LMFDB - Embedded newform 720.3.bs.c.641.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,3,Mod(401,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.401"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	720.bs (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-4] 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:	$19.6185790339$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.2
Root			$-3.73655i$ of defining polynomial
Character	$\chi$	$=$	720.641
Dual form			720.3.bs.c.401.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.62117 - 1.45927i) q^{3} +(1.93649 - 1.11803i) q^{5} +(-3.63061 + 6.28840i) q^{7} +(4.74103 + 7.65001i) q^{9} +(-6.50668 - 3.75663i) q^{11} +(-1.46668 - 2.54036i) q^{13} +(-6.70739 + 0.104680i) q^{15} +1.90107i q^{17} +7.38378 q^{19} +(18.6929 - 11.1849i) q^{21} +(30.6549 - 17.6986i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-1.26358 - 26.9704i) q^{27} +(-14.2015 - 8.19922i) q^{29} +(13.3206 + 23.0720i) q^{31} +(11.5731 + 19.3418i) q^{33} +16.2366i q^{35} -44.6613 q^{37} +(0.137323 + 8.79899i) q^{39} +(14.8634 - 8.58140i) q^{41} +(20.5554 - 35.6031i) q^{43} +(17.7339 + 9.51354i) q^{45} +(-36.4950 - 21.0704i) q^{47} +(-1.86263 - 3.22616i) q^{49} +(2.77419 - 4.98303i) q^{51} -100.474i q^{53} -16.8002 q^{55} +(-19.3541 - 10.7750i) q^{57} +(4.12003 - 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} +(-65.3191 + 2.03933i) q^{63} +(-5.68041 - 3.27959i) q^{65} +(-41.9225 - 72.6119i) q^{67} +(-106.179 + 1.65710i) q^{69} -23.1134i q^{71} -103.753 q^{73} +(-12.8718 + 7.70180i) q^{75} +(47.2464 - 27.2777i) q^{77} +(40.2610 - 69.7340i) q^{79} +(-36.0452 + 72.5379i) q^{81} +(17.1034 + 9.87463i) q^{83} +(2.12546 + 3.68141i) q^{85} +(25.2595 + 42.2153i) q^{87} -29.0566i q^{89} +21.2997 q^{91} +(-1.24719 - 79.9139i) q^{93} +(14.2986 - 8.25532i) q^{95} +(47.7972 - 82.7872i) q^{97} +(-2.11011 - 67.5864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 2 q^{7} + 8 q^{9} + 18 q^{11} - 10 q^{13} - 10 q^{15} + 52 q^{19} + 72 q^{21} + 54 q^{23} + 40 q^{25} - 34 q^{27} - 54 q^{29} - 32 q^{31} + 62 q^{33} + 44 q^{37} - 160 q^{39} + 144 q^{41}+ \cdots + 824 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 - 2 * q^7 + 8 * q^9 + 18 * q^11 - 10 * q^13 - 10 * q^15 + 52 * q^19 + 72 * q^21 + 54 * q^23 + 40 * q^25 - 34 * q^27 - 54 * q^29 - 32 * q^31 + 62 * q^33 + 44 * q^37 - 160 * q^39 + 144 * q^41 + 124 * q^43 + 140 * q^45 + 216 * q^47 - 54 * q^49 + 106 * q^51 - 236 * q^57 + 486 * q^59 + 62 * q^61 + 132 * q^63 - 90 * q^65 - 14 * q^67 + 90 * q^69 - 268 * q^73 + 20 * q^75 + 702 * q^77 + 40 * q^79 - 112 * q^81 - 522 * q^83 + 30 * q^85 - 106 * q^87 - 136 * q^91 + 90 * q^93 - 180 * q^95 - 142 * q^97 + 824 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.62117	−	1.45927i	−0.873722	−	0.486425i
$3$	−2.62117	−	1.45927i	−0.873722	−	0.486425i
$4$		0			0
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		0			0
$7$	−3.63061	+	6.28840i	−0.518658	+	0.898342i	0.481107	+	0.876662i	$0.340235\pi$
$7$	−3.63061	+	6.28840i	−0.518658	+	0.898342i	−0.999765	+	0.0216804i	$0.993098\pi$
$8$		0			0
$9$	4.74103	+	7.65001i	0.526781	+	0.850001i
$10$		0			0
$11$	−6.50668	−	3.75663i	−0.591516	−	0.341512i	0.174181	−	0.984714i	$-0.444272\pi$
$11$	−6.50668	−	3.75663i	−0.591516	−	0.341512i	−0.765697	+	0.643202i	$0.777606\pi$
$12$		0			0
$13$	−1.46668	−	2.54036i	−0.112821	−	0.195412i	0.804085	−	0.594514i	$-0.202655\pi$
$13$	−1.46668	−	2.54036i	−0.112821	−	0.195412i	−0.916907	+	0.399102i	$0.869322\pi$
$14$		0			0
$15$	−6.70739	+	0.104680i	−0.447159	+	0.00697867i
$16$		0			0
$17$			1.90107i			0.111828i	0.998436	+	0.0559139i	$0.0178072\pi$
$17$			1.90107i			0.111828i	−0.998436	+	0.0559139i	$0.982193\pi$
$18$		0			0
$19$	7.38378			0.388620			0.194310	−	0.980940i	$-0.437753\pi$
$19$	7.38378			0.388620			0.194310	+	0.980940i	$0.437753\pi$
$20$		0			0
$21$	18.6929	−	11.1849i	0.890140	−	0.532614i
$22$		0			0
$23$	30.6549	−	17.6986i	1.33282	−	0.769506i	0.347091	−	0.937831i	$-0.387169\pi$
$23$	30.6549	−	17.6986i	1.33282	−	0.769506i	0.985731	+	0.168326i	$0.0538360\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		0			0
$27$	−1.26358	−	26.9704i	−0.0467992	−	0.998904i
$28$		0			0
$29$	−14.2015	−	8.19922i	−0.489705	−	0.282732i	0.234747	−	0.972057i	$-0.424574\pi$
$29$	−14.2015	−	8.19922i	−0.489705	−	0.282732i	−0.724452	+	0.689325i	$0.757907\pi$
$30$		0			0
$31$	13.3206	+	23.0720i	0.429697	+	0.744257i	0.996846	−	0.0793581i	$-0.0252871\pi$
$31$	13.3206	+	23.0720i	0.429697	+	0.744257i	−0.567149	+	0.823615i	$0.691954\pi$
$32$		0			0
$33$	11.5731	+	19.3418i	0.350701	+	0.586115i
$34$		0			0
$35$			16.2366i			0.463902i
$36$		0			0
$37$	−44.6613			−1.20706			−0.603531	−	0.797340i	$-0.706240\pi$
$37$	−44.6613			−1.20706			−0.603531	+	0.797340i	$0.706240\pi$
$38$		0			0
$39$	0.137323	+	8.79899i	0.00352110	+	0.225615i
$40$		0			0
$41$	14.8634	−	8.58140i	0.362522	−	0.209302i	−0.307664	−	0.951495i	$-0.599547\pi$
$41$	14.8634	−	8.58140i	0.362522	−	0.209302i	0.670187	+	0.742193i	$0.266214\pi$
$42$		0			0
$43$	20.5554	−	35.6031i	0.478033	−	0.827978i	−0.521650	−	0.853160i	$-0.674683\pi$
$43$	20.5554	−	35.6031i	0.478033	−	0.827978i	0.999683	+	0.0251818i	$0.00801646\pi$
$44$		0			0
$45$	17.7339	+	9.51354i	0.394088	+	0.211412i
$46$		0			0
$47$	−36.4950	−	21.0704i	−0.776490	−	0.448307i	0.0586949	−	0.998276i	$-0.481306\pi$
$47$	−36.4950	−	21.0704i	−0.776490	−	0.448307i	−0.835185	+	0.549969i	$0.814639\pi$
$48$		0			0
$49$	−1.86263	−	3.22616i	−0.0380128	−	0.0658401i
$50$		0			0
$51$	2.77419	−	4.98303i	0.0543959	−	0.0977065i
$52$		0			0
$53$		−	100.474i		−	1.89573i	−0.318671	−	0.947865i	$-0.603236\pi$
$53$		−	100.474i		−	1.89573i	0.318671	−	0.947865i	$-0.396764\pi$
$54$		0			0
$55$	−16.8002			−0.305458
$56$		0			0
$57$	−19.3541	−	10.7750i	−0.339546	−	0.189035i
$58$		0			0
$59$	4.12003	−	2.37870i	0.0698310	−	0.0403169i	−0.464678	−	0.885480i	$-0.653830\pi$
$59$	4.12003	−	2.37870i	0.0698310	−	0.0403169i	0.534509	+	0.845163i	$0.320497\pi$
$60$		0			0
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	−0.356902	−	0.934142i	$-0.616167\pi$
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	0.987442	−	0.157985i	$-0.0504996\pi$
$62$		0			0
$63$	−65.3191	+	2.03933i	−1.03681	+	0.0323703i
$64$		0			0
$65$	−5.68041	−	3.27959i	−0.0873910	−	0.0504552i
$66$		0			0
$67$	−41.9225	−	72.6119i	−0.625709	−	1.08376i	−0.988403	−	0.151852i	$-0.951476\pi$
$67$	−41.9225	−	72.6119i	−0.625709	−	1.08376i	0.362694	−	0.931908i	$-0.381857\pi$
$68$		0			0
$69$	−106.179	+	1.65710i	−1.53882	+	0.0240159i
$70$		0			0
$71$		−	23.1134i		−	0.325540i	−0.986664	−	0.162770i	$-0.947957\pi$
$71$		−	23.1134i		−	0.325540i	0.986664	−	0.162770i	$-0.0520429\pi$
$72$		0			0
$73$	−103.753			−1.42127			−0.710637	−	0.703559i	$-0.751593\pi$
$73$	−103.753			−1.42127			−0.710637	+	0.703559i	$0.751593\pi$
$74$		0			0
$75$	−12.8718	+	7.70180i	−0.171624	+	0.102691i
$76$		0			0
$77$	47.2464	−	27.2777i	0.613589	−	0.354256i
$78$		0			0
$79$	40.2610	−	69.7340i	0.509633	−	0.882709i	−0.490305	−	0.871551i	$-0.663115\pi$
$79$	40.2610	−	69.7340i	0.509633	−	0.882709i	0.999938	−	0.0111586i	$-0.00355198\pi$
$80$		0			0
$81$	−36.0452	+	72.5379i	−0.445003	+	0.895529i
$82$		0			0
$83$	17.1034	+	9.87463i	0.206065	+	0.118971i	0.599481	−	0.800389i	$-0.295374\pi$
$83$	17.1034	+	9.87463i	0.206065	+	0.118971i	−0.393417	+	0.919360i	$0.628707\pi$
$84$		0			0
$85$	2.12546	+	3.68141i	0.0250055	+	0.0433107i
$86$		0			0
$87$	25.2595	+	42.2153i	0.290339	+	0.485234i
$88$		0			0
$89$		−	29.0566i		−	0.326478i	−0.986587	−	0.163239i	$-0.947806\pi$
$89$		−	29.0566i		−	0.326478i	0.986587	−	0.163239i	$-0.0521942\pi$
$90$		0			0
$91$	21.2997			0.234063
$92$		0			0
$93$	−1.24719	−	79.9139i	−0.0134107	−	0.859289i
$94$		0			0
$95$	14.2986	−	8.25532i	0.150512	−	0.0868981i
$96$		0			0
$97$	47.7972	−	82.7872i	0.492755	−	0.853476i	−0.507210	−	0.861822i	$-0.669323\pi$
$97$	47.7972	−	82.7872i	0.492755	−	0.853476i	0.999965	+	0.00834602i	$0.00265665\pi$
$98$		0			0
$99$	−2.11011	−	67.5864i	−0.0213143	−	0.682691i
$100$		0			0
$101$	117.817	+	68.0219i	1.16651	+	0.673484i	0.952855	−	0.303426i	$-0.0981305\pi$
$101$	117.817	+	68.0219i	1.16651	+	0.673484i	0.213653	+	0.976910i	$0.431464\pi$
$102$		0			0
$103$	−85.9401	−	148.853i	−0.834370	−	1.44517i	−0.894542	−	0.446983i	$-0.852498\pi$
$103$	−85.9401	−	148.853i	−0.834370	−	1.44517i	0.0601721	−	0.998188i	$-0.480835\pi$
$104$		0			0
$105$	23.6936	−	42.5588i	0.225654	−	0.405322i
$106$		0			0
$107$			98.6056i			0.921548i	0.887518	+	0.460774i	$0.152428\pi$
$107$			98.6056i			0.921548i	−0.887518	+	0.460774i	$0.847572\pi$
$108$		0			0
$109$	2.62651			0.0240965			0.0120482	−	0.999927i	$-0.496165\pi$
$109$	2.62651			0.0240965			0.0120482	+	0.999927i	$0.496165\pi$
$110$		0			0
$111$	117.065	+	65.1731i	1.05464	+	0.587145i
$112$		0			0
$113$	2.36782	−	1.36706i	0.0209542	−	0.0120979i	−0.489486	−	0.872011i	$-0.662816\pi$
$113$	2.36782	−	1.36706i	0.0209542	−	0.0120979i	0.510440	+	0.859913i	$0.329482\pi$
$114$		0			0
$115$	39.5753	−	68.5465i	0.344133	−	0.596056i
$116$		0			0
$117$	12.4802	−	23.2640i	0.106668	−	0.198838i
$118$		0			0
$119$	−11.9547	−	6.90205i	−0.100460	−	0.0580004i
$120$		0			0
$121$	−32.2754	−	55.9027i	−0.266739	−	0.462006i
$122$		0			0
$123$	−51.4821	+	0.803465i	−0.418554	+	0.00653224i
$124$		0			0
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−193.060			−1.52015			−0.760077	−	0.649833i	$-0.774839\pi$
$127$	−193.060			−1.52015			−0.760077	+	0.649833i	$0.774839\pi$
$128$		0			0
$129$	−105.834	+	63.3255i	−0.820418	+	0.490896i
$130$		0			0
$131$	201.259	−	116.197i	1.53633	−	0.886999i	0.537278	−	0.843405i	$-0.319453\pi$
$131$	201.259	−	116.197i	1.53633	−	0.886999i	0.999049	−	0.0435937i	$-0.0138807\pi$
$132$		0			0
$133$	−26.8076	+	46.4322i	−0.201561	+	0.349114i
$134$		0			0
$135$	−32.6007	−	50.8153i	−0.241487	−	0.376409i
$136$		0			0
$137$	154.172	+	89.0111i	1.12534	+	0.649716i	0.942759	−	0.333475i	$-0.108221\pi$
$137$	154.172	+	89.0111i	1.12534	+	0.649716i	0.182582	+	0.983191i	$0.441555\pi$
$138$		0			0
$139$	16.0343	+	27.7722i	0.115355	+	0.199800i	0.917922	−	0.396762i	$-0.129866\pi$
$139$	16.0343	+	27.7722i	0.115355	+	0.199800i	−0.802567	+	0.596562i	$0.796533\pi$
$140$		0			0
$141$	64.9120	+	108.485i	0.460369	+	0.769400i
$142$		0			0
$143$			22.0390i			0.154119i
$144$		0			0
$145$	−36.6680			−0.252883
$146$		0			0
$147$	0.174395	+	11.1744i	0.00118636	+	0.0760163i
$148$		0			0
$149$	80.4653	−	46.4567i	0.540036	−	0.311790i	−0.205058	−	0.978750i	$-0.565738\pi$
$149$	80.4653	−	46.4567i	0.540036	−	0.311790i	0.745093	+	0.666960i	$0.232405\pi$
$150$		0			0
$151$	−113.614	+	196.785i	−0.752408	+	1.30321i	0.194245	+	0.980953i	$0.437774\pi$
$151$	−113.614	+	196.785i	−0.752408	+	1.30321i	−0.946653	+	0.322256i	$0.895559\pi$
$152$		0			0
$153$	−14.5432	+	9.01305i	−0.0950537	+	0.0589088i
$154$		0			0
$155$	51.5905	+	29.7858i	0.332842	+	0.192166i
$156$		0			0
$157$	0.792406	+	1.37249i	0.00504717	+	0.00874196i	0.868538	−	0.495623i	$-0.165060\pi$
$157$	0.792406	+	1.37249i	0.00504717	+	0.00874196i	−0.863491	+	0.504365i	$0.831727\pi$
$158$		0			0
$159$	−146.619	+	263.358i	−0.922131	+	1.65634i
$160$		0			0
$161$			257.027i			1.59644i
$162$		0			0
$163$	41.6801			0.255706			0.127853	−	0.991793i	$-0.459191\pi$
$163$	41.6801			0.255706			0.127853	+	0.991793i	$0.459191\pi$
$164$		0			0
$165$	44.0360	+	24.5161i	0.266885	+	0.148582i
$166$		0			0
$167$	−8.01405	+	4.62692i	−0.0479884	+	0.0277061i	−0.523802	−	0.851840i	$-0.675487\pi$
$167$	−8.01405	+	4.62692i	−0.0479884	+	0.0277061i	0.475814	+	0.879546i	$0.342154\pi$
$168$		0			0
$169$	80.1977	−	138.907i	0.474543	−	0.821932i
$170$		0			0
$171$	35.0068	+	56.4860i	0.204718	+	0.330327i
$172$		0			0
$173$	−127.637	−	73.6913i	−0.737787	−	0.425962i	0.0834771	−	0.996510i	$-0.473397\pi$
$173$	−127.637	−	73.6913i	−0.737787	−	0.425962i	−0.821264	+	0.570548i	$0.806731\pi$
$174$		0			0
$175$	18.1530	+	31.4420i	0.103732	+	0.179668i
$176$		0			0
$177$	−14.2705	+	0.222714i	−0.0806240	+	0.00125827i
$178$		0			0
$179$		−	160.022i		−	0.893977i	−0.894540	−	0.446988i	$-0.852496\pi$
$179$		−	160.022i		−	0.893977i	0.894540	−	0.446988i	$-0.147504\pi$
$180$		0			0
$181$	−30.3346			−0.167595			−0.0837973	−	0.996483i	$-0.526705\pi$
$181$	−30.3346			−0.167595			−0.0837973	+	0.996483i	$0.526705\pi$
$182$		0			0
$183$	−198.034	+	118.493i	−1.08215	+	0.647505i
$184$		0			0
$185$	−86.4862	+	49.9328i	−0.467493	+	0.269907i
$186$		0			0
$187$	7.14163	−	12.3697i	0.0381905	−	0.0661480i
$188$		0			0
$189$	174.188	+	89.9731i	0.921631	+	0.476048i
$190$		0			0
$191$	249.938	+	144.302i	1.30857	+	0.755506i	0.981858	−	0.189617i	$-0.0607245\pi$
$191$	249.938	+	144.302i	1.30857	+	0.755506i	0.326716	+	0.945122i	$0.394058\pi$
$192$		0			0
$193$	47.3339	+	81.9847i	0.245253	+	0.424791i	0.962203	−	0.272334i	$-0.0877955\pi$
$193$	47.3339	+	81.9847i	0.245253	+	0.424791i	−0.716949	+	0.697125i	$0.754462\pi$
$194$		0			0
$195$	10.1035	+	16.8856i	0.0518128	+	0.0865930i
$196$		0			0
$197$			129.755i			0.658657i	0.944215	+	0.329329i	$0.106822\pi$
$197$			129.755i			0.658657i	−0.944215	+	0.329329i	$0.893178\pi$
$198$		0			0
$199$	−136.428			−0.685570			−0.342785	−	0.939414i	$-0.611370\pi$
$199$	−136.428			−0.685570			−0.342785	+	0.939414i	$0.611370\pi$
$200$		0			0
$201$	3.92515	+	251.504i	0.0195281	+	1.25127i
$202$		0			0
$203$	103.120	−	59.5363i	0.507980	−	0.293282i
$204$		0			0
$205$	19.1886	−	33.2356i	0.0936029	−	0.162125i
$206$		0			0
$207$	280.731	+	150.601i	1.35619	+	0.727539i
$208$		0			0
$209$	−48.0439	−	27.7382i	−0.229875	−	0.132718i
$210$		0			0
$211$	79.1144	+	137.030i	0.374950	+	0.649432i	0.990320	−	0.138806i	$-0.0443266\pi$
$211$	79.1144	+	137.030i	0.374950	+	0.649432i	−0.615370	+	0.788239i	$0.710993\pi$
$212$		0			0
$213$	−33.7287	+	60.5840i	−0.158351	+	0.284432i
$214$		0			0
$215$		−	91.9267i		−	0.427566i
$216$		0			0
$217$	−193.448			−0.891463
$218$		0			0
$219$	271.954	+	151.404i	1.24180	+	0.691343i
$220$		0			0
$221$	4.82941	−	2.78826i	0.0218525	−	0.0126166i
$222$		0			0
$223$	−103.124	+	178.616i	−0.462440	+	0.800969i	−0.999082	−	0.0428406i	$-0.986359\pi$
$223$	−103.124	+	178.616i	−0.462440	+	0.800969i	0.536642	+	0.843810i	$0.319693\pi$
$224$		0			0
$225$	44.9781	−	1.40426i	0.199903	−	0.00624115i
$226$		0			0
$227$	127.562	+	73.6481i	0.561948	+	0.324441i	0.753927	−	0.656958i	$-0.228157\pi$
$227$	127.562	+	73.6481i	0.561948	+	0.324441i	−0.191979	+	0.981399i	$0.561490\pi$
$228$		0			0
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	0.894142	−	0.447783i	$-0.147786\pi$
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	−0.834863	+	0.550458i	$0.814453\pi$
$230$		0			0
$231$	−163.646	+	2.55398i	−0.708426	+	0.0110562i
$232$		0			0
$233$		−	39.6011i		−	0.169962i	−0.996383	−	0.0849808i	$-0.972917\pi$
$233$		−	39.6011i		−	0.169962i	0.996383	−	0.0849808i	$-0.0270829\pi$
$234$		0			0
$235$	−94.2298			−0.400978
$236$		0			0
$237$	−207.292	+	124.033i	−0.874649	+	0.523345i
$238$		0			0
$239$	−54.9394	+	31.7193i	−0.229872	+	0.132717i	−0.610513	−	0.792006i	$-0.709037\pi$
$239$	−54.9394	+	31.7193i	−0.229872	+	0.132717i	0.380641	+	0.924723i	$0.375703\pi$
$240$		0			0
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	−0.686253	−	0.727363i	$-0.740746\pi$
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	0.973041	+	0.230630i	$0.0740789\pi$
$242$		0			0
$243$	200.333	−	137.534i	0.824416	−	0.565984i
$244$		0			0
$245$	−7.21392	−	4.16496i	−0.0294446	−	0.0169998i
$246$		0			0
$247$	−10.8296	−	18.7575i	−0.0438446	−	0.0759411i
$248$		0			0
$249$	−30.4210	−	50.8415i	−0.122173	−	0.204183i
$250$		0			0
$251$		−	186.477i		−	0.742936i	−0.928446	−	0.371468i	$-0.878855\pi$
$251$		−	186.477i		−	0.742936i	0.928446	−	0.371468i	$-0.121145\pi$
$252$		0			0
$253$	−265.949			−1.05118
$254$		0			0
$255$	−0.199004	−	12.7512i	−0.000780410	−	0.0500048i
$256$		0			0
$257$	201.713	−	116.459i	0.784877	−	0.453149i	−0.0532790	−	0.998580i	$-0.516967\pi$
$257$	201.713	−	116.459i	0.784877	−	0.453149i	0.838156	+	0.545431i	$0.183634\pi$
$258$		0			0
$259$	162.148	−	280.848i	0.626053	−	1.08435i
$260$		0			0
$261$	−4.60553	−	147.514i	−0.0176457	−	0.565188i
$262$		0			0
$263$	9.34728	+	5.39665i	0.0355410	+	0.0205196i	0.517665	−	0.855583i	$-0.326801\pi$
$263$	9.34728	+	5.39665i	0.0355410	+	0.0205196i	−0.482124	+	0.876103i	$0.660135\pi$
$264$		0			0
$265$	−112.333	−	194.567i	−0.423898	−	0.734213i
$266$		0			0
$267$	−42.4015	+	76.1622i	−0.158807	+	0.285252i
$268$		0			0
$269$			58.4601i			0.217324i	0.994079	+	0.108662i	$0.0346566\pi$
$269$			58.4601i			0.217324i	−0.994079	+	0.108662i	$0.965343\pi$
$270$		0			0
$271$	65.5995			0.242065			0.121032	−	0.992649i	$-0.461380\pi$
$271$	65.5995			0.242065			0.121032	+	0.992649i	$0.461380\pi$
$272$		0			0
$273$	−55.8301	−	31.0821i	−0.204506	−	0.113854i
$274$		0			0
$275$	−32.5334	+	18.7832i	−0.118303	+	0.0683024i
$276$		0			0
$277$	−134.128	+	232.317i	−0.484218	+	0.838690i	−0.999836	−	0.0181286i	$-0.994229\pi$
$277$	−134.128	+	232.317i	−0.484218	+	0.838690i	0.515618	+	0.856819i	$0.327562\pi$
$278$		0			0
$279$	−113.347	+	211.288i	−0.406263	+	0.757303i
$280$		0			0
$281$	159.428	+	92.0461i	0.567361	+	0.327566i	0.756095	−	0.654462i	$-0.227105\pi$
$281$	159.428	+	92.0461i	0.567361	+	0.327566i	−0.188734	+	0.982028i	$0.560438\pi$
$282$		0			0
$283$	−231.303	−	400.628i	−0.817324	−	1.41565i	−0.907647	−	0.419734i	$-0.862123\pi$
$283$	−231.303	−	400.628i	−0.817324	−	1.41565i	0.0903234	−	0.995912i	$-0.471210\pi$
$284$		0			0
$285$	−49.5259	+	0.772935i	−0.173775	+	0.00271205i
$286$		0			0
$287$			124.623i			0.434226i
$288$		0			0
$289$	285.386			0.987495
$290$		0			0
$291$	−246.094	+	147.250i	−0.845683	+	0.506013i
$292$		0			0
$293$	248.349	−	143.384i	0.847608	−	0.489367i	−0.0122351	−	0.999925i	$-0.503895\pi$
$293$	248.349	−	143.384i	0.847608	−	0.489367i	0.859843	+	0.510559i	$0.170561\pi$
$294$		0			0
$295$	5.31893	−	9.21266i	0.0180303	−	0.0312294i
$296$		0			0
$297$	−93.0962	+	180.235i	−0.313455	+	0.606850i
$298$		0			0
$299$	−89.9217	−	51.9163i	−0.300741	−	0.173633i
$300$		0			0
$301$	149.257	+	258.521i	0.495872	+	0.858875i
$302$		0			0
$303$	−209.556	−	350.225i	−0.691605	−	1.15586i
$304$		0			0
$305$		−	172.011i		−	0.563972i
$306$		0			0
$307$	236.738			0.771133			0.385567	−	0.922680i	$-0.374006\pi$
$307$	236.738			0.771133			0.385567	+	0.922680i	$0.374006\pi$
$308$		0			0
$309$	8.04646	+	515.578i	0.0260403	+	1.66854i
$310$		0			0
$311$	−448.597	+	258.997i	−1.44243	+	0.832789i	−0.998012	−	0.0630292i	$-0.979924\pi$
$311$	−448.597	+	258.997i	−1.44243	+	0.832789i	−0.444421	+	0.895818i	$0.646591\pi$
$312$		0			0
$313$	247.615	−	428.882i	0.791102	−	1.37023i	−0.134183	−	0.990957i	$-0.542841\pi$
$313$	247.615	−	428.882i	0.791102	−	1.37023i	0.925285	−	0.379272i	$-0.123826\pi$
$314$		0			0
$315$	−124.210	+	76.9781i	−0.394317	+	0.244375i
$316$		0			0
$317$	−189.840	−	109.604i	−0.598864	−	0.345754i	0.169731	−	0.985491i	$-0.445710\pi$
$317$	−189.840	−	109.604i	−0.598864	−	0.345754i	−0.768595	+	0.639736i	$0.779044\pi$
$318$		0			0
$319$	61.6029	+	106.699i	0.193112	+	0.334481i
$320$		0			0
$321$	143.893	−	258.462i	0.448264	−	0.805177i
$322$		0			0
$323$			14.0371i			0.0434586i
$324$		0			0
$325$	−14.6668			−0.0451285
$326$		0			0
$327$	−6.88453	−	3.83281i	−0.0210536	−	0.0117211i
$328$		0			0
$329$	264.998	−	152.997i	0.805466	−	0.465036i
$330$		0			0
$331$	−47.4838	+	82.2443i	−0.143455	+	0.248472i	−0.928796	−	0.370592i	$-0.879155\pi$
$331$	−47.4838	+	82.2443i	−0.143455	+	0.248472i	0.785340	+	0.619064i	$0.212488\pi$
$332$		0			0
$333$	−211.741	−	341.659i	−0.635858	−	1.02600i
$334$		0			0
$335$	−162.365	−	93.7416i	−0.484672	−	0.279826i
$336$		0			0
$337$	257.989	+	446.850i	0.765547	+	1.32597i	0.939957	+	0.341293i	$0.110865\pi$
$337$	257.989	+	446.850i	0.765547	+	1.32597i	−0.174411	+	0.984673i	$0.555802\pi$
$338$		0			0
$339$	−8.20138	+	0.127996i	−0.0241929	+	0.000377570i
$340$		0			0
$341$		−	200.162i		−	0.586986i
$342$		0			0
$343$	−328.750			−0.958454
$344$		0			0
$345$	−203.762	+	121.921i	−0.590614	+	0.353393i
$346$		0			0
$347$	96.4994	−	55.7140i	0.278096	−	0.160559i	−0.354465	−	0.935069i	$-0.615337\pi$
$347$	96.4994	−	55.7140i	0.278096	−	0.160559i	0.632561	+	0.774510i	$0.282004\pi$
$348$		0			0
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.0471279	+	0.998889i	$0.515007\pi$
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.841499	+	0.540258i	$0.818327\pi$
$350$		0			0
$351$	−66.6613	+	42.7668i	−0.189918	+	0.121843i
$352$		0			0
$353$	488.067	+	281.786i	1.38263	+	0.798260i	0.992470	−	0.122488i	$-0.0390873\pi$
$353$	488.067	+	281.786i	1.38263	+	0.798260i	0.390157	+	0.920748i	$0.372421\pi$
$354$		0			0
$355$	−25.8415	−	44.7588i	−0.0727930	−	0.126081i
$356$		0			0
$357$	21.2633	+	35.5366i	0.0595610	+	0.0995424i
$358$		0			0
$359$			415.128i			1.15635i	0.815915	+	0.578173i	$0.196234\pi$
$359$			415.128i			1.15635i	−0.815915	+	0.578173i	$0.803766\pi$
$360$		0			0
$361$	−306.480			−0.848974
$362$		0			0
$363$	3.02191	+	193.629i	0.00832482	+	0.533413i
$364$		0			0
$365$	−200.917	+	115.999i	−0.550457	+	0.317807i
$366$		0			0
$367$	313.940	−	543.761i	0.855423	−	1.48164i	−0.0208286	−	0.999783i	$-0.506630\pi$
$367$	313.940	−	543.761i	0.855423	−	1.48164i	0.876252	−	0.481853i	$-0.160036\pi$
$368$		0			0
$369$	136.116	+	73.0205i	0.368877	+	0.197888i
$370$		0			0
$371$	631.819	+	364.781i	1.70302	+	0.983237i
$372$		0			0
$373$	−195.467	−	338.559i	−0.524040	−	0.907665i	−0.999608	−	0.0279857i	$-0.991091\pi$
$373$	−195.467	−	338.559i	−0.524040	−	0.907665i	0.475568	−	0.879679i	$-0.342243\pi$
$374$		0			0
$375$	−16.3152	+	29.3055i	−0.0435072	+	0.0781481i
$376$		0			0
$377$			48.1024i			0.127593i
$378$		0			0
$379$	−52.4430			−0.138372			−0.0691860	−	0.997604i	$-0.522040\pi$
$379$	−52.4430			−0.138372			−0.0691860	+	0.997604i	$0.522040\pi$
$380$		0			0
$381$	506.042	+	281.727i	1.32819	+	0.739441i
$382$		0			0
$383$	96.0614	−	55.4610i	0.250813	−	0.144807i	−0.369324	−	0.929301i	$-0.620411\pi$
$383$	96.0614	−	55.4610i	0.250813	−	0.144807i	0.620136	+	0.784494i	$0.287077\pi$
$384$		0			0
$385$	60.9948	−	105.646i	0.158428	−	0.274405i
$386$		0			0
$387$	369.818	−	11.5461i	0.955601	−	0.0298348i
$388$		0			0
$389$	−91.6114	−	52.8918i	−0.235505	−	0.135969i	0.377604	−	0.925967i	$-0.376748\pi$
$389$	−91.6114	−	52.8918i	−0.235505	−	0.135969i	−0.613109	+	0.789998i	$0.710081\pi$
$390$		0			0
$391$	33.6464	+	58.2773i	0.0860521	+	0.149047i
$392$		0			0
$393$	−697.096	+	10.8794i	−1.77378	+	0.0276829i
$394$		0			0
$395$		−	180.053i		−	0.455829i
$396$		0			0
$397$	99.8892			0.251610			0.125805	−	0.992055i	$-0.459849\pi$
$397$	99.8892			0.251610			0.125805	+	0.992055i	$0.459849\pi$
$398$		0			0
$399$	138.025	−	82.5868i	0.345926	−	0.206984i
$400$		0			0
$401$	−136.080	+	78.5658i	−0.339352	+	0.195925i	−0.659985	−	0.751279i	$-0.729437\pi$
$401$	−136.080	+	78.5658i	−0.339352	+	0.195925i	0.320634	+	0.947203i	$0.396104\pi$
$402$		0			0
$403$	39.0740	−	67.6782i	0.0969579	−	0.167936i
$404$		0			0
$405$	11.2986	+	180.769i	0.0278977	+	0.446343i
$406$		0			0
$407$	290.597	+	167.776i	0.713996	+	0.412226i
$408$		0			0
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	−0.891813	−	0.452404i	$-0.850567\pi$
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	0.0541134	−	0.998535i	$-0.482767\pi$
$410$		0			0
$411$	−274.218	−	458.292i	−0.667197	−	1.11506i
$412$		0			0
$413$			34.5445i			0.0836428i
$414$		0			0
$415$	44.1607			0.106411
$416$		0			0
$417$	−1.50127	−	96.1942i	−0.00360017	−	0.230681i
$418$		0			0
$419$	44.6836	−	25.7981i	0.106643	−	0.0615706i	−0.445730	−	0.895168i	$-0.647056\pi$
$419$	44.6836	−	25.7981i	0.106643	−	0.0615706i	0.552373	+	0.833597i	$0.313722\pi$
$420$		0			0
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	−0.874653	−	0.484750i	$-0.838911\pi$
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	0.857132	+	0.515097i	$0.172244\pi$
$422$		0			0
$423$	−11.8353	−	379.083i	−0.0279795	−	0.896177i
$424$		0			0
$425$	8.23189	+	4.75268i	0.0193691	+	0.0111828i
$426$		0			0
$427$	279.287	+	483.740i	0.654069	+	1.13288i
$428$		0			0
$429$	32.1610	−	57.7680i	0.0749674	−	0.134657i
$430$		0			0
$431$			38.6810i			0.0897472i	0.998993	+	0.0448736i	$0.0142885\pi$
$431$			38.6810i			0.0897472i	−0.998993	+	0.0448736i	$0.985711\pi$
$432$		0			0
$433$	−544.647			−1.25784			−0.628922	−	0.777468i	$-0.716504\pi$
$433$	−544.647			−1.25784			−0.628922	+	0.777468i	$0.716504\pi$
$434$		0			0
$435$	96.1130	+	53.5087i	0.220949	+	0.123009i
$436$		0			0
$437$	226.349	−	130.683i	0.517962	−	0.299045i
$438$		0			0
$439$	125.709	−	217.735i	0.286353	−	0.495978i	−0.686583	−	0.727051i	$-0.740890\pi$
$439$	125.709	−	217.735i	0.286353	−	0.495978i	0.972936	+	0.231073i	$0.0742236\pi$
$440$		0			0
$441$	15.8494	−	29.5444i	0.0359397	−	0.0669942i
$442$		0			0
$443$	−632.952	−	365.435i	−1.42878	−	0.824909i	−0.431760	−	0.901989i	$-0.642107\pi$
$443$	−632.952	−	365.435i	−1.42878	−	0.824909i	−0.997025	+	0.0770796i	$0.975440\pi$
$444$		0			0
$445$	−32.4862	−	56.2678i	−0.0730028	−	0.126445i
$446$		0			0
$447$	−278.706	+	4.34968i	−0.623504	+	0.00973083i
$448$		0			0
$449$		−	94.7211i		−	0.210960i	−0.994421	−	0.105480i	$-0.966362\pi$
$449$		−	94.7211i		−	0.210960i	0.994421	−	0.105480i	$-0.0336379\pi$
$450$		0			0
$451$	−128.949			−0.285917
$452$		0			0
$453$	584.963	−	350.012i	1.29131	−	0.772653i
$454$		0			0
$455$	41.2467	−	23.8138i	0.0906521	−	0.0523380i
$456$		0			0
$457$	204.206	−	353.695i	0.446840	−	0.773949i	−0.551339	−	0.834282i	$-0.685883\pi$
$457$	204.206	−	353.695i	0.446840	−	0.773949i	0.998178	+	0.0603323i	$0.0192160\pi$
$458$		0			0
$459$	51.2727	−	2.40215i	0.111705	−	0.00523345i
$460$		0			0
$461$	−511.735	−	295.450i	−1.11005	−	0.640890i	−0.171211	−	0.985234i	$-0.554768\pi$
$461$	−511.735	−	295.450i	−1.11005	−	0.640890i	−0.938843	+	0.344344i	$0.888101\pi$
$462$		0			0
$463$	400.967	+	694.496i	0.866020	+	1.49999i	0.866031	+	0.499991i	$0.166663\pi$
$463$	400.967	+	694.496i	0.866020	+	1.49999i	−1.04649e−5		1.00000i	$0.500003\pi$
$464$		0			0
$465$	−91.7616	−	153.358i	−0.197337	−	0.329803i
$466$		0			0
$467$			20.6432i			0.0442039i	0.999756	+	0.0221019i	$0.00703584\pi$
$467$			20.6432i			0.0442039i	−0.999756	+	0.0221019i	$0.992964\pi$
$468$		0			0
$469$	608.817			1.29812
$470$		0			0
$471$	−0.0741920	−	4.75386i	−0.000157520	−	0.0100931i
$472$		0			0
$473$	−267.495	+	154.438i	−0.565529	+	0.326508i
$474$		0			0
$475$	18.4595	−	31.9727i	0.0388620	−	0.0673110i
$476$		0			0
$477$	768.625	−	476.349i	1.61137	−	0.998636i
$478$		0			0
$479$	−435.378	−	251.366i	−0.908931	−	0.524771i	−0.0288439	−	0.999584i	$-0.509183\pi$
$479$	−435.378	−	251.366i	−0.908931	−	0.524771i	−0.880087	+	0.474812i	$0.842516\pi$
$480$		0			0
$481$	65.5037	+	113.456i	0.136182	+	0.235875i
$482$		0			0
$483$	375.073	−	673.711i	0.776549	−	1.39485i
$484$		0			0
$485$		−	213.756i		−	0.440733i
$486$		0			0
$487$	−80.4336			−0.165161			−0.0825807	−	0.996584i	$-0.526316\pi$
$487$	−80.4336			−0.165161			−0.0825807	+	0.996584i	$0.526316\pi$
$488$		0			0
$489$	−109.250	−	60.8227i	−0.223416	−	0.124382i
$490$		0			0
$491$	417.972	−	241.316i	0.851267	−	0.491479i	−0.00981129	−	0.999952i	$-0.503123\pi$
$491$	417.972	−	241.316i	0.851267	−	0.491479i	0.861078	+	0.508473i	$0.169790\pi$
$492$		0			0
$493$	15.5873	−	26.9980i	0.0316173	−	0.0547627i
$494$		0			0
$495$	−79.6501	−	128.521i	−0.160909	−	0.259639i
$496$		0			0
$497$	145.346	+	83.9155i	0.292447	+	0.168844i
$498$		0			0
$499$	−17.5059	−	30.3212i	−0.0350820	−	0.0607638i	0.847951	−	0.530074i	$-0.177836\pi$
$499$	−17.5059	−	30.3212i	−0.0350820	−	0.0607638i	−0.883033	+	0.469310i	$0.844503\pi$
$500$		0			0
$501$	27.7581	−	0.433212i	0.0554054	−	0.000864695i
$502$		0			0
$503$		−	211.016i		−	0.419514i	−0.977754	−	0.209757i	$-0.932733\pi$
$503$		−	211.016i		−	0.419514i	0.977754	−	0.209757i	$-0.0672673\pi$
$504$		0			0
$505$	304.203			0.602382
$506$		0			0
$507$	−412.914	+	247.067i	−0.814427	+	0.487311i
$508$		0			0
$509$	−732.292	+	422.789i	−1.43869	+	0.830627i	−0.997759	−	0.0669144i	$-0.978685\pi$
$509$	−732.292	+	422.789i	−1.43869	+	0.830627i	−0.440930	+	0.897542i	$0.645351\pi$
$510$		0			0
$511$	376.687	−	652.440i	0.737156	−	1.27679i
$512$		0			0
$513$	−9.32998	−	199.144i	−0.0181871	−	0.388194i
$514$		0			0
$515$	−332.845	−	192.168i	−0.646300	−	0.373142i
$516$		0			0
$517$	158.308	+	274.197i	0.306204	+	0.530361i
$518$		0			0
$519$	227.022	+	379.415i	0.437423	+	0.731050i
$520$		0			0
$521$			260.960i			0.500883i	0.968132	+	0.250442i	$0.0805758\pi$
$521$			260.960i			0.500883i	−0.968132	+	0.250442i	$0.919424\pi$
$522$		0			0
$523$	−553.330			−1.05799			−0.528996	−	0.848624i	$-0.677431\pi$
$523$	−553.330			−1.05799			−0.528996	+	0.848624i	$0.677431\pi$
$524$		0			0
$525$	−1.69965	−	108.905i	−0.00323742	−	0.207438i
$526$		0			0
$527$	−43.8615	+	25.3234i	−0.0832286	+	0.0480521i
$528$		0			0
$529$	361.983	−	626.973i	0.684278	−	1.18520i
$530$		0			0
$531$	37.7302	+	20.2407i	0.0710551	+	0.0381182i
$532$		0			0
$533$	−43.5996	−	25.1723i	−0.0818005	−	0.0472275i
$534$		0			0
$535$	110.244	+	190.949i	0.206064	+	0.356914i
$536$		0			0
$537$	−233.516	+	419.444i	−0.434853	+	0.781088i
$538$		0			0
$539$			27.9888i			0.0519273i
$540$		0			0
$541$	−795.168			−1.46981			−0.734906	−	0.678169i	$-0.762774\pi$
$541$	−795.168			−1.46981			−0.734906	+	0.678169i	$0.762774\pi$
$542$		0			0
$543$	79.5121	+	44.2665i	0.146431	+	0.0815222i
$544$		0			0
$545$	5.08622	−	2.93653i	0.00933252	−	0.00538813i
$546$		0			0
$547$	−303.604	+	525.858i	−0.555035	+	0.961348i	0.442866	+	0.896588i	$0.353962\pi$
$547$	−303.604	+	525.858i	−0.555035	+	0.961348i	−0.997901	+	0.0647606i	$0.979372\pi$
$548$		0			0
$549$	691.995	−	21.6048i	1.26046	−	0.0393529i
$550$		0			0
$551$	−104.861	−	60.5412i	−0.190309	−	0.109875i
$552$		0			0
$553$	292.344	+	506.354i	0.528650	+	0.915649i
$554$		0			0
$555$	299.561	−	4.67515i	0.539749	−	0.00842369i
$556$		0			0
$557$		−	686.808i		−	1.23305i	−0.787336	−	0.616524i	$-0.788540\pi$
$557$		−	686.808i		−	1.23305i	0.787336	−	0.616524i	$-0.211460\pi$
$558$		0			0
$559$	−120.593			−0.215729
$560$		0			0
$561$	−36.7702	+	22.0014i	−0.0655439	+	0.0392181i
$562$		0			0
$563$	208.976	−	120.652i	0.371182	−	0.214302i	−0.302792	−	0.953057i	$-0.597919\pi$
$563$	208.976	−	120.652i	0.371182	−	0.214302i	0.673975	+	0.738754i	$0.264586\pi$
$564$		0			0
$565$	3.05685	−	5.29461i	0.00541035	−	0.00937099i
$566$		0			0
$567$	−325.281	−	490.023i	−0.573688	−	0.864238i
$568$		0			0
$569$	−666.084	−	384.564i	−1.17062	−	0.675859i	−0.216796	−	0.976217i	$-0.569561\pi$
$569$	−666.084	−	384.564i	−1.17062	−	0.675859i	−0.953827	+	0.300358i	$0.902894\pi$
$570$		0			0
$571$	48.7253	+	84.3947i	0.0853333	+	0.147802i	0.905533	−	0.424275i	$-0.139471\pi$
$571$	48.7253	+	84.3947i	0.0853333	+	0.147802i	−0.820200	+	0.572077i	$0.806138\pi$
$572$		0			0
$573$	−444.553	−	742.966i	−0.775834	−	1.29663i
$574$		0			0
$575$		−	176.986i		−	0.307802i
$576$		0			0
$577$	277.283			0.480560			0.240280	−	0.970704i	$-0.422761\pi$
$577$	277.283			0.480560			0.240280	+	0.970704i	$0.422761\pi$
$578$		0			0
$579$	−4.43181	−	283.969i	−0.00765425	−	0.490447i
$580$		0			0
$581$	−124.191	+	71.7018i	−0.213754	+	0.123411i
$582$		0			0
$583$	−377.443	+	653.750i	−0.647415	+	1.12136i
$584$		0			0
$585$	−1.84216	−	59.0038i	−0.00314899	−	0.100861i
$586$		0			0
$587$	−405.017	−	233.836i	−0.689977	−	0.398358i	0.113626	−	0.993524i	$-0.463753\pi$
$587$	−405.017	−	233.836i	−0.689977	−	0.398358i	−0.803603	+	0.595165i	$0.797087\pi$
$588$		0			0
$589$	98.3565	+	170.358i	0.166989	+	0.289233i
$590$		0			0
$591$	189.349	−	340.111i	0.320387	−	0.575483i
$592$		0			0
$593$			254.411i			0.429023i	0.976721	+	0.214512i	$0.0688160\pi$
$593$			254.411i			0.429023i	−0.976721	+	0.214512i	$0.931184\pi$
$594$		0			0
$595$	−30.8669			−0.0518772
$596$		0			0
$597$	357.602	+	199.087i	0.598998	+	0.333478i
$598$		0			0
$599$	−352.081	+	203.274i	−0.587780	+	0.339355i	−0.764219	−	0.644956i	$-0.776876\pi$
$599$	−352.081	+	203.274i	−0.587780	+	0.339355i	0.176439	+	0.984312i	$0.443542\pi$
$600$		0			0
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	−0.995524	−	0.0945042i	$-0.969873\pi$
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	0.579605	+	0.814897i	$0.303207\pi$
$602$		0			0
$603$	356.726	−	664.963i	0.591585	−	1.10276i
$604$		0			0
$605$	−125.002	−	72.1701i	−0.206615	−	0.119289i
$606$		0			0
$607$	29.9627	+	51.8970i	0.0493620	+	0.0854975i	0.889651	−	0.456642i	$-0.150948\pi$
$607$	29.9627	+	51.8970i	0.0493620	+	0.0854975i	−0.840289	+	0.542139i	$0.817615\pi$
$608$		0			0
$609$	−357.174	+	5.57430i	−0.586493	+	0.00915321i
$610$		0			0
$611$			123.614i			0.202314i
$612$		0			0
$613$	−373.866			−0.609896			−0.304948	−	0.952369i	$-0.598639\pi$
$613$	−373.866			−0.609896			−0.304948	+	0.952369i	$0.598639\pi$
$614$		0			0
$615$	−98.7964	+	59.1147i	−0.160645	+	0.0961214i
$616$		0			0
$617$	−320.088	+	184.803i	−0.518782	+	0.299519i	−0.736436	−	0.676507i	$-0.763493\pi$
$617$	−320.088	+	184.803i	−0.518782	+	0.299519i	0.217654	+	0.976026i	$0.430159\pi$
$618$		0			0
$619$	598.225	−	1036.16i	0.966438	−	1.67392i	0.260738	−	0.965410i	$-0.416034\pi$
$619$	598.225	−	1036.16i	0.966438	−	1.67392i	0.705701	−	0.708510i	$-0.250632\pi$
$620$		0			0
$621$	−516.074	−	804.413i	−0.831037	−	1.29535i
$622$		0			0
$623$	182.719	+	105.493i	0.293289	+	0.169331i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	85.4535	+	142.816i	0.136289	+	0.227776i
$628$		0			0
$629$		−	84.9044i		−	0.134983i
$630$		0			0
$631$	−628.525			−0.996078			−0.498039	−	0.867155i	$-0.665946\pi$
$631$	−628.525			−0.996078			−0.498039	+	0.867155i	$0.665946\pi$
$632$		0			0
$633$	−7.40738	−	474.629i	−0.0117020	−	0.749808i
$634$		0			0
$635$	−373.858	+	215.847i	−0.588753	+	0.339917i
$636$		0			0
$637$	−5.46374	+	9.46347i	−0.00857730	+	0.0148563i
$638$		0			0
$639$	176.817	−	109.581i	0.276709	−	0.171489i
$640$		0			0
$641$	824.417	+	475.977i	1.28614	+	0.742554i	0.977964	−	0.208774i	$-0.0669474\pi$
$641$	824.417	+	475.977i	1.28614	+	0.742554i	0.308178	+	0.951329i	$0.400281\pi$
$642$		0			0
$643$	−35.7759	−	61.9656i	−0.0556390	−	0.0963696i	0.836864	−	0.547410i	$-0.184386\pi$
$643$	−35.7759	−	61.9656i	−0.0556390	−	0.0963696i	−0.892503	+	0.451041i	$0.851053\pi$
$644$		0			0
$645$	−134.146	+	240.955i	−0.207979	+	0.373574i
$646$		0			0
$647$		−	900.292i		−	1.39149i	−0.718290	−	0.695744i	$-0.755075\pi$
$647$		−	900.292i		−	1.39149i	0.718290	−	0.695744i	$-0.244925\pi$
$648$		0			0
$649$	−35.7436			−0.0550748
$650$		0			0
$651$	507.058	+	282.293i	0.778892	+	0.433630i
$652$		0			0
$653$	−222.825	+	128.648i	−0.341233	+	0.197011i	−0.660817	−	0.750547i	$-0.729790\pi$
$653$	−222.825	+	128.648i	−0.341233	+	0.197011i	0.319584	+	0.947558i	$0.396457\pi$
$654$		0			0
$655$	259.824	−	450.029i	0.396678	−	0.687066i
$656$		0			0
$657$	−491.897	−	793.711i	−0.748701	−	1.20808i
$658$		0			0
$659$	−477.967	−	275.954i	−0.725291	−	0.418747i	0.0914057	−	0.995814i	$-0.470864\pi$
$659$	−477.967	−	275.954i	−0.725291	−	0.418747i	−0.816697	+	0.577067i	$0.804197\pi$
$660$		0			0
$661$	523.413	+	906.578i	0.791851	+	1.37153i	0.924820	+	0.380405i	$0.124216\pi$
$661$	523.413	+	906.578i	0.791851	+	1.37153i	−0.132969	+	0.991120i	$0.542451\pi$
$662$		0			0
$663$	−16.7275	+	0.261061i	−0.0252300	+	0.000393757i
$664$		0			0
$665$			119.887i			0.180282i
$666$		0			0
$667$	−580.460			−0.870254
$668$		0			0
$669$	530.956	−	317.696i	0.793656	−	0.474883i
$670$		0			0
$671$	−500.531	+	288.982i	−0.745948	+	0.430673i
$672$		0			0
$673$	−118.875	+	205.898i	−0.176635	+	0.305940i	−0.940726	−	0.339168i	$-0.889854\pi$
$673$	−118.875	+	205.898i	−0.176635	+	0.305940i	0.764091	+	0.645108i	$0.223188\pi$
$674$		0			0
$675$	−119.944	−	61.9546i	−0.177695	−	0.0917846i
$676$		0			0
$677$	−145.591	−	84.0570i	−0.215053	−	0.124161i	0.388605	−	0.921405i	$-0.372957\pi$
$677$	−145.591	−	84.0570i	−0.215053	−	0.124161i	−0.603658	+	0.797244i	$0.706291\pi$
$678$		0			0
$679$	347.066	+	601.136i	0.511143	+	0.885325i
$680$		0			0
$681$	−226.889	−	379.192i	−0.333171	−	0.556817i
$682$		0			0
$683$			995.446i			1.45746i	0.684800	+	0.728731i	$0.259889\pi$
$683$			995.446i			1.45746i	−0.684800	+	0.728731i	$0.740111\pi$
$684$		0			0
$685$	398.070			0.581123
$686$		0			0
$687$	−1.27102	−	81.4405i	−0.00185010	−	0.118545i
$688$		0			0
$689$	−255.239	+	147.362i	−0.370449	+	0.213879i
$690$		0			0
$691$	−298.570	+	517.138i	−0.432084	+	0.748391i	−0.997053	−	0.0767211i	$-0.975555\pi$
$691$	−298.570	+	517.138i	−0.432084	+	0.748391i	0.564969	+	0.825112i	$0.308888\pi$
$692$		0			0
$693$	432.671	+	232.111i	0.624345	+	0.334936i
$694$		0			0
$695$	62.1006	+	35.8538i	0.0893534	+	0.0515882i
$696$		0			0
$697$	16.3139	+	28.2564i	0.0234058	+	0.0405401i
$698$		0			0
$699$	−57.7888	+	103.801i	−0.0826736	+	0.148499i
$700$		0			0
$701$		−	413.729i		−	0.590199i	−0.955467	−	0.295099i	$-0.904647\pi$
$701$		−	413.729i		−	0.590199i	0.955467	−	0.295099i	$-0.0953528\pi$
$702$		0			0
$703$	−329.769			−0.469089
$704$		0			0
$705$	246.992	+	137.507i	0.350343	+	0.195046i
$706$		0			0
$707$	−855.497	+	493.921i	−1.21004	+	0.698616i
$708$		0			0
$709$	328.568	−	569.096i	0.463424	−	0.802674i	−0.535705	−	0.844405i	$-0.679954\pi$
$709$	328.568	−	569.096i	0.463424	−	0.802674i	0.999129	+	0.0417311i	$0.0132873\pi$
$710$		0			0
$711$	724.345	−	22.6147i	1.01877	−	0.0318070i
$712$		0			0
$713$	816.684	+	471.513i	1.14542	+	0.661308i
$714$		0			0
$715$	24.6404	+	42.6784i	0.0344621	+	0.0596901i
$716$		0			0
$717$	190.293	−	2.96984i	0.265401	−	0.00414203i
$718$		0			0
$719$		−	217.226i		−	0.302122i	−0.988524	−	0.151061i	$-0.951731\pi$
$719$		−	217.226i		−	0.302122i	0.988524	−	0.151061i	$-0.0482690\pi$
$720$		0			0
$721$	1248.06			1.73101
$722$		0			0
$723$	−355.858	+	212.927i	−0.492197	+	0.294505i
$724$		0			0
$725$	−71.0073	+	40.9961i	−0.0979411	+	0.0565463i
$726$		0			0
$727$	304.437	−	527.300i	0.418757	−	0.725309i	−0.577057	−	0.816704i	$-0.695799\pi$
$727$	304.437	−	527.300i	0.418757	−	0.725309i	0.995815	+	0.0913946i	$0.0291325\pi$
$728$		0			0
$729$	−725.807	+	68.1584i	−0.995620	+	0.0934958i
$730$		0			0
$731$	67.6840	+	39.0774i	0.0925910	+	0.0534574i
$732$		0			0
$733$	440.351	+	762.709i	0.600751	+	1.04053i	0.992708	+	0.120548i	$0.0384650\pi$
$733$	440.351	+	762.709i	0.600751	+	1.04053i	−0.391957	+	0.919984i	$0.628202\pi$
$734$		0			0
$735$	12.8311	+	21.4441i	0.0174572	+	0.0291757i
$736$		0			0
$737$			629.950i			0.854749i
$738$		0			0
$739$	917.157			1.24108			0.620540	−	0.784175i	$-0.286914\pi$
$739$	917.157			1.24108			0.620540	+	0.784175i	$0.286914\pi$
$740$		0			0
$741$	1.01396	+	64.9698i	0.00136837	+	0.0876786i
$742$		0			0
$743$	956.492	−	552.231i	1.28734	−	0.743245i	0.309159	−	0.951010i	$-0.399952\pi$
$743$	956.492	−	552.231i	1.28734	−	0.743245i	0.978179	+	0.207765i	$0.0666191\pi$
$744$		0			0
$745$	103.880	−	179.926i	0.139437	−	0.241511i
$746$		0			0
$747$	5.54662	+	177.657i	0.00742519	+	0.237827i
$748$		0			0
$749$	−620.071	−	357.998i	−0.827866	−	0.477968i
$750$		0			0
$751$	330.239	+	571.990i	0.439732	+	0.761638i	0.997669	−	0.0682453i	$-0.0217401\pi$
$751$	330.239	+	571.990i	0.439732	+	0.761638i	−0.557936	+	0.829884i	$0.688407\pi$
$752$		0			0
$753$	−272.121	+	488.787i	−0.361383	+	0.649120i
$754$		0			0
$755$			508.096i			0.672974i
$756$		0			0
$757$	−353.728			−0.467276			−0.233638	−	0.972324i	$-0.575063\pi$
$757$	−353.728			−0.467276			−0.233638	+	0.972324i	$0.575063\pi$
$758$		0			0
$759$	697.096	+	388.093i	0.918441	+	0.511321i
$760$		0			0
$761$	708.380	−	408.983i	0.930854	−	0.537429i	0.0437722	−	0.999042i	$-0.486062\pi$
$761$	708.380	−	408.983i	0.930854	−	0.537429i	0.887081	+	0.461613i	$0.152729\pi$
$762$		0			0
$763$	−9.53584	+	16.5166i	−0.0124978	+	0.0216469i
$764$		0			0
$765$	−18.0859	+	33.7135i	−0.0236417	+	0.0440700i
$766$		0			0
$767$	−12.0855	−	6.97756i	−0.0157568	−	0.00909721i
$768$		0			0
$769$	500.408	+	866.732i	0.650725	+	1.12709i	0.982947	+	0.183888i	$0.0588684\pi$
$769$	500.408	+	866.732i	0.650725	+	1.12709i	−0.332222	+	0.943201i	$0.607798\pi$
$770$		0			0
$771$	−698.670	+	10.9039i	−0.906187	+	0.0141426i
$772$		0			0
$773$		−	860.440i		−	1.11312i	−0.830808	−	0.556559i	$-0.812121\pi$
$773$		−	860.440i		−	1.11312i	0.830808	−	0.556559i	$-0.187879\pi$
$774$		0			0
$775$	133.206			0.171879
$776$		0			0
$777$	−834.850	+	499.531i	−1.07445	+	0.642898i
$778$		0			0
$779$	109.748	−	63.3632i	0.140884	−	0.0813391i
$780$		0			0
$781$	−86.8283	+	150.391i	−0.111176	+	0.192562i
$782$		0			0
$783$	−203.192	+	393.380i	−0.259504	+	0.502401i
$784$		0			0
$785$	3.06898	+	1.77187i	0.00390952	+	0.00225716i
$786$		0			0
$787$	463.491	+	802.789i	0.588933	+	1.02006i	0.994372	+	0.105940i	$0.0337853\pi$
$787$	463.491	+	802.789i	0.588933	+	1.02006i	−0.405439	+	0.914122i	$0.632881\pi$
$788$		0			0
$789$	−16.6256	−	27.7858i	−0.0210717	−	0.0352165i
$790$		0			0
$791$			19.8531i			0.0250987i
$792$		0			0
$793$	−225.651			−0.284553
$794$		0			0
$795$	10.5176	+	673.916i	0.0132297	+	0.847693i
$796$		0			0
$797$	−825.230	+	476.447i	−1.03542	+	0.597800i	−0.918533	−	0.395345i	$-0.870625\pi$
$797$	−825.230	+	476.447i	−1.03542	+	0.597800i	−0.116888	+	0.993145i	$0.537292\pi$
$798$		0			0
$799$	40.0564	−	69.3797i	0.0501332	−	0.0868332i
$800$		0			0
$801$	222.283	−	137.758i	0.277507	−	0.171983i
$802$		0			0
$803$	675.087	+	389.762i	0.840707	+	0.485382i
$804$		0			0
$805$	287.365	+	497.731i	0.356975	+	0.618299i
$806$		0			0
$807$	85.3094	−	153.234i	0.105712	−	0.189881i
$808$		0			0
$809$			1425.22i			1.76171i	0.473387	+	0.880855i	$0.343031\pi$
$809$			1425.22i			1.76171i	−0.473387	+	0.880855i	$0.656969\pi$
$810$		0			0
$811$	473.774			0.584185			0.292093	−	0.956390i	$-0.405648\pi$
$811$	473.774			0.584185			0.292093	+	0.956390i	$0.405648\pi$
$812$		0			0
$813$	−171.947	−	95.7277i	−0.211497	−	0.117746i
$814$		0			0
$815$	80.7131	−	46.5997i	0.0990345	−	0.0571776i
$816$		0			0
$817$	151.777	−	262.885i	0.185773	−	0.321769i
$818$		0			0
$819$	100.983	+	162.943i	0.123300	+	0.198953i
$820$		0			0
$821$	−63.4905	−	36.6562i	−0.0773331	−	0.0446483i	0.460835	−	0.887486i	$-0.347550\pi$
$821$	−63.4905	−	36.6562i	−0.0773331	−	0.0446483i	−0.538168	+	0.842838i	$0.680883\pi$
$822$		0			0
$823$	316.027	+	547.374i	0.383994	+	0.665096i	0.991629	−	0.129120i	$-0.0412151\pi$
$823$	316.027	+	547.374i	0.383994	+	0.665096i	−0.607635	+	0.794216i	$0.707882\pi$
$824$		0			0
$825$	112.685	−	1.75864i	0.136588	−	0.00213169i
$826$		0			0
$827$			226.153i			0.273462i	0.990608	+	0.136731i	$0.0436597\pi$
$827$			226.153i			0.273462i	−0.990608	+	0.136731i	$0.956340\pi$
$828$		0			0
$829$	−522.396			−0.630152			−0.315076	−	0.949067i	$-0.602030\pi$
$829$	−522.396			−0.630152			−0.315076	+	0.949067i	$0.602030\pi$
$830$		0			0
$831$	690.588	−	413.212i	0.831032	−	0.497247i
$832$		0			0
$833$	6.13317	−	3.54099i	0.00736275	−	0.00425089i
$834$		0			0
$835$	−10.3461	+	17.9200i	−0.0123905	+	0.0214610i
$836$		0			0
$837$	605.429	−	388.415i	0.723332	−	0.464057i
$838$		0			0
$839$	−511.329	−	295.216i	−0.609450	−	0.351866i	0.163300	−	0.986576i	$-0.447786\pi$
$839$	−511.329	−	295.216i	−0.609450	−	0.351866i	−0.772750	+	0.634710i	$0.781119\pi$
$840$		0			0
$841$	−286.046	−	495.446i	−0.340126	−	0.589115i
$842$		0			0
$843$	−283.568	−	473.918i	−0.336380	−	0.562180i
$844$		0			0
$845$		−	358.655i		−	0.424444i
$846$		0			0
$847$	468.718			0.553386
$848$		0			0
$849$	21.6566	+	1387.65i	0.0255083	+	1.63445i
$850$		0			0
$851$	−1369.09	+	790.444i	−1.60880	+	0.928841i
$852$		0			0
$853$	−693.749	+	1201.61i	−0.813305	+	1.40869i	0.0972332	+	0.995262i	$0.469001\pi$
$853$	−693.749	+	1201.61i	−0.813305	+	1.40869i	−0.910538	+	0.413424i	$0.864333\pi$
$854$		0			0
$855$	130.944	+	70.2459i	0.153150	+	0.0821590i
$856$		0			0
$857$	−683.058	−	394.363i	−0.797033	−	0.460167i	0.0453994	−	0.998969i	$-0.485544\pi$
$857$	−683.058	−	394.363i	−0.797033	−	0.460167i	−0.842433	+	0.538801i	$0.818877\pi$
$858$		0			0
$859$	413.601	+	716.378i	0.481491	+	0.833968i	0.999774	−	0.0212416i	$-0.00676191\pi$
$859$	413.601	+	716.378i	0.481491	+	0.833968i	−0.518283	+	0.855209i	$0.673429\pi$
$860$		0			0
$861$	181.859	−	326.657i	0.211218	−	0.379393i
$862$		0			0
$863$			1089.70i			1.26268i	0.775504	+	0.631342i	$0.217496\pi$
$863$			1089.70i			1.26268i	−0.775504	+	0.631342i	$0.782504\pi$
$864$		0			0
$865$	−329.558			−0.380992
$866$		0			0
$867$	−748.044	−	416.457i	−0.862796	−	0.480342i
$868$		0			0
$869$	−523.930	+	302.491i	−0.602912	+	0.348091i
$870$		0			0
$871$	−122.974	+	212.996i	−0.141187	+	0.244542i
$872$		0			0
$873$	859.931	−	26.8479i	0.985029	−	0.0307536i
$874$		0			0
$875$	70.3064	+	40.5914i	0.0803502	+	0.0463902i
$876$		0			0
$877$	−213.875	−	370.443i	−0.243872	−	0.422398i	0.717942	−	0.696103i	$-0.245084\pi$
$877$	−213.875	−	370.443i	−0.243872	−	0.422398i	−0.961814	+	0.273705i	$0.911751\pi$
$878$		0			0
$879$	−860.202	+	13.4249i	−0.978614	+	0.0152729i
$880$		0			0
$881$			1113.87i			1.26432i	0.774837	+	0.632161i	$0.217832\pi$
$881$			1113.87i			1.26432i	−0.774837	+	0.632161i	$0.782168\pi$
$882$		0			0
$883$	408.581			0.462719			0.231359	−	0.972868i	$-0.425683\pi$
$883$	408.581			0.462719			0.231359	+	0.972868i	$0.425683\pi$
$884$		0			0
$885$	−27.3856	+	16.3861i	−0.0309442	+	0.0185154i
$886$		0			0
$887$	755.098	−	435.956i	0.851294	−	0.491495i	−0.00979311	−	0.999952i	$-0.503117\pi$
$887$	755.098	−	435.956i	0.851294	−	0.491495i	0.861087	+	0.508457i	$0.169784\pi$
$888$		0			0
$889$	700.924	−	1214.04i	0.788441	−	1.36562i
$890$		0			0
$891$	507.033	−	336.572i	0.569060	−	0.377746i
$892$		0			0
$893$	−269.471	−	155.579i	−0.301760	−	0.174221i
$894$		0			0
$895$	−178.910	−	309.881i	−0.199899	−	0.346236i
$896$		0			0
$897$	159.940	+	267.302i	0.178305	+	0.297995i
$898$		0			0
$899$		−	436.874i		−	0.485956i
$900$		0			0
$901$	191.008			0.211995
$902$		0			0
$903$	−13.9748	−	895.436i	−0.0154759	−	0.991623i
$904$		0			0
$905$	−58.7427	+	33.9151i	−0.0649091	+	0.0374753i
$906$		0			0
$907$	−843.097	+	1460.29i	−0.929544	+	1.61002i	−0.145459	+	0.989364i	$0.546466\pi$
$907$	−843.097	+	1460.29i	−0.929544	+	1.61002i	−0.784085	+	0.620653i	$0.786867\pi$
$908$		0			0
$909$	38.2081	+	1223.80i	0.0420332	+	1.34631i
$910$		0			0
$911$	383.084	+	221.173i	0.420509	+	0.242781i	0.695295	−	0.718724i	$-0.255274\pi$
$911$	383.084	+	221.173i	0.420509	+	0.242781i	−0.274786	+	0.961505i	$0.588607\pi$
$912$		0			0
$913$	−74.1907	−	128.502i	−0.0812603	−	0.140747i
$914$		0			0
$915$	−251.012	+	450.870i	−0.274330	+	0.492755i
$916$		0			0
$917$			1687.46i			1.84020i
$918$		0			0
$919$	182.236			0.198298			0.0991489	−	0.995073i	$-0.468388\pi$
$919$	182.236			0.198298			0.0991489	+	0.995073i	$0.468388\pi$
$920$		0			0
$921$	−620.530	−	345.466i	−0.673757	−	0.375099i
$922$		0			0
$923$	−58.7162	+	33.8998i	−0.0636145	+	0.0367279i
$924$		0			0
$925$	−111.653	+	193.389i	−0.120706	+	0.209069i
$926$		0			0
$927$	731.279	−	1363.16i	0.788866	−	1.47050i
$928$		0			0
$929$	−1150.27	−	664.111i	−1.23819	−	0.714867i	−0.269463	−	0.963011i	$-0.586846\pi$
$929$	−1150.27	−	664.111i	−1.23819	−	0.714867i	−0.968723	+	0.248144i	$0.920179\pi$
$930$		0			0
$931$	−13.7532	−	23.8213i	−0.0147725	−	0.0255868i
$932$		0			0
$933$	1553.79	−	24.2496i	1.66537	−	0.0259910i
$934$		0			0
$935$		−	31.9383i		−	0.0341587i
$936$		0			0
$937$	−276.582			−0.295178			−0.147589	−	0.989049i	$-0.547151\pi$
$937$	−276.582			−0.295178			−0.147589	+	0.989049i	$0.547151\pi$
$938$		0			0
$939$	−1274.90	+	762.832i	−1.35772	+	0.812388i
$940$		0			0
$941$	1083.50	−	625.557i	1.15143	−	0.664779i	0.202196	−	0.979345i	$-0.435192\pi$
$941$	1083.50	−	625.557i	1.15143	−	0.664779i	0.949236	+	0.314566i	$0.101859\pi$
$942$		0			0
$943$	303.758	−	526.124i	0.322119	−	0.557926i
$944$		0			0
$945$	437.907	−	20.5162i	0.463394	−	0.0217102i
$946$		0			0
$947$	935.323	+	540.009i	0.987670	+	0.570232i	0.904577	−	0.426310i	$-0.140187\pi$
$947$	935.323	+	540.009i	0.987670	+	0.570232i	0.0830930	+	0.996542i	$0.473520\pi$
$948$		0			0
$949$	152.172	+	263.570i	0.160350	+	0.277734i
$950$		0			0
$951$	337.660	+	564.319i	0.355057	+	0.593396i
$952$		0			0
$953$			328.534i			0.344737i	0.985033	+	0.172369i	$0.0551420\pi$
$953$			328.534i			0.344737i	−0.985033	+	0.172369i	$0.944858\pi$
$954$		0			0
$955$	645.336			0.675745
$956$		0			0
$957$	−5.76780	−	369.572i	−0.00602696	−	0.386178i
$958$		0			0
$959$	−1119.47	+	646.328i	−1.16733	+	0.673961i
$960$		0			0
$961$	125.623	−	217.585i	0.130721	−	0.226416i
$962$		0			0
$963$	−754.334	+	467.493i	−0.783316	+	0.485454i
$964$		0			0
$965$	183.323	+	105.842i	0.189972	+	0.109681i
$966$		0			0
$967$	−298.854	−	517.631i	−0.309053	−	0.535296i	0.669102	−	0.743170i	$-0.266679\pi$
$967$	−298.854	−	517.631i	−0.309053	−	0.535296i	−0.978155	+	0.207875i	$0.933345\pi$
$968$		0			0
$969$	20.4840	−	36.7936i	0.0211393	−	0.0379707i
$970$		0			0
$971$		−	711.597i		−	0.732850i	−0.930448	−	0.366425i	$-0.880582\pi$
$971$		−	711.597i		−	0.732850i	0.930448	−	0.366425i	$-0.119418\pi$
$972$		0			0
$973$	−232.857			−0.239319
$974$		0			0
$975$	38.4440	+	21.4028i	0.0394298	+	0.0219516i
$976$		0			0
$977$	292.262	−	168.738i	0.299142	−	0.172710i	−0.342915	−	0.939366i	$-0.611414\pi$
$977$	292.262	−	168.738i	0.299142	−	0.172710i	0.642058	+	0.766656i	$0.278081\pi$
$978$		0			0
$979$	−109.155	+	189.062i	−0.111496	+	0.193117i
$980$		0			0
$981$	12.4524	+	20.0928i	0.0126936	+	0.0204820i
$982$		0			0
$983$	274.504	+	158.485i	0.279252	+	0.161226i	0.633085	−	0.774083i	$-0.281789\pi$
$983$	274.504	+	158.485i	0.279252	+	0.161226i	−0.353833	+	0.935309i	$0.615122\pi$
$984$		0			0
$985$	145.071	+	251.270i	0.147280	+	0.255097i
$986$		0			0
$987$	−917.869	+	14.3249i	−0.929959	+	0.0145136i
$988$		0			0
$989$		−	1455.21i		−	1.47140i
$990$		0			0
$991$	−685.922			−0.692152			−0.346076	−	0.938207i	$-0.612486\pi$
$991$	−685.922			−0.692152			−0.346076	+	0.938207i	$0.612486\pi$
$992$		0			0
$993$	244.480	−	146.284i	0.246203	−	0.147315i
$994$		0			0
$995$	−264.192	+	152.532i	−0.265520	+	0.153298i
$996$		0			0
$997$	−293.035	+	507.551i	−0.293917	+	0.509078i	−0.974732	−	0.223376i	$-0.928292\pi$
$997$	−293.035	+	507.551i	−0.293917	+	0.509078i	0.680816	+	0.732455i	$0.261625\pi$
$998$		0			0
$999$	56.4330	+	1204.53i	0.0564895	+	1.20574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.3.bs.c.641.2		16
3.2	odd	2		2160.3.bs.c.1601.1		16
4.3	odd	2		45.3.i.a.11.1	✓	16
9.4	even	3		2160.3.bs.c.881.1		16
9.5	odd	6	inner	720.3.bs.c.401.2		16
12.11	even	2		135.3.i.a.116.8		16
20.3	even	4		225.3.i.b.74.1		32
20.7	even	4		225.3.i.b.74.16		32
20.19	odd	2		225.3.j.b.101.8		16
36.7	odd	6		405.3.c.a.161.16		16
36.11	even	6		405.3.c.a.161.1		16
36.23	even	6		45.3.i.a.41.1	yes	16
36.31	odd	6		135.3.i.a.71.8		16
60.23	odd	4		675.3.i.c.224.16		32
60.47	odd	4		675.3.i.c.224.1		32
60.59	even	2		675.3.j.b.251.1		16
180.23	odd	12		225.3.i.b.149.16		32
180.59	even	6		225.3.j.b.176.8		16
180.67	even	12		675.3.i.c.449.16		32
180.103	even	12		675.3.i.c.449.1		32
180.139	odd	6		675.3.j.b.476.1		16
180.167	odd	12		225.3.i.b.149.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	4.3	odd	2
45.3.i.a.41.1	yes	16	36.23	even	6
135.3.i.a.71.8		16	36.31	odd	6
135.3.i.a.116.8		16	12.11	even	2
225.3.i.b.74.1		32	20.3	even	4
225.3.i.b.74.16		32	20.7	even	4
225.3.i.b.149.1		32	180.167	odd	12
225.3.i.b.149.16		32	180.23	odd	12
225.3.j.b.101.8		16	20.19	odd	2
225.3.j.b.176.8		16	180.59	even	6
405.3.c.a.161.1		16	36.11	even	6
405.3.c.a.161.16		16	36.7	odd	6
675.3.i.c.224.1		32	60.47	odd	4
675.3.i.c.224.16		32	60.23	odd	4
675.3.i.c.449.1		32	180.103	even	12
675.3.i.c.449.16		32	180.67	even	12
675.3.j.b.251.1		16	60.59	even	2
675.3.j.b.476.1		16	180.139	odd	6
720.3.bs.c.401.2		16	9.5	odd	6	inner
720.3.bs.c.641.2		16	1.1	even	1	trivial
2160.3.bs.c.881.1		16	9.4	even	3
2160.3.bs.c.1601.1		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	720.bs (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.62117 - 1.45927i) q^{3} +(1.93649 - 1.11803i) q^{5} +(-3.63061 + 6.28840i) q^{7} +(4.74103 + 7.65001i) q^{9} +(-6.50668 - 3.75663i) q^{11} +(-1.46668 - 2.54036i) q^{13} +(-6.70739 + 0.104680i) q^{15} +1.90107i q^{17} +7.38378 q^{19} +(18.6929 - 11.1849i) q^{21} +(30.6549 - 17.6986i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-1.26358 - 26.9704i) q^{27} +(-14.2015 - 8.19922i) q^{29} +(13.3206 + 23.0720i) q^{31} +(11.5731 + 19.3418i) q^{33} +16.2366i q^{35} -44.6613 q^{37} +(0.137323 + 8.79899i) q^{39} +(14.8634 - 8.58140i) q^{41} +(20.5554 - 35.6031i) q^{43} +(17.7339 + 9.51354i) q^{45} +(-36.4950 - 21.0704i) q^{47} +(-1.86263 - 3.22616i) q^{49} +(2.77419 - 4.98303i) q^{51} -100.474i q^{53} -16.8002 q^{55} +(-19.3541 - 10.7750i) q^{57} +(4.12003 - 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} +(-65.3191 + 2.03933i) q^{63} +(-5.68041 - 3.27959i) q^{65} +(-41.9225 - 72.6119i) q^{67} +(-106.179 + 1.65710i) q^{69} -23.1134i q^{71} -103.753 q^{73} +(-12.8718 + 7.70180i) q^{75} +(47.2464 - 27.2777i) q^{77} +(40.2610 - 69.7340i) q^{79} +(-36.0452 + 72.5379i) q^{81} +(17.1034 + 9.87463i) q^{83} +(2.12546 + 3.68141i) q^{85} +(25.2595 + 42.2153i) q^{87} -29.0566i q^{89} +21.2997 q^{91} +(-1.24719 - 79.9139i) q^{93} +(14.2986 - 8.25532i) q^{95} +(47.7972 - 82.7872i) q^{97} +(-2.11011 - 67.5864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 2 q^{7} + 8 q^{9} + 18 q^{11} - 10 q^{13} - 10 q^{15} + 52 q^{19} + 72 q^{21} + 54 q^{23} + 40 q^{25} - 34 q^{27} - 54 q^{29} - 32 q^{31} + 62 q^{33} + 44 q^{37} - 160 q^{39} + 144 q^{41}+ \cdots + 824 q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 - 2 * q^7 + 8 * q^9 + 18 * q^11 - 10 * q^13 - 10 * q^15 + 52 * q^19 + 72 * q^21 + 54 * q^23 + 40 * q^25 - 34 * q^27 - 54 * q^29 - 32 * q^31 + 62 * q^33 + 44 * q^37 - 160 * q^39 + 144 * q^41 + 124 * q^43 + 140 * q^45 + 216 * q^47 - 54 * q^49 + 106 * q^51 - 236 * q^57 + 486 * q^59 + 62 * q^61 + 132 * q^63 - 90 * q^65 - 14 * q^67 + 90 * q^69 - 268 * q^73 + 20 * q^75 + 702 * q^77 + 40 * q^79 - 112 * q^81 - 522 * q^83 + 30 * q^85 - 106 * q^87 - 136 * q^91 + 90 * q^93 - 180 * q^95 - 142 * q^97 + 824 * q^99

Introduction

L-functions

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