LMFDB - Embedded newform 720.3.bs.c.401.4

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)

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);

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")

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			401.4
Root			$-1.83391i$ of defining polynomial
Character	$\chi$	$=$	720.401
Dual form			720.3.bs.c.641.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.822398 + 2.88508i) q^{3} +(-1.93649 - 1.11803i) q^{5} +(-3.23398 - 5.60142i) q^{7} +(-7.64732 - 4.74536i) q^{9} +(-9.24701 + 5.33876i) q^{11} +(-5.53374 + 9.58473i) q^{13} +(4.81818 - 4.66746i) q^{15} -12.6328i q^{17} +32.1403 q^{19} +(18.8201 - 4.72368i) q^{21} +(9.82266 + 5.67112i) q^{23} +(2.50000 + 4.33013i) q^{25} +(19.9799 - 18.1605i) q^{27} +(35.2234 - 20.3362i) q^{29} +(-15.9429 + 27.6139i) q^{31} +(-7.79801 - 31.0689i) q^{33} +14.4628i q^{35} +45.4499 q^{37} +(-23.1017 - 23.8477i) q^{39} +(-25.4781 - 14.7098i) q^{41} +(-18.8093 - 32.5786i) q^{43} +(9.50350 + 17.7393i) q^{45} +(49.8119 - 28.7589i) q^{47} +(3.58274 - 6.20548i) q^{49} +(36.4465 + 10.3891i) q^{51} +33.3940i q^{53} +23.8757 q^{55} +(-26.4321 + 92.7272i) q^{57} +(-3.54909 - 2.04907i) q^{59} +(33.1195 + 57.3647i) q^{61} +(-1.84945 + 58.1823i) q^{63} +(21.4321 - 12.3738i) q^{65} +(35.4890 - 61.4687i) q^{67} +(-24.4397 + 23.6752i) q^{69} +13.1123i q^{71} +109.273 q^{73} +(-14.5487 + 3.65160i) q^{75} +(59.8093 + 34.5309i) q^{77} +(49.8891 + 86.4104i) q^{79} +(35.9631 + 72.5786i) q^{81} +(-74.2472 + 42.8667i) q^{83} +(-14.1238 + 24.4632i) q^{85} +(29.7039 + 118.347i) q^{87} -63.6372i q^{89} +71.5841 q^{91} +(-66.5567 - 68.7060i) q^{93} +(-62.2394 - 35.9339i) q^{95} +(-43.2064 - 74.8357i) q^{97} +(96.0492 + 3.05314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.822398	+	2.88508i	−0.274133	+	0.961692i
$3$	−0.822398	+	2.88508i	−0.274133	+	0.961692i
$4$		0			0
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$6$		0			0
$7$	−3.23398	−	5.60142i	−0.461997	−	0.800203i	0.537063	−	0.843542i	$-0.319534\pi$
$7$	−3.23398	−	5.60142i	−0.461997	−	0.800203i	−0.999060	+	0.0433393i	$0.986200\pi$
$8$		0			0
$9$	−7.64732	−	4.74536i	−0.849703	−	0.527262i
$10$		0			0
$11$	−9.24701	+	5.33876i	−0.840637	+	0.485342i	−0.857481	−	0.514516i	$-0.827972\pi$
$11$	−9.24701	+	5.33876i	−0.840637	+	0.485342i	0.0168436	+	0.999858i	$0.494638\pi$
$12$		0			0
$13$	−5.53374	+	9.58473i	−0.425673	+	0.737287i	−0.996483	−	0.0837952i	$-0.973296\pi$
$13$	−5.53374	+	9.58473i	−0.425673	+	0.737287i	0.570810	+	0.821082i	$0.306629\pi$
$14$		0			0
$15$	4.81818	−	4.66746i	0.321212	−	0.311164i
$16$		0			0
$17$		−	12.6328i		−	0.743103i	−0.928412	−	0.371552i	$-0.878826\pi$
$17$		−	12.6328i		−	0.743103i	0.928412	−	0.371552i	$-0.121174\pi$
$18$		0			0
$19$	32.1403			1.69159			0.845797	−	0.533505i	$-0.179125\pi$
$19$	32.1403			1.69159			0.845797	+	0.533505i	$0.179125\pi$
$20$		0			0
$21$	18.8201	−	4.72368i	0.896197	−	0.224937i
$22$		0			0
$23$	9.82266	+	5.67112i	0.427072	+	0.246570i	0.698099	−	0.716002i	$-0.254030\pi$
$23$	9.82266	+	5.67112i	0.427072	+	0.246570i	−0.271026	+	0.962572i	$0.587363\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$		0			0
$27$	19.9799	−	18.1605i	0.739995	−	0.672612i
$28$		0			0
$29$	35.2234	−	20.3362i	1.21460	−	0.701249i	0.250841	−	0.968028i	$-0.419293\pi$
$29$	35.2234	−	20.3362i	1.21460	−	0.701249i	0.963758	+	0.266779i	$0.0859594\pi$
$30$		0			0
$31$	−15.9429	+	27.6139i	−0.514286	+	0.890770i	0.485576	+	0.874194i	$0.338610\pi$
$31$	−15.9429	+	27.6139i	−0.514286	+	0.890770i	−0.999863	+	0.0165759i	$0.994723\pi$
$32$		0			0
$33$	−7.79801	−	31.0689i	−0.236303	−	0.941482i
$34$		0			0
$35$			14.4628i			0.413223i
$36$		0			0
$37$	45.4499			1.22837			0.614187	−	0.789160i	$-0.289484\pi$
$37$	45.4499			1.22837			0.614187	+	0.789160i	$0.289484\pi$
$38$		0			0
$39$	−23.1017	−	23.8477i	−0.592352	−	0.611480i
$40$		0			0
$41$	−25.4781	−	14.7098i	−0.621418	−	0.358776i	0.156003	−	0.987757i	$-0.450139\pi$
$41$	−25.4781	−	14.7098i	−0.621418	−	0.358776i	−0.777421	+	0.628981i	$0.783472\pi$
$42$		0			0
$43$	−18.8093	−	32.5786i	−0.437424	−	0.757641i	0.560066	−	0.828448i	$-0.310776\pi$
$43$	−18.8093	−	32.5786i	−0.437424	−	0.757641i	−0.997490	+	0.0708069i	$0.977443\pi$
$44$		0			0
$45$	9.50350	+	17.7393i	0.211189	+	0.394207i
$46$		0			0
$47$	49.8119	−	28.7589i	1.05983	−	0.611892i	0.134443	−	0.990921i	$-0.457075\pi$
$47$	49.8119	−	28.7589i	1.05983	−	0.611892i	0.925385	+	0.379029i	$0.123742\pi$
$48$		0			0
$49$	3.58274	−	6.20548i	0.0731171	−	0.126642i
$50$		0			0
$51$	36.4465	+	10.3891i	0.714636	+	0.203709i
$52$		0			0
$53$			33.3940i			0.630075i	0.949079	+	0.315038i	$0.102017\pi$
$53$			33.3940i			0.630075i	−0.949079	+	0.315038i	$0.897983\pi$
$54$		0			0
$55$	23.8757			0.434103
$56$		0			0
$57$	−26.4321	+	92.7272i	−0.463721	+	1.62679i
$58$		0			0
$59$	−3.54909	−	2.04907i	−0.0601541	−	0.0347300i	0.469621	−	0.882868i	$-0.344390\pi$
$59$	−3.54909	−	2.04907i	−0.0601541	−	0.0347300i	−0.529775	+	0.848138i	$0.677724\pi$
$60$		0			0
$61$	33.1195	+	57.3647i	0.542943	+	0.940404i	0.998733	+	0.0503172i	$0.0160232\pi$
$61$	33.1195	+	57.3647i	0.542943	+	0.940404i	−0.455791	+	0.890087i	$0.650643\pi$
$62$		0			0
$63$	−1.84945	+	58.1823i	−0.0293564	+	0.923528i
$64$		0			0
$65$	21.4321	−	12.3738i	0.329725	−	0.190367i
$66$		0			0
$67$	35.4890	−	61.4687i	0.529686	−	0.917444i	−0.469714	−	0.882819i	$-0.655643\pi$
$67$	35.4890	−	61.4687i	0.529686	−	0.917444i	0.999400	−	0.0346251i	$-0.0110237\pi$
$68$		0			0
$69$	−24.4397	+	23.6752i	−0.354199	+	0.343119i
$70$		0			0
$71$			13.1123i			0.184680i	0.995728	+	0.0923400i	$0.0294347\pi$
$71$			13.1123i			0.184680i	−0.995728	+	0.0923400i	$0.970565\pi$
$72$		0			0
$73$	109.273			1.49688			0.748442	−	0.663200i	$-0.230802\pi$
$73$	109.273			1.49688			0.748442	+	0.663200i	$0.230802\pi$
$74$		0			0
$75$	−14.5487	+	3.65160i	−0.193983	+	0.0486880i
$76$		0			0
$77$	59.8093	+	34.5309i	0.776744	+	0.448453i
$78$		0			0
$79$	49.8891	+	86.4104i	0.631507	+	1.09380i	0.987244	+	0.159217i	$0.0508968\pi$
$79$	49.8891	+	86.4104i	0.631507	+	1.09380i	−0.355736	+	0.934586i	$0.615770\pi$
$80$		0			0
$81$	35.9631	+	72.5786i	0.443989	+	0.896032i
$82$		0			0
$83$	−74.2472	+	42.8667i	−0.894545	+	0.516466i	−0.875426	−	0.483351i	$-0.839419\pi$
$83$	−74.2472	+	42.8667i	−0.894545	+	0.516466i	−0.0191187	+	0.999817i	$0.506086\pi$
$84$		0			0
$85$	−14.1238	+	24.4632i	−0.166163	+	0.287803i
$86$		0			0
$87$	29.7039	+	118.347i	0.341424	+	1.36031i
$88$		0			0
$89$		−	63.6372i		−	0.715025i	−0.933908	−	0.357513i	$-0.883625\pi$
$89$		−	63.6372i		−	0.715025i	0.933908	−	0.357513i	$-0.116375\pi$
$90$		0			0
$91$	71.5841			0.786638
$92$		0			0
$93$	−66.5567	−	68.7060i	−0.715664	−	0.738774i
$94$		0			0
$95$	−62.2394	−	35.9339i	−0.655152	−	0.378252i
$96$		0			0
$97$	−43.2064	−	74.8357i	−0.445427	−	0.771503i	0.552655	−	0.833410i	$-0.313615\pi$
$97$	−43.2064	−	74.8357i	−0.445427	−	0.771503i	−0.998082	+	0.0619078i	$0.980282\pi$
$98$		0			0
$99$	96.0492	+	3.05314i	0.970194	+	0.0308398i
$100$		0			0
$101$	−38.1796	+	22.0430i	−0.378015	+	0.218247i	−0.676954	−	0.736025i	$-0.736701\pi$
$101$	−38.1796	+	22.0430i	−0.378015	+	0.218247i	0.298939	+	0.954272i	$0.403367\pi$
$102$		0			0
$103$	46.9358	−	81.2952i	0.455688	−	0.789274i	−0.543040	−	0.839707i	$-0.682727\pi$
$103$	46.9358	−	81.2952i	0.455688	−	0.789274i	0.998727	+	0.0504329i	$0.0160601\pi$
$104$		0			0
$105$	−41.7263	−	11.8942i	−0.397393	−	0.113278i
$106$		0			0
$107$		−	138.518i		−	1.29456i	−0.762252	−	0.647280i	$-0.775906\pi$
$107$		−	138.518i		−	1.29456i	0.762252	−	0.647280i	$-0.224094\pi$
$108$		0			0
$109$	176.733			1.62140			0.810700	−	0.585461i	$-0.199087\pi$
$109$	176.733			1.62140			0.810700	+	0.585461i	$0.199087\pi$
$110$		0			0
$111$	−37.3779	+	131.126i	−0.336738	+	1.18132i
$112$		0			0
$113$	−76.8430	−	44.3653i	−0.680026	−	0.392613i	0.119839	−	0.992793i	$-0.461762\pi$
$113$	−76.8430	−	44.3653i	−0.680026	−	0.392613i	−0.799865	+	0.600180i	$0.795096\pi$
$114$		0			0
$115$	−12.6810	−	21.9641i	−0.110270	−	0.190992i
$116$		0			0
$117$	87.8013	−	47.0379i	0.750439	−	0.402033i
$118$		0			0
$119$	−70.7613	+	40.8541i	−0.594633	+	0.343312i
$120$		0			0
$121$	−3.49522	+	6.05390i	−0.0288861	+	0.0500323i
$122$		0			0
$123$	63.3921	−	61.4090i	0.515383	−	0.499260i
$124$		0			0
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−92.0203			−0.724569			−0.362285	−	0.932068i	$-0.618003\pi$
$127$	−92.0203			−0.724569			−0.362285	+	0.932068i	$0.618003\pi$
$128$		0			0
$129$	109.460	−	27.4736i	0.848530	−	0.212973i
$130$		0			0
$131$	138.979	+	80.2398i	1.06091	+	0.612518i	0.925684	−	0.378297i	$-0.123490\pi$
$131$	138.979	+	80.2398i	1.06091	+	0.612518i	0.135228	+	0.990815i	$0.456823\pi$
$132$		0			0
$133$	−103.941	−	180.031i	−0.781512	−	1.35362i
$134$		0			0
$135$	−58.9949	+	12.8296i	−0.437000	+	0.0950337i
$136$		0			0
$137$	−78.6907	+	45.4321i	−0.574385	+	0.331621i	−0.758899	−	0.651209i	$-0.774262\pi$
$137$	−78.6907	+	45.4321i	−0.574385	+	0.331621i	0.184514	+	0.982830i	$0.440929\pi$
$138$		0			0
$139$	−32.4865	+	56.2682i	−0.233716	+	0.404807i	−0.958899	−	0.283749i	$-0.908422\pi$
$139$	−32.4865	+	56.2682i	−0.233716	+	0.404807i	0.725183	+	0.688556i	$0.241755\pi$
$140$		0			0
$141$	42.0065	+	167.362i	0.297918	+	1.18697i
$142$		0			0
$143$		−	118.173i		−	0.826387i
$144$		0			0
$145$	−90.9464			−0.627216
$146$		0			0
$147$	14.9568	+	15.4398i	0.101747	+	0.105033i
$148$		0			0
$149$	−124.965	−	72.1483i	−0.838688	−	0.484217i	0.0181301	−	0.999836i	$-0.494229\pi$
$149$	−124.965	−	72.1483i	−0.838688	−	0.484217i	−0.856818	+	0.515619i	$0.827562\pi$
$150$		0			0
$151$	68.3876	+	118.451i	0.452898	+	0.784442i	0.998565	−	0.0535600i	$-0.0170568\pi$
$151$	68.3876	+	118.451i	0.452898	+	0.784442i	−0.545667	+	0.838002i	$0.683724\pi$
$152$		0			0
$153$	−59.9470	+	96.6068i	−0.391810	+	0.631417i
$154$		0			0
$155$	61.7465	−	35.6494i	0.398365	−	0.229996i
$156$		0			0
$157$	26.0965	−	45.2004i	0.166220	−	0.287901i	−0.770868	−	0.636995i	$-0.780177\pi$
$157$	26.0965	−	45.2004i	0.166220	−	0.287901i	0.937088	+	0.349094i	$0.113511\pi$
$158$		0			0
$159$	−96.3442	−	27.4631i	−0.605938	−	0.172724i
$160$		0			0
$161$		−	73.3611i		−	0.455659i
$162$		0			0
$163$	103.226			0.633287			0.316643	−	0.948545i	$-0.397444\pi$
$163$	103.226			0.633287			0.316643	+	0.948545i	$0.397444\pi$
$164$		0			0
$165$	−19.6353	+	68.8831i	−0.119002	+	0.417473i
$166$		0			0
$167$	−97.7044	−	56.4096i	−0.585056	−	0.337782i	0.178084	−	0.984015i	$-0.443010\pi$
$167$	−97.7044	−	56.4096i	−0.585056	−	0.337782i	−0.763140	+	0.646233i	$0.776343\pi$
$168$		0			0
$169$	23.2553	+	40.2794i	0.137606	+	0.238340i
$170$		0			0
$171$	−245.787	−	152.517i	−1.43735	−	0.891914i
$172$		0			0
$173$	113.723	−	65.6580i	0.657359	−	0.379526i	−0.133911	−	0.990993i	$-0.542754\pi$
$173$	113.723	−	65.6580i	0.657359	−	0.379526i	0.791270	+	0.611467i	$0.209420\pi$
$174$		0			0
$175$	16.1699	−	28.0071i	0.0923995	−	0.160041i
$176$		0			0
$177$	8.83049	−	8.55425i	0.0498898	−	0.0483291i
$178$		0			0
$179$		−	297.076i		−	1.65964i	−0.558028	−	0.829822i	$-0.688442\pi$
$179$		−	297.076i		−	1.65964i	0.558028	−	0.829822i	$-0.311558\pi$
$180$		0			0
$181$	28.1168			0.155342			0.0776708	−	0.996979i	$-0.475252\pi$
$181$	28.1168			0.155342			0.0776708	+	0.996979i	$0.475252\pi$
$182$		0			0
$183$	−192.739	+	48.3757i	−1.05322	+	0.264348i
$184$		0			0
$185$	−88.0133	−	50.8145i	−0.475748	−	0.274673i
$186$		0			0
$187$	67.4433	+	116.815i	0.360659	+	0.624680i
$188$		0			0
$189$	−166.339	−	53.1848i	−0.880102	−	0.281401i
$190$		0			0
$191$	−7.94176	+	4.58518i	−0.0415799	+	0.0240062i	−0.520646	−	0.853773i	$-0.674309\pi$
$191$	−7.94176	+	4.58518i	−0.0415799	+	0.0240062i	0.479066	+	0.877779i	$0.340975\pi$
$192$		0			0
$193$	−47.3830	+	82.0697i	−0.245508	+	0.425232i	−0.962274	−	0.272082i	$-0.912288\pi$
$193$	−47.3830	+	82.0697i	−0.245508	+	0.425232i	0.716767	+	0.697313i	$0.245621\pi$
$194$		0			0
$195$	18.0737	+	72.0094i	0.0926857	+	0.369279i
$196$		0			0
$197$		−	267.330i		−	1.35701i	−0.734597	−	0.678504i	$-0.762629\pi$
$197$		−	267.330i		−	1.35701i	0.734597	−	0.678504i	$-0.237371\pi$
$198$		0			0
$199$	158.327			0.795615			0.397808	−	0.917469i	$-0.369771\pi$
$199$	158.327			0.795615			0.397808	+	0.917469i	$0.369771\pi$
$200$		0			0
$201$	148.156	+	152.940i	0.737094	+	0.760896i
$202$		0			0
$203$	−227.823	−	131.534i	−1.12228	−	0.647950i
$204$		0			0
$205$	32.8921	+	56.9708i	0.160449	+	0.277907i
$206$		0			0
$207$	−48.2056	−	89.9809i	−0.232877	−	0.434690i
$208$		0			0
$209$	−297.202	+	171.589i	−1.42202	+	0.821002i
$210$		0			0
$211$	158.786	−	275.026i	0.752542	−	1.30344i	−0.194045	−	0.980993i	$-0.562161\pi$
$211$	158.786	−	275.026i	0.752542	−	1.30344i	0.946587	−	0.322448i	$-0.104506\pi$
$212$		0			0
$213$	−37.8299	−	10.7835i	−0.177605	−	0.0506268i
$214$		0			0
$215$			84.1175i			0.391244i
$216$		0			0
$217$	206.236			0.950396
$218$		0			0
$219$	−89.8656	+	315.260i	−0.410345	+	1.43954i
$220$		0			0
$221$	121.081	+	69.9064i	0.547880	+	0.316319i
$222$		0			0
$223$	−61.9955	−	107.379i	−0.278007	−	0.481522i	0.692883	−	0.721050i	$-0.256340\pi$
$223$	−61.9955	−	107.379i	−0.278007	−	0.481522i	−0.970889	+	0.239529i	$0.923007\pi$
$224$		0			0
$225$	1.42970	−	44.9773i	0.00635424	−	0.199899i
$226$		0			0
$227$	188.341	−	108.739i	0.829695	−	0.479025i	−0.0240532	−	0.999711i	$-0.507657\pi$
$227$	188.341	−	108.739i	0.829695	−	0.479025i	0.853748	+	0.520686i	$0.174324\pi$
$228$		0			0
$229$	−37.4773	+	64.9126i	−0.163656	+	0.283461i	−0.936177	−	0.351528i	$-0.885662\pi$
$229$	−37.4773	+	64.9126i	−0.163656	+	0.283461i	0.772521	+	0.634989i	$0.218995\pi$
$230$		0			0
$231$	−148.811	+	144.156i	−0.644205	+	0.624053i
$232$		0			0
$233$		−	142.781i		−	0.612792i	−0.951904	−	0.306396i	$-0.900877\pi$
$233$		−	142.781i		−	0.612792i	0.951904	−	0.306396i	$-0.0991232\pi$
$234$		0			0
$235$	−128.614			−0.547293
$236$		0			0
$237$	−290.329	+	72.8700i	−1.22502	+	0.307469i
$238$		0			0
$239$	−173.362	−	100.090i	−0.725363	−	0.418789i	0.0913604	−	0.995818i	$-0.470878\pi$
$239$	−173.362	−	100.090i	−0.725363	−	0.418789i	−0.816723	+	0.577029i	$0.804212\pi$
$240$		0			0
$241$	−96.9600	−	167.940i	−0.402324	−	0.696845i	0.591682	−	0.806171i	$-0.298464\pi$
$241$	−96.9600	−	167.940i	−0.402324	−	0.696845i	−0.994006	+	0.109326i	$0.965131\pi$
$242$		0			0
$243$	−238.971	+	44.0678i	−0.983419	+	0.181349i
$244$		0			0
$245$	−13.8759	+	8.01124i	−0.0566362	+	0.0326989i
$246$		0			0
$247$	−177.856	+	308.056i	−0.720065	+	1.24719i
$248$		0			0
$249$	−62.6128	−	249.462i	−0.251457	−	1.00186i
$250$		0			0
$251$			301.288i			1.20035i	0.799868	+	0.600176i	$0.204903\pi$
$251$			301.288i			1.20035i	−0.799868	+	0.600176i	$0.795097\pi$
$252$		0			0
$253$	−121.107			−0.478684
$254$		0			0
$255$	−58.9628	−	60.8669i	−0.231227	−	0.238694i
$256$		0			0
$257$	181.874	+	105.005i	0.707679	+	0.408579i	0.810201	−	0.586152i	$-0.199358\pi$
$257$	181.874	+	105.005i	0.707679	+	0.408579i	−0.102522	+	0.994731i	$0.532691\pi$
$258$		0			0
$259$	−146.984	−	254.584i	−0.567506	−	0.982949i
$260$		0			0
$261$	−365.867	−	11.6299i	−1.40179	−	0.0445591i
$262$		0			0
$263$	−131.132	+	75.7092i	−0.498601	+	0.287868i	−0.728136	−	0.685433i	$-0.759613\pi$
$263$	−131.132	+	75.7092i	−0.498601	+	0.287868i	0.229534	+	0.973301i	$0.426280\pi$
$264$		0			0
$265$	37.3356	−	64.6672i	0.140889	−	0.244027i
$266$		0			0
$267$	183.598	+	52.3351i	0.687634	+	0.196012i
$268$		0			0
$269$			411.264i			1.52886i	0.644706	+	0.764431i	$0.276980\pi$
$269$			411.264i			1.52886i	−0.644706	+	0.764431i	$0.723020\pi$
$270$		0			0
$271$	255.156			0.941534			0.470767	−	0.882257i	$-0.343977\pi$
$271$	255.156			0.941534			0.470767	+	0.882257i	$0.343977\pi$
$272$		0			0
$273$	−58.8706	+	206.526i	−0.215643	+	0.756504i
$274$		0			0
$275$	−46.2350	−	26.6938i	−0.168127	−	0.0970684i
$276$		0			0
$277$	92.7798	+	160.699i	0.334945	+	0.580142i	0.983474	−	0.181048i	$-0.0579488\pi$
$277$	92.7798	+	160.699i	0.334945	+	0.580142i	−0.648529	+	0.761190i	$0.724615\pi$
$278$		0			0
$279$	252.958	−	135.518i	0.906660	−	0.485726i
$280$		0			0
$281$	90.1892	−	52.0708i	0.320958	−	0.185305i	−0.330862	−	0.943679i	$-0.607339\pi$
$281$	90.1892	−	52.0708i	0.320958	−	0.185305i	0.651820	+	0.758374i	$0.274006\pi$
$282$		0			0
$283$	−25.9282	+	44.9089i	−0.0916189	+	0.158689i	−0.908192	−	0.418553i	$-0.862537\pi$
$283$	−25.9282	+	44.9089i	−0.0916189	+	0.158689i	0.816574	+	0.577241i	$0.195871\pi$
$284$		0			0
$285$	154.858	−	150.013i	0.543360	−	0.526363i
$286$		0			0
$287$			190.285i			0.663014i
$288$		0			0
$289$	129.414			0.447798
$290$		0			0
$291$	251.440	−	63.1091i	0.864054	−	0.216870i
$292$		0			0
$293$	−287.235	−	165.835i	−0.980323	−	0.565990i	−0.0779553	−	0.996957i	$-0.524839\pi$
$293$	−287.235	−	165.835i	−0.980323	−	0.565990i	−0.902368	+	0.430967i	$0.858172\pi$
$294$		0			0
$295$	4.58186	+	7.93602i	0.0155317	+	0.0269017i
$296$		0			0
$297$	−87.7992	+	274.598i	−0.295620	+	0.924574i
$298$		0			0
$299$	−108.712	+	62.7650i	−0.363586	+	0.209916i
$300$		0			0
$301$	−121.658	+	210.717i	−0.404178	+	0.700057i
$302$		0			0
$303$	−32.1969	−	128.279i	−0.106260	−	0.423363i
$304$		0			0
$305$		−	148.115i		−	0.485623i
$306$		0			0
$307$	292.274			0.952031			0.476016	−	0.879437i	$-0.342081\pi$
$307$	292.274			0.952031			0.476016	+	0.879437i	$0.342081\pi$
$308$		0			0
$309$	195.943	+	202.270i	0.634120	+	0.654597i
$310$		0			0
$311$	−171.292	−	98.8956i	−0.550779	−	0.317992i	0.198657	−	0.980069i	$-0.436342\pi$
$311$	−171.292	−	98.8956i	−0.550779	−	0.317992i	−0.749436	+	0.662077i	$0.769675\pi$
$312$		0			0
$313$	−107.849	−	186.800i	−0.344565	−	0.596804i	0.640710	−	0.767783i	$-0.278640\pi$
$313$	−107.849	−	186.800i	−0.344565	−	0.596804i	−0.985275	+	0.170979i	$0.945307\pi$
$314$		0			0
$315$	68.6312	−	110.602i	0.217877	−	0.351117i
$316$		0			0
$317$	−176.354	+	101.818i	−0.556321	+	0.321192i	−0.751668	−	0.659542i	$-0.770750\pi$
$317$	−176.354	+	101.818i	−0.556321	+	0.321192i	0.195346	+	0.980734i	$0.437417\pi$
$318$		0			0
$319$	−217.141	+	376.098i	−0.680691	+	1.17899i
$320$		0			0
$321$	399.635	+	113.917i	1.24497	+	0.354881i
$322$		0			0
$323$		−	406.020i		−	1.25703i
$324$		0			0
$325$	−55.3374			−0.170269
$326$		0			0
$327$	−145.345	+	509.887i	−0.444479	+	1.55929i
$328$		0			0
$329$	−322.182	−	186.012i	−0.979275	−	0.565385i
$330$		0			0
$331$	47.0115	+	81.4264i	0.142029	+	0.246001i	0.928260	−	0.371931i	$-0.121304\pi$
$331$	47.0115	+	81.4264i	0.142029	+	0.246001i	−0.786232	+	0.617932i	$0.787971\pi$
$332$		0			0
$333$	−347.570	−	215.676i	−1.04375	−	0.647676i
$334$		0			0
$335$	−137.448	+	79.3558i	−0.410293	+	0.236883i
$336$		0			0
$337$	168.068	−	291.103i	0.498719	−	0.863807i	−0.501280	−	0.865285i	$-0.667137\pi$
$337$	168.068	−	291.103i	0.498719	−	0.863807i	0.999999	+	0.00147845i	$0.000470606\pi$
$338$		0			0
$339$	191.193	−	185.212i	0.563990	−	0.546348i
$340$		0			0
$341$		−	340.461i		−	0.998419i
$342$		0			0
$343$	−363.276			−1.05911
$344$		0			0
$345$	73.7970	−	18.5224i	0.213904	−	0.0536881i
$346$		0			0
$347$	−54.1469	−	31.2617i	−0.156043	−	0.0900914i	0.419945	−	0.907549i	$-0.362049\pi$
$347$	−54.1469	−	31.2617i	−0.156043	−	0.0900914i	−0.575988	+	0.817458i	$0.695383\pi$
$348$		0			0
$349$	160.475	+	277.951i	0.459815	+	0.796422i	0.998951	−	0.0457962i	$-0.0145825\pi$
$349$	160.475	+	277.951i	0.459815	+	0.796422i	−0.539136	+	0.842219i	$0.681249\pi$
$350$		0			0
$351$	63.5003	+	291.997i	0.180912	+	0.831901i
$352$		0			0
$353$	−143.945	+	83.1067i	−0.407776	+	0.235430i	−0.689834	−	0.723968i	$-0.742316\pi$
$353$	−143.945	+	83.1067i	−0.407776	+	0.235430i	0.282058	+	0.959397i	$0.408983\pi$
$354$		0			0
$355$	14.6600	−	25.3918i	0.0412957	−	0.0715263i
$356$		0			0
$357$	−59.6731	−	237.750i	−0.167152	−	0.665967i
$358$		0			0
$359$			199.670i			0.556183i	0.960555	+	0.278091i	$0.0897018\pi$
$359$			199.670i			0.556183i	−0.960555	+	0.278091i	$0.910298\pi$
$360$		0			0
$361$	671.998			1.86149
$362$		0			0
$363$	−14.5915	−	15.0627i	−0.0401970	−	0.0414950i
$364$		0			0
$365$	−211.605	−	122.170i	−0.579741	−	0.334714i
$366$		0			0
$367$	−80.3209	−	139.120i	−0.218858	−	0.379073i	0.735601	−	0.677415i	$-0.236900\pi$
$367$	−80.3209	−	139.120i	−0.218858	−	0.379073i	−0.954459	+	0.298342i	$0.903567\pi$
$368$		0			0
$369$	125.036	+	233.394i	0.338852	+	0.632503i
$370$		0			0
$371$	187.054	−	107.996i	0.504188	−	0.291093i
$372$		0			0
$373$	85.6188	−	148.296i	0.229541	−	0.397577i	−0.728131	−	0.685438i	$-0.759611\pi$
$373$	85.6188	−	148.296i	0.229541	−	0.397577i	0.957672	+	0.287861i	$0.0929442\pi$
$374$		0			0
$375$	32.2561	+	9.19469i	0.0860163	+	0.0245192i
$376$		0			0
$377$			450.142i			1.19401i
$378$		0			0
$379$	297.486			0.784922			0.392461	−	0.919769i	$-0.371624\pi$
$379$	297.486			0.784922			0.392461	+	0.919769i	$0.371624\pi$
$380$		0			0
$381$	75.6773	−	265.485i	0.198628	−	0.696812i
$382$		0			0
$383$	416.340	+	240.374i	1.08705	+	0.627608i	0.932789	−	0.360423i	$-0.117368\pi$
$383$	416.340	+	240.374i	1.08705	+	0.627608i	0.154259	+	0.988030i	$0.450701\pi$
$384$		0			0
$385$	−77.2135	−	133.738i	−0.200554	−	0.347371i
$386$		0			0
$387$	−10.7567	+	338.396i	−0.0277950	+	0.874407i
$388$		0			0
$389$	514.801	−	297.220i	1.32340	−	0.764062i	0.339126	−	0.940741i	$-0.389869\pi$
$389$	514.801	−	297.220i	1.32340	−	0.764062i	0.984269	+	0.176678i	$0.0565352\pi$
$390$		0			0
$391$	71.6418	−	124.087i	0.183227	−	0.317359i
$392$		0			0
$393$	−345.794	+	334.977i	−0.879884	+	0.852359i
$394$		0			0
$395$		−	223.111i		−	0.564837i
$396$		0			0
$397$	−106.303			−0.267765			−0.133883	−	0.990997i	$-0.542745\pi$
$397$	−106.303			−0.267765			−0.133883	+	0.990997i	$0.542745\pi$
$398$		0			0
$399$	604.885	−	151.821i	1.51600	−	0.380503i
$400$		0			0
$401$	−26.3207	−	15.1963i	−0.0656376	−	0.0378959i	0.466822	−	0.884351i	$-0.345399\pi$
$401$	−26.3207	−	15.1963i	−0.0656376	−	0.0378959i	−0.532460	+	0.846455i	$0.678732\pi$
$402$		0			0
$403$	−176.448	−	305.616i	−0.437835	−	0.758353i
$404$		0			0
$405$	11.5031	−	180.756i	0.0284027	−	0.446311i
$406$		0			0
$407$	−420.275	+	242.646i	−1.03262	+	0.596182i
$408$		0			0
$409$	−36.7195	+	63.6000i	−0.0897787	+	0.155501i	−0.907418	−	0.420230i	$-0.861949\pi$
$409$	−36.7195	+	63.6000i	−0.0897787	+	0.155501i	0.817639	+	0.575732i	$0.195283\pi$
$410$		0			0
$411$	−66.3600	−	264.392i	−0.161460	−	0.643290i
$412$		0			0
$413$			26.5066i			0.0641807i
$414$		0			0
$415$	191.706			0.461941
$416$		0			0
$417$	−135.621	−	140.001i	−0.325231	−	0.335733i
$418$		0			0
$419$	−144.551	−	83.4568i	−0.344992	−	0.199181i	0.317486	−	0.948263i	$-0.397162\pi$
$419$	−144.551	−	83.4568i	−0.344992	−	0.199181i	−0.662477	+	0.749082i	$0.730495\pi$
$420$		0			0
$421$	152.746	+	264.563i	0.362816	+	0.628416i	0.988423	−	0.151722i	$-0.0484820\pi$
$421$	152.746	+	264.563i	0.362816	+	0.628416i	−0.625607	+	0.780138i	$0.715149\pi$
$422$		0			0
$423$	−517.399	−	16.4467i	−1.22317	−	0.0388811i
$424$		0			0
$425$	54.7014	−	31.5819i	0.128709	−	0.0743103i
$426$		0			0
$427$	214.216	−	371.032i	0.501676	−	0.868928i
$428$		0			0
$429$	340.939	+	97.1856i	0.794730	+	0.226540i
$430$		0			0
$431$			221.026i			0.512820i	0.966568	+	0.256410i	$0.0825398\pi$
$431$			221.026i			0.512820i	−0.966568	+	0.256410i	$0.917460\pi$
$432$		0			0
$433$	194.055			0.448164			0.224082	−	0.974570i	$-0.428062\pi$
$433$	194.055			0.448164			0.224082	+	0.974570i	$0.428062\pi$
$434$		0			0
$435$	74.7941	−	262.387i	0.171940	−	0.603189i
$436$		0			0
$437$	315.703	+	182.271i	0.722433	+	0.417097i
$438$		0			0
$439$	−77.3450	−	133.965i	−0.176184	−	0.305160i	0.764386	−	0.644759i	$-0.223042\pi$
$439$	−77.3450	−	133.965i	−0.176184	−	0.305160i	−0.940571	+	0.339598i	$0.889709\pi$
$440$		0			0
$441$	−56.8456	+	30.4539i	−0.128902	+	0.0690566i
$442$		0			0
$443$	418.418	−	241.573i	0.944509	−	0.545313i	0.0531381	−	0.998587i	$-0.483078\pi$
$443$	418.418	−	241.573i	0.944509	−	0.545313i	0.891371	+	0.453275i	$0.149744\pi$
$444$		0			0
$445$	−71.1486	+	123.233i	−0.159884	+	0.276928i
$446$		0			0
$447$	310.924	−	301.197i	0.695579	−	0.673820i
$448$		0			0
$449$		−	679.146i		−	1.51257i	−0.654240	−	0.756287i	$-0.727011\pi$
$449$		−	679.146i		−	1.51257i	0.654240	−	0.756287i	$-0.272989\pi$
$450$		0			0
$451$	314.129			0.696516
$452$		0			0
$453$	−397.981	+	99.8897i	−0.878546	+	0.220507i
$454$		0			0
$455$	−138.622	−	80.0335i	−0.304664	−	0.175898i
$456$		0			0
$457$	40.2569	+	69.7270i	0.0880896	+	0.152576i	0.906704	−	0.421768i	$-0.138590\pi$
$457$	40.2569	+	69.7270i	0.0880896	+	0.152576i	−0.818614	+	0.574344i	$0.805257\pi$
$458$		0			0
$459$	−229.418	−	252.401i	−0.499820	−	0.549893i
$460$		0			0
$461$	535.846	−	309.371i	1.16236	−	0.671087i	0.210489	−	0.977596i	$-0.432495\pi$
$461$	535.846	−	309.371i	1.16236	−	0.671087i	0.951868	+	0.306510i	$0.0991612\pi$
$462$		0			0
$463$	164.729	−	285.318i	0.355785	−	0.616238i	−0.631467	−	0.775403i	$-0.717547\pi$
$463$	164.729	−	285.318i	0.355785	−	0.616238i	0.987252	+	0.159165i	$0.0508801\pi$
$464$		0			0
$465$	52.0709	+	207.461i	0.111980	+	0.446153i
$466$		0			0
$467$			216.349i			0.463275i	0.972802	+	0.231637i	$0.0744083\pi$
$467$			216.349i			0.463275i	−0.972802	+	0.231637i	$0.925592\pi$
$468$		0			0
$469$	−459.083			−0.978855
$470$		0			0
$471$	108.945	+	112.463i	0.231306	+	0.238775i
$472$		0			0
$473$	347.859	+	200.836i	0.735430	+	0.424601i
$474$		0			0
$475$	80.3507	+	139.172i	0.169159	+	0.292993i
$476$		0			0
$477$	158.467	−	255.375i	0.332215	−	0.535377i
$478$		0			0
$479$	119.965	−	69.2617i	0.250448	−	0.144596i	−0.369521	−	0.929222i	$-0.620478\pi$
$479$	119.965	−	69.2617i	0.250448	−	0.144596i	0.619970	+	0.784626i	$0.287145\pi$
$480$		0			0
$481$	−251.508	+	435.625i	−0.522886	+	0.905665i
$482$		0			0
$483$	211.652	+	60.3320i	0.438204	+	0.124911i
$484$		0			0
$485$			193.225i			0.398402i
$486$		0			0
$487$	−93.0290			−0.191025			−0.0955123	−	0.995428i	$-0.530449\pi$
$487$	−93.0290			−0.191025			−0.0955123	+	0.995428i	$0.530449\pi$
$488$		0			0
$489$	−84.8927	+	297.814i	−0.173605	+	0.609027i
$490$		0			0
$491$	203.168	+	117.299i	0.413783	+	0.238898i	0.692414	−	0.721501i	$-0.256547\pi$
$491$	203.168	+	117.299i	0.413783	+	0.238898i	−0.278631	+	0.960398i	$0.589881\pi$
$492$		0			0
$493$	−256.902	−	444.968i	−0.521100	−	0.902572i
$494$		0			0
$495$	−182.585	−	113.299i	−0.368859	−	0.228886i
$496$		0			0
$497$	73.4474	−	42.4049i	0.147781	−	0.0853217i
$498$		0			0
$499$	−330.575	+	572.573i	−0.662476	+	1.14744i	0.317487	+	0.948262i	$0.397161\pi$
$499$	−330.575	+	572.573i	−0.662476	+	1.14744i	−0.979963	+	0.199179i	$0.936172\pi$
$500$		0			0
$501$	243.098	−	235.493i	0.485225	−	0.470047i
$502$		0			0
$503$			184.352i			0.366504i	0.983066	+	0.183252i	$0.0586624\pi$
$503$			184.352i			0.366504i	−0.983066	+	0.183252i	$0.941338\pi$
$504$		0			0
$505$	98.5792			0.195206
$506$		0			0
$507$	−135.334	+	33.9677i	−0.266932	+	0.0669974i
$508$		0			0
$509$	702.274	+	405.458i	1.37971	+	0.796578i	0.992125	−	0.125255i	$-0.0399749\pi$
$509$	702.274	+	405.458i	1.37971	+	0.796578i	0.387588	+	0.921833i	$0.373308\pi$
$510$		0			0
$511$	−353.385	−	612.082i	−0.691557	−	1.19781i
$512$		0			0
$513$	642.159	−	583.685i	1.25177	−	1.13779i
$514$		0			0
$515$	−181.782	+	104.952i	−0.352974	+	0.203790i
$516$		0			0
$517$	−307.074	+	531.868i	−0.593954	+	1.02876i
$518$		0			0
$519$	95.9028	+	382.097i	0.184784	+	0.736217i
$520$		0			0
$521$			787.925i			1.51233i	0.654379	+	0.756167i	$0.272930\pi$
$521$			787.925i			1.51233i	−0.654379	+	0.756167i	$0.727070\pi$
$522$		0			0
$523$	−495.806			−0.948004			−0.474002	−	0.880524i	$-0.657191\pi$
$523$	−495.806			−0.948004			−0.474002	+	0.880524i	$0.657191\pi$
$524$		0			0
$525$	67.5045	+	69.6844i	0.128580	+	0.132732i
$526$		0			0
$527$	348.839	+	201.402i	0.661934	+	0.382168i
$528$		0			0
$529$	−200.177	−	346.717i	−0.378406	−	0.655419i
$530$		0			0
$531$	17.4175	+	32.5116i	0.0328013	+	0.0612272i
$532$		0			0
$533$	281.979	−	162.801i	0.529041	−	0.305442i
$534$		0			0
$535$	−154.868	+	268.239i	−0.289472	+	0.501381i
$536$		0			0
$537$	857.088	+	244.315i	1.59607	+	0.454963i
$538$		0			0
$539$			76.5095i			0.141947i
$540$		0			0
$541$	−395.636			−0.731305			−0.365652	−	0.930751i	$-0.619154\pi$
$541$	−395.636			−0.731305			−0.365652	+	0.930751i	$0.619154\pi$
$542$		0			0
$543$	−23.1232	+	81.1192i	−0.0425842	+	0.149391i
$544$		0			0
$545$	−342.241	−	197.593i	−0.627966	−	0.362556i
$546$		0			0
$547$	80.8992	+	140.121i	0.147896	+	0.256164i	0.930450	−	0.366420i	$-0.119417\pi$
$547$	80.8992	+	140.121i	0.147896	+	0.256164i	−0.782554	+	0.622583i	$0.786083\pi$
$548$		0			0
$549$	18.9404	−	595.850i	0.0344999	−	1.08534i
$550$		0			0
$551$	1132.09	−	653.612i	2.05461	−	1.18623i
$552$		0			0
$553$	322.681	−	558.899i	0.583509	−	1.01067i
$554$		0			0
$555$	218.986	−	212.135i	0.394569	−	0.382226i
$556$		0			0
$557$			199.042i			0.357347i	0.983908	+	0.178673i	$0.0571806\pi$
$557$			199.042i			0.357347i	−0.983908	+	0.178673i	$0.942819\pi$
$558$		0			0
$559$	416.342			0.744799
$560$		0			0
$561$	−392.486	+	98.5104i	−0.699618	+	0.175598i
$562$		0			0
$563$	785.990	+	453.792i	1.39608	+	0.806024i	0.993979	−	0.109573i	$-0.0349484\pi$
$563$	785.990	+	453.792i	1.39608	+	0.806024i	0.402096	+	0.915597i	$0.368282\pi$
$564$		0			0
$565$	99.2038	+	171.826i	0.175582	+	0.304117i
$566$		0			0
$567$	290.239	−	436.162i	0.511886	−	0.769246i
$568$		0			0
$569$	−776.399	+	448.254i	−1.36450	+	0.787793i	−0.990219	−	0.139523i	$-0.955443\pi$
$569$	−776.399	+	448.254i	−1.36450	+	0.787793i	−0.374279	+	0.927316i	$0.622110\pi$
$570$		0			0
$571$	−304.808	+	527.943i	−0.533815	+	0.924594i	0.465405	+	0.885098i	$0.345909\pi$
$571$	−304.808	+	527.943i	−0.533815	+	0.924594i	−0.999220	+	0.0394965i	$0.987425\pi$
$572$		0			0
$573$	−6.69729	−	26.6834i	−0.0116881	−	0.0465679i
$574$		0			0
$575$			56.7112i			0.0986281i
$576$		0			0
$577$	477.854			0.828170			0.414085	−	0.910238i	$-0.364102\pi$
$577$	477.854			0.828170			0.414085	+	0.910238i	$0.364102\pi$
$578$		0			0
$579$	−197.810	−	204.197i	−0.341640	−	0.352673i
$580$		0			0
$581$	480.228	+	277.260i	0.826555	+	0.477212i
$582$		0			0
$583$	−178.283	−	308.795i	−0.305802	−	0.529665i
$584$		0			0
$585$	−222.616	−	7.07637i	−0.380541	−	0.0120964i
$586$		0			0
$587$	220.698	−	127.420i	0.375976	−	0.217070i	−0.300090	−	0.953911i	$-0.597017\pi$
$587$	220.698	−	127.420i	0.375976	−	0.217070i	0.676066	+	0.736841i	$0.263683\pi$
$588$		0			0
$589$	−512.409	+	887.518i	−0.869964	+	1.50682i
$590$		0			0
$591$	771.268	+	219.852i	1.30502	+	0.372000i
$592$		0			0
$593$			604.184i			1.01886i	0.860512	+	0.509430i	$0.170144\pi$
$593$			604.184i			1.01886i	−0.860512	+	0.509430i	$0.829856\pi$
$594$		0			0
$595$	182.705			0.307067
$596$		0			0
$597$	−130.208	+	456.787i	−0.218104	+	0.765137i
$598$		0			0
$599$	164.832	+	95.1657i	0.275178	+	0.158874i	0.631239	−	0.775589i	$-0.282547\pi$
$599$	164.832	+	95.1657i	0.275178	+	0.158874i	−0.356060	+	0.934463i	$0.615880\pi$
$600$		0			0
$601$	−468.662	−	811.746i	−0.779804	−	1.35066i	−0.932055	−	0.362318i	$-0.881986\pi$
$601$	−468.662	−	811.746i	−0.779804	−	1.35066i	0.152251	−	0.988342i	$-0.451348\pi$
$602$		0			0
$603$	−563.087	+	301.663i	−0.933809	+	0.500271i
$604$		0			0
$605$	13.5369	−	7.81556i	0.0223751	−	0.0129183i
$606$		0			0
$607$	−483.997	+	838.308i	−0.797360	+	1.38107i	0.123970	+	0.992286i	$0.460437\pi$
$607$	−483.997	+	838.308i	−0.797360	+	1.38107i	−0.921330	+	0.388781i	$0.872896\pi$
$608$		0			0
$609$	566.847	−	549.115i	0.930783	−	0.901666i
$610$		0			0
$611$			636.578i			1.04186i
$612$		0			0
$613$	14.3244			0.0233677			0.0116839	−	0.999932i	$-0.496281\pi$
$613$	14.3244			0.0233677			0.0116839	+	0.999932i	$0.496281\pi$
$614$		0			0
$615$	−191.416	+	48.0436i	−0.311245	+	0.0781197i
$616$		0			0
$617$	−924.580	−	533.807i	−1.49851	−	0.865165i	−0.498511	−	0.866884i	$-0.666119\pi$
$617$	−924.580	−	533.807i	−1.49851	−	0.865165i	−0.999999	+	0.00171906i	$0.999453\pi$
$618$		0			0
$619$	582.166	+	1008.34i	0.940494	+	1.62898i	0.764531	+	0.644586i	$0.222970\pi$
$619$	582.166	+	1008.34i	0.940494	+	1.62898i	0.175963	+	0.984397i	$0.443696\pi$
$620$		0			0
$621$	299.246	−	65.0766i	0.481877	−	0.104793i
$622$		0			0
$623$	−356.459	+	205.802i	−0.572165	+	0.330340i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−250.630	−	998.564i	−0.399730	−	1.59261i
$628$		0			0
$629$		−	574.157i		−	0.912809i
$630$		0			0
$631$	88.9538			0.140973			0.0704864	−	0.997513i	$-0.477545\pi$
$631$	88.9538			0.140973			0.0704864	+	0.997513i	$0.477545\pi$
$632$		0			0
$633$	662.885	+	684.291i	1.04721	+	1.08103i
$634$		0			0
$635$	178.196	+	102.882i	0.280624	+	0.162019i
$636$		0			0
$637$	39.6519	+	68.6791i	0.0622479	+	0.107816i
$638$		0			0
$639$	62.2225	−	100.274i	0.0973748	−	0.156923i
$640$		0			0
$641$	115.362	−	66.6040i	0.179971	−	0.103906i	−0.407308	−	0.913291i	$-0.633532\pi$
$641$	115.362	−	66.6040i	0.179971	−	0.103906i	0.587279	+	0.809384i	$0.300199\pi$
$642$		0			0
$643$	−241.729	+	418.686i	−0.375939	+	0.651145i	−0.990467	−	0.137750i	$-0.956013\pi$
$643$	−241.729	+	418.686i	−0.375939	+	0.651145i	0.614528	+	0.788895i	$0.289346\pi$
$644$		0			0
$645$	−242.685	−	69.1781i	−0.376257	−	0.107253i
$646$		0			0
$647$		−	347.759i		−	0.537495i	−0.963211	−	0.268748i	$-0.913390\pi$
$647$		−	347.759i		−	0.537495i	0.963211	−	0.268748i	$-0.0866097\pi$
$648$		0			0
$649$	43.7580			0.0674237
$650$		0			0
$651$	−169.608	+	595.006i	−0.260534	+	0.913988i
$652$		0			0
$653$	751.488	+	433.872i	1.15082	+	0.664428i	0.949088	−	0.315011i	$-0.102008\pi$
$653$	751.488	+	433.872i	1.15082	+	0.664428i	0.201736	+	0.979440i	$0.435342\pi$
$654$		0			0
$655$	−179.422	−	310.768i	−0.273926	−	0.474454i
$656$		0			0
$657$	−835.643	−	518.538i	−1.27191	−	0.789251i
$658$		0			0
$659$	−804.603	+	464.538i	−1.22095	+	0.704913i	−0.965120	−	0.261810i	$-0.915681\pi$
$659$	−804.603	+	464.538i	−1.22095	+	0.704913i	−0.255826	+	0.966723i	$0.582347\pi$
$660$		0			0
$661$	463.561	−	802.912i	0.701303	−	1.21469i	−0.266706	−	0.963778i	$-0.585935\pi$
$661$	463.561	−	802.912i	0.701303	−	1.21469i	0.968009	−	0.250915i	$-0.0807314\pi$
$662$		0			0
$663$	−301.263	+	291.838i	−0.454393	+	0.440179i
$664$		0			0
$665$			464.839i			0.699005i
$666$		0			0
$667$	461.316			0.691629
$668$		0			0
$669$	360.783	−	90.5531i	0.539286	−	0.135356i
$670$		0			0
$671$	−612.513	−	353.634i	−0.912836	−	0.527026i
$672$		0			0
$673$	−472.996	−	819.253i	−0.702817	−	1.21732i	−0.967473	−	0.252973i	$-0.918592\pi$
$673$	−472.996	−	819.253i	−0.702817	−	1.21732i	0.264656	−	0.964343i	$-0.414742\pi$
$674$		0			0
$675$	128.587	+	41.1140i	0.190499	+	0.0609097i
$676$		0			0
$677$	532.245	−	307.292i	0.786182	−	0.453902i	−0.0524349	−	0.998624i	$-0.516698\pi$
$677$	532.245	−	307.292i	0.786182	−	0.453902i	0.838617	+	0.544722i	$0.183365\pi$
$678$		0			0
$679$	−279.458	+	484.035i	−0.411572	+	0.712864i
$680$		0			0
$681$	158.828	+	632.804i	0.233228	+	0.929227i
$682$		0			0
$683$		−	258.893i		−	0.379053i	−0.981876	−	0.189527i	$-0.939305\pi$
$683$		−	258.893i		−	0.379053i	0.981876	−	0.189527i	$-0.0606954\pi$
$684$		0			0
$685$	203.179			0.296611
$686$		0			0
$687$	−156.456	−	161.509i	−0.227739	−	0.235093i
$688$		0			0
$689$	−320.072	−	184.794i	−0.464546	−	0.268206i
$690$		0			0
$691$	−485.487	−	840.888i	−0.702586	−	1.21691i	−0.967556	−	0.252658i	$-0.918695\pi$
$691$	−485.487	−	840.888i	−0.702586	−	1.21691i	0.264969	−	0.964257i	$-0.414638\pi$
$692$		0			0
$693$	−293.519	−	547.886i	−0.423549	−	0.790600i
$694$		0			0
$695$	125.820	−	72.6420i	0.181035	−	0.104521i
$696$		0			0
$697$	−185.825	+	321.859i	−0.266607	+	0.461778i
$698$		0			0
$699$	411.933	+	117.422i	0.589317	+	0.167986i
$700$		0			0
$701$			718.418i			1.02485i	0.858733	+	0.512424i	$0.171252\pi$
$701$			718.418i			1.02485i	−0.858733	+	0.512424i	$0.828748\pi$
$702$		0			0
$703$	1460.77			2.07791
$704$		0			0
$705$	105.772	−	371.061i	0.150031	−	0.526327i
$706$		0			0
$707$	246.944	+	142.573i	0.349284	+	0.201659i
$708$		0			0
$709$	494.222	+	856.018i	0.697070	+	1.20736i	0.969478	+	0.245178i	$0.0788465\pi$
$709$	494.222	+	856.018i	0.697070	+	1.20736i	−0.272408	+	0.962182i	$0.587820\pi$
$710$		0			0
$711$	28.5307	−	897.550i	0.0401275	−	1.26238i
$712$		0			0
$713$	−313.203	+	180.828i	−0.439275	+	0.253615i
$714$		0			0
$715$	−132.122	+	228.842i	−0.184786	+	0.320058i
$716$		0			0
$717$	431.341	−	417.848i	0.601591	−	0.582772i
$718$		0			0
$719$		−	1280.53i		−	1.78099i	−0.454994	−	0.890495i	$-0.650358\pi$
$719$		−	1280.53i		−	1.78099i	0.454994	−	0.890495i	$-0.349642\pi$
$720$		0			0
$721$	−607.158			−0.842106
$722$		0			0
$723$	564.258	−	141.624i	0.780440	−	0.195883i
$724$		0			0
$725$	176.117	+	101.681i	0.242920	+	0.140250i
$726$		0			0
$727$	−324.824	−	562.611i	−0.446800	−	0.773881i	0.551376	−	0.834257i	$-0.314103\pi$
$727$	−324.824	−	562.611i	−0.446800	−	0.773881i	−0.998176	+	0.0603766i	$0.980770\pi$
$728$		0			0
$729$	69.3901	−	725.690i	0.0951853	−	0.995460i
$730$		0			0
$731$	−411.557	+	237.613i	−0.563006	+	0.325052i
$732$		0			0
$733$	−585.044	+	1013.33i	−0.798150	+	1.38244i	0.122669	+	0.992448i	$0.460855\pi$
$733$	−585.044	+	1013.33i	−0.798150	+	1.38244i	−0.920820	+	0.389989i	$0.872479\pi$
$734$		0			0
$735$	−11.7015	−	46.6214i	−0.0159205	−	0.0634305i
$736$		0			0
$737$			757.869i			1.02832i
$738$		0			0
$739$	−1175.25			−1.59033			−0.795164	−	0.606394i	$-0.792615\pi$
$739$	−1175.25			−1.59033			−0.795164	+	0.606394i	$0.792615\pi$
$740$		0			0
$741$	−742.496	−	766.473i	−1.00202	−	1.03438i
$742$		0			0
$743$	881.124	+	508.717i	1.18590	+	0.684680i	0.957372	−	0.288858i	$-0.0932754\pi$
$743$	881.124	+	508.717i	1.18590	+	0.684680i	0.228528	+	0.973537i	$0.426609\pi$
$744$		0			0
$745$	161.328	+	279.429i	0.216548	+	0.375073i
$746$		0			0
$747$	771.211	+	24.5147i	1.03241	+	0.0328175i
$748$		0			0
$749$	−775.897	+	447.964i	−1.03591	+	0.598083i
$750$		0			0
$751$	−497.229	+	861.226i	−0.662089	+	1.14677i	0.317977	+	0.948099i	$0.396997\pi$
$751$	−497.229	+	861.226i	−0.662089	+	1.14677i	−0.980066	+	0.198673i	$0.936337\pi$
$752$		0			0
$753$	−869.240	−	247.779i	−1.15437	−	0.329056i
$754$		0			0
$755$		−	305.839i		−	0.405084i
$756$		0			0
$757$	−659.088			−0.870658			−0.435329	−	0.900271i	$-0.643368\pi$
$757$	−659.088			−0.870658			−0.435329	+	0.900271i	$0.643368\pi$
$758$		0			0
$759$	99.5981	−	349.403i	0.131223	−	0.460346i
$760$		0			0
$761$	559.677	+	323.130i	0.735450	+	0.424612i	0.820413	−	0.571772i	$-0.193744\pi$
$761$	559.677	+	323.130i	0.735450	+	0.424612i	−0.0849628	+	0.996384i	$0.527077\pi$
$762$		0			0
$763$	−571.550	−	989.954i	−0.749083	−	1.29745i
$764$		0			0
$765$	224.096	−	120.055i	0.292937	−	0.156935i
$766$		0			0
$767$	39.2796	−	22.6781i	0.0512119	−	0.0295672i
$768$		0			0
$769$	123.429	−	213.784i	0.160505	−	0.278003i	−0.774545	−	0.632519i	$-0.782021\pi$
$769$	123.429	−	213.784i	0.160505	−	0.278003i	0.935050	+	0.354516i	$0.115354\pi$
$770$		0			0
$771$	−452.519	+	438.363i	−0.586925	+	0.568565i
$772$		0			0
$773$		−	263.071i		−	0.340325i	−0.985416	−	0.170162i	$-0.945571\pi$
$773$		−	263.071i		−	0.340325i	0.985416	−	0.170162i	$-0.0544292\pi$
$774$		0			0
$775$	−159.429			−0.205715
$776$		0			0
$777$	855.373	−	214.691i	1.10087	−	0.276307i
$778$		0			0
$779$	−818.875	−	472.777i	−1.05119	−	0.606903i
$780$		0			0
$781$	−70.0034	−	121.249i	−0.0896330	−	0.155249i
$782$		0			0
$783$	334.442	−	1045.99i	0.427128	−	1.33588i
$784$		0			0
$785$	−101.071	+	58.3535i	−0.128753	+	0.0743356i
$786$		0			0
$787$	538.388	−	932.515i	0.684102	−	1.18490i	−0.289617	−	0.957143i	$-0.593528\pi$
$787$	538.388	−	932.515i	0.684102	−	1.18490i	0.973718	−	0.227756i	$-0.0731388\pi$
$788$		0			0
$789$	−110.584	−	440.589i	−0.140157	−	0.558415i
$790$		0			0
$791$			573.906i			0.725545i
$792$		0			0
$793$	−733.100			−0.924463
$794$		0			0
$795$	155.865	+	160.898i	0.196057	+	0.202388i
$796$		0			0
$797$	791.487	+	456.965i	0.993082	+	0.573356i	0.906194	−	0.422862i	$-0.138974\pi$
$797$	791.487	+	456.965i	0.993082	+	0.573356i	0.0868882	+	0.996218i	$0.472308\pi$
$798$		0			0
$799$	−363.304	−	629.262i	−0.454699	−	0.787562i
$800$		0			0
$801$	−301.982	+	486.654i	−0.377006	+	0.607559i
$802$		0			0
$803$	−1010.44	+	583.381i	−1.25834	+	0.726501i
$804$		0			0
$805$	−82.0202	+	142.063i	−0.101888	+	0.176476i
$806$		0			0
$807$	−1186.53	−	338.222i	−1.47029	−	0.419111i
$808$		0			0
$809$		−	1008.67i		−	1.24681i	−0.781897	−	0.623407i	$-0.785748\pi$
$809$		−	1008.67i		−	1.24681i	0.781897	−	0.623407i	$-0.214252\pi$
$810$		0			0
$811$	−952.468			−1.17444			−0.587218	−	0.809429i	$-0.699777\pi$
$811$	−952.468			−1.17444			−0.587218	+	0.809429i	$0.699777\pi$
$812$		0			0
$813$	−209.840	+	736.144i	−0.258105	+	0.905466i
$814$		0			0
$815$	−199.896	−	115.410i	−0.245271	−	0.141607i
$816$		0			0
$817$	−604.535	−	1047.08i	−0.739945	−	1.28162i
$818$		0			0
$819$	−547.427	−	339.692i	−0.668409	−	0.414765i
$820$		0			0
$821$	−1222.35	+	705.724i	−1.48885	+	0.859590i	−0.999919	−	0.0127295i	$-0.995948\pi$
$821$	−1222.35	+	705.724i	−1.48885	+	0.859590i	−0.488935	+	0.872320i	$0.662615\pi$
$822$		0			0
$823$	380.867	−	659.680i	0.462778	−	0.801556i	−0.536320	−	0.844015i	$-0.680186\pi$
$823$	380.867	−	659.680i	0.462778	−	0.801556i	0.999098	+	0.0424591i	$0.0135192\pi$
$824$		0			0
$825$	115.037	−	111.439i	0.139439	−	0.135077i
$826$		0			0
$827$			718.144i			0.868373i	0.900823	+	0.434186i	$0.142964\pi$
$827$			718.144i			0.868373i	−0.900823	+	0.434186i	$0.857036\pi$
$828$		0			0
$829$	400.411			0.483005			0.241503	−	0.970400i	$-0.422360\pi$
$829$	400.411			0.483005			0.241503	+	0.970400i	$0.422360\pi$
$830$		0			0
$831$	−539.932	+	135.518i	−0.649738	+	0.163078i
$832$		0			0
$833$	−78.3923	−	45.2598i	−0.0941084	−	0.0543335i
$834$		0			0
$835$	126.136	+	218.474i	0.151061	+	0.261645i
$836$		0			0
$837$	182.946	+	841.253i	0.218574	+	1.00508i
$838$		0			0
$839$	614.302	−	354.667i	0.732183	−	0.422726i	−0.0870370	−	0.996205i	$-0.527740\pi$
$839$	614.302	−	354.667i	0.732183	−	0.422726i	0.819220	+	0.573479i	$0.194407\pi$
$840$		0			0
$841$	406.624	−	704.293i	0.483500	−	0.837447i
$842$		0			0
$843$	76.0567	+	303.026i	0.0902214	+	0.359461i
$844$		0			0
$845$		−	104.001i		−	0.123078i
$846$		0			0
$847$	45.2139			0.0533813
$848$		0			0
$849$	−108.242	−	111.738i	−0.127494	−	0.131611i
$850$		0			0
$851$	446.439	+	257.751i	0.524605	+	0.302881i
$852$		0			0
$853$	−443.113	−	767.495i	−0.519476	−	0.899760i	−0.999744	−	0.0226375i	$-0.992794\pi$
$853$	−443.113	−	767.495i	−0.519476	−	0.899760i	0.480267	−	0.877122i	$-0.340540\pi$
$854$		0			0
$855$	305.445	+	570.147i	0.357246	+	0.666838i
$856$		0			0
$857$	283.635	−	163.757i	0.330963	−	0.191081i	−0.325306	−	0.945609i	$-0.605467\pi$
$857$	283.635	−	163.757i	0.330963	−	0.191081i	0.656268	+	0.754527i	$0.272134\pi$
$858$		0			0
$859$	−35.0835	+	60.7664i	−0.0408423	+	0.0707409i	−0.885724	−	0.464212i	$-0.846337\pi$
$859$	−35.0835	+	60.7664i	−0.0408423	+	0.0707409i	0.844882	+	0.534953i	$0.179671\pi$
$860$		0			0
$861$	−548.987	−	156.490i	−0.637615	−	0.181754i
$862$		0			0
$863$			982.709i			1.13871i	0.822091	+	0.569356i	$0.192807\pi$
$863$			982.709i			1.13871i	−0.822091	+	0.569356i	$0.807193\pi$
$864$		0			0
$865$	−293.632			−0.339459
$866$		0			0
$867$	−106.429	+	373.368i	−0.122756	+	0.430643i
$868$		0			0
$869$	−922.650	−	532.692i	−1.06174	−	0.612994i
$870$		0			0
$871$	392.774	+	680.305i	0.450946	+	0.781062i
$872$		0			0
$873$	−24.7090	+	777.323i	−0.0283035	+	0.890405i
$874$		0			0
$875$	−62.6258	+	36.1570i	−0.0715723	+	0.0413223i
$876$		0			0
$877$	−463.447	+	802.714i	−0.528446	+	0.915296i	0.471004	+	0.882131i	$0.343892\pi$
$877$	−463.447	+	802.714i	−0.528446	+	0.915296i	−0.999450	+	0.0331646i	$0.989441\pi$
$878$		0			0
$879$	714.668	−	692.311i	0.813046	−	0.787612i
$880$		0			0
$881$		−	766.920i		−	0.870510i	−0.900307	−	0.435255i	$-0.856658\pi$
$881$		−	766.920i		−	0.870510i	0.900307	−	0.435255i	$-0.143342\pi$
$882$		0			0
$883$	−1206.08			−1.36589			−0.682946	−	0.730469i	$-0.739301\pi$
$883$	−1206.08			−1.36589			−0.682946	+	0.730469i	$0.739301\pi$
$884$		0			0
$885$	−26.6641	+	6.69245i	−0.0301289	+	0.00756209i
$886$		0			0
$887$	−651.741	−	376.283i	−0.734771	−	0.424220i	0.0853943	−	0.996347i	$-0.472785\pi$
$887$	−651.741	−	376.283i	−0.734771	−	0.424220i	−0.820165	+	0.572127i	$0.806118\pi$
$888$		0			0
$889$	297.592	+	515.444i	0.334749	+	0.579802i
$890$		0			0
$891$	−720.031	−	479.136i	−0.808116	−	0.537751i
$892$		0			0
$893$	1600.97	−	924.320i	1.79280	−	1.03507i
$894$		0			0
$895$	−332.142	+	575.286i	−0.371108	+	0.642778i
$896$		0			0
$897$	−91.6771	−	365.261i	−0.102204	−	0.407203i
$898$		0			0
$899$			1296.87i			1.44257i
$900$		0			0
$901$	421.858			0.468211
$902$		0			0
$903$	−507.884	−	524.284i	−0.562440	−	0.580603i
$904$		0			0
$905$	−54.4480	−	31.4356i	−0.0601635	−	0.0347354i
$906$		0			0
$907$	−177.370	−	307.213i	−0.195556	−	0.338713i	0.751526	−	0.659703i	$-0.229318\pi$
$907$	−177.370	−	307.213i	−0.195556	−	0.338713i	−0.947083	+	0.320989i	$0.895985\pi$
$908$		0			0
$909$	396.573	+	12.6060i	0.436274	+	0.0138680i
$910$		0			0
$911$	−280.940	+	162.201i	−0.308387	+	0.178047i	−0.646204	−	0.763164i	$-0.723645\pi$
$911$	−280.940	+	162.201i	−0.308387	+	0.178047i	0.337818	+	0.941212i	$0.390311\pi$
$912$		0			0
$913$	457.710	−	792.777i	0.501325	−	0.868321i
$914$		0			0
$915$	427.323	+	121.809i	0.467019	+	0.133125i
$916$		0			0
$917$		−	1037.98i		−	1.13193i
$918$		0			0
$919$	604.200			0.657453			0.328727	−	0.944425i	$-0.393381\pi$
$919$	604.200			0.657453			0.328727	+	0.944425i	$0.393381\pi$
$920$		0			0
$921$	−240.365	+	843.232i	−0.260983	+	0.915561i
$922$		0			0
$923$	−125.678	−	72.5600i	−0.136162	−	0.0786133i
$924$		0			0
$925$	113.625	+	196.804i	0.122837	+	0.212761i
$926$		0			0
$927$	−744.709	+	398.964i	−0.803353	+	0.430381i
$928$		0			0
$929$	−1417.48	+	818.384i	−1.52582	+	0.880930i	−0.526285	+	0.850308i	$0.676415\pi$
$929$	−1417.48	+	818.384i	−1.52582	+	0.880930i	−0.999531	+	0.0306220i	$0.990251\pi$
$930$		0			0
$931$	115.150	−	199.446i	0.123684	−	0.214228i
$932$		0			0
$933$	426.192	−	412.859i	0.456797	−	0.442507i
$934$		0			0
$935$		−	301.615i		−	0.322583i
$936$		0			0
$937$	−266.212			−0.284111			−0.142055	−	0.989859i	$-0.545371\pi$
$937$	−266.212			−0.284111			−0.142055	+	0.989859i	$0.545371\pi$
$938$		0			0
$939$	627.626	−	157.528i	0.668398	−	0.167762i
$940$		0			0
$941$	140.374	+	81.0449i	0.149175	+	0.0861264i	0.572730	−	0.819744i	$-0.305884\pi$
$941$	140.374	+	81.0449i	0.149175	+	0.0861264i	−0.423554	+	0.905871i	$0.639218\pi$
$942$		0			0
$943$	−166.842	−	288.979i	−0.176927	−	0.306446i
$944$		0			0
$945$	262.652	+	288.965i	0.277939	+	0.305783i
$946$		0			0
$947$	690.598	−	398.717i	0.729248	−	0.421032i	−0.0888989	−	0.996041i	$-0.528335\pi$
$947$	690.598	−	398.717i	0.729248	−	0.421032i	0.818147	+	0.575009i	$0.195001\pi$
$948$		0			0
$949$	−604.687	+	1047.35i	−0.637183	+	1.10363i
$950$		0			0
$951$	−148.719	−	592.529i	−0.156382	−	0.623059i
$952$		0			0
$953$			1382.90i			1.45110i	0.688168	+	0.725551i	$0.258415\pi$
$953$			1382.90i			1.45110i	−0.688168	+	0.725551i	$0.741585\pi$
$954$		0			0
$955$	20.5055			0.0214718
$956$		0			0
$957$	−906.497	−	935.769i	−0.947227	−	0.977816i
$958$		0			0
$959$	508.969	+	293.853i	0.530729	+	0.306416i
$960$		0			0
$961$	−27.8509	−	48.2391i	−0.0289811	−	0.0501968i
$962$		0			0
$963$	−657.317	+	1059.29i	−0.682573	+	1.09999i
$964$		0			0
$965$	183.513	−	105.952i	0.190169	−	0.109794i
$966$		0			0
$967$	184.756	−	320.006i	0.191061	−	0.330927i	−0.754541	−	0.656252i	$-0.772141\pi$
$967$	184.756	−	320.006i	0.191061	−	0.330927i	0.945602	+	0.325326i	$0.105474\pi$
$968$		0			0
$969$	1171.40	+	333.910i	1.20887	+	0.344593i
$970$		0			0
$971$		−	961.450i		−	0.990165i	−0.868846	−	0.495082i	$-0.835138\pi$
$971$		−	961.450i		−	0.990165i	0.868846	−	0.495082i	$-0.164862\pi$
$972$		0			0
$973$	420.243			0.431904
$974$		0			0
$975$	45.5094	−	159.653i	0.0466763	−	0.163746i
$976$		0			0
$977$	−1487.96	−	859.076i	−1.52299	−	0.879300i	−0.999630	−	0.0271901i	$-0.991344\pi$
$977$	−1487.96	−	859.076i	−1.52299	−	0.879300i	−0.523362	−	0.852110i	$-0.675323\pi$
$978$		0			0
$979$	339.744	+	588.454i	0.347032	+	0.601077i
$980$		0			0
$981$	−1351.53	−	838.660i	−1.37771	−	0.854903i
$982$		0			0
$983$	1109.96	−	640.833i	1.12915	−	0.651915i	0.185430	−	0.982658i	$-0.440632\pi$
$983$	1109.96	−	640.833i	1.12915	−	0.651915i	0.943721	+	0.330742i	$0.107299\pi$
$984$		0			0
$985$	−298.884	+	517.683i	−0.303436	+	0.525567i
$986$		0			0
$987$	801.619	−	776.543i	0.812177	−	0.786771i
$988$		0			0
$989$		−	426.678i		−	0.431423i
$990$		0			0
$991$	−952.926			−0.961581			−0.480790	−	0.876836i	$-0.659650\pi$
$991$	−952.926			−0.961581			−0.480790	+	0.876836i	$0.659650\pi$
$992$		0			0
$993$	−273.583	+	68.6670i	−0.275512	+	0.0691510i
$994$		0			0
$995$	−306.600	−	177.015i	−0.308140	−	0.177905i
$996$		0			0
$997$	−884.833	−	1532.57i	−0.887495	−	1.53719i	−0.842827	−	0.538185i	$-0.819110\pi$
$997$	−884.833	−	1532.57i	−0.887495	−	1.53719i	−0.0446679	−	0.999002i	$-0.514223\pi$
$998$		0			0
$999$	908.082	−	825.394i	0.908991	−	0.826220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.3.bs.c.401.4		16
3.2	odd	2		2160.3.bs.c.881.6		16
4.3	odd	2		45.3.i.a.41.6	yes	16
9.2	odd	6	inner	720.3.bs.c.641.4		16
9.7	even	3		2160.3.bs.c.1601.6		16
12.11	even	2		135.3.i.a.71.3		16
20.3	even	4		225.3.i.b.149.5		32
20.7	even	4		225.3.i.b.149.12		32
20.19	odd	2		225.3.j.b.176.3		16
36.7	odd	6		135.3.i.a.116.3		16
36.11	even	6		45.3.i.a.11.6	✓	16
36.23	even	6		405.3.c.a.161.5		16
36.31	odd	6		405.3.c.a.161.12		16
60.23	odd	4		675.3.i.c.449.12		32
60.47	odd	4		675.3.i.c.449.5		32
60.59	even	2		675.3.j.b.476.6		16
180.7	even	12		675.3.i.c.224.12		32
180.43	even	12		675.3.i.c.224.5		32
180.47	odd	12		225.3.i.b.74.5		32
180.79	odd	6		675.3.j.b.251.6		16
180.83	odd	12		225.3.i.b.74.12		32
180.119	even	6		225.3.j.b.101.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.6	✓	16	36.11	even	6
45.3.i.a.41.6	yes	16	4.3	odd	2
135.3.i.a.71.3		16	12.11	even	2
135.3.i.a.116.3		16	36.7	odd	6
225.3.i.b.74.5		32	180.47	odd	12
225.3.i.b.74.12		32	180.83	odd	12
225.3.i.b.149.5		32	20.3	even	4
225.3.i.b.149.12		32	20.7	even	4
225.3.j.b.101.3		16	180.119	even	6
225.3.j.b.176.3		16	20.19	odd	2
405.3.c.a.161.5		16	36.23	even	6
405.3.c.a.161.12		16	36.31	odd	6
675.3.i.c.224.5		32	180.43	even	12
675.3.i.c.224.12		32	180.7	even	12
675.3.i.c.449.5		32	60.47	odd	4
675.3.i.c.449.12		32	60.23	odd	4
675.3.j.b.251.6		16	180.79	odd	6
675.3.j.b.476.6		16	60.59	even	2
720.3.bs.c.401.4		16	1.1	even	1	trivial
720.3.bs.c.641.4		16	9.2	odd	6	inner
2160.3.bs.c.881.6		16	3.2	odd	2
2160.3.bs.c.1601.6		16	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-0.822398 + 2.88508i) q^{3} +(-1.93649 - 1.11803i) q^{5} +(-3.23398 - 5.60142i) q^{7} +(-7.64732 - 4.74536i) q^{9} +(-9.24701 + 5.33876i) q^{11} +(-5.53374 + 9.58473i) q^{13} +(4.81818 - 4.66746i) q^{15} -12.6328i q^{17} +32.1403 q^{19} +(18.8201 - 4.72368i) q^{21} +(9.82266 + 5.67112i) q^{23} +(2.50000 + 4.33013i) q^{25} +(19.9799 - 18.1605i) q^{27} +(35.2234 - 20.3362i) q^{29} +(-15.9429 + 27.6139i) q^{31} +(-7.79801 - 31.0689i) q^{33} +14.4628i q^{35} +45.4499 q^{37} +(-23.1017 - 23.8477i) q^{39} +(-25.4781 - 14.7098i) q^{41} +(-18.8093 - 32.5786i) q^{43} +(9.50350 + 17.7393i) q^{45} +(49.8119 - 28.7589i) q^{47} +(3.58274 - 6.20548i) q^{49} +(36.4465 + 10.3891i) q^{51} +33.3940i q^{53} +23.8757 q^{55} +(-26.4321 + 92.7272i) q^{57} +(-3.54909 - 2.04907i) q^{59} +(33.1195 + 57.3647i) q^{61} +(-1.84945 + 58.1823i) q^{63} +(21.4321 - 12.3738i) q^{65} +(35.4890 - 61.4687i) q^{67} +(-24.4397 + 23.6752i) q^{69} +13.1123i q^{71} +109.273 q^{73} +(-14.5487 + 3.65160i) q^{75} +(59.8093 + 34.5309i) q^{77} +(49.8891 + 86.4104i) q^{79} +(35.9631 + 72.5786i) q^{81} +(-74.2472 + 42.8667i) q^{83} +(-14.1238 + 24.4632i) q^{85} +(29.7039 + 118.347i) q^{87} -63.6372i q^{89} +71.5841 q^{91} +(-66.5567 - 68.7060i) q^{93} +(-62.2394 - 35.9339i) q^{95} +(-43.2064 - 74.8357i) q^{97} +(96.0492 + 3.05314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 2 q^{7} + 8 q^{9} + 18 q^{11} - 10 q^{13} - 10 q^{15} + 52 q^{19} + 72 q^{21} + 54 q^{23} + 40 q^{25} - 34 q^{27} - 54 q^{29} - 32 q^{31} + 62 q^{33} + 44 q^{37} - 160 q^{39} + 144 q^{41}+ \cdots + 824 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

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Groups

Database

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