$		0			0
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	0.931383	−	0.364040i	$-0.118603\pi$
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	−0.780960	+	0.624582i	$0.785270\pi$
$840$		0			0
$841$	−5.14749	+	8.91571i	−0.177500	+	0.307438i
$842$		0			0
$843$	−38.0558	+	6.71026i	−1.31071	+	0.231114i
$844$		0			0
$845$	−2.21751			−0.0762847
$846$		0			0
$847$	8.26857			0.284111
$848$		0			0
$849$	20.7020	+	24.6717i	0.710492	+	0.846731i
$850$		0			0
$851$	41.2943	−	71.5239i	1.41555	−	2.45181i
$852$		0			0
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	0.950170	−	0.311733i	$-0.100909\pi$
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	−0.745053	+	0.667005i	$0.767576\pi$
$854$		0			0
$855$	12.2554	−	4.46059i	0.419125	−	0.152549i
$856$		0			0
$857$	−3.25015	−	5.62943i	−0.111023	−	0.192298i	0.805160	−	0.593058i	$-0.202079\pi$
$857$	−3.25015	−	5.62943i	−0.111023	−	0.192298i	−0.916183	+	0.400760i	$0.868746\pi$
$858$		0			0
$859$	−26.7763	+	46.3779i	−0.913596	+	1.58239i	−0.104652	+	0.994509i	$0.533373\pi$
$859$	−26.7763	+	46.3779i	−0.913596	+	1.58239i	−0.808944	+	0.587886i	$0.799960\pi$
$860$		0			0
$861$	−2.02094	+	5.55250i	−0.0688736	+	0.189229i
$862$		0			0
$863$	−3.69965			−0.125937			−0.0629687	−	0.998016i	$-0.520057\pi$
$863$	−3.69965			−0.125937			−0.0629687	+	0.998016i	$0.520057\pi$
$864$		0			0
$865$	−6.40230			−0.217685
$866$		0			0
$867$	−9.94104	+	27.3128i	−0.337615	+	0.927590i
$868$		0			0
$869$	1.98633	−	3.44042i	0.0673816	−	0.116708i
$870$		0			0
$871$	−1.00459	−	1.73999i	−0.0340391	−	0.0589574i
$872$		0			0
$873$	0.989266	−	5.61041i	0.0334816	−	0.189884i
$874$		0			0
$875$	−5.51367	−	9.54996i	−0.186396	−	0.322847i
$876$		0			0
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	−0.749178	−	0.662369i	$-0.769551\pi$
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	0.948217	+	0.317622i	$0.102884\pi$
$878$		0			0
$879$	14.5753	+	17.3702i	0.491613	+	0.585882i
$880$		0			0
$881$	49.4858			1.66722			0.833609	−	0.552355i	$-0.186271\pi$
$881$	49.4858			1.66722			0.833609	+	0.552355i	$0.186271\pi$
$882$		0			0
$883$	21.5357			0.724734			0.362367	−	0.932035i	$-0.381969\pi$
$883$	21.5357			0.724734			0.362367	+	0.932035i	$0.381969\pi$
$884$		0			0
$885$	−23.8935	+	4.21307i	−0.803172	+	0.141621i
$886$		0			0
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	−0.748849	−	0.662741i	$-0.769393\pi$
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	0.948375	+	0.317152i	$0.102727\pi$
$888$		0			0
$889$	10.3858	+	17.9887i	0.348328	+	0.603322i
$890$		0			0
$891$	−11.3944	+	9.56104i	−0.381727	+	0.320307i
$892$		0			0
$893$	15.0929	+	26.1416i	0.505063	+	0.874795i
$894$		0			0
$895$	−5.74763	+	9.95518i	−0.192122	+	0.332765i
$896$		0			0
$897$	−51.4043	+	9.06396i	−1.71634	+	0.302637i
$898$		0			0
$899$	−57.8866			−1.93063
$900$		0			0
$901$	−0.268571			−0.00894739
$902$		0			0
$903$	−4.91147	−	5.85327i	−0.163444	−	0.194785i
$904$		0			0
$905$	11.6099	−	20.1090i	0.385927	−	0.668446i
$906$		0			0
$907$	−13.0107	−	22.5353i	−0.432014	−	0.748271i	0.565032	−	0.825069i	$-0.308864\pi$
$907$	−13.0107	−	22.5353i	−0.432014	−	0.748271i	−0.997047	+	0.0767980i	$0.975530\pi$
$908$		0			0
$909$	0.890367	−	5.04952i	0.0295316	−	0.167482i
$910$		0			0
$911$	−2.01636	−	3.49244i	−0.0668050	−	0.115710i	0.830688	−	0.556738i	$-0.187947\pi$
$911$	−2.01636	−	3.49244i	−0.0668050	−	0.115710i	−0.897493	+	0.441028i	$0.854614\pi$
$912$		0			0
$913$	12.4363	−	21.5403i	0.411581	−	0.712879i
$914$		0			0
$915$	6.09627	−	16.7494i	0.201536	−	0.553717i
$916$		0			0
$917$	−7.16519			−0.236615
$918$		0			0
$919$	−27.4270			−0.904732			−0.452366	−	0.891832i	$-0.649420\pi$
$919$	−27.4270			−0.904732			−0.452366	+	0.891832i	$0.649420\pi$
$920$		0			0
$921$	−3.73829	+	10.2709i	−0.123181	+	0.338437i
$922$		0			0
$923$	0.934011	−	1.61775i	0.0307434	−	0.0532491i
$924$		0			0
$925$	14.7049	+	25.4696i	0.483493	+	0.837434i
$926$		0			0
$927$	10.2562	−	3.73297i	0.336859	−	0.122607i
$928$		0			0
$929$	−3.83837	−	6.64826i	−0.125933	−	0.218122i	0.796164	−	0.605081i	$-0.206859\pi$
$929$	−3.83837	−	6.64826i	−0.125933	−	0.218122i	−0.922097	+	0.386958i	$0.873526\pi$
$930$		0			0
$931$	−1.61334	+	2.79439i	−0.0528751	+	0.0915824i
$932$		0			0
$933$	10.6038	+	12.6372i	0.347154	+	0.413722i
$934$		0			0
$935$	−1.04189			−0.0340734
$936$		0			0
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$		0			0
$939$	30.0699	−	5.30213i	0.981293	−	0.173028i
$940$		0			0
$941$	3.06964	−	5.31677i	0.100067	−	0.173322i	−0.811645	−	0.584151i	$-0.801427\pi$
$941$	3.06964	−	5.31677i	0.100067	−	0.173322i	0.911712	+	0.410829i	$0.134761\pi$
$942$		0			0
$943$	15.2554	+	26.4231i	0.496783	+	0.860454i
$944$		0			0
$945$	6.06283	−	3.50038i	0.197224	−	0.113867i
$946$		0			0
$947$	2.78224	+	4.81898i	0.0904107	+	0.156596i	0.907684	−	0.419654i	$-0.137849\pi$
$947$	2.78224	+	4.81898i	0.0904107	+	0.156596i	−0.817273	+	0.576250i	$0.804515\pi$
$948$		0			0
$949$	3.45320	−	5.98112i	0.112096	−	0.194155i
$950$		0			0
$951$	−13.7772	+	2.42929i	−0.446756	+	0.0787751i
$952$		0			0
$953$	−8.72018			−0.282474			−0.141237	−	0.989976i	$-0.545108\pi$
$953$	−8.72018			−0.282474			−0.141237	+	0.989976i	$0.545108\pi$
$954$		0			0
$955$	−17.3928			−0.562818
$956$		0			0
$957$	−11.5343	−	13.7461i	−0.372851	−	0.444347i
$958$		0			0
$959$	1.28446	−	2.22475i	0.0414775	−	0.0718411i
$960$		0			0
$961$	−27.1373	−	47.0031i	−0.875396	−	1.51623i
$962$		0			0
$963$	16.3819	+	13.7461i	0.527900	+	0.442960i
$964$		0			0
$965$	0.429892	+	0.744596i	0.0138387	+	0.0239694i
$966$		0			0
$967$	−28.8849	+	50.0301i	−0.928876	+	1.60886i	−0.143670	+	0.989626i	$0.545890\pi$
$967$	−28.8849	+	50.0301i	−0.928876	+	1.60886i	−0.785206	+	0.619235i	$0.787443\pi$
$968$		0			0
$969$	0.894400	−	2.45734i	0.0287323	−	0.0789413i
$970$		0			0
$971$	30.7192			0.985828			0.492914	−	0.870078i	$-0.335932\pi$
$971$	30.7192			0.985828			0.492914	+	0.870078i	$0.335932\pi$
$972$		0			0
$973$	−6.13341			−0.196628
$974$		0			0
$975$	6.35726	−	17.4664i	0.203595	−	0.559373i
$976$		0			0
$977$	−5.15002	+	8.92009i	−0.164764	+	0.285379i	−0.936571	−	0.350477i	$-0.886019\pi$
$977$	−5.15002	+	8.92009i	−0.164764	+	0.285379i	0.771808	+	0.635856i	$0.219353\pi$
$978$		0			0
$979$	7.50862	+	13.0053i	0.239976	+	0.415651i
$980$		0			0
$981$	−0.927833	−	0.778544i	−0.0296234	−	0.0248570i
$982$		0			0
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	0.954326	−	0.298767i	$-0.0965755\pi$
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	−0.735903	+	0.677087i	$0.763242\pi$
$984$		0			0
$985$	−7.71032	+	13.3547i	−0.245671	+	0.425515i
$986$		0			0
$987$	10.4153	+	12.4125i	0.331524	+	0.395095i
$988$		0			0
$989$	−39.4543			−1.25457
$990$		0			0
$991$	−57.9813			−1.84184			−0.920919	−	0.389754i	$-0.872560\pi$
$991$	−57.9813			−1.84184			−0.920919	+	0.389754i	$0.872560\pi$
$992$		0			0
$993$	39.3166	−	6.93258i	1.24767	−	0.219999i
$994$		0			0
$995$	−2.45084	+	4.24497i	−0.0776968	+	0.134575i
$996$		0			0
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	0.708578	−	0.705633i	$-0.249337\pi$
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	−0.965385	+	0.260830i	$0.916004\pi$
$998$		0			0
$999$	−41.5549	+	23.9917i	−1.31474	+	0.759065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.h.337.2		6
3.2	odd	2		3024.2.r.k.1009.2		6
4.3	odd	2		63.2.f.a.22.3	✓	6
9.2	odd	6		3024.2.r.k.2017.2		6
9.4	even	3		9072.2.a.ca.1.2		3
9.5	odd	6		9072.2.a.bs.1.2		3
9.7	even	3	inner	1008.2.r.h.673.2		6
12.11	even	2		189.2.f.b.64.1		6
28.3	even	6		441.2.h.e.373.1		6
28.11	odd	6		441.2.h.d.373.1		6
28.19	even	6		441.2.g.b.67.3		6
28.23	odd	6		441.2.g.c.67.3		6
28.27	even	2		441.2.f.c.148.3		6
36.7	odd	6		63.2.f.a.43.3	yes	6
36.11	even	6		189.2.f.b.127.1		6
36.23	even	6		567.2.a.c.1.3		3
36.31	odd	6		567.2.a.h.1.1		3
84.11	even	6		1323.2.h.c.226.3		6
84.23	even	6		1323.2.g.d.361.1		6
84.47	odd	6		1323.2.g.e.361.1		6
84.59	odd	6		1323.2.h.b.226.3		6
84.83	odd	2		1323.2.f.d.442.1		6
252.11	even	6		1323.2.g.d.667.1		6
252.47	odd	6		1323.2.h.b.802.3		6
252.79	odd	6		441.2.h.d.214.1		6
252.83	odd	6		1323.2.f.d.883.1		6
252.115	even	6		441.2.g.b.79.3		6
252.139	even	6		3969.2.a.q.1.1		3
252.151	odd	6		441.2.g.c.79.3		6
252.167	odd	6		3969.2.a.l.1.3		3
252.187	even	6		441.2.h.e.214.1		6
252.191	even	6		1323.2.h.c.802.3		6
252.223	even	6		441.2.f.c.295.3		6
252.227	odd	6		1323.2.g.e.667.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	4.3	odd	2
63.2.f.a.43.3	yes	6	36.7	odd	6
189.2.f.b.64.1		6	12.11	even	2
189.2.f.b.127.1		6	36.11	even	6
441.2.f.c.148.3		6	28.27	even	2
441.2.f.c.295.3		6	252.223	even	6
441.2.g.b.67.3		6	28.19	even	6
441.2.g.b.79.3		6	252.115	even	6
441.2.g.c.67.3		6	28.23	odd	6
441.2.g.c.79.3		6	252.151	odd	6
441.2.h.d.214.1		6	252.79	odd	6
441.2.h.d.373.1		6	28.11	odd	6
441.2.h.e.214.1		6	252.187	even	6
441.2.h.e.373.1		6	28.3	even	6
567.2.a.c.1.3		3	36.23	even	6
567.2.a.h.1.1		3	36.31	odd	6
1008.2.r.h.337.2		6	1.1	even	1	trivial
1008.2.r.h.673.2		6	9.7	even	3	inner
1323.2.f.d.442.1		6	84.83	odd	2
1323.2.f.d.883.1		6	252.83	odd	6
1323.2.g.d.361.1		6	84.23	even	6
1323.2.g.d.667.1		6	252.11	even	6
1323.2.g.e.361.1		6	84.47	odd	6
1323.2.g.e.667.1		6	252.227	odd	6
1323.2.h.b.226.3		6	84.59	odd	6
1323.2.h.b.802.3		6	252.47	odd	6
1323.2.h.c.226.3		6	84.11	even	6
1323.2.h.c.802.3		6	252.191	even	6
3024.2.r.k.1009.2		6	3.2	odd	2
3024.2.r.k.2017.2		6	9.2	odd	6
3969.2.a.l.1.3		3	252.167	odd	6
3969.2.a.q.1.1		3	252.139	even	6
9072.2.a.bs.1.2		3	9.5	odd	6
9072.2.a.ca.1.2		3	9.4	even	3

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.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.592396 - 1.62760i) q^{3} +(-0.673648 + 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\)	\(q+(0.592396 - 1.62760i) q^{3} +(-0.673648 + 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-2.29813 - 1.92836i) q^{9} +(0.826352 + 1.43128i) q^{11} +(1.68479 - 2.91815i) q^{13} +(1.50000 + 1.78763i) q^{15} +0.467911 q^{17} +3.22668 q^{19} +(1.70574 - 0.300767i) q^{21} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(4.61721 - 7.99724i) q^{31} +(2.81908 - 0.497079i) q^{33} -1.34730 q^{35} +9.23442 q^{37} +(-3.75150 - 4.47086i) q^{39} +(-1.70574 + 2.95442i) q^{41} +(-2.20574 - 3.82045i) q^{43} +(3.79813 - 1.38241i) q^{45} +(4.67752 + 8.10170i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.277189 - 0.761570i) q^{51} -0.573978 q^{53} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +(0.520945 - 2.95442i) q^{63} +(2.26991 + 3.93161i) q^{65} +(0.298133 - 0.516382i) q^{67} +(-9.95723 - 11.8666i) q^{69} +0.554378 q^{71} +2.04963 q^{73} +(5.43242 - 0.957882i) q^{75} +(-0.826352 + 1.43128i) q^{77} +(-1.20187 - 2.08169i) q^{79} +(1.56283 + 8.86327i) q^{81} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(-10.6925 + 1.88538i) q^{87} +9.08647 q^{89} +3.36959 q^{91} +(-10.2811 - 12.2525i) q^{93} +(-2.17365 + 3.76487i) q^{95} +(0.949493 + 1.64457i) q^{97} +(0.860967 - 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 + 3 * q^7	\( 6 q - 3 q^{5} + 3 q^{7} + 6 q^{11} + 3 q^{13} + 9 q^{15} + 12 q^{17} + 6 q^{19} + 12 q^{23} + 6 q^{25} - 27 q^{27} - 9 q^{29} - 3 q^{31} - 6 q^{35} - 6 q^{37} + 18 q^{39} - 3 q^{43} + 9 q^{45} + 3 q^{47} - 3 q^{49} - 9 q^{51} + 12 q^{53} - 9 q^{57} - 3 q^{59} - 6 q^{61} - 15 q^{65} - 12 q^{67} - 9 q^{69} - 18 q^{71} - 42 q^{73} + 9 q^{75} - 6 q^{77} - 21 q^{79} - 18 q^{83} - 9 q^{85} - 9 q^{87} + 24 q^{89} + 6 q^{91} - 27 q^{93} - 12 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 + 3 * q^7 + 6 * q^11 + 3 * q^13 + 9 * q^15 + 12 * q^17 + 6 * q^19 + 12 * q^23 + 6 * q^25 - 27 * q^27 - 9 * q^29 - 3 * q^31 - 6 * q^35 - 6 * q^37 + 18 * q^39 - 3 * q^43 + 9 * q^45 + 3 * q^47 - 3 * q^49 - 9 * q^51 + 12 * q^53 - 9 * q^57 - 3 * q^59 - 6 * q^61 - 15 * q^65 - 12 * q^67 - 9 * q^69 - 18 * q^71 - 42 * q^73 + 9 * q^75 - 6 * q^77 - 21 * q^79 - 18 * q^83 - 9 * q^85 - 9 * q^87 + 24 * q^89 + 6 * q^91 - 27 * q^93 - 12 * q^95 + 3 * q^97 - 18 * q^99

Introduction

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