LMFDB - Embedded newform 432.2.u.c.337.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(49,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.1
Root			$0.500000 + 1.00210i$ of defining polynomial
Character	$\chi$	$=$	432.337
Dual form			432.2.u.c.241.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.210069 - 1.71926i) q^{3} +(0.0713060 + 0.0598329i) q^{5} +(-0.544891 - 0.198324i) q^{7} +(-2.91174 - 0.722330i) q^{9} +(2.36944 - 1.98820i) q^{11} +(0.729623 - 4.13790i) q^{13} +(0.117848 - 0.110025i) q^{15} +(0.995493 - 1.72424i) q^{17} +(-1.92271 - 3.33023i) q^{19} +(-0.455437 + 0.895151i) q^{21} +(-4.18428 + 1.52295i) q^{23} +(-0.866736 - 4.91551i) q^{25} +(-1.85354 + 4.85432i) q^{27} +(1.11126 + 6.30229i) q^{29} +(1.55754 - 0.566898i) q^{31} +(-2.92049 - 4.49135i) q^{33} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(-6.96087 - 2.12366i) q^{39} +(-0.190345 + 1.07950i) q^{41} +(5.28657 - 4.43596i) q^{43} +(-0.164406 - 0.225724i) q^{45} +(3.37650 + 1.22894i) q^{47} +(-5.10474 - 4.28338i) q^{49} +(-2.75531 - 2.07373i) q^{51} +5.40034 q^{53} +0.287915 q^{55} +(-6.12946 + 2.60607i) q^{57} +(7.87850 + 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(1.44333 + 0.971060i) q^{63} +(0.299609 - 0.251402i) q^{65} +(1.53458 - 8.70304i) q^{67} +(1.73937 + 7.51381i) q^{69} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(-8.63313 + 0.457552i) q^{75} +(-1.68539 + 0.613433i) q^{77} +(1.25166 + 7.09849i) q^{79} +(7.95648 + 4.20647i) q^{81} +(2.58744 + 14.6741i) q^{83} +(0.174151 - 0.0633858i) q^{85} +(11.0687 - 0.586638i) q^{87} +(0.776563 + 1.34505i) q^{89} +(-1.21821 + 2.11000i) q^{91} +(-0.647457 - 2.79691i) q^{93} +(0.0621565 - 0.352507i) q^{95} +(4.05661 - 3.40390i) q^{97} +(-8.33533 + 4.07760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41}+ \cdots + 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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
$3$	0.210069	−	1.71926i	0.121284	−	0.992618i
$3$	0.210069	−	1.71926i	0.121284	−	0.992618i
$4$		0			0
$5$	0.0713060	+	0.0598329i	0.0318890	+	0.0267581i	0.658593	−	0.752499i	$-0.271152\pi$
$5$	0.0713060	+	0.0598329i	0.0318890	+	0.0267581i	−0.626704	+	0.779258i	$0.715596\pi$
$6$		0			0
$7$	−0.544891	−	0.198324i	−0.205950	−	0.0749595i	0.236986	−	0.971513i	$-0.423841\pi$
$7$	−0.544891	−	0.198324i	−0.205950	−	0.0749595i	−0.442935	+	0.896554i	$0.646063\pi$
$8$		0			0
$9$	−2.91174	−	0.722330i	−0.970581	−	0.240777i
$10$		0			0
$11$	2.36944	−	1.98820i	0.714413	−	0.599464i	−0.211421	−	0.977395i	$-0.567809\pi$
$11$	2.36944	−	1.98820i	0.714413	−	0.599464i	0.925834	+	0.377932i	$0.123365\pi$
$12$		0			0
$13$	0.729623	−	4.13790i	0.202361	−	1.14765i	−0.699178	−	0.714948i	$-0.746450\pi$
$13$	0.729623	−	4.13790i	0.202361	−	1.14765i	0.901539	−	0.432699i	$-0.142439\pi$
$14$		0			0
$15$	0.117848	−	0.110025i	0.0304282	−	0.0284083i
$16$		0			0
$17$	0.995493	−	1.72424i	0.241443	−	0.418191i	−0.719683	−	0.694303i	$-0.755713\pi$
$17$	0.995493	−	1.72424i	0.241443	−	0.418191i	0.961125	+	0.276112i	$0.0890461\pi$
$18$		0			0
$19$	−1.92271	−	3.33023i	−0.441100	−	0.764008i	0.556671	−	0.830733i	$-0.312078\pi$
$19$	−1.92271	−	3.33023i	−0.441100	−	0.764008i	−0.997771	+	0.0667249i	$0.978745\pi$
$20$		0			0
$21$	−0.455437	+	0.895151i	−0.0993845	+	0.195338i
$22$		0			0
$23$	−4.18428	+	1.52295i	−0.872482	+	0.317558i	−0.739172	−	0.673517i	$-0.764783\pi$
$23$	−4.18428	+	1.52295i	−0.872482	+	0.317558i	−0.133310	+	0.991074i	$0.542561\pi$
$24$		0			0
$25$	−0.866736	−	4.91551i	−0.173347	−	0.983101i
$26$		0			0
$27$	−1.85354	+	4.85432i	−0.356715	+	0.934213i
$28$		0			0
$29$	1.11126	+	6.30229i	0.206356	+	1.17031i	0.895291	+	0.445482i	$0.146968\pi$
$29$	1.11126	+	6.30229i	0.206356	+	1.17031i	−0.688935	+	0.724823i	$0.741921\pi$
$30$		0			0
$31$	1.55754	−	0.566898i	0.279743	−	0.101818i	−0.198339	−	0.980134i	$-0.563555\pi$
$31$	1.55754	−	0.566898i	0.279743	−	0.101818i	0.478081	+	0.878316i	$0.341332\pi$
$32$		0			0
$33$	−2.92049	−	4.49135i	−0.508392	−	0.781844i
$34$		0			0
$35$	−0.0269877	−	0.0467441i	−0.00456176	−	0.00790120i
$36$		0			0
$37$	−2.01505	+	3.49016i	−0.331272	+	0.573779i	−0.982761	−	0.184878i	$-0.940811\pi$
$37$	−2.01505	+	3.49016i	−0.331272	+	0.573779i	0.651490	+	0.758657i	$0.274144\pi$
$38$		0			0
$39$	−6.96087	−	2.12366i	−1.11463	−	0.340058i
$40$		0			0
$41$	−0.190345	+	1.07950i	−0.0297270	+	0.168590i	−0.996057	−	0.0887159i	$-0.971724\pi$
$41$	−0.190345	+	1.07950i	−0.0297270	+	0.168590i	0.966330	+	0.257306i	$0.0828348\pi$
$42$		0			0
$43$	5.28657	−	4.43596i	0.806194	−	0.676477i	−0.143502	−	0.989650i	$-0.545836\pi$
$43$	5.28657	−	4.43596i	0.806194	−	0.676477i	0.949696	+	0.313173i	$0.101392\pi$
$44$		0			0
$45$	−0.164406	−	0.225724i	−0.0245082	−	0.0336490i
$46$		0			0
$47$	3.37650	+	1.22894i	0.492513	+	0.179260i	0.576323	−	0.817222i	$-0.304487\pi$
$47$	3.37650	+	1.22894i	0.492513	+	0.179260i	−0.0838106	+	0.996482i	$0.526709\pi$
$48$		0			0
$49$	−5.10474	−	4.28338i	−0.729248	−	0.611912i
$50$		0			0
$51$	−2.75531	−	2.07373i	−0.385821	−	0.290380i
$52$		0			0
$53$	5.40034			0.741793			0.370897	−	0.928674i	$-0.379050\pi$
$53$	5.40034			0.741793			0.370897	+	0.928674i	$0.379050\pi$
$54$		0			0
$55$	0.287915			0.0388224
$56$		0			0
$57$	−6.12946	+	2.60607i	−0.811866	+	0.345182i
$58$		0			0
$59$	7.87850	+	6.61085i	1.02569	+	0.860659i	0.990332	−	0.138715i	$-0.0442973\pi$
$59$	7.87850	+	6.61085i	1.02569	+	0.860659i	0.0353615	+	0.999375i	$0.488742\pi$
$60$		0			0
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.976864	−	0.213860i	$-0.0686036\pi$
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.610855	+	0.791742i	$0.290826\pi$
$62$		0			0
$63$	1.44333	+	0.971060i	0.181842	+	0.122342i
$64$		0			0
$65$	0.299609	−	0.251402i	0.0371619	−	0.0311825i
$66$		0			0
$67$	1.53458	−	8.70304i	0.187479	−	1.06324i	−0.735250	−	0.677796i	$-0.762935\pi$
$67$	1.53458	−	8.70304i	0.187479	−	1.06324i	0.922729	−	0.385449i	$-0.125954\pi$
$68$		0			0
$69$	1.73937	+	7.51381i	0.209396	+	0.904556i
$70$		0			0
$71$	0.572473	−	0.991553i	0.0679401	−	0.117676i	−0.830054	−	0.557683i	$-0.811691\pi$
$71$	0.572473	−	0.991553i	0.0679401	−	0.117676i	0.897994	+	0.440007i	$0.145024\pi$
$72$		0			0
$73$	−0.0977361	−	0.169284i	−0.0114391	−	0.0198132i	0.860249	−	0.509874i	$-0.170308\pi$
$73$	−0.0977361	−	0.169284i	−0.0114391	−	0.0198132i	−0.871688	+	0.490061i	$0.836975\pi$
$74$		0			0
$75$	−8.63313	+	0.457552i	−0.996868	+	0.0528336i
$76$		0			0
$77$	−1.68539	+	0.613433i	−0.192069	+	0.0699072i
$78$		0			0
$79$	1.25166	+	7.09849i	0.140822	+	0.798642i	0.970627	+	0.240589i	$0.0773405\pi$
$79$	1.25166	+	7.09849i	0.140822	+	0.798642i	−0.829805	+	0.558054i	$0.811548\pi$
$80$		0			0
$81$	7.95648	+	4.20647i	0.884053	+	0.467386i
$82$		0			0
$83$	2.58744	+	14.6741i	0.284008	+	1.61069i	0.708808	+	0.705402i	$0.249233\pi$
$83$	2.58744	+	14.6741i	0.284008	+	1.61069i	−0.424800	+	0.905287i	$0.639656\pi$
$84$		0			0
$85$	0.174151	−	0.0633858i	0.0188893	−	0.00687516i
$86$		0			0
$87$	11.0687	−	0.586638i	1.18669	−	0.0628942i
$88$		0			0
$89$	0.776563	+	1.34505i	0.0823155	+	0.142575i	0.904244	−	0.427016i	$-0.140435\pi$
$89$	0.776563	+	1.34505i	0.0823155	+	0.142575i	−0.821929	+	0.569590i	$0.807102\pi$
$90$		0			0
$91$	−1.21821	+	2.11000i	−0.127703	+	0.221189i
$92$		0			0
$93$	−0.647457	−	2.79691i	−0.0671381	−	0.290026i
$94$		0			0
$95$	0.0621565	−	0.352507i	0.00637712	−	0.0361665i
$96$		0			0
$97$	4.05661	−	3.40390i	0.411887	−	0.345614i	−0.413180	−	0.910649i	$-0.635582\pi$
$97$	4.05661	−	3.40390i	0.411887	−	0.345614i	0.825067	+	0.565035i	$0.191137\pi$
$98$		0			0
$99$	−8.33533	+	4.07760i	−0.837732	+	0.409814i
$100$		0			0
$101$	6.83061	+	2.48614i	0.679671	+	0.247380i	0.658706	−	0.752400i	$-0.271104\pi$
$101$	6.83061	+	2.48614i	0.679671	+	0.247380i	0.0209647	+	0.999780i	$0.493326\pi$
$102$		0			0
$103$	−4.90374	−	4.11472i	−0.483179	−	0.405436i	0.368395	−	0.929669i	$-0.379907\pi$
$103$	−4.90374	−	4.11472i	−0.483179	−	0.405436i	−0.851574	+	0.524234i	$0.824352\pi$
$104$		0			0
$105$	−0.0860348	+	0.0365796i	−0.00839614	+	0.00356980i
$106$		0			0
$107$	5.54365			0.535925			0.267963	−	0.963429i	$-0.413650\pi$
$107$	5.54365			0.535925			0.267963	+	0.963429i	$0.413650\pi$
$108$		0			0
$109$	−6.23137			−0.596857			−0.298428	−	0.954432i	$-0.596462\pi$
$109$	−6.23137			−0.596857			−0.298428	+	0.954432i	$0.596462\pi$
$110$		0			0
$111$	5.57722	+	4.19758i	0.529366	+	0.398416i
$112$		0			0
$113$	−9.07301	−	7.61316i	−0.853517	−	0.716186i	0.107044	−	0.994254i	$-0.465861\pi$
$113$	−9.07301	−	7.61316i	−0.853517	−	0.716186i	−0.960561	+	0.278068i	$0.910306\pi$
$114$		0			0
$115$	−0.389487	−	0.141762i	−0.0363198	−	0.0132193i
$116$		0			0
$117$	−5.11340	+	11.5215i	−0.472734	+	1.06516i
$118$		0			0
$119$	−0.884395	+	0.742096i	−0.0810724	+	0.0680278i
$120$		0			0
$121$	−0.248809	+	1.41107i	−0.0226190	+	0.128279i
$122$		0			0
$123$	1.81597	+	0.554025i	0.163740	+	0.0499547i
$124$		0			0
$125$	0.465014	−	0.805428i	0.0415921	−	0.0720396i
$126$		0			0
$127$	5.76469	+	9.98473i	0.511533	+	0.886002i	0.999911	+	0.0133693i	$0.00425570\pi$
$127$	5.76469	+	9.98473i	0.511533	+	0.886002i	−0.488377	+	0.872633i	$0.662411\pi$
$128$		0			0
$129$	−6.51604	−	10.0209i	−0.573705	−	0.882288i
$130$		0			0
$131$	−8.46830	+	3.08221i	−0.739879	+	0.269294i	−0.684340	−	0.729163i	$-0.739910\pi$
$131$	−8.46830	+	3.08221i	−0.739879	+	0.269294i	−0.0555383	+	0.998457i	$0.517688\pi$
$132$		0			0
$133$	0.387203	+	2.19594i	0.0335747	+	0.190412i
$134$		0			0
$135$	−0.422616	+	0.235239i	−0.0363730	+	0.0202462i
$136$		0			0
$137$	2.00047	+	11.3452i	0.170911	+	0.969287i	0.942758	+	0.333478i	$0.108222\pi$
$137$	2.00047	+	11.3452i	0.170911	+	0.969287i	−0.771846	+	0.635809i	$0.780667\pi$
$138$		0			0
$139$	1.60108	−	0.582746i	0.135802	−	0.0494279i	−0.273225	−	0.961950i	$-0.588090\pi$
$139$	1.60108	−	0.582746i	0.135802	−	0.0494279i	0.409027	+	0.912522i	$0.365868\pi$
$140$		0			0
$141$	2.82218	−	5.54693i	0.237670	−	0.467136i
$142$		0			0
$143$	−6.49816	−	11.2551i	−0.543403	−	0.941202i
$144$		0			0
$145$	−0.297844	+	0.515881i	−0.0247346	+	0.0428416i
$146$		0			0
$147$	−8.43662	+	7.87659i	−0.695840	+	0.649650i
$148$		0			0
$149$	−3.75996	+	21.3238i	−0.308028	+	1.74691i	0.300869	+	0.953666i	$0.402723\pi$
$149$	−3.75996	+	21.3238i	−0.308028	+	1.74691i	−0.608897	+	0.793249i	$0.708388\pi$
$150$		0			0
$151$	3.63222	−	3.04779i	0.295586	−	0.248026i	−0.482918	−	0.875665i	$-0.660423\pi$
$151$	3.63222	−	3.04779i	0.295586	−	0.248026i	0.778504	+	0.627640i	$0.215979\pi$
$152$		0			0
$153$	−4.14409	+	4.30148i	−0.335030	+	0.347754i
$154$		0			0
$155$	0.144981	+	0.0527688i	0.0116452	+	0.00423849i
$156$		0			0
$157$	−0.160261	−	0.134475i	−0.0127902	−	0.0107323i	0.636370	−	0.771384i	$-0.280435\pi$
$157$	−0.160261	−	0.134475i	−0.0127902	−	0.0107323i	−0.649160	+	0.760652i	$0.724880\pi$
$158$		0			0
$159$	1.13444	−	9.28461i	0.0899673	−	0.736317i
$160$		0			0
$161$	2.58202			0.203491
$162$		0			0
$163$	−5.62384			−0.440493			−0.220247	−	0.975444i	$-0.570686\pi$
$163$	−5.62384			−0.440493			−0.220247	+	0.975444i	$0.570686\pi$
$164$		0			0
$165$	0.0604821	−	0.495002i	0.00470852	−	0.0385358i
$166$		0			0
$167$	−12.7780	−	10.7220i	−0.988791	−	0.829695i	−0.00339914	−	0.999994i	$-0.501082\pi$
$167$	−12.7780	−	10.7220i	−0.988791	−	0.829695i	−0.985392	+	0.170300i	$0.945526\pi$
$168$		0			0
$169$	−4.37386	−	1.59195i	−0.336451	−	0.122458i
$170$		0			0
$171$	3.19291	+	11.0856i	0.244168	+	0.847738i
$172$		0			0
$173$	14.5565	−	12.2143i	1.10671	−	0.928639i	0.108851	−	0.994058i	$-0.465283\pi$
$173$	14.5565	−	12.2143i	1.10671	−	0.928639i	0.997858	+	0.0654187i	$0.0208383\pi$
$174$		0			0
$175$	−0.502587	+	2.85031i	−0.0379920	+	0.215463i
$176$		0			0
$177$	13.0208	−	12.1565i	0.978706	−	0.913738i
$178$		0			0
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	−0.385035	−	0.922902i	$-0.625811\pi$
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	0.991774	−	0.128001i	$-0.0408560\pi$
$180$		0			0
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$182$		0			0
$183$	10.3647	−	20.3716i	0.766181	−	1.50591i
$184$		0			0
$185$	−0.352512	+	0.128304i	−0.0259172	+	0.00943308i
$186$		0			0
$187$	−1.06938	−	6.06473i	−0.0782005	−	0.443497i
$188$		0			0
$189$	1.97271	−	2.27747i	0.143493	−	0.165662i
$190$		0			0
$191$	0.391371	+	2.21958i	0.0283186	+	0.160603i	0.995688	−	0.0927685i	$-0.0295716\pi$
$191$	0.391371	+	2.21958i	0.0283186	+	0.160603i	−0.967369	+	0.253371i	$0.918461\pi$
$192$		0			0
$193$	0.827186	−	0.301071i	0.0595422	−	0.0216716i	−0.312077	−	0.950057i	$-0.601025\pi$
$193$	0.827186	−	0.301071i	0.0595422	−	0.0216716i	0.371620	+	0.928385i	$0.378803\pi$
$194$		0			0
$195$	−0.369287	−	0.567919i	−0.0264452	−	0.0406695i
$196$		0			0
$197$	−10.1383	−	17.5600i	−0.722322	−	1.25110i	−0.960067	−	0.279771i	$-0.909741\pi$
$197$	−10.1383	−	17.5600i	−0.722322	−	1.25110i	0.237744	−	0.971328i	$-0.423592\pi$
$198$		0			0
$199$	−9.50472	+	16.4627i	−0.673772	+	1.16701i	0.303054	+	0.952973i	$0.401994\pi$
$199$	−9.50472	+	16.4627i	−0.673772	+	1.16701i	−0.976826	+	0.214034i	$0.931340\pi$
$200$		0			0
$201$	−14.6405	−	4.46659i	−1.03266	−	0.315049i
$202$		0			0
$203$	0.644379	−	3.65445i	0.0452265	−	0.256492i
$204$		0			0
$205$	−0.0781625	+	0.0655862i	−0.00545911	+	0.00458074i
$206$		0			0
$207$	13.2836	−	1.41202i	0.923275	−	0.0981420i
$208$		0			0
$209$	−11.1769	−	4.06806i	−0.773123	−	0.281394i
$210$		0			0
$211$	−12.3977	−	10.4029i	−0.853494	−	0.716166i	0.107062	−	0.994252i	$-0.465856\pi$
$211$	−12.3977	−	10.4029i	−0.853494	−	0.716166i	−0.960556	+	0.278086i	$0.910300\pi$
$212$		0			0
$213$	−1.58448	−	1.19253i	−0.108567	−	0.0817107i
$214$		0			0
$215$	0.642380			0.0438100
$216$		0			0
$217$	−0.961120			−0.0652451
$218$		0			0
$219$	−0.311575	+	0.132473i	−0.0210543	+	0.00895168i
$220$		0			0
$221$	−6.40842	−	5.37730i	−0.431077	−	0.361716i
$222$		0			0
$223$	20.1633	+	7.33883i	1.35023	+	0.491444i	0.913020	−	0.407914i	$-0.133744\pi$
$223$	20.1633	+	7.33883i	1.35023	+	0.491444i	0.437212	+	0.899359i	$0.355966\pi$
$224$		0			0
$225$	−1.02690	+	14.9388i	−0.0684602	+	0.995917i
$226$		0			0
$227$	14.6424	−	12.2864i	0.971848	−	0.815477i	−0.0109918	−	0.999940i	$-0.503499\pi$
$227$	14.6424	−	12.2864i	0.971848	−	0.815477i	0.982840	+	0.184462i	$0.0590544\pi$
$228$		0			0
$229$	3.90190	−	22.1288i	0.257845	−	1.46231i	−0.530818	−	0.847486i	$-0.678115\pi$
$229$	3.90190	−	22.1288i	0.257845	−	1.46231i	0.788663	−	0.614826i	$-0.210774\pi$
$230$		0			0
$231$	0.700605	+	3.02650i	0.0460964	+	0.199129i
$232$		0			0
$233$	8.84074	−	15.3126i	0.579176	−	1.00316i	−0.416398	−	0.909182i	$-0.636708\pi$
$233$	8.84074	−	15.3126i	0.579176	−	1.00316i	0.995574	−	0.0939796i	$-0.0299589\pi$
$234$		0			0
$235$	0.167233	+	0.289657i	0.0109091	+	0.0188951i
$236$		0			0
$237$	12.4671	−	0.660752i	0.809826	−	0.0429204i
$238$		0			0
$239$	−14.4904	+	5.27406i	−0.937303	+	0.341151i	−0.765100	−	0.643911i	$-0.777311\pi$
$239$	−14.4904	+	5.27406i	−0.937303	+	0.341151i	−0.172203	+	0.985061i	$0.555088\pi$
$240$		0			0
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	0.965651	+	0.259844i	$0.0836711\pi$
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	−0.818543	+	0.574445i	$0.805218\pi$
$242$		0			0
$243$	8.90345	−	12.7956i	0.571157	−	0.820841i
$244$		0			0
$245$	−0.107711	−	0.610862i	−0.00688143	−	0.0390265i
$246$		0			0
$247$	−15.1830	+	5.52617i	−0.966073	+	0.351622i
$248$		0			0
$249$	25.7722	−	1.36591i	1.63324	−	0.0865612i
$250$		0			0
$251$	8.70830	+	15.0832i	0.549663	+	0.952045i	0.998297	+	0.0583292i	$0.0185773\pi$
$251$	8.70830	+	15.0832i	0.549663	+	0.952045i	−0.448634	+	0.893716i	$0.648089\pi$
$252$		0			0
$253$	−6.88646	+	11.9277i	−0.432948	+	0.749889i
$254$		0			0
$255$	−0.0723932	−	0.312727i	−0.00453344	−	0.0195837i
$256$		0			0
$257$	1.94270	−	11.0176i	0.121182	−	0.687260i	−0.862320	−	0.506364i	$-0.830989\pi$
$257$	1.94270	−	11.0176i	0.121182	−	0.687260i	0.983502	−	0.180896i	$-0.0578997\pi$
$258$		0			0
$259$	1.79017	−	1.50213i	0.111236	−	0.0933377i
$260$		0			0
$261$	1.31662	−	19.1533i	0.0814965	−	1.18556i
$262$		0			0
$263$	−19.4619	−	7.08354i	−1.20007	−	0.436790i	−0.336821	−	0.941569i	$-0.609352\pi$
$263$	−19.4619	−	7.08354i	−1.20007	−	0.436790i	−0.863249	+	0.504779i	$0.831574\pi$
$264$		0			0
$265$	0.385077	+	0.323118i	0.0236551	+	0.0198490i
$266$		0			0
$267$	2.47562	−	1.05256i	0.151506	−	0.0644159i
$268$		0			0
$269$	−28.2449			−1.72212			−0.861060	−	0.508504i	$-0.830199\pi$
$269$	−28.2449			−1.72212			−0.861060	+	0.508504i	$0.830199\pi$
$270$		0			0
$271$	−17.2626			−1.04863			−0.524316	−	0.851524i	$-0.675679\pi$
$271$	−17.2626			−1.04863			−0.524316	+	0.851524i	$0.675679\pi$
$272$		0			0
$273$	3.37175	+	2.53767i	0.204067	+	0.153587i
$274$		0			0
$275$	−11.8267	−	9.92375i	−0.713175	−	0.598425i
$276$		0			0
$277$	−4.85725	−	1.76789i	−0.291844	−	0.106222i	0.191949	−	0.981405i	$-0.438519\pi$
$277$	−4.85725	−	1.76789i	−0.291844	−	0.106222i	−0.483793	+	0.875182i	$0.660741\pi$
$278$		0			0
$279$	−4.94464	+	0.525604i	−0.296028	+	0.0314671i
$280$		0			0
$281$	−2.52522	+	2.11891i	−0.150642	+	0.126404i	−0.714994	−	0.699131i	$-0.753571\pi$
$281$	−2.52522	+	2.11891i	−0.150642	+	0.126404i	0.564352	+	0.825534i	$0.309126\pi$
$282$		0			0
$283$	1.58553	−	8.99200i	0.0942501	−	0.534519i	−0.900724	−	0.434391i	$-0.856964\pi$
$283$	1.58553	−	8.99200i	0.0942501	−	0.534519i	0.994975	−	0.100128i	$-0.0319253\pi$
$284$		0			0
$285$	−0.592996	−	0.180914i	−0.0351260	−	0.0107164i
$286$		0			0
$287$	0.317809	−	0.550462i	0.0187597	−	0.0324927i
$288$		0			0
$289$	6.51799	+	11.2895i	0.383411	+	0.664087i
$290$		0			0
$291$	−5.00004	−	7.68945i	−0.293108	−	0.450764i
$292$		0			0
$293$	2.65598	−	0.966697i	0.155164	−	0.0564750i	−0.263271	−	0.964722i	$-0.584801\pi$
$293$	2.65598	−	0.966697i	0.155164	−	0.0564750i	0.418434	+	0.908247i	$0.362579\pi$
$294$		0			0
$295$	0.166239	+	0.942787i	0.00967880	+	0.0548912i
$296$		0			0
$297$	5.25947	+	15.1872i	0.305185	+	0.881251i
$298$		0			0
$299$	3.24888	+	18.4253i	0.187887	+	1.06556i
$300$		0			0
$301$	−3.76036	+	1.36866i	−0.216744	+	0.0788882i
$302$		0			0
$303$	5.70923	−	11.2214i	0.327987	−	0.644650i
$304$		0			0
$305$	0.614179	+	1.06379i	0.0351678	+	0.0609124i
$306$		0			0
$307$	3.14723	−	5.45116i	0.179622	−	0.311114i	−0.762129	−	0.647425i	$-0.775846\pi$
$307$	3.14723	−	5.45116i	0.179622	−	0.311114i	0.941751	+	0.336311i	$0.109179\pi$
$308$		0			0
$309$	−8.10442	+	7.56644i	−0.461045	+	0.430440i
$310$		0			0
$311$	1.28029	−	7.26088i	0.0725985	−	0.411727i	−0.926751	−	0.375675i	$-0.877411\pi$
$311$	1.28029	−	7.26088i	0.0725985	−	0.411727i	0.999350	−	0.0360515i	$-0.0114780\pi$
$312$		0			0
$313$	−3.27159	+	2.74519i	−0.184921	+	0.155167i	−0.730549	−	0.682860i	$-0.760736\pi$
$313$	−3.27159	+	2.74519i	−0.184921	+	0.155167i	0.545628	+	0.838028i	$0.316291\pi$
$314$		0			0
$315$	0.0448167	+	0.155601i	0.00252513	+	0.00876712i
$316$		0			0
$317$	−15.1738	−	5.52279i	−0.852243	−	0.310191i	−0.121288	−	0.992617i	$-0.538703\pi$
$317$	−15.1738	−	5.52279i	−0.852243	−	0.310191i	−0.730954	+	0.682426i	$0.760925\pi$
$318$		0			0
$319$	15.1632	+	12.7235i	0.848979	+	0.712378i
$320$		0			0
$321$	1.16455	−	9.53101i	0.0649989	−	0.531969i
$322$		0			0
$323$	−7.65618			−0.426001
$324$		0			0
$325$	−20.9723			−1.16333
$326$		0			0
$327$	−1.30902	+	10.7134i	−0.0723890	+	0.592451i
$328$		0			0
$329$	−1.59610	−	1.33928i	−0.0879956	−	0.0738371i
$330$		0			0
$331$	18.0686	+	6.57644i	0.993142	+	0.361474i	0.786936	−	0.617035i	$-0.211666\pi$
$331$	18.0686	+	6.57644i	0.993142	+	0.361474i	0.206206	+	0.978509i	$0.433888\pi$
$332$		0			0
$333$	8.38834	−	8.70693i	0.459678	−	0.477137i
$334$		0			0
$335$	0.630152	−	0.528761i	0.0344289	−	0.0288893i
$336$		0			0
$337$	−5.11615	+	29.0152i	−0.278695	+	1.58056i	0.448281	+	0.893893i	$0.352036\pi$
$337$	−5.11615	+	29.0152i	−0.278695	+	1.58056i	−0.726976	+	0.686663i	$0.759075\pi$
$338$		0			0
$339$	−14.9950	+	13.9996i	−0.814417	+	0.760355i
$340$		0			0
$341$	2.56339	−	4.43993i	0.138815	−	0.240435i
$342$		0			0
$343$	3.96154	+	6.86159i	0.213903	+	0.370491i
$344$		0			0
$345$	−0.325545	+	0.639851i	−0.0175268	+	0.0344484i
$346$		0			0
$347$	10.7097	−	3.89801i	0.574927	−	0.209256i	−0.0381600	−	0.999272i	$-0.512150\pi$
$347$	10.7097	−	3.89801i	0.574927	−	0.209256i	0.613087	+	0.790015i	$0.289927\pi$
$348$		0			0
$349$	4.89021	+	27.7338i	0.261767	+	1.48456i	0.778085	+	0.628158i	$0.216191\pi$
$349$	4.89021	+	27.7338i	0.261767	+	1.48456i	−0.516318	+	0.856397i	$0.672698\pi$
$350$		0			0
$351$	18.7343	+	11.2116i	0.999962	+	0.598431i
$352$		0			0
$353$	4.97573	+	28.2188i	0.264831	+	1.50193i	0.769515	+	0.638629i	$0.220498\pi$
$353$	4.97573	+	28.2188i	0.264831	+	1.50193i	−0.504683	+	0.863305i	$0.668391\pi$
$354$		0			0
$355$	0.100148	−	0.0364510i	0.00531532	−	0.00193462i
$356$		0			0
$357$	1.09007	+	1.67640i	0.0576929	+	0.0887245i
$358$		0			0
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	−0.906486	−	0.422235i	$-0.861246\pi$
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	0.0875770	−	0.996158i	$-0.472088\pi$
$360$		0			0
$361$	2.10636	−	3.64833i	0.110861	−	0.192017i
$362$		0			0
$363$	2.37373	+	0.724191i	0.124589	+	0.0380102i
$364$		0			0
$365$	0.00315957	−	0.0179188i	0.000165379	−	0.000937912i
$366$		0			0
$367$	−18.4802	+	15.5067i	−0.964660	+	0.809446i	−0.981705	−	0.190409i	$-0.939019\pi$
$367$	−18.4802	+	15.5067i	−0.964660	+	0.809446i	0.0170450	+	0.999855i	$0.494574\pi$
$368$		0			0
$369$	1.33399	−	3.00574i	0.0694449	−	0.156473i
$370$		0			0
$371$	−2.94260	−	1.07102i	−0.152772	−	0.0556045i
$372$		0			0
$373$	−9.64114	−	8.08988i	−0.499199	−	0.418878i	0.358110	−	0.933679i	$-0.383421\pi$
$373$	−9.64114	−	8.08988i	−0.499199	−	0.418878i	−0.857309	+	0.514801i	$0.827866\pi$
$374$		0			0
$375$	−1.28706	−	0.968677i	−0.0664634	−	0.0500223i
$376$		0			0
$377$	26.8890			1.38486
$378$		0			0
$379$	7.70522			0.395790			0.197895	−	0.980223i	$-0.436589\pi$
$379$	7.70522			0.395790			0.197895	+	0.980223i	$0.436589\pi$
$380$		0			0
$381$	18.3774	−	7.81354i	0.941502	−	0.400300i
$382$		0			0
$383$	13.6828	+	11.4812i	0.699159	+	0.586664i	0.921534	−	0.388297i	$-0.126937\pi$
$383$	13.6828	+	11.4812i	0.699159	+	0.586664i	−0.222376	+	0.974961i	$0.571381\pi$
$384$		0			0
$385$	−0.156882	−	0.0571005i	−0.00799546	−	0.00291011i
$386$		0			0
$387$	−18.5973	+	9.09771i	−0.945356	+	0.462463i
$388$		0			0
$389$	20.9808	−	17.6050i	1.06377	−	0.892607i	0.0692941	−	0.997596i	$-0.477925\pi$
$389$	20.9808	−	17.6050i	1.06377	−	0.892607i	0.994473	+	0.104989i	$0.0334809\pi$
$390$		0			0
$391$	−1.53948	+	8.73081i	−0.0778547	+	0.441536i
$392$		0			0
$393$	3.52020	+	15.2067i	0.177571	+	0.767078i
$394$		0			0
$395$	−0.335472	+	0.581055i	−0.0168794	+	0.0292361i
$396$		0			0
$397$	−2.10799	−	3.65115i	−0.105797	−	0.183246i	0.808266	−	0.588817i	$-0.200406\pi$
$397$	−2.10799	−	3.65115i	−0.105797	−	0.183246i	−0.914064	+	0.405571i	$0.867073\pi$
$398$		0			0
$399$	3.85673	−	0.204405i	0.193078	−	0.0102331i
$400$		0			0
$401$	−14.2575	+	5.18930i	−0.711985	+	0.259141i	−0.672519	−	0.740080i	$-0.734788\pi$
$401$	−14.2575	+	5.18930i	−0.711985	+	0.259141i	−0.0394656	+	0.999221i	$0.512566\pi$
$402$		0			0
$403$	−1.20935	−	6.85857i	−0.0602420	−	0.341650i
$404$		0			0
$405$	0.315660	+	0.776006i	0.0156853	+	0.0385600i
$406$		0			0
$407$	2.16460	+	12.2760i	0.107295	+	0.608501i
$408$		0			0
$409$	−4.42559	+	1.61078i	−0.218831	+	0.0796481i	−0.449109	−	0.893477i	$-0.648259\pi$
$409$	−4.42559	+	1.61078i	−0.218831	+	0.0796481i	0.230278	+	0.973125i	$0.426036\pi$
$410$		0			0
$411$	19.9257	−	1.05605i	0.982860	−	0.0520912i
$412$		0			0
$413$	−2.98184	−	5.16469i	−0.146727	−	0.254138i
$414$		0			0
$415$	−0.693492	+	1.20116i	−0.0340422	+	0.0589628i
$416$		0			0
$417$	−0.665556	−	2.87510i	−0.0325924	−	0.140794i
$418$		0			0
$419$	−3.43669	+	19.4905i	−0.167894	+	0.952171i	0.778137	+	0.628094i	$0.216165\pi$
$419$	−3.43669	+	19.4905i	−0.167894	+	0.952171i	−0.946031	+	0.324077i	$0.894946\pi$
$420$		0			0
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.0589715	−	0.998260i	$-0.481218\pi$
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.993334	+	0.115270i	$0.0367734\pi$
$422$		0			0
$423$	−8.94379	−	6.01731i	−0.434862	−	0.292572i
$424$		0			0
$425$	−9.33836	−	3.39889i	−0.452977	−	0.164870i
$426$		0			0
$427$	−5.86180	−	4.91863i	−0.283672	−	0.238029i
$428$		0			0
$429$	−20.7156	+	8.80769i	−1.00016	+	0.425239i
$430$		0			0
$431$	5.19681			0.250321			0.125161	−	0.992136i	$-0.460055\pi$
$431$	5.19681			0.250321			0.125161	+	0.992136i	$0.460055\pi$
$432$		0			0
$433$	25.3285			1.21721			0.608605	−	0.793473i	$-0.291730\pi$
$433$	25.3285			1.21721			0.608605	+	0.793473i	$0.291730\pi$
$434$		0			0
$435$	0.824368	+	0.620444i	0.0395254	+	0.0297480i
$436$		0			0
$437$	13.1169	+	11.0064i	0.627469	+	0.526509i
$438$		0			0
$439$	−14.7167	−	5.35646i	−0.702392	−	0.255650i	−0.0339602	−	0.999423i	$-0.510812\pi$
$439$	−14.7167	−	5.35646i	−0.702392	−	0.255650i	−0.668432	+	0.743773i	$0.733034\pi$
$440$		0			0
$441$	11.7697	+	16.1594i	0.560460	+	0.769496i
$442$		0			0
$443$	13.9833	−	11.7333i	0.664365	−	0.557468i	−0.247027	−	0.969009i	$-0.579454\pi$
$443$	13.9833	−	11.7333i	0.664365	−	0.557468i	0.911391	+	0.411541i	$0.135009\pi$
$444$		0			0
$445$	−0.0251044	+	0.142374i	−0.00119006	+	0.00674917i
$446$		0			0
$447$	35.8714	+	10.9439i	1.69666	+	0.517626i
$448$		0			0
$449$	−14.3608	+	24.8737i	−0.677729	+	1.17386i	0.297934	+	0.954586i	$0.403702\pi$
$449$	−14.3608	+	24.8737i	−0.677729	+	1.17386i	−0.975663	+	0.219274i	$0.929631\pi$
$450$		0			0
$451$	1.69525	+	2.93626i	0.0798262	+	0.138263i
$452$		0			0
$453$	−4.47694	−	6.88499i	−0.210345	−	0.323485i
$454$		0			0
$455$	−0.213113	+	0.0775669i	−0.00999091	+	0.00363639i
$456$		0			0
$457$	−6.14505	−	34.8503i	−0.287453	−	1.63023i	−0.696389	−	0.717665i	$-0.745211\pi$
$457$	−6.14505	−	34.8503i	−0.287453	−	1.63023i	0.408936	−	0.912563i	$-0.365900\pi$
$458$		0			0
$459$	6.52484	+	8.02840i	0.304553	+	0.374734i
$460$		0			0
$461$	0.395350	+	2.24214i	0.0184133	+	0.104427i	0.992629	−	0.121190i	$-0.0386712\pi$
$461$	0.395350	+	2.24214i	0.0184133	+	0.104427i	−0.974216	+	0.225617i	$0.927560\pi$
$462$		0			0
$463$	17.2664	−	6.28446i	0.802438	−	0.292064i	0.0919417	−	0.995764i	$-0.470693\pi$
$463$	17.2664	−	6.28446i	0.802438	−	0.292064i	0.710496	+	0.703701i	$0.248470\pi$
$464$		0			0
$465$	0.121180	−	0.238176i	0.00561957	−	0.0110451i
$466$		0			0
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	0.914874	−	0.403738i	$-0.132289\pi$
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	−0.807085	+	0.590435i	$0.798956\pi$
$468$		0			0
$469$	−2.56220	+	4.43786i	−0.118312	+	0.204922i
$470$		0			0
$471$	−0.264864	+	0.247282i	−0.0122043	+	0.0113941i
$472$		0			0
$473$	3.70665	−	21.0215i	0.170432	−	0.966568i
$474$		0			0
$475$	−14.7033	+	12.3375i	−0.674634	+	0.566085i
$476$		0			0
$477$	−15.7244	−	3.90082i	−0.719970	−	0.178606i
$478$		0			0
$479$	−13.3210	−	4.84844i	−0.608651	−	0.221531i	0.0192617	−	0.999814i	$-0.493868\pi$
$479$	−13.3210	−	4.84844i	−0.608651	−	0.221531i	−0.627913	+	0.778283i	$0.716091\pi$
$480$		0			0
$481$	12.9717	+	10.8846i	0.591460	+	0.496294i
$482$		0			0
$483$	0.542402	−	4.43917i	0.0246802	−	0.201989i
$484$		0			0
$485$	0.492926			0.0223826
$486$		0			0
$487$	21.4338			0.971258			0.485629	−	0.874165i	$-0.338591\pi$
$487$	21.4338			0.971258			0.485629	+	0.874165i	$0.338591\pi$
$488$		0			0
$489$	−1.18140	+	9.66888i	−0.0534246	+	0.437242i
$490$		0			0
$491$	10.7919	+	9.05550i	0.487033	+	0.408669i	0.852961	−	0.521974i	$-0.174804\pi$
$491$	10.7919	+	9.05550i	0.487033	+	0.408669i	−0.365929	+	0.930643i	$0.619249\pi$
$492$		0			0
$493$	11.9729	+	4.35779i	0.539234	+	0.196265i
$494$		0			0
$495$	−0.838333	−	0.207969i	−0.0376803	−	0.00934753i
$496$		0			0
$497$	−0.508585	+	0.426753i	−0.0228131	+	0.0191425i
$498$		0			0
$499$	−2.58898	+	14.6828i	−0.115899	+	0.657294i	0.870403	+	0.492340i	$0.163858\pi$
$499$	−2.58898	+	14.6828i	−0.115899	+	0.657294i	−0.986301	+	0.164953i	$0.947253\pi$
$500$		0			0
$501$	−21.1182	+	19.7164i	−0.943494	+	0.880864i
$502$		0			0
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	−0.986886	−	0.161420i	$-0.948393\pi$
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	0.633236	+	0.773958i	$0.281726\pi$
$504$		0			0
$505$	0.338311	+	0.585972i	0.0150546	+	0.0260754i
$506$		0			0
$507$	−3.65580	+	7.18540i	−0.162360	+	0.319115i
$508$		0			0
$509$	−31.8807	+	11.6036i	−1.41309	+	0.514321i	−0.932034	−	0.362371i	$-0.881967\pi$
$509$	−31.8807	+	11.6036i	−1.41309	+	0.514321i	−0.481052	+	0.876692i	$0.659745\pi$
$510$		0			0
$511$	0.0196825	+	0.111625i	0.000870700	+	0.00493799i
$512$		0			0
$513$	19.7298	−	3.16072i	0.871093	−	0.139549i
$514$		0			0
$515$	−0.103470	−	0.586809i	−0.00455945	−	0.0258579i
$516$		0			0
$517$	10.4438	−	3.80123i	0.459317	−	0.167178i
$518$		0			0
$519$	−17.9418	−	27.5923i	−0.787558	−	1.21117i
$520$		0			0
$521$	21.3899	+	37.0484i	0.937108	+	1.62312i	0.770831	+	0.637040i	$0.219841\pi$
$521$	21.3899	+	37.0484i	0.937108	+	1.62312i	0.166277	+	0.986079i	$0.446825\pi$
$522$		0			0
$523$	−1.38893	+	2.40569i	−0.0607335	+	0.105193i	−0.894793	−	0.446480i	$-0.852677\pi$
$523$	−1.38893	+	2.40569i	−0.0607335	+	0.105193i	0.834060	+	0.551674i	$0.186011\pi$
$524$		0			0
$525$	4.79486	+	1.46284i	0.209265	+	0.0638437i
$526$		0			0
$527$	0.573049	−	3.24992i	0.0249624	−	0.141569i
$528$		0			0
$529$	−2.43023	+	2.03920i	−0.105662	+	0.0886609i
$530$		0			0
$531$	−18.1650	−	24.9400i	−0.788292	−	1.08230i
$532$		0			0
$533$	4.32799	+	1.57526i	0.187466	+	0.0682321i
$534$		0			0
$535$	0.395296	+	0.331693i	0.0170901	+	0.0143403i
$536$		0			0
$537$	−22.4678	−	16.9099i	−0.969557	−	0.729717i
$538$		0			0
$539$	−20.6116			−0.887803
$540$		0			0
$541$	−3.59390			−0.154514			−0.0772570	−	0.997011i	$-0.524616\pi$
$541$	−3.59390			−0.154514			−0.0772570	+	0.997011i	$0.524616\pi$
$542$		0			0
$543$	4.76846	−	2.02741i	0.204634	−	0.0870047i
$544$		0			0
$545$	−0.444334	−	0.372841i	−0.0190332	−	0.0159707i
$546$		0			0
$547$	−37.1985	−	13.5392i	−1.59049	−	0.578892i	−0.613042	−	0.790051i	$-0.710054\pi$
$547$	−37.1985	−	13.5392i	−1.59049	−	0.578892i	−0.977452	+	0.211158i	$0.932276\pi$
$548$		0			0
$549$	−32.8468	−	22.0991i	−1.40187	−	0.943167i
$550$		0			0
$551$	18.8514	−	15.8182i	0.803099	−	0.673880i
$552$		0			0
$553$	0.725786	−	4.11614i	0.0308636	−	0.175036i
$554$		0			0
$555$	0.146536	+	0.633013i	0.00622011	+	0.0268699i
$556$		0			0
$557$	5.71731	−	9.90267i	0.242250	−	0.419590i	−0.719105	−	0.694902i	$-0.755448\pi$
$557$	5.71731	−	9.90267i	0.242250	−	0.419590i	0.961355	+	0.275312i	$0.0887812\pi$
$558$		0			0
$559$	−14.4983	−	25.1119i	−0.613214	−	1.06212i
$560$		0			0
$561$	−10.6515	+	0.564526i	−0.449707	+	0.0238343i
$562$		0			0
$563$	13.6357	−	4.96298i	0.574676	−	0.209165i	−0.0383005	−	0.999266i	$-0.512194\pi$
$563$	13.6357	−	4.96298i	0.574676	−	0.209165i	0.612976	+	0.790101i	$0.289972\pi$
$564$		0			0
$565$	−0.191443	−	1.08573i	−0.00805408	−	0.0456770i
$566$		0			0
$567$	−3.50117	−	3.87003i	−0.147035	−	0.162526i
$568$		0			0
$569$	−0.225601	−	1.27945i	−0.00945767	−	0.0536371i	0.979714	−	0.200402i	$-0.0642249\pi$
$569$	−0.225601	−	1.27945i	−0.00945767	−	0.0536371i	−0.989171	+	0.146765i	$0.953114\pi$
$570$		0			0
$571$	15.0890	−	5.49193i	0.631453	−	0.229830i	−0.00641065	−	0.999979i	$-0.502041\pi$
$571$	15.0890	−	5.49193i	0.631453	−	0.229830i	0.637864	+	0.770149i	$0.279818\pi$
$572$		0			0
$573$	3.89825	−	0.206606i	0.162852	−	0.00863108i
$574$		0			0
$575$	11.1127	+	19.2478i	0.463434	+	0.802691i
$576$		0			0
$577$	4.23017	−	7.32686i	0.176104	−	0.305021i	−0.764439	−	0.644696i	$-0.776984\pi$
$577$	4.23017	−	7.32686i	0.176104	−	0.305021i	0.940543	+	0.339675i	$0.110317\pi$
$578$		0			0
$579$	−0.343854	−	1.48540i	−0.0142901	−	0.0617310i
$580$		0			0
$581$	1.50035	−	8.50893i	0.0622452	−	0.353010i
$582$		0			0
$583$	12.7958	−	10.7369i	0.529947	−	0.444678i
$584$		0			0
$585$	−1.05398	+	0.515601i	−0.0435767	+	0.0213175i
$586$		0			0
$587$	−17.2764	−	6.28811i	−0.713075	−	0.259538i	−0.0400919	−	0.999196i	$-0.512765\pi$
$587$	−17.2764	−	6.28811i	−0.713075	−	0.259538i	−0.672983	+	0.739658i	$0.734987\pi$
$588$		0			0
$589$	−4.88260	−	4.09699i	−0.201184	−	0.168814i
$590$		0			0
$591$	−32.3200	+	13.7416i	−1.32947	+	0.565252i
$592$		0			0
$593$	13.5128			0.554905			0.277452	−	0.960739i	$-0.410510\pi$
$593$	13.5128			0.554905			0.277452	+	0.960739i	$0.410510\pi$
$594$		0			0
$595$	−0.107464			−0.00440561
$596$		0			0
$597$	26.3070	+	19.7994i	1.07667	+	0.810337i
$598$		0			0
$599$	−8.44772	−	7.08848i	−0.345165	−	0.289627i	0.453680	−	0.891164i	$-0.350111\pi$
$599$	−8.44772	−	7.08848i	−0.345165	−	0.289627i	−0.798845	+	0.601537i	$0.794555\pi$
$600$		0			0
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.203579	−	0.979058i	$-0.565257\pi$
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.785277	+	0.619144i	$0.787480\pi$
$602$		0			0
$603$	−10.7548	+	24.2325i	−0.437968	+	0.986824i
$604$		0			0
$605$	−0.102170	+	0.0857306i	−0.00415379	+	0.00348545i
$606$		0			0
$607$	2.56823	−	14.5652i	0.104241	−	0.591182i	−0.887279	−	0.461233i	$-0.847407\pi$
$607$	2.56823	−	14.5652i	0.104241	−	0.591182i	0.991521	−	0.129950i	$-0.0414816\pi$
$608$		0			0
$609$	−6.14761	−	1.87555i	−0.249114	−	0.0760009i
$610$		0			0
$611$	7.54882	−	13.0749i	0.305393	−	0.528956i
$612$		0			0
$613$	−18.1370	−	31.4141i	−0.732545	−	1.26880i	−0.955792	−	0.294043i	$-0.904999\pi$
$613$	−18.1370	−	31.4141i	−0.732545	−	1.26880i	0.223248	−	0.974762i	$-0.428334\pi$
$614$		0			0
$615$	0.0963404	+	0.148160i	0.00388482	+	0.00597438i
$616$		0			0
$617$	37.9387	−	13.8086i	1.52736	−	0.555912i	0.564383	−	0.825513i	$-0.309114\pi$
$617$	37.9387	−	13.8086i	1.52736	−	0.555912i	0.962972	+	0.269601i	$0.0868918\pi$
$618$		0			0
$619$	1.19701	+	6.78858i	0.0481119	+	0.272856i	0.999368	−	0.0355458i	$-0.0113170\pi$
$619$	1.19701	+	6.78858i	0.0481119	+	0.272856i	−0.951256	+	0.308402i	$0.900206\pi$
$620$		0			0
$621$	0.362848	−	23.1347i	0.0145606	−	0.928362i
$622$		0			0
$623$	−0.156387	−	0.886916i	−0.00626552	−	0.0355335i
$624$		0			0
$625$	−23.3703	+	8.50608i	−0.934810	+	0.340243i
$626$		0			0
$627$	−9.34200	+	18.3615i	−0.373083	+	0.733287i
$628$		0			0
$629$	4.01193	+	6.94887i	0.159966	+	0.277070i
$630$		0			0
$631$	14.9095	−	25.8241i	0.593539	−	1.02804i	−0.400212	−	0.916423i	$-0.631064\pi$
$631$	14.9095	−	25.8241i	0.593539	−	1.02804i	0.993751	−	0.111617i	$-0.0356031\pi$
$632$		0			0
$633$	−20.4897	+	19.1296i	−0.814394	+	0.760334i
$634$		0			0
$635$	−0.186358	+	1.05689i	−0.00739540	+	0.0419414i
$636$		0			0
$637$	−21.4487	+	17.9976i	−0.849830	+	0.713092i
$638$		0			0
$639$	−2.38312	+	2.47363i	−0.0942749	+	0.0978554i
$640$		0			0
$641$	−40.2947	−	14.6661i	−1.59155	−	0.579275i	−0.613872	−	0.789406i	$-0.710389\pi$
$641$	−40.2947	−	14.6661i	−1.59155	−	0.579275i	−0.977673	+	0.210131i	$0.932611\pi$
$642$		0			0
$643$	20.9998	+	17.6209i	0.828150	+	0.694901i	0.954866	−	0.297038i	$-0.0959989\pi$
$643$	20.9998	+	17.6209i	0.828150	+	0.694901i	−0.126715	+	0.991939i	$0.540443\pi$
$644$		0			0
$645$	0.134944	−	1.10442i	0.00531343	−	0.0434865i
$646$		0			0
$647$	16.1623			0.635407			0.317703	−	0.948190i	$-0.397088\pi$
$647$	16.1623			0.635407			0.317703	+	0.948190i	$0.397088\pi$
$648$		0			0
$649$	31.8113			1.24870
$650$		0			0
$651$	−0.201902	+	1.65242i	−0.00791316	+	0.0647634i
$652$		0			0
$653$	24.7021	+	20.7275i	0.966668	+	0.811130i	0.982025	−	0.188752i	$-0.0604441\pi$
$653$	24.7021	+	20.7275i	0.966668	+	0.811130i	−0.0153573	+	0.999882i	$0.504889\pi$
$654$		0			0
$655$	−0.788258	−	0.286903i	−0.0307998	−	0.0112102i
$656$		0			0
$657$	0.162303	+	0.563508i	0.00633206	+	0.0219846i
$658$		0			0
$659$	−21.3103	+	17.8814i	−0.830130	+	0.696562i	−0.955321	−	0.295571i	$-0.904490\pi$
$659$	−21.3103	+	17.8814i	−0.830130	+	0.696562i	0.125191	+	0.992133i	$0.460046\pi$
$660$		0			0
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	−0.684779	−	0.728751i	$-0.740101\pi$
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	0.892729	−	0.450594i	$-0.148788\pi$
$662$		0			0
$663$	−10.5912	+	9.88816i	−0.411329	+	0.384024i
$664$		0			0
$665$	−0.103779	+	0.179751i	−0.00402439	+	0.00697044i
$666$		0			0
$667$	−14.2479	−	24.6781i	−0.551682	−	0.955540i
$668$		0			0
$669$	16.8531	−	33.1243i	0.651577	−	1.28066i
$670$		0			0
$671$	38.3557	−	13.9603i	1.48071	−	0.538933i
$672$		0			0
$673$	−4.53753	−	25.7336i	−0.174909	−	0.991959i	−0.938249	−	0.345961i	$-0.887553\pi$
$673$	−4.53753	−	25.7336i	−0.174909	−	0.991959i	0.763340	−	0.645997i	$-0.223558\pi$
$674$		0			0
$675$	25.4679	+	4.90369i	0.980262	+	0.188743i
$676$		0			0
$677$	3.15944	+	17.9181i	0.121427	+	0.688648i	0.983366	+	0.181635i	$0.0581391\pi$
$677$	3.15944	+	17.9181i	0.121427	+	0.688648i	−0.861939	+	0.507012i	$0.830750\pi$
$678$		0			0
$679$	−2.88549	+	1.05023i	−0.110735	+	0.0403042i
$680$		0			0
$681$	−18.0477	−	27.7551i	−0.691588	−	1.06358i
$682$		0			0
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	0.998356	−	0.0573104i	$-0.0182525\pi$
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	−0.548811	+	0.835947i	$0.684919\pi$
$684$		0			0
$685$	−0.536171	+	0.928676i	−0.0204860	+	0.0354829i
$686$		0			0
$687$	−37.2256	−	11.3570i	−1.42024	−	0.433296i
$688$		0			0
$689$	3.94021	−	22.3460i	0.150110	−	0.851317i
$690$		0			0
$691$	34.1180	−	28.6284i	1.29791	−	1.08908i	0.307409	−	0.951577i	$-0.400538\pi$
$691$	34.1180	−	28.6284i	1.29791	−	1.08908i	0.990502	−	0.137499i	$-0.0439065\pi$
$692$		0			0
$693$	5.35054	−	0.568750i	0.203250	−	0.0216050i
$694$		0			0
$695$	0.149034	+	0.0542440i	0.00565318	+	0.00205759i
$696$		0			0
$697$	1.67184	+	1.40284i	0.0633254	+	0.0531363i
$698$		0			0
$699$	−24.4692	−	18.4163i	−0.925512	−	0.696567i
$700$		0			0
$701$	−25.2567			−0.953934			−0.476967	−	0.878921i	$-0.658264\pi$
$701$	−25.2567			−0.953934			−0.476967	+	0.878921i	$0.658264\pi$
$702$		0			0
$703$	15.4974			0.584496
$704$		0			0
$705$	0.533127	−	0.226670i	0.0200787	−	0.00853690i
$706$		0			0
$707$	−3.22888	−	2.70935i	−0.121434	−	0.101896i
$708$		0			0
$709$	14.7382	+	5.36425i	0.553503	+	0.201459i	0.603602	−	0.797286i	$-0.293731\pi$
$709$	14.7382	+	5.36425i	0.553503	+	0.201459i	−0.0500991	+	0.998744i	$0.515954\pi$
$710$		0			0
$711$	1.48295	−	21.5731i	0.0556150	−	0.809053i
$712$		0			0
$713$	−5.65382	+	4.74412i	−0.211737	+	0.177669i
$714$		0			0
$715$	0.210069	−	1.19136i	0.00785615	−	0.0445544i
$716$		0			0
$717$	6.02352	+	26.0207i	0.224953	+	0.971760i
$718$		0			0
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.381523	+	0.924359i	$0.624600\pi$
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.609757	+	0.792588i	$0.708733\pi$
$720$		0			0
$721$	1.85595	+	3.21461i	0.0691194	+	0.119718i
$722$		0			0
$723$	22.7471	−	1.20558i	0.845972	−	0.0448361i
$724$		0			0
$725$	30.0158	−	10.9248i	1.11476	−	0.405738i
$726$		0			0
$727$	−0.0814709	−	0.462044i	−0.00302159	−	0.0171363i	0.983260	−	0.182210i	$-0.0583250\pi$
$727$	−0.0814709	−	0.462044i	−0.00302159	−	0.0171363i	−0.986281	+	0.165073i	$0.947214\pi$
$728$		0			0
$729$	−20.1288	−	17.9954i	−0.745509	−	0.666495i
$730$		0			0
$731$	−2.38593	−	13.5313i	−0.0882469	−	0.500473i
$732$		0			0
$733$	43.6076	−	15.8719i	1.61068	−	0.586241i	0.629109	−	0.777317i	$-0.283420\pi$
$733$	43.6076	−	15.8719i	1.61068	−	0.586241i	0.981575	+	0.191075i	$0.0611975\pi$
$734$		0			0
$735$	−1.07286	+	0.0568611i	−0.0395731	+	0.00209735i
$736$		0			0
$737$	−13.6672	−	23.6724i	−0.503439	−	0.871983i
$738$		0			0
$739$	12.9047	−	22.3515i	0.474706	−	0.822214i	−0.524875	−	0.851179i	$-0.675888\pi$
$739$	12.9047	−	22.3515i	0.474706	−	0.822214i	0.999580	+	0.0289653i	$0.00922124\pi$
$740$		0			0
$741$	6.31146	+	27.2645i	0.231857	+	1.00159i
$742$		0			0
$743$	−6.02726	+	34.1823i	−0.221119	+	1.25403i	0.648848	+	0.760918i	$0.275251\pi$
$743$	−6.02726	+	34.1823i	−0.221119	+	1.25403i	−0.869967	+	0.493110i	$0.835860\pi$
$744$		0			0
$745$	−1.54397	+	1.29555i	−0.0565668	+	0.0474652i
$746$		0			0
$747$	3.06557	−	44.5961i	0.112163	−	1.63169i
$748$		0			0
$749$	−3.02069	−	1.09944i	−0.110374	−	0.0401727i
$750$		0			0
$751$	−18.3742	−	15.4178i	−0.670485	−	0.562604i	0.242724	−	0.970095i	$-0.421959\pi$
$751$	−18.3742	−	15.4178i	−0.670485	−	0.562604i	−0.913209	+	0.407492i	$0.866404\pi$
$752$		0			0
$753$	27.7614	−	11.8034i	1.01168	−	0.430138i
$754$		0			0
$755$	0.441357			0.0160626
$756$		0			0
$757$	−8.78780			−0.319398			−0.159699	−	0.987166i	$-0.551052\pi$
$757$	−8.78780			−0.319398			−0.159699	+	0.987166i	$0.551052\pi$
$758$		0			0
$759$	19.0603	+	14.3453i	0.691843	+	0.520701i
$760$		0			0
$761$	10.5361	+	8.84082i	0.381933	+	0.320479i	0.813461	−	0.581620i	$-0.197581\pi$
$761$	10.5361	+	8.84082i	0.381933	+	0.320479i	−0.431528	+	0.902100i	$0.642025\pi$
$762$		0			0
$763$	3.39542	+	1.23583i	0.122922	+	0.0447401i
$764$		0			0
$765$	−0.552869	+	0.0587687i	−0.0199890	+	0.00212479i
$766$		0			0
$767$	33.1034	−	27.7770i	1.19529	−	1.00297i
$768$		0			0
$769$	−5.44525	+	30.8815i	−0.196361	+	1.11362i	0.714107	+	0.700036i	$0.246833\pi$
$769$	−5.44525	+	30.8815i	−0.196361	+	1.11362i	−0.910468	+	0.413580i	$0.864278\pi$
$770$		0			0
$771$	−18.5341	−	5.65448i	−0.667489	−	0.203641i
$772$		0			0
$773$	−14.0607	+	24.3539i	−0.505729	+	0.875948i	0.494249	+	0.869320i	$0.335443\pi$
$773$	−14.0607	+	24.3539i	−0.505729	+	0.875948i	−0.999978	+	0.00662776i	$0.997890\pi$
$774$		0			0
$775$	−4.13657	−	7.16475i	−0.148590	−	0.257365i
$776$		0			0
$777$	−2.20650	−	3.39332i	−0.0791576	−	0.121735i
$778$		0			0
$779$	3.96098	−	1.44168i	0.141917	−	0.0516535i
$780$		0			0
$781$	−0.614960	−	3.48761i	−0.0220050	−	0.124797i
$782$		0			0
$783$	−32.6531	−	6.28714i	−1.16693	−	0.224684i
$784$		0			0
$785$	−0.00338155	−	0.0191777i	−0.000120693	−	0.000684483i
$786$		0			0
$787$	−34.0170	+	12.3812i	−1.21258	+	0.441342i	−0.867597	−	0.497269i	$-0.834336\pi$
$787$	−34.0170	+	12.3812i	−1.21258	+	0.441342i	−0.344979	+	0.938610i	$0.612114\pi$
$788$		0			0
$789$	−16.2668	+	31.9721i	−0.579114	+	1.13824i
$790$		0			0
$791$	3.43393	+	5.94775i	0.122097	+	0.211478i
$792$		0			0
$793$	27.7237	−	48.0189i	0.984498	−	1.70520i
$794$		0			0
$795$	0.636417	−	0.594171i	0.0225714	−	0.0210731i
$796$		0			0
$797$	−5.14000	+	29.1504i	−0.182068	+	1.03256i	0.747596	+	0.664153i	$0.231208\pi$
$797$	−5.14000	+	29.1504i	−0.182068	+	1.03256i	−0.929665	+	0.368407i	$0.879903\pi$
$798$		0			0
$799$	5.48028	−	4.59850i	0.193878	−	0.162683i
$800$		0			0
$801$	−1.28958	−	4.47736i	−0.0455652	−	0.158200i
$802$		0			0
$803$	−0.568149	−	0.206789i	−0.0200495	−	0.00729744i
$804$		0			0
$805$	0.184113	+	0.154489i	0.00648914	+	0.00544504i
$806$		0			0
$807$	−5.93338	+	48.5604i	−0.208865	+	1.70941i
$808$		0			0
$809$	−5.75943			−0.202491			−0.101245	−	0.994861i	$-0.532283\pi$
$809$	−5.75943			−0.202491			−0.101245	+	0.994861i	$0.532283\pi$
$810$		0			0
$811$	−12.4896			−0.438569			−0.219284	−	0.975661i	$-0.570372\pi$
$811$	−12.4896			−0.438569			−0.219284	+	0.975661i	$0.570372\pi$
$812$		0			0
$813$	−3.62635	+	29.6791i	−0.127182	+	1.04089i
$814$		0			0
$815$	−0.401014	−	0.336491i	−0.0140469	−	0.0117868i
$816$		0			0
$817$	−24.9373	−	9.07644i	−0.872446	−	0.317544i
$818$		0			0
$819$	5.07123	−	5.26384i	0.177203	−	0.183933i
$820$		0			0
$821$	32.9911	−	27.6828i	1.15140	−	0.966136i	0.151644	−	0.988435i	$-0.451543\pi$
$821$	32.9911	−	27.6828i	1.15140	−	0.966136i	0.999751	+	0.0222995i	$0.00709873\pi$
$822$		0			0
$823$	−1.78581	+	10.1279i	−0.0622496	+	0.353035i	0.937734	+	0.347353i	$0.112920\pi$
$823$	−1.78581	+	10.1279i	−0.0622496	+	0.353035i	−0.999984	+	0.00568141i	$0.998192\pi$
$824$		0			0
$825$	−19.5460	+	18.2485i	−0.680504	+	0.635331i
$826$		0			0
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	−0.808167	−	0.588954i	$-0.799540\pi$
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	0.914132	+	0.405416i	$0.132873\pi$
$828$		0			0
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	0.994852	+	0.101339i	$0.0323126\pi$
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	−0.409664	+	0.912236i	$0.634354\pi$
$830$		0			0
$831$	−4.05984	+	7.97952i	−0.140834	+	0.276806i
$832$		0			0
$833$	−12.4673	+	4.53774i	−0.431967	+	0.157223i
$834$		0			0
$835$	−0.269620	−	1.52909i	−0.00933057	−	0.0529163i
$836$		0			0
$837$	−0.135065	+	8.61156i	−0.00466853	+	0.297659i
$838$		0			0
$839$	7.33250	+	41.5847i	0.253146	+	1.43566i	0.800787	+	0.598950i	$0.204415\pi$
$839$	7.33250	+	41.5847i	0.253146	+	1.43566i	−0.547641	+	0.836714i	$0.684474\pi$
$840$		0			0
$841$	−11.2328	+	4.08841i	−0.387339	+	0.140980i
$842$		0			0
$843$	3.11250	+	4.78664i	0.107200	+	0.164861i
$844$		0			0
$845$	−0.216631	−	0.375216i	−0.00745234	−	0.0129078i
$846$		0			0
$847$	0.415423	−	0.719533i	0.0142741	−	0.0247235i
$848$		0			0
$849$	−15.1266	−	4.61489i	−0.519142	−	0.158383i
$850$		0			0
$851$	3.11616	−	17.6726i	0.106821	−	0.605810i
$852$		0			0
$853$	−27.3705	+	22.9665i	−0.937147	+	0.786359i	−0.977086	−	0.212843i	$-0.931728\pi$
$853$	−27.3705	+	22.9665i	−0.937147	+	0.786359i	0.0399399	+	0.999202i	$0.487283\pi$
$854$		0			0
$855$	−0.435610	+	0.981512i	−0.0148975	+	0.0335670i
$856$		0			0
$857$	−7.43170	−	2.70492i	−0.253862	−	0.0923983i	0.211954	−	0.977280i	$-0.432017\pi$
$857$	−7.43170	−	2.70492i	−0.253862	−	0.0923983i	−0.465817	+	0.884881i	$0.654239\pi$
$858$		0			0
$859$	34.2569	+	28.7449i	1.16883	+	0.980764i	0.999988	−	0.00487963i	$-0.00155324\pi$
$859$	34.2569	+	28.7449i	1.16883	+	0.980764i	0.168841	+	0.985643i	$0.445998\pi$
$860$		0			0
$861$	−0.879627	−	0.662033i	−0.0299776	−	0.0225620i
$862$		0			0
$863$	22.9170			0.780103			0.390052	−	0.920793i	$-0.372457\pi$
$863$	22.9170			0.780103			0.390052	+	0.920793i	$0.372457\pi$
$864$		0			0
$865$	1.76878			0.0601405
$866$		0			0
$867$	20.7788	−	8.83457i	0.705686	−	0.300038i
$868$		0			0
$869$	17.0789	+	14.3309i	0.579362	+	0.486143i
$870$		0			0
$871$	−34.8926	−	12.6999i	−1.18229	−	0.430319i
$872$		0			0
$873$	−14.2706	+	6.98108i	−0.482985	+	0.236274i
$874$		0			0
$875$	−0.413118	+	0.346647i	−0.0139659	+	0.0117188i
$876$		0			0
$877$	−3.84416	+	21.8013i	−0.129808	+	0.736178i	0.848527	+	0.529152i	$0.177490\pi$
$877$	−3.84416	+	21.8013i	−0.129808	+	0.736178i	−0.978335	+	0.207026i	$0.933621\pi$
$878$		0			0
$879$	−1.10407	−	4.76940i	−0.0372393	−	0.160868i
$880$		0			0
$881$	−4.93202	+	8.54251i	−0.166164	+	0.287804i	−0.937068	−	0.349147i	$-0.886471\pi$
$881$	−4.93202	+	8.54251i	−0.166164	+	0.287804i	0.770904	+	0.636951i	$0.219805\pi$
$882$		0			0
$883$	23.7865	+	41.1995i	0.800481	+	1.38647i	0.919300	+	0.393558i	$0.128756\pi$
$883$	23.7865	+	41.1995i	0.800481	+	1.38647i	−0.118819	+	0.992916i	$0.537911\pi$
$884$		0			0
$885$	1.65582	−	0.0877578i	0.0556598	−	0.00294995i
$886$		0			0
$887$	12.5517	−	4.56846i	0.421446	−	0.153394i	−0.122587	−	0.992458i	$-0.539119\pi$
$887$	12.5517	−	4.56846i	0.421446	−	0.153394i	0.544033	+	0.839064i	$0.316897\pi$
$888$		0			0
$889$	−1.16091	−	6.58387i	−0.0389358	−	0.220816i
$890$		0			0
$891$	27.2157	−	5.85205i	0.911760	−	0.196051i
$892$		0			0
$893$	−2.39936	−	13.6074i	−0.0802914	−	0.455355i
$894$		0			0
$895$	1.42009	−	0.516871i	0.0474684	−	0.0172771i
$896$		0			0
$897$	32.3605	−	1.71509i	1.08048	−	0.0572652i
$898$		0			0
$899$	5.30359	+	9.18609i	0.176885	+	0.306373i
$900$		0			0
$901$	5.37600	−	9.31150i	0.179100	−	0.310211i
$902$		0			0
$903$	1.56315	+	6.75257i	0.0520184	+	0.224712i
$904$		0			0
$905$	−0.0483552	+	0.274236i	−0.00160738	+	0.00911591i
$906$		0			0
$907$	−28.3135	+	23.7578i	−0.940134	+	0.788866i	−0.977609	−	0.210431i	$-0.932513\pi$
$907$	−28.3135	+	23.7578i	−0.940134	+	0.788866i	0.0374746	+	0.999298i	$0.488069\pi$
$908$		0			0
$909$	−18.0932	−	12.1729i	−0.600112	−	0.403751i
$910$		0			0
$911$	−45.4916	−	16.5576i	−1.50720	−	0.548577i	−0.549288	−	0.835633i	$-0.685101\pi$
$911$	−45.4916	−	16.5576i	−1.50720	−	0.548577i	−0.957914	+	0.287056i	$0.907323\pi$
$912$		0			0
$913$	35.3057	+	29.6250i	1.16845	+	0.980445i
$914$		0			0
$915$	1.95796	−	0.832467i	0.0647280	−	0.0275205i
$916$		0			0
$917$	5.22558			0.172564
$918$		0			0
$919$	−8.93459			−0.294725			−0.147363	−	0.989083i	$-0.547078\pi$
$919$	−8.93459			−0.294725			−0.147363	+	0.989083i	$0.547078\pi$
$920$		0			0
$921$	−8.71086	−	6.55604i	−0.287032	−	0.216029i
$922$		0			0
$923$	−3.68526	−	3.09230i	−0.121302	−	0.101784i
$924$		0			0
$925$	18.9024	+	6.87992i	0.621508	+	0.226211i
$926$		0			0
$927$	11.3062	+	15.5231i	0.371345	+	0.509846i
$928$		0			0
$929$	−4.78330	+	4.01366i	−0.156935	+	0.131684i	−0.717874	−	0.696173i	$-0.754885\pi$
$929$	−4.78330	+	4.01366i	−0.156935	+	0.131684i	0.560939	+	0.827857i	$0.310440\pi$
$930$		0			0
$931$	−4.44973	+	25.2357i	−0.145834	+	0.827066i
$932$		0			0
$933$	−12.2144	−	3.72644i	−0.399882	−	0.121998i
$934$		0			0
$935$	0.286617	−	0.496435i	0.00937338	−	0.0162352i
$936$		0			0
$937$	−22.9212	−	39.7006i	−0.748802	−	1.29696i	−0.948397	−	0.317085i	$-0.897296\pi$
$937$	−22.9212	−	39.7006i	−0.748802	−	1.29696i	0.199595	−	0.979878i	$-0.436037\pi$
$938$		0			0
$939$	4.03244	+	6.20140i	0.131594	+	0.202375i
$940$		0			0
$941$	4.09014	−	1.48869i	0.133335	−	0.0485298i	−0.274491	−	0.961590i	$-0.588509\pi$
$941$	4.09014	−	1.48869i	0.133335	−	0.0485298i	0.407826	+	0.913060i	$0.366287\pi$
$942$		0			0
$943$	−0.847573	−	4.80683i	−0.0276008	−	0.156532i
$944$		0			0
$945$	0.276934	−	0.0443647i	0.00900865	−	0.00144318i
$946$		0			0
$947$	−0.350202	−	1.98610i	−0.0113800	−	0.0645395i	0.978589	−	0.205825i	$-0.0659877\pi$
$947$	−0.350202	−	1.98610i	−0.0113800	−	0.0645395i	−0.989969	+	0.141285i	$0.954877\pi$
$948$		0			0
$949$	−0.771790	+	0.280909i	−0.0250534	+	0.00911868i
$950$		0			0
$951$	−12.6827	+	24.9275i	−0.411264	+	0.808331i
$952$		0			0
$953$	17.8644	+	30.9420i	0.578684	+	1.00231i	0.995631	+	0.0933786i	$0.0297667\pi$
$953$	17.8644	+	30.9420i	0.578684	+	1.00231i	−0.416947	+	0.908931i	$0.636900\pi$
$954$		0			0
$955$	−0.104896	+	0.181686i	−0.00339437	+	0.00587922i
$956$		0			0
$957$	25.0604	−	23.3968i	0.810086	−	0.756312i
$958$		0			0
$959$	1.15999	−	6.57865i	0.0374581	−	0.212436i
$960$		0			0
$961$	−21.6428	+	18.1605i	−0.698155	+	0.585822i
$962$		0			0
$963$	−16.1417	−	4.00434i	−0.520159	−	0.129038i
$964$		0			0
$965$	0.0769973	+	0.0280247i	0.00247863	+	0.000902148i
$966$		0			0
$967$	0.531112	+	0.445656i	0.0170794	+	0.0143313i	0.651287	−	0.758831i	$-0.274229\pi$
$967$	0.531112	+	0.445656i	0.0170794	+	0.0143313i	−0.634208	+	0.773163i	$0.718674\pi$
$968$		0			0
$969$	−1.60833	+	13.1630i	−0.0516670	+	0.422857i
$970$		0			0
$971$	−47.4942			−1.52416			−0.762081	−	0.647482i	$-0.775822\pi$
$971$	−47.4942			−1.52416			−0.762081	+	0.647482i	$0.775822\pi$
$972$		0			0
$973$	−0.987988			−0.0316734
$974$		0			0
$975$	−4.40563	+	36.0569i	−0.141093	+	1.15474i
$976$		0			0
$977$	−9.65470	−	8.10126i	−0.308881	−	0.259182i	0.475148	−	0.879906i	$-0.342394\pi$
$977$	−9.65470	−	8.10126i	−0.308881	−	0.259182i	−0.784029	+	0.620724i	$0.786839\pi$
$978$		0			0
$979$	4.51423	+	1.64305i	0.144276	+	0.0525120i
$980$		0			0
$981$	18.1441	+	4.50110i	0.579298	+	0.143709i
$982$		0			0
$983$	−8.84400	+	7.42100i	−0.282080	+	0.236693i	−0.772839	−	0.634602i	$-0.781164\pi$
$983$	−8.84400	+	7.42100i	−0.282080	+	0.236693i	0.490759	+	0.871295i	$0.336720\pi$
$984$		0			0
$985$	0.327745	−	1.85874i	0.0104428	−	0.0592243i
$986$		0			0
$987$	−2.63787	+	2.46277i	−0.0839644	+	0.0783908i
$988$		0			0
$989$	−15.3647	+	26.6125i	−0.488569	+	0.846227i
$990$		0			0
$991$	9.34676	+	16.1891i	0.296910	+	0.514263i	0.975427	−	0.220322i	$-0.0707107\pi$
$991$	9.34676	+	16.1891i	0.296910	+	0.514263i	−0.678518	+	0.734584i	$0.737377\pi$
$992$		0			0
$993$	15.1023	−	29.6832i	0.479257	−	0.941969i
$994$		0			0
$995$	−1.66275	+	0.605192i	−0.0527128	+	0.0191859i
$996$		0			0
$997$	0.583250	+	3.30778i	0.0184717	+	0.104758i	0.992650	−	0.121023i	$-0.0386175\pi$
$997$	0.583250	+	3.30778i	0.0184717	+	0.104758i	−0.974178	+	0.225782i	$0.927506\pi$
$998$		0			0
$999$	−13.2074	−	16.2508i	−0.417863	−	0.514154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.c.337.1		12
4.3	odd	2		27.2.e.a.13.1	✓	12
12.11	even	2		81.2.e.a.10.2		12
20.3	even	4		675.2.u.b.499.1		24
20.7	even	4		675.2.u.b.499.4		24
20.19	odd	2		675.2.l.c.526.2		12
27.25	even	9	inner	432.2.u.c.241.1		12
36.7	odd	6		243.2.e.c.109.1		12
36.11	even	6		243.2.e.b.109.2		12
36.23	even	6		243.2.e.a.190.1		12
36.31	odd	6		243.2.e.d.190.2		12
108.7	odd	18		243.2.e.c.136.1		12
108.11	even	18		243.2.e.a.55.1		12
108.23	even	18		729.2.c.b.487.1		12
108.31	odd	18		729.2.c.e.487.6		12
108.43	odd	18		243.2.e.d.55.2		12
108.47	even	18		243.2.e.b.136.2		12
108.59	even	18		729.2.a.d.1.6		6
108.67	odd	18		729.2.c.e.244.6		12
108.79	odd	18		27.2.e.a.25.1	yes	12
108.83	even	18		81.2.e.a.73.2		12
108.95	even	18		729.2.c.b.244.1		12
108.103	odd	18		729.2.a.a.1.1		6
540.79	odd	18		675.2.l.c.376.2		12
540.187	even	36		675.2.u.b.349.1		24
540.403	even	36		675.2.u.b.349.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	4.3	odd	2
27.2.e.a.25.1	yes	12	108.79	odd	18
81.2.e.a.10.2		12	12.11	even	2
81.2.e.a.73.2		12	108.83	even	18
243.2.e.a.55.1		12	108.11	even	18
243.2.e.a.190.1		12	36.23	even	6
243.2.e.b.109.2		12	36.11	even	6
243.2.e.b.136.2		12	108.47	even	18
243.2.e.c.109.1		12	36.7	odd	6
243.2.e.c.136.1		12	108.7	odd	18
243.2.e.d.55.2		12	108.43	odd	18
243.2.e.d.190.2		12	36.31	odd	6
432.2.u.c.241.1		12	27.25	even	9	inner
432.2.u.c.337.1		12	1.1	even	1	trivial
675.2.l.c.376.2		12	540.79	odd	18
675.2.l.c.526.2		12	20.19	odd	2
675.2.u.b.349.1		24	540.187	even	36
675.2.u.b.349.4		24	540.403	even	36
675.2.u.b.499.1		24	20.3	even	4
675.2.u.b.499.4		24	20.7	even	4
729.2.a.a.1.1		6	108.103	odd	18
729.2.a.d.1.6		6	108.59	even	18
729.2.c.b.244.1		12	108.95	even	18
729.2.c.b.487.1		12	108.23	even	18
729.2.c.e.244.6		12	108.67	odd	18
729.2.c.e.487.6		12	108.31	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.210069 - 1.71926i) q^{3} +(0.0713060 + 0.0598329i) q^{5} +(-0.544891 - 0.198324i) q^{7} +(-2.91174 - 0.722330i) q^{9} +(2.36944 - 1.98820i) q^{11} +(0.729623 - 4.13790i) q^{13} +(0.117848 - 0.110025i) q^{15} +(0.995493 - 1.72424i) q^{17} +(-1.92271 - 3.33023i) q^{19} +(-0.455437 + 0.895151i) q^{21} +(-4.18428 + 1.52295i) q^{23} +(-0.866736 - 4.91551i) q^{25} +(-1.85354 + 4.85432i) q^{27} +(1.11126 + 6.30229i) q^{29} +(1.55754 - 0.566898i) q^{31} +(-2.92049 - 4.49135i) q^{33} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(-6.96087 - 2.12366i) q^{39} +(-0.190345 + 1.07950i) q^{41} +(5.28657 - 4.43596i) q^{43} +(-0.164406 - 0.225724i) q^{45} +(3.37650 + 1.22894i) q^{47} +(-5.10474 - 4.28338i) q^{49} +(-2.75531 - 2.07373i) q^{51} +5.40034 q^{53} +0.287915 q^{55} +(-6.12946 + 2.60607i) q^{57} +(7.87850 + 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(1.44333 + 0.971060i) q^{63} +(0.299609 - 0.251402i) q^{65} +(1.53458 - 8.70304i) q^{67} +(1.73937 + 7.51381i) q^{69} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(-8.63313 + 0.457552i) q^{75} +(-1.68539 + 0.613433i) q^{77} +(1.25166 + 7.09849i) q^{79} +(7.95648 + 4.20647i) q^{81} +(2.58744 + 14.6741i) q^{83} +(0.174151 - 0.0633858i) q^{85} +(11.0687 - 0.586638i) q^{87} +(0.776563 + 1.34505i) q^{89} +(-1.21821 + 2.11000i) q^{91} +(-0.647457 - 2.79691i) q^{93} +(0.0621565 - 0.352507i) q^{95} +(4.05661 - 3.40390i) q^{97} +(-8.33533 + 4.07760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41}+ \cdots + 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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