LMFDB - Embedded newform 72.3.m.b.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Root			$1.91950 - 3.32468i$ of defining polynomial
Character	$\chi$	$=$	72.41
Dual form			72.3.m.b.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.419504 - 2.97052i) q^{3} +(-8.20800 - 4.73889i) q^{5} +(1.05671 + 1.83027i) q^{7} +(-8.64803 + 2.49230i) q^{9} +O(q^{10})$	\(q+(-0.419504 - 2.97052i) q^{3} +(-8.20800 - 4.73889i) q^{5} +(1.05671 + 1.83027i) q^{7} +(-8.64803 + 2.49230i) q^{9} +(13.7064 - 7.91342i) q^{11} +(4.70337 - 8.14648i) q^{13} +(-10.6337 + 26.3701i) q^{15} -11.6027i q^{17} +12.9707 q^{19} +(4.99357 - 3.90678i) q^{21} +(-5.27427 - 3.04510i) q^{23} +(32.4142 + 56.1431i) q^{25} +(11.0313 + 24.6437i) q^{27} +(-24.7667 + 14.2991i) q^{29} +(8.75365 - 15.1618i) q^{31} +(-29.2569 - 37.3956i) q^{33} -20.0305i q^{35} -15.6207 q^{37} +(-26.1724 - 10.5540i) q^{39} +(14.8062 + 8.54836i) q^{41} +(-21.7157 - 37.6127i) q^{43} +(82.7938 + 20.5253i) q^{45} +(20.6696 - 11.9336i) q^{47} +(22.2667 - 38.5671i) q^{49} +(-34.4661 + 4.86739i) q^{51} -14.1051i q^{53} -150.003 q^{55} +(-5.44126 - 38.5297i) q^{57} +(38.5788 + 22.2735i) q^{59} +(-1.86057 - 3.22260i) q^{61} +(-13.7000 - 13.1946i) q^{63} +(-77.2105 + 44.5775i) q^{65} +(21.0090 - 36.3887i) q^{67} +(-6.83297 + 16.9448i) q^{69} +120.440i q^{71} +5.48692 q^{73} +(153.176 - 119.839i) q^{75} +(28.9674 + 16.7243i) q^{77} +(60.5480 + 104.872i) q^{79} +(68.5769 - 43.1069i) q^{81} +(46.5861 - 26.8965i) q^{83} +(-54.9840 + 95.2351i) q^{85} +(52.8655 + 67.5717i) q^{87} +102.195i q^{89} +19.8803 q^{91} +(-48.7106 - 19.6425i) q^{93} +(-106.463 - 61.4667i) q^{95} +(-58.9377 - 102.083i) q^{97} +(-98.8112 + 102.596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) $ 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9	$ 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9} + 36 q^{11} + 14 q^{13} + 10 q^{15} + 4 q^{19} - 54 q^{21} - 102 q^{23} + 10 q^{25} - 20 q^{27} - 114 q^{29} - 50 q^{31} - 104 q^{33} + 120 q^{37} + 82 q^{39} + 264 q^{41} - 28 q^{43} + 206 q^{45} + 150 q^{47} + 94 q^{49} + 170 q^{51} - 244 q^{55} - 178 q^{57} - 108 q^{59} + 14 q^{61} - 210 q^{63} - 198 q^{65} - 20 q^{67} - 14 q^{69} - 76 q^{73} + 326 q^{75} + 66 q^{77} + 26 q^{79} + 194 q^{81} + 246 q^{83} - 224 q^{85} - 18 q^{87} + 108 q^{91} - 130 q^{93} - 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) $ 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9 + 36 * q^11 + 14 * q^13 + 10 * q^15 + 4 * q^19 - 54 * q^21 - 102 * q^23 + 10 * q^25 - 20 * q^27 - 114 * q^29 - 50 * q^31 - 104 * q^33 + 120 * q^37 + 82 * q^39 + 264 * q^41 - 28 * q^43 + 206 * q^45 + 150 * q^47 + 94 * q^49 + 170 * q^51 - 244 * q^55 - 178 * q^57 - 108 * q^59 + 14 * q^61 - 210 * q^63 - 198 * q^65 - 20 * q^67 - 14 * q^69 - 76 * q^73 + 326 * q^75 + 66 * q^77 + 26 * q^79 + 194 * q^81 + 246 * q^83 - 224 * q^85 - 18 * q^87 + 108 * q^91 - 130 * q^93 - 456 * q^95 - 236 * q^97 - 634 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.419504	−	2.97052i	−0.139835	−	0.990175i
$3$	−0.419504	−	2.97052i	−0.139835	−	0.990175i
$4$		0			0
$5$	−8.20800	−	4.73889i	−1.64160	−	0.947779i	−0.980265	−	0.197688i	$-0.936657\pi$
$5$	−8.20800	−	4.73889i	−1.64160	−	0.947779i	−0.661336	−	0.750090i	$-0.730010\pi$
$6$		0			0
$7$	1.05671	+	1.83027i	0.150958	+	0.261467i	0.931580	−	0.363537i	$-0.118431\pi$
$7$	1.05671	+	1.83027i	0.150958	+	0.261467i	−0.780622	+	0.625004i	$0.785097\pi$
$8$		0			0
$9$	−8.64803	+	2.49230i	−0.960892	+	0.276922i
$10$		0			0
$11$	13.7064	−	7.91342i	1.24604	−	0.719401i	0.275723	−	0.961237i	$-0.411083\pi$
$11$	13.7064	−	7.91342i	1.24604	−	0.719401i	0.970317	+	0.241836i	$0.0777495\pi$
$12$		0			0
$13$	4.70337	−	8.14648i	0.361798	−	0.626652i	−0.626459	−	0.779454i	$-0.715496\pi$
$13$	4.70337	−	8.14648i	0.361798	−	0.626652i	0.988257	+	0.152802i	$0.0488298\pi$
$14$		0			0
$15$	−10.6337	+	26.3701i	−0.708914	+	1.75800i
$16$		0			0
$17$		−	11.6027i		−	0.682513i	−0.939970	−	0.341256i	$-0.889148\pi$
$17$		−	11.6027i		−	0.682513i	0.939970	−	0.341256i	$-0.110852\pi$
$18$		0			0
$19$	12.9707			0.682667			0.341334	−	0.939942i	$-0.389121\pi$
$19$	12.9707			0.682667			0.341334	+	0.939942i	$0.389121\pi$
$20$		0			0
$21$	4.99357	−	3.90678i	0.237789	−	0.186037i
$22$		0			0
$23$	−5.27427	−	3.04510i	−0.229316	−	0.132396i	0.380940	−	0.924600i	$-0.375600\pi$
$23$	−5.27427	−	3.04510i	−0.229316	−	0.132396i	−0.610256	+	0.792204i	$0.708934\pi$
$24$		0			0
$25$	32.4142	+	56.1431i	1.29657	+	2.24572i
$26$		0			0
$27$	11.0313	+	24.6437i	0.408567	+	0.912728i
$28$		0			0
$29$	−24.7667	+	14.2991i	−0.854026	+	0.493072i	−0.862007	−	0.506896i	$-0.830793\pi$
$29$	−24.7667	+	14.2991i	−0.854026	+	0.493072i	0.00798151	+	0.999968i	$0.497459\pi$
$30$		0			0
$31$	8.75365	−	15.1618i	0.282376	−	0.489089i	−0.689594	−	0.724196i	$-0.742211\pi$
$31$	8.75365	−	15.1618i	0.282376	−	0.489089i	0.971969	+	0.235107i	$0.0755442\pi$
$32$		0			0
$33$	−29.2569	−	37.3956i	−0.886573	−	1.13320i
$34$		0			0
$35$		−	20.0305i		−	0.572299i
$36$		0			0
$37$	−15.6207			−0.422181			−0.211091	−	0.977467i	$-0.567702\pi$
$37$	−15.6207			−0.422181			−0.211091	+	0.977467i	$0.567702\pi$
$38$		0			0
$39$	−26.1724	−	10.5540i	−0.671087	−	0.270615i
$40$		0			0
$41$	14.8062	+	8.54836i	0.361127	+	0.208497i	0.669575	−	0.742745i	$-0.266476\pi$
$41$	14.8062	+	8.54836i	0.361127	+	0.208497i	−0.308448	+	0.951241i	$0.599810\pi$
$42$		0			0
$43$	−21.7157	−	37.6127i	−0.505016	−	0.874714i	−0.999983	−	0.00580217i	$-0.998153\pi$
$43$	−21.7157	−	37.6127i	−0.505016	−	0.874714i	0.494967	−	0.868912i	$-0.335180\pi$
$44$		0			0
$45$	82.7938	+	20.5253i	1.83986	+	0.456118i
$46$		0			0
$47$	20.6696	−	11.9336i	0.439778	−	0.253906i	−0.263726	−	0.964598i	$-0.584951\pi$
$47$	20.6696	−	11.9336i	0.439778	−	0.253906i	0.703503	+	0.710692i	$0.251618\pi$
$48$		0			0
$49$	22.2667	−	38.5671i	0.454423	−	0.787084i
$50$		0			0
$51$	−34.4661	+	4.86739i	−0.675807	+	0.0954390i
$52$		0			0
$53$		−	14.1051i		−	0.266134i	−0.991107	−	0.133067i	$-0.957517\pi$
$53$		−	14.1051i		−	0.266134i	0.991107	−	0.133067i	$-0.0424825\pi$
$54$		0			0
$55$	−150.003			−2.72733
$56$		0			0
$57$	−5.44126	−	38.5297i	−0.0954607	−	0.675960i
$58$		0			0
$59$	38.5788	+	22.2735i	0.653877	+	0.377516i	0.789940	−	0.613184i	$-0.210112\pi$
$59$	38.5788	+	22.2735i	0.653877	+	0.377516i	−0.136063	+	0.990700i	$0.543445\pi$
$60$		0			0
$61$	−1.86057	−	3.22260i	−0.0305012	−	0.0528296i	0.850372	−	0.526182i	$-0.176377\pi$
$61$	−1.86057	−	3.22260i	−0.0305012	−	0.0528296i	−0.880873	+	0.473353i	$0.843044\pi$
$62$		0			0
$63$	−13.7000	−	13.1946i	−0.217460	−	0.209438i
$64$		0			0
$65$	−77.2105	+	44.5775i	−1.18785	+	0.685808i
$66$		0			0
$67$	21.0090	−	36.3887i	0.313568	−	0.543115i	−0.665564	−	0.746340i	$-0.731809\pi$
$67$	21.0090	−	36.3887i	0.313568	−	0.543115i	0.979132	+	0.203225i	$0.0651424\pi$
$68$		0			0
$69$	−6.83297	+	16.9448i	−0.0990285	+	0.245576i
$70$		0			0
$71$			120.440i			1.69634i	0.529724	+	0.848170i	$0.322295\pi$
$71$			120.440i			1.69634i	−0.529724	+	0.848170i	$0.677705\pi$
$72$		0			0
$73$	5.48692			0.0751633			0.0375817	−	0.999294i	$-0.488035\pi$
$73$	5.48692			0.0751633			0.0375817	+	0.999294i	$0.488035\pi$
$74$		0			0
$75$	153.176	−	119.839i	2.04235	−	1.59786i
$76$		0			0
$77$	28.9674	+	16.7243i	0.376200	+	0.217199i
$78$		0			0
$79$	60.5480	+	104.872i	0.766430	+	1.32750i	0.939487	+	0.342585i	$0.111302\pi$
$79$	60.5480	+	104.872i	0.766430	+	1.32750i	−0.173056	+	0.984912i	$0.555364\pi$
$80$		0			0
$81$	68.5769	−	43.1069i	0.846629	−	0.532184i
$82$		0			0
$83$	46.5861	−	26.8965i	0.561279	−	0.324054i	−0.192380	−	0.981321i	$-0.561621\pi$
$83$	46.5861	−	26.8965i	0.561279	−	0.324054i	0.753659	+	0.657266i	$0.228287\pi$
$84$		0			0
$85$	−54.9840	+	95.2351i	−0.646871	+	1.12041i
$86$		0			0
$87$	52.8655	+	67.5717i	0.607650	+	0.776686i
$88$		0			0
$89$			102.195i			1.14825i	0.818766	+	0.574127i	$0.194658\pi$
$89$			102.195i			1.14825i	−0.818766	+	0.574127i	$0.805342\pi$
$90$		0			0
$91$	19.8803			0.218465
$92$		0			0
$93$	−48.7106	−	19.6425i	−0.523770	−	0.211210i
$94$		0			0
$95$	−106.463	−	61.4667i	−1.12067	−	0.647018i
$96$		0			0
$97$	−58.9377	−	102.083i	−0.607605	−	1.05240i	−0.991634	−	0.129081i	$-0.958797\pi$
$97$	−58.9377	−	102.083i	−0.607605	−	1.05240i	0.384029	−	0.923321i	$-0.374536\pi$
$98$		0			0
$99$	−98.8112	+	102.596i	−0.998092	+	1.03632i
$100$		0			0
$101$	118.181	−	68.2317i	1.17011	−	0.675561i	0.216401	−	0.976304i	$-0.430568\pi$
$101$	118.181	−	68.2317i	1.17011	−	0.675561i	0.953705	+	0.300743i	$0.0972347\pi$
$102$		0			0
$103$	60.8511	−	105.397i	0.590787	−	1.02327i	−0.403340	−	0.915050i	$-0.632151\pi$
$103$	60.8511	−	105.397i	0.590787	−	1.02327i	0.994127	−	0.108223i	$-0.0345160\pi$
$104$		0			0
$105$	−59.5010	+	8.40287i	−0.566677	+	0.0800274i
$106$		0			0
$107$			82.1437i			0.767698i	0.923396	+	0.383849i	$0.125402\pi$
$107$			82.1437i			0.767698i	−0.923396	+	0.383849i	$0.874598\pi$
$108$		0			0
$109$	−165.603			−1.51929			−0.759646	−	0.650337i	$-0.774628\pi$
$109$	−165.603			−1.51929			−0.759646	+	0.650337i	$0.774628\pi$
$110$		0			0
$111$	6.55295	+	46.4017i	0.0590356	+	0.418033i
$112$		0			0
$113$	68.7460	+	39.6905i	0.608372	+	0.351244i	0.772328	−	0.635224i	$-0.219092\pi$
$113$	68.7460	+	39.6905i	0.608372	+	0.351244i	−0.163956	+	0.986468i	$0.552426\pi$
$114$		0			0
$115$	28.8608	+	49.9884i	0.250964	+	0.434682i
$116$		0			0
$117$	−20.3715	+	82.1732i	−0.174115	+	0.702335i
$118$		0			0
$119$	21.2361	−	12.2607i	0.178455	−	0.103031i
$120$		0			0
$121$	64.7443	−	112.140i	0.535077	−	0.926781i
$122$		0			0
$123$	19.1818	−	47.5682i	0.155950	−	0.386733i
$124$		0			0
$125$		−	377.485i		−	3.01988i
$126$		0			0
$127$	147.235			1.15933			0.579666	−	0.814854i	$-0.303183\pi$
$127$	147.235			1.15933			0.579666	+	0.814854i	$0.303183\pi$
$128$		0			0
$129$	−102.620	+	80.2857i	−0.795501	+	0.622370i
$130$		0			0
$131$	−145.857	−	84.2103i	−1.11341	−	0.642827i	−0.173699	−	0.984799i	$-0.555572\pi$
$131$	−145.857	−	84.2103i	−1.11341	−	0.642827i	−0.939710	+	0.341972i	$0.888905\pi$
$132$		0			0
$133$	13.7062	+	23.7398i	0.103054	+	0.178495i
$134$		0			0
$135$	26.2386	−	254.551i	0.194360	−	1.88557i
$136$		0			0
$137$	−174.984	+	101.027i	−1.27726	+	0.737426i	−0.976343	−	0.216225i	$-0.930625\pi$
$137$	−174.984	+	101.027i	−1.27726	+	0.737426i	−0.300915	+	0.953651i	$0.597292\pi$
$138$		0			0
$139$	−129.193	+	223.768i	−0.929443	+	1.60984i	−0.145189	+	0.989404i	$0.546379\pi$
$139$	−129.193	+	223.768i	−0.929443	+	1.60984i	−0.784255	+	0.620439i	$0.786954\pi$
$140$		0			0
$141$	−44.1199	−	56.3932i	−0.312907	−	0.399952i
$142$		0			0
$143$		−	148.879i		−	1.04111i
$144$		0			0
$145$	271.047			1.86929
$146$		0			0
$147$	−123.906	−	49.9648i	−0.842895	−	0.339897i
$148$		0			0
$149$	68.6316	+	39.6245i	0.460615	+	0.265936i	0.712303	−	0.701872i	$-0.247652\pi$
$149$	68.6316	+	39.6245i	0.460615	+	0.265936i	−0.251688	+	0.967808i	$0.580986\pi$
$150$		0			0
$151$	4.73094	+	8.19422i	0.0313307	+	0.0542664i	0.881266	−	0.472621i	$-0.156692\pi$
$151$	4.73094	+	8.19422i	0.0313307	+	0.0542664i	−0.849935	+	0.526888i	$0.823359\pi$
$152$		0			0
$153$	28.9174	+	100.341i	0.189003	+	0.655821i
$154$		0			0
$155$	−143.700	+	82.9652i	−0.927096	+	0.535259i
$156$		0			0
$157$	34.3561	−	59.5066i	0.218829	−	0.379023i	−0.735621	−	0.677393i	$-0.763110\pi$
$157$	34.3561	−	59.5066i	0.218829	−	0.379023i	0.954450	+	0.298370i	$0.0964430\pi$
$158$		0			0
$159$	−41.8995	+	5.91715i	−0.263519	+	0.0372148i
$160$		0			0
$161$		−	12.8711i		−	0.0799448i
$162$		0			0
$163$	209.391			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$163$	209.391			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$164$		0			0
$165$	62.9271	+	445.589i	0.381376	+	2.70054i
$166$		0			0
$167$	21.3682	+	12.3369i	0.127953	+	0.0738739i	0.562610	−	0.826722i	$-0.309797\pi$
$167$	21.3682	+	12.3369i	0.127953	+	0.0738739i	−0.434657	+	0.900596i	$0.643130\pi$
$168$		0			0
$169$	40.2566	+	69.7265i	0.238205	+	0.412583i
$170$		0			0
$171$	−112.171	+	32.3268i	−0.655970	+	0.189045i
$172$		0			0
$173$	129.186	−	74.5855i	0.746739	−	0.431130i	−0.0777754	−	0.996971i	$-0.524782\pi$
$173$	129.186	−	74.5855i	0.746739	−	0.431130i	0.824514	+	0.565841i	$0.191448\pi$
$174$		0			0
$175$	−68.5046	+	118.654i	−0.391455	+	0.678020i
$176$		0			0
$177$	49.9799	−	123.943i	0.282372	−	0.700243i
$178$		0			0
$179$		−	65.1600i		−	0.364022i	−0.983296	−	0.182011i	$-0.941739\pi$
$179$		−	65.1600i		−	0.364022i	0.983296	−	0.182011i	$-0.0582607\pi$
$180$		0			0
$181$	−95.5019			−0.527635			−0.263817	−	0.964573i	$-0.584982\pi$
$181$	−95.5019			−0.527635			−0.263817	+	0.964573i	$0.584982\pi$
$182$		0			0
$183$	−8.79231	+	6.87877i	−0.0480454	+	0.0375889i
$184$		0			0
$185$	128.215	+	74.0248i	0.693053	+	0.400134i
$186$		0			0
$187$	−91.8171	−	159.032i	−0.491001	−	0.850438i
$188$		0			0
$189$	−33.4477	+	46.2314i	−0.176972	+	0.244611i
$190$		0			0
$191$	160.947	−	92.9225i	0.842652	−	0.486505i	−0.0155129	−	0.999880i	$-0.504938\pi$
$191$	160.947	−	92.9225i	0.842652	−	0.486505i	0.858165	+	0.513374i	$0.171605\pi$
$192$		0			0
$193$	−48.1579	+	83.4119i	−0.249523	+	0.432186i	−0.963393	−	0.268091i	$-0.913607\pi$
$193$	−48.1579	+	83.4119i	−0.249523	+	0.432186i	0.713871	+	0.700277i	$0.246940\pi$
$194$		0			0
$195$	164.809	+	210.655i	0.845173	+	1.08028i
$196$		0			0
$197$			126.121i			0.640209i	0.947382	+	0.320105i	$0.103718\pi$
$197$			126.121i			0.640209i	−0.947382	+	0.320105i	$0.896282\pi$
$198$		0			0
$199$	131.718			0.661899			0.330950	−	0.943648i	$-0.392631\pi$
$199$	131.718			0.661899			0.330950	+	0.943648i	$0.392631\pi$
$200$		0			0
$201$	−116.907	−	47.1426i	−0.581627	−	0.234540i
$202$		0			0
$203$	−52.3424	−	30.2199i	−0.257844	−	0.148866i
$204$		0			0
$205$	−81.0195	−	140.330i	−0.395217	−	0.684536i
$206$		0			0
$207$	53.2013	+	13.1891i	0.257011	+	0.0637154i
$208$		0			0
$209$	177.782	−	102.642i	0.850631	−	0.491112i
$210$		0			0
$211$	−5.15331	+	8.92579i	−0.0244233	+	0.0423023i	−0.877979	−	0.478700i	$-0.841108\pi$
$211$	−5.15331	+	8.92579i	−0.0244233	+	0.0423023i	0.853555	+	0.521002i	$0.174442\pi$
$212$		0			0
$213$	357.770	−	50.5252i	1.67967	−	0.237207i
$214$		0			0
$215$			411.634i			1.91457i
$216$		0			0
$217$	37.0001			0.170508
$218$		0			0
$219$	−2.30179	−	16.2990i	−0.0105104	−	0.0744248i
$220$		0			0
$221$	−94.5212	−	54.5718i	−0.427698	−	0.246931i
$222$		0			0
$223$	−86.4202	−	149.684i	−0.387535	−	0.671230i	0.604583	−	0.796542i	$-0.293340\pi$
$223$	−86.4202	−	149.684i	−0.387535	−	0.671230i	−0.992117	+	0.125313i	$0.960007\pi$
$224$		0			0
$225$	−420.244	−	404.741i	−1.86775	−	1.79885i
$226$		0			0
$227$	−173.974	+	100.444i	−0.766403	+	0.442483i	−0.831590	−	0.555390i	$-0.812569\pi$
$227$	−173.974	+	100.444i	−0.766403	+	0.442483i	0.0651869	+	0.997873i	$0.479236\pi$
$228$		0			0
$229$	−130.630	+	226.259i	−0.570439	+	0.988029i	0.426082	+	0.904684i	$0.359893\pi$
$229$	−130.630	+	226.259i	−0.570439	+	0.988029i	−0.996521	+	0.0833443i	$0.973440\pi$
$230$		0			0
$231$	37.5281	−	93.0642i	0.162459	−	0.402875i
$232$		0			0
$233$			130.530i			0.560214i	0.959969	+	0.280107i	$0.0903700\pi$
$233$			130.530i			0.560214i	−0.959969	+	0.280107i	$0.909630\pi$
$234$		0			0
$235$	−226.208			−0.962586
$236$		0			0
$237$	286.125	−	223.854i	1.20728	−	0.944530i
$238$		0			0
$239$	−231.586	−	133.706i	−0.968981	−	0.559441i	−0.0700553	−	0.997543i	$-0.522318\pi$
$239$	−231.586	−	133.706i	−0.968981	−	0.559441i	−0.898925	+	0.438102i	$0.855651\pi$
$240$		0			0
$241$	−50.8188	−	88.0207i	−0.210866	−	0.365231i	0.741120	−	0.671373i	$-0.234295\pi$
$241$	−50.8188	−	88.0207i	−0.210866	−	0.365231i	−0.951986	+	0.306142i	$0.900962\pi$
$242$		0			0
$243$	−156.818	−	185.626i	−0.645343	−	0.763893i
$244$		0			0
$245$	−365.531	+	211.039i	−1.49196	+	0.861385i
$246$		0			0
$247$	61.0059	−	105.665i	0.246987	−	0.427795i
$248$		0			0
$249$	−99.4398	−	127.102i	−0.399357	−	0.510450i
$250$		0			0
$251$		−	137.033i		−	0.545946i	−0.962022	−	0.272973i	$-0.911993\pi$
$251$		−	137.033i		−	0.545946i	0.962022	−	0.272973i	$-0.0880070\pi$
$252$		0			0
$253$	−96.3886			−0.380983
$254$		0			0
$255$	305.964	+	123.380i	1.19986	+	0.483842i
$256$		0			0
$257$	−217.737	−	125.711i	−0.847226	−	0.489146i	0.0124876	−	0.999922i	$-0.496025\pi$
$257$	−217.737	−	125.711i	−0.847226	−	0.489146i	−0.859714	+	0.510776i	$0.829358\pi$
$258$		0			0
$259$	−16.5065	−	28.5901i	−0.0637317	−	0.110387i
$260$		0			0
$261$	178.546	−	185.385i	0.684084	−	0.710287i
$262$		0			0
$263$	416.538	−	240.488i	1.58379	−	0.914404i	0.589496	−	0.807771i	$-0.299326\pi$
$263$	416.538	−	240.488i	1.58379	−	0.914404i	0.994298	−	0.106633i	$-0.0340069\pi$
$264$		0			0
$265$	−66.8425	+	115.775i	−0.252236	+	0.436885i
$266$		0			0
$267$	303.572	−	42.8711i	1.13697	−	0.160566i
$268$		0			0
$269$			182.939i			0.680071i	0.940413	+	0.340036i	$0.110439\pi$
$269$			182.939i			0.680071i	−0.940413	+	0.340036i	$0.889561\pi$
$270$		0			0
$271$	−31.0146			−0.114445			−0.0572225	−	0.998361i	$-0.518224\pi$
$271$	−31.0146			−0.114445			−0.0572225	+	0.998361i	$0.518224\pi$
$272$		0			0
$273$	−8.33989	−	59.0550i	−0.0305490	−	0.216319i
$274$		0			0
$275$	888.567	+	513.014i	3.23115	+	1.86551i
$276$		0			0
$277$	−206.382	−	357.464i	−0.745060	−	1.29048i	−0.950167	−	0.311743i	$-0.899087\pi$
$277$	−206.382	−	357.464i	−0.745060	−	1.29048i	0.205106	−	0.978740i	$-0.434246\pi$
$278$		0			0
$279$	−37.9142	+	152.936i	−0.135893	+	0.548158i
$280$		0			0
$281$	−107.255	+	61.9236i	−0.381690	+	0.220369i	−0.678553	−	0.734551i	$-0.737393\pi$
$281$	−107.255	+	61.9236i	−0.381690	+	0.220369i	0.296863	+	0.954920i	$0.404059\pi$
$282$		0			0
$283$	−4.23689	+	7.33850i	−0.0149713	+	0.0259311i	−0.873414	−	0.486978i	$-0.838099\pi$
$283$	−4.23689	+	7.33850i	−0.0149713	+	0.0259311i	0.858443	+	0.512910i	$0.171432\pi$
$284$		0			0
$285$	−137.926	+	342.038i	−0.483952	+	1.20013i
$286$		0			0
$287$			36.1324i			0.125897i
$288$		0			0
$289$	154.377			0.534177
$290$		0			0
$291$	−278.516	+	217.900i	−0.957098	+	0.748797i
$292$		0			0
$293$	−93.2120	−	53.8160i	−0.318130	−	0.183672i	0.332429	−	0.943128i	$-0.392132\pi$
$293$	−93.2120	−	53.8160i	−0.318130	−	0.183672i	−0.650559	+	0.759456i	$0.725465\pi$
$294$		0			0
$295$	−211.103	−	365.641i	−0.715604	−	1.23946i
$296$		0			0
$297$	346.216	+	250.481i	1.16571	+	0.843372i
$298$		0			0
$299$	−49.6137	+	28.6445i	−0.165932	+	0.0958009i
$300$		0			0
$301$	45.8943	−	79.4912i	0.152473	−	0.264090i
$302$		0			0
$303$	−252.261	−	322.435i	−0.832545	−	1.06414i
$304$		0			0
$305$			35.2682i			0.115633i
$306$		0			0
$307$	−530.715			−1.72871			−0.864357	−	0.502878i	$-0.832274\pi$
$307$	−530.715			−1.72871			−0.864357	+	0.502878i	$0.832274\pi$
$308$		0			0
$309$	−338.612	−	136.545i	−1.09583	−	0.441893i
$310$		0			0
$311$	142.535	+	82.2926i	0.458312	+	0.264606i	0.711334	−	0.702854i	$-0.248091\pi$
$311$	142.535	+	82.2926i	0.458312	+	0.264606i	−0.253022	+	0.967460i	$0.581425\pi$
$312$		0			0
$313$	273.833	+	474.293i	0.874866	+	1.51531i	0.856905	+	0.515474i	$0.172384\pi$
$313$	273.833	+	474.293i	0.874866	+	1.51531i	0.0179611	+	0.999839i	$0.494283\pi$
$314$		0			0
$315$	49.9219	+	173.224i	0.158482	+	0.549918i
$316$		0			0
$317$	67.7106	−	39.0928i	0.213598	−	0.123321i	−0.389384	−	0.921075i	$-0.627312\pi$
$317$	67.7106	−	39.0928i	0.213598	−	0.123321i	0.602983	+	0.797754i	$0.293979\pi$
$318$		0			0
$319$	−226.309	+	391.979i	−0.709433	+	1.22877i
$320$		0			0
$321$	244.010	−	34.4596i	0.760155	−	0.107351i
$322$		0			0
$323$		−	150.495i		−	0.465929i
$324$		0			0
$325$	609.824			1.87638
$326$		0			0
$327$	69.4711	+	491.927i	0.212450	+	1.50437i
$328$		0			0
$329$	43.6833	+	25.2206i	0.132776	+	0.0766583i
$330$		0			0
$331$	274.898	+	476.137i	0.830507	+	1.43848i	0.897637	+	0.440736i	$0.145283\pi$
$331$	274.898	+	476.137i	0.830507	+	1.43848i	−0.0671297	+	0.997744i	$0.521384\pi$
$332$		0			0
$333$	135.088	−	38.9314i	0.405671	−	0.116911i
$334$		0			0
$335$	−344.884	+	199.119i	−1.02951	+	0.594385i
$336$		0			0
$337$	36.8057	−	63.7494i	0.109216	−	0.189167i	−0.806237	−	0.591593i	$-0.798499\pi$
$337$	36.8057	−	63.7494i	0.109216	−	0.189167i	0.915453	+	0.402425i	$0.131833\pi$
$338$		0			0
$339$	89.0624	−	220.862i	0.262721	−	0.651511i
$340$		0			0
$341$		−	277.085i		−	0.812566i
$342$		0			0
$343$	197.675			0.576312
$344$		0			0
$345$	136.384	−	106.702i	0.395317	−	0.309281i
$346$		0			0
$347$	−367.796	−	212.347i	−1.05993	−	0.611951i	−0.134517	−	0.990911i	$-0.542948\pi$
$347$	−367.796	−	212.347i	−1.05993	−	0.611951i	−0.925413	+	0.378960i	$0.876282\pi$
$348$		0			0
$349$	267.361	+	463.082i	0.766077	+	1.32688i	0.939676	+	0.342067i	$0.111127\pi$
$349$	267.361	+	463.082i	0.766077	+	1.32688i	−0.173599	+	0.984816i	$0.555540\pi$
$350$		0			0
$351$	252.643	+	26.0419i	0.719782	+	0.0741935i
$352$		0			0
$353$	−155.165	+	89.5845i	−0.439561	+	0.253781i	−0.703411	−	0.710783i	$-0.748341\pi$
$353$	−155.165	+	89.5845i	−0.439561	+	0.253781i	0.263851	+	0.964564i	$0.415007\pi$
$354$		0			0
$355$	570.753	−	988.573i	1.60775	−	2.78471i
$356$		0			0
$357$	−45.3292	−	57.9389i	−0.126973	−	0.162294i
$358$		0			0
$359$		−	351.534i		−	0.979204i	−0.871946	−	0.489602i	$-0.837142\pi$
$359$		−	351.534i		−	0.979204i	0.871946	−	0.489602i	$-0.162858\pi$
$360$		0			0
$361$	−192.761			−0.533965
$362$		0			0
$363$	−360.276	−	145.281i	−0.992497	−	0.400224i
$364$		0			0
$365$	−45.0367	−	26.0019i	−0.123388	−	0.0712382i
$366$		0			0
$367$	41.9855	+	72.7210i	0.114402	+	0.198150i	0.917541	−	0.397642i	$-0.130171\pi$
$367$	41.9855	+	72.7210i	0.114402	+	0.198150i	−0.803139	+	0.595792i	$0.796838\pi$
$368$		0			0
$369$	−149.349	−	37.0251i	−0.404741	−	0.100339i
$370$		0			0
$371$	25.8161	−	14.9050i	0.0695853	−	0.0401751i
$372$		0			0
$373$	−218.337	+	378.171i	−0.585354	+	1.01386i	0.409477	+	0.912320i	$0.365711\pi$
$373$	−218.337	+	378.171i	−0.585354	+	1.01386i	−0.994831	+	0.101543i	$0.967622\pi$
$374$		0			0
$375$	−1121.33	+	158.357i	−2.99021	+	0.422284i
$376$		0			0
$377$			269.016i			0.713569i
$378$		0			0
$379$	273.455			0.721516			0.360758	−	0.932659i	$-0.382518\pi$
$379$	273.455			0.721516			0.360758	+	0.932659i	$0.382518\pi$
$380$		0			0
$381$	−61.7658	−	437.366i	−0.162115	−	1.14794i
$382$		0			0
$383$	−192.544	−	111.166i	−0.502727	−	0.290249i	0.227112	−	0.973869i	$-0.427072\pi$
$383$	−192.544	−	111.166i	−0.502727	−	0.290249i	−0.729839	+	0.683619i	$0.760405\pi$
$384$		0			0
$385$	−158.510	−	274.547i	−0.411713	−	0.713108i
$386$		0			0
$387$	281.540	+	271.154i	0.727494	+	0.700656i
$388$		0			0
$389$	522.471	−	301.649i	1.34311	−	0.775447i	0.355851	−	0.934543i	$-0.384191\pi$
$389$	522.471	−	301.649i	1.34311	−	0.775447i	0.987263	+	0.159096i	$0.0508578\pi$
$390$		0			0
$391$	−35.3314	+	61.1958i	−0.0903617	+	0.156511i
$392$		0			0
$393$	−188.961	+	468.597i	−0.480818	+	1.19236i
$394$		0			0
$395$		−	1147.72i		−	2.90563i
$396$		0			0
$397$	−138.804			−0.349633			−0.174816	−	0.984601i	$-0.555933\pi$
$397$	−138.804			−0.349633			−0.174816	+	0.984601i	$0.555933\pi$
$398$		0			0
$399$	64.7700	−	50.6736i	0.162331	−	0.127001i
$400$		0			0
$401$	−281.903	−	162.757i	−0.702999	−	0.405877i	0.105464	−	0.994423i	$-0.466367\pi$
$401$	−281.903	−	162.757i	−0.702999	−	0.405877i	−0.808464	+	0.588546i	$0.799700\pi$
$402$		0			0
$403$	−82.3433	−	142.623i	−0.204326	−	0.353903i
$404$		0			0
$405$	−767.159	+	28.8430i	−1.89422	+	0.0712173i
$406$		0			0
$407$	−214.104	+	123.613i	−0.526055	+	0.303718i
$408$		0			0
$409$	257.442	−	445.903i	0.629443	−	1.09023i	−0.358220	−	0.933637i	$-0.616616\pi$
$409$	257.442	−	445.903i	0.629443	−	1.09023i	0.987664	−	0.156591i	$-0.0500504\pi$
$410$		0			0
$411$	373.511	+	477.414i	0.908785	+	1.16159i
$412$		0			0
$413$			94.1461i			0.227957i
$414$		0			0
$415$	−509.839			−1.22853
$416$		0			0
$417$	718.906	+	289.898i	1.72399	+	0.695199i
$418$		0			0
$419$	107.340	+	61.9726i	0.256181	+	0.147906i	0.622591	−	0.782547i	$-0.286080\pi$
$419$	107.340	+	61.9726i	0.256181	+	0.147906i	−0.366410	+	0.930453i	$0.619413\pi$
$420$		0			0
$421$	255.924	+	443.273i	0.607895	+	1.05291i	0.991587	+	0.129444i	$0.0413194\pi$
$421$	255.924	+	443.273i	0.607895	+	1.05291i	−0.383691	+	0.923461i	$0.625347\pi$
$422$		0			0
$423$	−149.009	+	154.717i	−0.352267	+	0.365760i
$424$		0			0
$425$	651.412	−	376.093i	1.53273	−	0.884924i
$426$		0			0
$427$	3.93216	−	6.81070i	0.00920880	−	0.0159501i
$428$		0			0
$429$	−442.248	+	62.4553i	−1.03088	+	0.145584i
$430$		0			0
$431$			650.840i			1.51007i	0.655684	+	0.755035i	$0.272380\pi$
$431$			650.840i			1.51007i	−0.655684	+	0.755035i	$0.727620\pi$
$432$		0			0
$433$	−432.455			−0.998742			−0.499371	−	0.866388i	$-0.666435\pi$
$433$	−432.455			−0.998742			−0.499371	+	0.866388i	$0.666435\pi$
$434$		0			0
$435$	−113.706	−	805.153i	−0.261392	−	1.85093i
$436$		0			0
$437$	−68.4108	−	39.4970i	−0.156547	−	0.0903822i
$438$		0			0
$439$	190.663	+	330.238i	0.434312	+	0.752251i	0.997239	−	0.0742559i	$-0.0236582\pi$
$439$	190.663	+	330.238i	0.434312	+	0.752251i	−0.562927	+	0.826507i	$0.690325\pi$
$440$		0			0
$441$	−96.4428	+	389.025i	−0.218691	+	0.882143i
$442$		0			0
$443$	−33.3781	+	19.2708i	−0.0753455	+	0.0435007i	−0.537199	−	0.843455i	$-0.680518\pi$
$443$	−33.3781	+	19.2708i	−0.0753455	+	0.0435007i	0.461854	+	0.886956i	$0.347184\pi$
$444$		0			0
$445$	484.289	−	838.813i	1.08829	−	1.88497i
$446$		0			0
$447$	88.9143	−	220.495i	0.198913	−	0.493277i
$448$		0			0
$449$		−	373.577i		−	0.832019i	−0.909360	−	0.416010i	$-0.863428\pi$
$449$		−	373.577i		−	0.832019i	0.909360	−	0.416010i	$-0.136572\pi$
$450$		0			0
$451$	270.587			0.599971
$452$		0			0
$453$	22.3565	−	17.4909i	0.0493521	−	0.0386112i
$454$		0			0
$455$	−163.178	−	94.2108i	−0.358633	−	0.207057i
$456$		0			0
$457$	−121.482	−	210.414i	−0.265826	−	0.460423i	0.701954	−	0.712222i	$-0.252311\pi$
$457$	−121.482	−	210.414i	−0.265826	−	0.460423i	−0.967780	+	0.251799i	$0.918978\pi$
$458$		0			0
$459$	285.933	−	127.993i	0.622948	−	0.278852i
$460$		0			0
$461$	−116.211	+	67.0942i	−0.252084	+	0.145541i	−0.620718	−	0.784034i	$-0.713159\pi$
$461$	−116.211	+	67.0942i	−0.252084	+	0.145541i	0.368634	+	0.929574i	$0.379825\pi$
$462$		0			0
$463$	−155.129	+	268.691i	−0.335051	+	0.580326i	−0.983495	−	0.180937i	$-0.942087\pi$
$463$	−155.129	+	268.691i	−0.335051	+	0.580326i	0.648443	+	0.761263i	$0.275420\pi$
$464$		0			0
$465$	306.733	+	392.060i	0.659640	+	0.843139i
$466$		0			0
$467$			765.680i			1.63957i	0.572670	+	0.819786i	$0.305908\pi$
$467$			765.680i			1.63957i	−0.572670	+	0.819786i	$0.694092\pi$
$468$		0			0
$469$	88.8015			0.189342
$470$		0			0
$471$	−191.178	−	77.0925i	−0.405899	−	0.163678i
$472$		0			0
$473$	−595.290	−	343.691i	−1.25854	−	0.726619i
$474$		0			0
$475$	420.434	+	728.214i	0.885125	+	1.53308i
$476$		0			0
$477$	35.1541	+	121.981i	0.0736983	+	0.255726i
$478$		0			0
$479$	442.124	−	255.260i	0.923014	−	0.532902i	0.0384186	−	0.999262i	$-0.487768\pi$
$479$	442.124	−	255.260i	0.923014	−	0.532902i	0.884595	+	0.466359i	$0.154435\pi$
$480$		0			0
$481$	−73.4699	+	127.254i	−0.152744	+	0.264561i
$482$		0			0
$483$	−38.2340	+	5.39949i	−0.0791593	+	0.0111791i
$484$		0			0
$485$			1117.20i			2.30350i
$486$		0			0
$487$	669.532			1.37481			0.687405	−	0.726274i	$-0.258750\pi$
$487$	669.532			1.37481			0.687405	+	0.726274i	$0.258750\pi$
$488$		0			0
$489$	−87.8405	−	622.001i	−0.179633	−	1.27199i
$490$		0			0
$491$	640.537	+	369.814i	1.30456	+	0.753186i	0.981182	−	0.193085i	$-0.0618492\pi$
$491$	640.537	+	369.814i	1.30456	+	0.753186i	0.323375	+	0.946271i	$0.395183\pi$
$492$		0			0
$493$	165.908	+	287.361i	0.336528	+	0.582883i
$494$		0			0
$495$	1297.23	−	373.853i	2.62067	−	0.755258i
$496$		0			0
$497$	−220.438	+	127.270i	−0.443537	+	0.256076i
$498$		0			0
$499$	−461.405	+	799.176i	−0.924659	+	1.60156i	−0.132550	+	0.991176i	$0.542316\pi$
$499$	−461.405	+	799.176i	−0.924659	+	1.60156i	−0.792109	+	0.610380i	$0.791017\pi$
$500$		0			0
$501$	27.6831	−	68.6502i	0.0552557	−	0.137026i
$502$		0			0
$503$			223.098i			0.443534i	0.975100	+	0.221767i	$0.0711824\pi$
$503$			223.098i			0.443534i	−0.975100	+	0.221767i	$0.928818\pi$
$504$		0			0
$505$	−1293.37			−2.56113
$506$		0			0
$507$	190.237	−	148.834i	0.375220	−	0.293558i
$508$		0			0
$509$	125.233	+	72.3030i	0.246036	+	0.142049i	0.617948	−	0.786219i	$-0.287964\pi$
$509$	125.233	+	72.3030i	0.246036	+	0.142049i	−0.371912	+	0.928268i	$0.621298\pi$
$510$		0			0
$511$	5.79807	+	10.0425i	0.0113465	+	0.0196527i
$512$		0			0
$513$	143.084	+	319.645i	0.278916	+	0.623090i
$514$		0			0
$515$	−998.932	+	576.733i	−1.93967	+	1.11987i
$516$		0			0
$517$	188.871	−	327.134i	0.365320	−	0.632753i
$518$		0			0
$519$	−275.752	−	352.461i	−0.531314	−	0.679115i
$520$		0			0
$521$		−	452.382i		−	0.868296i	−0.900842	−	0.434148i	$-0.857050\pi$
$521$		−	452.382i		−	0.868296i	0.900842	−	0.434148i	$-0.142950\pi$
$522$		0			0
$523$	−168.242			−0.321686			−0.160843	−	0.986980i	$-0.551421\pi$
$523$	−168.242			−0.321686			−0.160843	+	0.986980i	$0.551421\pi$
$524$		0			0
$525$	381.201	+	153.719i	0.726097	+	0.292798i
$526$		0			0
$527$	−175.918	−	101.566i	−0.333809	−	0.192725i
$528$		0			0
$529$	−245.955	−	426.006i	−0.464943	−	0.805305i
$530$		0			0
$531$	−389.142	−	96.4719i	−0.732848	−	0.181680i
$532$		0			0
$533$	139.278	−	80.4122i	0.261309	−	0.150867i
$534$		0			0
$535$	389.270	−	674.235i	0.727607	−	1.26025i
$536$		0			0
$537$	−193.559	+	27.3349i	−0.360446	+	0.0509030i
$538$		0			0
$539$		−	704.824i		−	1.30765i
$540$		0			0
$541$	−809.693			−1.49666			−0.748330	−	0.663327i	$-0.769144\pi$
$541$	−809.693			−1.49666			−0.748330	+	0.663327i	$0.769144\pi$
$542$		0			0
$543$	40.0634	+	283.691i	0.0737817	+	0.522450i
$544$		0			0
$545$	1359.27	+	784.774i	2.49407	+	1.43995i
$546$		0			0
$547$	−468.105	−	810.781i	−0.855767	−	1.48223i	−0.875931	−	0.482436i	$-0.839752\pi$
$547$	−468.105	−	810.781i	−0.855767	−	1.48223i	0.0201641	−	0.999797i	$-0.493581\pi$
$548$		0			0
$549$	24.1220	+	23.2321i	0.0439380	+	0.0423171i
$550$		0			0
$551$	−321.242	+	185.469i	−0.583015	+	0.336604i
$552$		0			0
$553$	−127.963	+	221.638i	−0.231398	+	0.400793i
$554$		0			0
$555$	166.106	−	411.919i	0.299290	−	0.742196i
$556$		0			0
$557$			318.572i			0.571942i	0.958238	+	0.285971i	$0.0923162\pi$
$557$			318.572i			0.571942i	−0.958238	+	0.285971i	$0.907684\pi$
$558$		0			0
$559$	−408.548			−0.730855
$560$		0			0
$561$	−433.890	+	339.460i	−0.773423	+	0.605097i
$562$		0			0
$563$	700.038	+	404.167i	1.24341	+	0.717882i	0.969786	−	0.243956i	$-0.0784452\pi$
$563$	700.038	+	404.167i	1.24341	+	0.717882i	0.273621	+	0.961838i	$0.411779\pi$
$564$		0			0
$565$	−376.178	−	651.560i	−0.665802	−	1.15320i
$566$		0			0
$567$	151.363	+	79.9629i	0.266954	+	0.141028i
$568$		0			0
$569$	895.501	−	517.017i	1.57381	−	0.908642i	0.578120	−	0.815952i	$-0.303787\pi$
$569$	895.501	−	517.017i	1.57381	−	0.908642i	0.995695	−	0.0926904i	$-0.0295467\pi$
$570$		0			0
$571$	24.0163	−	41.5974i	0.0420600	−	0.0728500i	−0.844229	−	0.535983i	$-0.819941\pi$
$571$	24.0163	−	41.5974i	0.0420600	−	0.0728500i	0.886289	+	0.463133i	$0.153275\pi$
$572$		0			0
$573$	−343.546	−	439.114i	−0.599557	−	0.766342i
$574$		0			0
$575$		−	394.818i		−	0.686640i
$576$		0			0
$577$	396.617			0.687378			0.343689	−	0.939084i	$-0.388323\pi$
$577$	396.617			0.687378			0.343689	+	0.939084i	$0.388323\pi$
$578$		0			0
$579$	267.980	+	108.063i	0.462832	+	0.186636i
$580$		0			0
$581$	98.4558	+	56.8435i	0.169459	+	0.0978373i
$582$		0			0
$583$	−111.619	−	193.331i	−0.191457	−	0.331613i
$584$		0			0
$585$	556.619	−	577.939i	0.951485	−	0.987931i
$586$		0			0
$587$	−560.569	+	323.645i	−0.954973	+	0.551354i	−0.894622	−	0.446823i	$-0.852555\pi$
$587$	−560.569	+	323.645i	−0.954973	+	0.551354i	−0.0603509	+	0.998177i	$0.519222\pi$
$588$		0			0
$589$	113.541	−	196.658i	0.192769	−	0.333885i
$590$		0			0
$591$	374.646	−	52.9084i	0.633919	−	0.0895236i
$592$		0			0
$593$		−	322.360i		−	0.543609i	−0.962352	−	0.271805i	$-0.912380\pi$
$593$		−	322.360i		−	0.543609i	0.962352	−	0.271805i	$-0.0876204\pi$
$594$		0			0
$595$	−232.408			−0.390602
$596$		0			0
$597$	−55.2563	−	391.271i	−0.0925566	−	0.655396i
$598$		0			0
$599$	−286.437	−	165.374i	−0.478191	−	0.276084i	0.241471	−	0.970408i	$-0.422370\pi$
$599$	−286.437	−	165.374i	−0.478191	−	0.276084i	−0.719662	+	0.694324i	$0.755703\pi$
$600$		0			0
$601$	−2.29683	−	3.97823i	−0.00382169	−	0.00661936i	0.864108	−	0.503306i	$-0.167883\pi$
$601$	−2.29683	−	3.97823i	−0.00382169	−	0.00661936i	−0.867930	+	0.496687i	$0.834550\pi$
$602$		0			0
$603$	−90.9953	+	367.051i	−0.150904	+	0.608709i
$604$		0			0
$605$	−1062.84	+	613.633i	−1.75677	+	1.01427i
$606$		0			0
$607$	100.896	−	174.756i	0.166220	−	0.287902i	−0.770868	−	0.636995i	$-0.780177\pi$
$607$	100.896	−	174.756i	0.166220	−	0.287902i	0.937088	+	0.349093i	$0.113510\pi$
$608$		0			0
$609$	−67.8110	+	168.162i	−0.111348	+	0.276128i
$610$		0			0
$611$		−	224.512i		−	0.367450i
$612$		0			0
$613$	594.531			0.969871			0.484936	−	0.874550i	$-0.338843\pi$
$613$	594.531			0.969871			0.484936	+	0.874550i	$0.338843\pi$
$614$		0			0
$615$	−382.865	+	299.539i	−0.622545	+	0.487056i
$616$		0			0
$617$	−562.741	−	324.899i	−0.912060	−	0.526578i	−0.0309665	−	0.999520i	$-0.509859\pi$
$617$	−562.741	−	324.899i	−0.912060	−	0.526578i	−0.881093	+	0.472942i	$0.843192\pi$
$618$		0			0
$619$	114.275	+	197.931i	0.184613	+	0.319759i	0.943446	−	0.331526i	$-0.107564\pi$
$619$	114.275	+	197.931i	0.184613	+	0.319759i	−0.758833	+	0.651285i	$0.774230\pi$
$620$		0			0
$621$	16.8603	−	163.569i	0.0271503	−	0.263396i
$622$		0			0
$623$	−187.044	+	107.990i	−0.300231	+	0.173338i
$624$		0			0
$625$	−978.507	+	1694.82i	−1.56561	+	2.71172i
$626$		0			0
$627$	−379.482	−	485.046i	−0.605235	−	0.773599i
$628$		0			0
$629$			181.243i			0.288144i
$630$		0			0
$631$	−555.448			−0.880266			−0.440133	−	0.897933i	$-0.645069\pi$
$631$	−555.448			−0.880266			−0.440133	+	0.897933i	$0.645069\pi$
$632$		0			0
$633$	28.6761	+	11.5636i	0.0453019	+	0.0182680i
$634$		0			0
$635$	−1208.51	−	697.732i	−1.90316	−	1.09879i
$636$		0			0
$637$	−209.457	−	362.791i	−0.328819	−	0.569530i
$638$		0			0
$639$	−300.172	−	1041.57i	−0.469753	−	1.63000i
$640$		0			0
$641$	374.507	−	216.222i	0.584254	−	0.337319i	−0.178568	−	0.983928i	$-0.557147\pi$
$641$	374.507	−	216.222i	0.584254	−	0.337319i	0.762822	+	0.646608i	$0.223813\pi$
$642$		0			0
$643$	170.831	−	295.888i	0.265678	−	0.460168i	−0.702063	−	0.712115i	$-0.747738\pi$
$643$	170.831	−	295.888i	0.265678	−	0.460168i	0.967741	+	0.251947i	$0.0810709\pi$
$644$		0			0
$645$	1222.77	−	172.682i	1.89576	−	0.267724i
$646$		0			0
$647$			1066.85i			1.64891i	0.565926	+	0.824456i	$0.308519\pi$
$647$			1066.85i			1.64891i	−0.565926	+	0.824456i	$0.691481\pi$
$648$		0			0
$649$	705.037			1.08634
$650$		0			0
$651$	−15.5217	−	109.910i	−0.0238429	−	0.168832i
$652$		0			0
$653$	576.545	+	332.868i	0.882917	+	0.509752i	0.871619	−	0.490184i	$-0.163070\pi$
$653$	576.545	+	332.868i	0.882917	+	0.509752i	0.0112977	+	0.999936i	$0.496404\pi$
$654$		0			0
$655$	798.128	+	1382.40i	1.21852	+	2.11053i
$656$		0			0
$657$	−47.4511	+	13.6750i	−0.0722239	+	0.0208144i
$658$		0			0
$659$	795.462	−	459.260i	1.20707	−	0.696905i	0.244955	−	0.969534i	$-0.421227\pi$
$659$	795.462	−	459.260i	1.20707	−	0.696905i	0.962119	+	0.272630i	$0.0878934\pi$
$660$		0			0
$661$	385.777	−	668.185i	0.583626	−	1.01087i	−0.411420	−	0.911446i	$-0.634967\pi$
$661$	385.777	−	668.185i	0.583626	−	1.01087i	0.995045	−	0.0994232i	$-0.0316998\pi$
$662$		0			0
$663$	−122.455	+	303.671i	−0.184698	+	0.458025i
$664$		0			0
$665$		−	259.809i		−	0.390690i
$666$		0			0
$667$	174.169			0.261122
$668$		0			0
$669$	−408.387	+	319.507i	−0.610444	+	0.477588i
$670$		0			0
$671$	−51.0036	−	29.4470i	−0.0760114	−	0.0438852i
$672$		0			0
$673$	559.767	+	969.546i	0.831750	+	1.44063i	0.896650	+	0.442741i	$0.145994\pi$
$673$	559.767	+	969.546i	0.831750	+	1.44063i	−0.0649002	+	0.997892i	$0.520673\pi$
$674$		0			0
$675$	−1026.00	+	1418.14i	−1.52000	+	2.10094i
$676$		0			0
$677$	−339.051	+	195.751i	−0.500815	+	0.289145i	−0.729050	−	0.684461i	$-0.760038\pi$
$677$	−339.051	+	195.751i	−0.500815	+	0.289145i	0.228235	+	0.973606i	$0.426704\pi$
$678$		0			0
$679$	124.560	−	215.744i	0.183446	−	0.317737i
$680$		0			0
$681$	371.353	+	474.656i	0.545305	+	0.696999i
$682$		0			0
$683$			661.278i			0.968196i	0.875014	+	0.484098i	$0.160852\pi$
$683$			661.278i			0.968196i	−0.875014	+	0.484098i	$0.839148\pi$
$684$		0			0
$685$	1915.03			2.79566
$686$		0			0
$687$	726.907	+	293.125i	1.05809	+	0.426673i
$688$		0			0
$689$	−114.907	−	66.3415i	−0.166773	−	0.0962866i
$690$		0			0
$691$	−412.836	−	715.053i	−0.597447	−	1.03481i	−0.993197	−	0.116450i	$-0.962849\pi$
$691$	−412.836	−	715.053i	−0.597447	−	1.03481i	0.395750	−	0.918358i	$-0.370485\pi$
$692$		0			0
$693$	−292.193	−	72.4372i	−0.421635	−	0.104527i
$694$		0			0
$695$	2120.83	−	1224.46i	3.05155	−	1.76181i
$696$		0			0
$697$	99.1841	−	171.792i	0.142301	−	0.246473i
$698$		0			0
$699$	387.742	−	54.7579i	0.554710	−	0.0783374i
$700$		0			0
$701$			236.167i			0.336900i	0.985710	+	0.168450i	$0.0538761\pi$
$701$			236.167i			0.336900i	−0.985710	+	0.168450i	$0.946124\pi$
$702$		0			0
$703$	−202.611			−0.288209
$704$		0			0
$705$	94.8951	+	671.955i	0.134603	+	0.953128i
$706$		0			0
$707$	249.765	+	144.202i	0.353274	+	0.203963i
$708$		0			0
$709$	−247.969	−	429.496i	−0.349745	−	0.605777i	0.636459	−	0.771311i	$-0.280399\pi$
$709$	−247.969	−	429.496i	−0.349745	−	0.605777i	−0.986204	+	0.165534i	$0.947065\pi$
$710$		0			0
$711$	−784.994	−	756.035i	−1.10407	−	1.06334i
$712$		0			0
$713$	−92.3381	+	53.3115i	−0.129507	+	0.0747706i
$714$		0			0
$715$	−705.521	+	1222.00i	−0.986743	+	1.70909i
$716$		0			0
$717$	−300.027	+	744.023i	−0.418447	+	1.03769i
$718$		0			0
$719$		−	1065.13i		−	1.48141i	−0.671830	−	0.740705i	$-0.734492\pi$
$719$		−	1065.13i		−	1.48141i	0.671830	−	0.740705i	$-0.265508\pi$
$720$		0			0
$721$	257.207			0.356736
$722$		0			0
$723$	−240.149	+	187.884i	−0.332156	+	0.259867i
$724$		0			0
$725$	−1605.59	−	926.987i	−2.21460	−	1.27860i
$726$		0			0
$727$	−549.525	−	951.806i	−0.755881	−	1.30922i	−0.944935	−	0.327257i	$-0.893876\pi$
$727$	−549.525	−	951.806i	−0.755881	−	1.30922i	0.189054	−	0.981967i	$-0.439458\pi$
$728$		0			0
$729$	−485.620	+	543.704i	−0.666146	+	0.745822i
$730$		0			0
$731$	−436.409	+	251.961i	−0.597003	+	0.344680i
$732$		0			0
$733$	−720.569	+	1248.06i	−0.983041	+	1.70268i	−0.332706	+	0.943031i	$0.607962\pi$
$733$	−720.569	+	1248.06i	−0.983041	+	1.70268i	−0.650336	+	0.759647i	$0.725372\pi$
$734$		0			0
$735$	780.240	+	997.287i	1.06155	+	1.35685i
$736$		0			0
$737$		−	665.013i		−	0.902324i
$738$		0			0
$739$	1095.72			1.48271			0.741356	−	0.671112i	$-0.234183\pi$
$739$	1095.72			1.48271			0.741356	+	0.671112i	$0.234183\pi$
$740$		0			0
$741$	−339.474	−	136.892i	−0.458129	−	0.184740i
$742$		0			0
$743$	857.848	+	495.279i	1.15457	+	0.666593i	0.949997	−	0.312258i	$-0.101085\pi$
$743$	857.848	+	495.279i	1.15457	+	0.666593i	0.204575	+	0.978851i	$0.434419\pi$
$744$		0			0
$745$	−375.552	−	650.476i	−0.504097	−	0.873122i
$746$		0			0
$747$	−335.844	+	348.708i	−0.449591	+	0.466812i
$748$		0			0
$749$	−150.345	+	86.8018i	−0.200728	+	0.115890i
$750$		0			0
$751$	177.884	−	308.103i	0.236862	−	0.410258i	−0.722950	−	0.690900i	$-0.757214\pi$
$751$	177.884	−	308.103i	0.236862	−	0.410258i	0.959812	+	0.280643i	$0.0905476\pi$
$752$		0			0
$753$	−407.058	+	57.4857i	−0.540582	+	0.0763423i
$754$		0			0
$755$		−	89.6776i		−	0.118778i
$756$		0			0
$757$	−231.917			−0.306364			−0.153182	−	0.988198i	$-0.548952\pi$
$757$	−231.917			−0.306364			−0.153182	+	0.988198i	$0.548952\pi$
$758$		0			0
$759$	40.4354	+	286.325i	0.0532746	+	0.377239i
$760$		0			0
$761$	−368.325	−	212.653i	−0.484002	−	0.279438i	0.238081	−	0.971245i	$-0.423482\pi$
$761$	−368.325	−	212.653i	−0.484002	−	0.279438i	−0.722083	+	0.691807i	$0.756815\pi$
$762$		0			0
$763$	−174.994	−	303.098i	−0.229350	−	0.397245i
$764$		0			0
$765$	238.149	−	960.633i	0.311306	−	1.25573i
$766$		0			0
$767$	362.900	−	209.521i	0.473143	−	0.273169i
$768$		0			0
$769$	422.147	−	731.179i	0.548955	−	0.950819i	−0.449391	−	0.893335i	$-0.648359\pi$
$769$	422.147	−	731.179i	0.548955	−	0.950819i	0.998346	−	0.0574834i	$-0.0183076\pi$
$770$		0			0
$771$	−282.085	+	699.530i	−0.365869	+	0.907302i
$772$		0			0
$773$		−	816.503i		−	1.05628i	−0.849158	−	0.528139i	$-0.822890\pi$
$773$		−	816.503i		−	1.05628i	0.849158	−	0.528139i	$-0.177110\pi$
$774$		0			0
$775$	1134.97			1.46448
$776$		0			0
$777$	−78.0031	+	61.0267i	−0.100390	+	0.0785414i
$778$		0			0
$779$	192.046	+	110.878i	0.246529	+	0.142334i
$780$		0			0
$781$	953.093	+	1650.81i	1.22035	+	2.11371i
$782$		0			0
$783$	−625.592	−	452.606i	−0.798967	−	0.578040i
$784$		0			0
$785$	−563.991	+	325.620i	−0.718459	+	0.414803i
$786$		0			0
$787$	−178.111	+	308.497i	−0.226316	+	0.391991i	−0.956713	−	0.291031i	$-0.906002\pi$
$787$	−178.111	+	308.497i	−0.226316	+	0.391991i	0.730397	+	0.683022i	$0.239335\pi$
$788$		0			0
$789$	−889.116	−	1136.45i	−1.12689	−	1.44037i
$790$		0			0
$791$			167.765i			0.212092i
$792$		0			0
$793$	−35.0038			−0.0441410
$794$		0			0
$795$	371.952	+	149.989i	0.467864	+	0.188666i
$796$		0			0
$797$	561.666	+	324.278i	0.704725	+	0.406873i	0.809105	−	0.587664i	$-0.199952\pi$
$797$	561.666	+	324.278i	0.704725	+	0.406873i	−0.104380	+	0.994537i	$0.533286\pi$
$798$		0			0
$799$	−138.462	−	239.823i	−0.173294	−	0.300154i
$800$		0			0
$801$	−254.699	−	883.782i	−0.317976	−	1.10335i
$802$		0			0
$803$	75.2062	−	43.4203i	0.0936565	−	0.0540726i
$804$		0			0
$805$	−60.9948	+	105.646i	−0.0757700	+	0.131237i
$806$		0			0
$807$	543.425	−	76.7438i	0.673389	−	0.0950976i
$808$		0			0
$809$			445.244i			0.550363i	0.961392	+	0.275182i	$0.0887380\pi$
$809$			445.244i			0.550363i	−0.961392	+	0.275182i	$0.911262\pi$
$810$		0			0
$811$	−373.366			−0.460377			−0.230189	−	0.973146i	$-0.573934\pi$
$811$	−373.366			−0.460377			−0.230189	+	0.973146i	$0.573934\pi$
$812$		0			0
$813$	13.0108	+	92.1296i	0.0160034	+	0.113321i
$814$		0			0
$815$	−1718.68	−	992.282i	−2.10881	−	1.21752i
$816$		0			0
$817$	−281.667	−	487.862i	−0.344758	−	0.597139i
$818$		0			0
$819$	−171.926	+	49.5477i	−0.209922	+	0.0604978i
$820$		0			0
$821$	−42.7001	+	24.6529i	−0.0520099	+	0.0300279i	−0.525779	−	0.850621i	$-0.676226\pi$
$821$	−42.7001	+	24.6529i	−0.0520099	+	0.0300279i	0.473770	+	0.880649i	$0.342893\pi$
$822$		0			0
$823$	289.224	−	500.950i	0.351426	−	0.608688i	−0.635074	−	0.772452i	$-0.719030\pi$
$823$	289.224	−	500.950i	0.351426	−	0.608688i	0.986500	+	0.163764i	$0.0523635\pi$
$824$		0			0
$825$	1151.16	−	2854.72i	1.39535	−	3.46027i
$826$		0			0
$827$		−	665.710i		−	0.804970i	−0.915427	−	0.402485i	$-0.868147\pi$
$827$		−	665.710i		−	0.804970i	0.915427	−	0.402485i	$-0.131853\pi$
$828$		0			0
$829$	133.042			0.160485			0.0802423	−	0.996775i	$-0.474431\pi$
$829$	133.042			0.160485			0.0802423	+	0.996775i	$0.474431\pi$
$830$		0			0
$831$	−975.276	+	763.019i	−1.17362	+	0.918194i
$832$		0			0
$833$	−447.483	−	258.355i	−0.537195	−	0.310150i
$834$		0			0
$835$	−116.927	−	202.523i	−0.140032	−	0.242543i
$836$		0			0
$837$	470.205	+	48.4678i	0.561775	+	0.0579065i
$838$		0			0
$839$	−707.636	+	408.554i	−0.843428	+	0.486954i	−0.858428	−	0.512934i	$-0.828559\pi$
$839$	−707.636	+	408.554i	−0.843428	+	0.486954i	0.0149998	+	0.999887i	$0.495225\pi$
$840$		0			0
$841$	−11.5724	+	20.0439i	−0.0137602	+	0.0238334i
$842$		0			0
$843$	228.939	+	292.626i	0.271577	+	0.347124i
$844$		0			0
$845$		−	763.087i		−	0.903062i
$846$		0			0
$847$	273.663			0.323097
$848$		0			0
$849$	23.5766	+	9.50724i	0.0277698	+	0.0111982i
$850$		0			0
$851$	82.3878	+	47.5666i	0.0968129	+	0.0558950i
$852$		0			0
$853$	−14.2616	−	24.7018i	−0.0167193	−	0.0289587i	0.857545	−	0.514409i	$-0.171989\pi$
$853$	−14.2616	−	24.7018i	−0.0167193	−	0.0289587i	−0.874264	+	0.485451i	$0.838656\pi$
$854$		0			0
$855$	1073.89	+	266.227i	1.25601	+	0.311377i
$856$		0			0
$857$	−1218.49	+	703.496i	−1.42181	+	0.820883i	−0.996454	−	0.0841433i	$-0.973185\pi$
$857$	−1218.49	+	703.496i	−1.42181	+	0.820883i	−0.425357	+	0.905026i	$0.639851\pi$
$858$		0			0
$859$	−296.573	+	513.680i	−0.345254	+	0.597998i	−0.985400	−	0.170256i	$-0.945541\pi$
$859$	−296.573	+	513.680i	−0.345254	+	0.597998i	0.640146	+	0.768254i	$0.278874\pi$
$860$		0			0
$861$	107.332	−	15.1577i	0.124660	−	0.0176048i
$862$		0			0
$863$			549.058i			0.636220i	0.948054	+	0.318110i	$0.103048\pi$
$863$			549.058i			0.636220i	−0.948054	+	0.318110i	$0.896952\pi$
$864$		0			0
$865$	−1413.81			−1.63446
$866$		0			0
$867$	−64.7619	−	458.581i	−0.0746965	−	0.528928i
$868$		0			0
$869$	1659.80	+	958.283i	1.91001	+	1.10274i
$870$		0			0
$871$	−197.626	−	342.299i	−0.226896	−	0.392996i
$872$		0			0
$873$	764.116	+	735.927i	0.875276	+	0.842987i
$874$		0			0
$875$	690.900	−	398.891i	0.789600	−	0.455876i
$876$		0			0
$877$	−481.413	+	833.831i	−0.548931	+	0.950776i	0.449417	+	0.893322i	$0.351632\pi$
$877$	−481.413	+	833.831i	−0.548931	+	0.950776i	−0.998348	+	0.0574544i	$0.981702\pi$
$878$		0			0
$879$	−120.759	+	299.464i	−0.137382	+	0.340688i
$880$		0			0
$881$			485.913i			0.551547i	0.961223	+	0.275774i	$0.0889340\pi$
$881$			485.913i			0.551547i	−0.961223	+	0.275774i	$0.911066\pi$
$882$		0			0
$883$	1020.25			1.15544			0.577720	−	0.816235i	$-0.303943\pi$
$883$	1020.25			1.15544			0.577720	+	0.816235i	$0.303943\pi$
$884$		0			0
$885$	−997.587	+	780.475i	−1.12722	+	0.881892i
$886$		0			0
$887$	896.965	+	517.863i	1.01123	+	0.583836i	0.911553	−	0.411183i	$-0.134884\pi$
$887$	896.965	+	517.863i	1.01123	+	0.583836i	0.0996814	+	0.995019i	$0.468218\pi$
$888$		0			0
$889$	155.584	+	269.480i	0.175011	+	0.303127i
$890$		0			0
$891$	598.822	−	1133.52i	0.672079	−	1.27219i
$892$		0			0
$893$	268.098	−	154.787i	0.300222	−	0.173333i
$894$		0			0
$895$	−308.786	+	534.834i	−0.345013	+	0.597580i
$896$		0			0
$897$	105.902	+	135.362i	0.118063	+	0.150905i
$898$		0			0
$899$			500.676i			0.556926i
$900$		0			0
$901$	−163.657			−0.181640
$902$		0			0
$903$	−255.383	−	102.983i	−0.282817	−	0.114046i
$904$		0			0
$905$	783.880	+	452.573i	0.866165	+	0.500081i
$906$		0			0
$907$	−794.936	−	1376.87i	−0.876445	−	1.51805i	−0.855215	−	0.518273i	$-0.826575\pi$
$907$	−794.936	−	1376.87i	−0.876445	−	1.51805i	−0.0212301	−	0.999775i	$-0.506758\pi$
$908$		0			0
$909$	−851.977	+	884.611i	−0.937269	+	0.973170i
$910$		0			0
$911$	362.743	−	209.430i	0.398181	−	0.229890i	−0.287518	−	0.957775i	$-0.592830\pi$
$911$	362.743	−	209.430i	0.398181	−	0.229890i	0.685699	+	0.727885i	$0.259497\pi$
$912$		0			0
$913$	425.687	−	737.311i	0.466250	−	0.807569i
$914$		0			0
$915$	104.765	−	14.7952i	0.114497	−	0.0161696i
$916$		0			0
$917$		−	355.943i		−	0.388160i
$918$		0			0
$919$	−1499.57			−1.63174			−0.815872	−	0.578233i	$-0.803743\pi$
$919$	−1499.57			−1.63174			−0.815872	+	0.578233i	$0.803743\pi$
$920$		0			0
$921$	222.637	+	1576.50i	0.241734	+	1.71173i
$922$		0			0
$923$	981.162	+	566.474i	1.06301	+	0.613732i
$924$		0			0
$925$	−506.333	−	876.994i	−0.547387	−	0.948102i
$926$		0			0
$927$	−263.561	+	1063.14i	−0.284316	+	1.14686i
$928$		0			0
$929$	−1046.99	+	604.481i	−1.12701	+	0.650679i	−0.943181	−	0.332279i	$-0.892183\pi$
$929$	−1046.99	+	604.481i	−1.12701	+	0.650679i	−0.183829	+	0.982958i	$0.558849\pi$
$930$		0			0
$931$	288.815	−	500.242i	0.310220	−	0.537317i
$932$		0			0
$933$	184.658	−	457.926i	0.197919	−	0.490810i
$934$		0			0
$935$			1740.45i			1.86144i
$936$		0			0
$937$	557.393			0.594870			0.297435	−	0.954742i	$-0.403869\pi$
$937$	557.393			0.594870			0.297435	+	0.954742i	$0.403869\pi$
$938$		0			0
$939$	1294.02	−	1012.40i	1.37809	−	1.07816i
$940$		0			0
$941$	465.315	+	268.650i	0.494490	+	0.285494i	0.726435	−	0.687235i	$-0.241176\pi$
$941$	465.315	+	268.650i	0.494490	+	0.285494i	−0.231945	+	0.972729i	$0.574509\pi$
$942$		0			0
$943$	−52.0612	−	90.1727i	−0.0552081	−	0.0956232i
$944$		0			0
$945$	493.624	−	220.963i	0.522354	−	0.233823i
$946$		0			0
$947$	515.416	−	297.575i	0.544261	−	0.314229i	−0.202543	−	0.979273i	$-0.564921\pi$
$947$	515.416	−	297.575i	0.544261	−	0.314229i	0.746804	+	0.665044i	$0.231587\pi$
$948$		0			0
$949$	25.8070	−	44.6991i	0.0271939	−	0.0471012i
$950$		0			0
$951$	−144.531	−	184.737i	−0.151978	−	0.194255i
$952$		0			0
$953$			88.9834i			0.0933718i	0.998910	+	0.0466859i	$0.0148660\pi$
$953$			88.9834i			0.0933718i	−0.998910	+	0.0466859i	$0.985134\pi$
$954$		0			0
$955$	−1761.40			−1.84440
$956$		0			0
$957$	1259.32	+	507.820i	1.31591	+	0.530638i
$958$		0			0
$959$	−369.814	−	213.512i	−0.385625	−	0.222641i
$960$		0			0
$961$	327.247	+	566.809i	0.340528	+	0.589812i
$962$		0			0
$963$	−204.726	−	710.381i	−0.212592	−	0.737675i
$964$		0			0
$965$	790.560	−	456.430i	0.819233	−	0.472985i
$966$		0			0
$967$	−658.074	+	1139.82i	−0.680532	+	1.17872i	0.294287	+	0.955717i	$0.404918\pi$
$967$	−658.074	+	1139.82i	−0.680532	+	1.17872i	−0.974819	+	0.222998i	$0.928416\pi$
$968$		0			0
$969$	−447.049	+	63.1333i	−0.461351	+	0.0651531i
$970$		0			0
$971$			361.433i			0.372228i	0.982528	+	0.186114i	$0.0595893\pi$
$971$			361.433i			0.372228i	−0.982528	+	0.186114i	$0.940411\pi$
$972$		0			0
$973$	−546.075			−0.561228
$974$		0			0
$975$	−255.824	−	1811.50i	−0.262383	−	1.85795i
$976$		0			0
$977$	883.148	+	509.885i	0.903938	+	0.521889i	0.878476	−	0.477787i	$-0.158561\pi$
$977$	883.148	+	509.885i	0.903938	+	0.521889i	0.0254624	+	0.999676i	$0.491894\pi$
$978$		0			0
$979$	808.708	+	1400.72i	0.826056	+	1.43077i
$980$		0			0
$981$	1432.14	−	412.731i	1.45988	−	0.420725i
$982$		0			0
$983$	−1144.21	+	660.612i	−1.16400	+	0.672037i	−0.952260	−	0.305289i	$-0.901247\pi$
$983$	−1144.21	+	660.612i	−1.16400	+	0.672037i	−0.211742	+	0.977326i	$0.567914\pi$
$984$		0			0
$985$	597.675	−	1035.20i	0.606777	−	1.05097i
$986$		0			0
$987$	56.5930	−	140.342i	0.0573384	−	0.142191i
$988$		0			0
$989$			264.506i			0.267448i
$990$		0			0
$991$	−6.11587			−0.00617141			−0.00308571	−	0.999995i	$-0.500982\pi$
$991$	−6.11587			−0.00617141			−0.00308571	+	0.999995i	$0.500982\pi$
$992$		0			0
$993$	1299.06	−	1016.33i	1.30821	−	1.02350i
$994$		0			0
$995$	−1081.14	−	624.197i	−1.08657	−	0.627334i
$996$		0			0
$997$	315.180	+	545.908i	0.316129	+	0.547551i	0.979677	−	0.200583i	$-0.0642835\pi$
$997$	315.180	+	545.908i	0.316129	+	0.547551i	−0.663548	+	0.748134i	$0.730950\pi$
$998$		0			0
$999$	−172.317	−	384.951i	−0.172489	−	0.385337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.m.b.41.1	✓	8
3.2	odd	2		216.3.m.b.17.4		8
4.3	odd	2		144.3.q.e.113.4		8
8.3	odd	2		576.3.q.j.257.1		8
8.5	even	2		576.3.q.i.257.4		8
9.2	odd	6	inner	72.3.m.b.65.1	yes	8
9.4	even	3		648.3.e.c.161.8		8
9.5	odd	6		648.3.e.c.161.1		8
9.7	even	3		216.3.m.b.89.4		8
12.11	even	2		432.3.q.e.17.4		8
24.5	odd	2		1728.3.q.j.449.1		8
24.11	even	2		1728.3.q.i.449.1		8
36.7	odd	6		432.3.q.e.305.4		8
36.11	even	6		144.3.q.e.65.4		8
36.23	even	6		1296.3.e.i.161.1		8
36.31	odd	6		1296.3.e.i.161.8		8
72.11	even	6		576.3.q.j.65.1		8
72.29	odd	6		576.3.q.i.65.4		8
72.43	odd	6		1728.3.q.i.1601.1		8
72.61	even	6		1728.3.q.j.1601.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.1	✓	8	1.1	even	1	trivial
72.3.m.b.65.1	yes	8	9.2	odd	6	inner
144.3.q.e.65.4		8	36.11	even	6
144.3.q.e.113.4		8	4.3	odd	2
216.3.m.b.17.4		8	3.2	odd	2
216.3.m.b.89.4		8	9.7	even	3
432.3.q.e.17.4		8	12.11	even	2
432.3.q.e.305.4		8	36.7	odd	6
576.3.q.i.65.4		8	72.29	odd	6
576.3.q.i.257.4		8	8.5	even	2
576.3.q.j.65.1		8	72.11	even	6
576.3.q.j.257.1		8	8.3	odd	2
648.3.e.c.161.1		8	9.5	odd	6
648.3.e.c.161.8		8	9.4	even	3
1296.3.e.i.161.1		8	36.23	even	6
1296.3.e.i.161.8		8	36.31	odd	6
1728.3.q.i.449.1		8	24.11	even	2
1728.3.q.i.1601.1		8	72.43	odd	6
1728.3.q.j.449.1		8	24.5	odd	2
1728.3.q.j.1601.1		8	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.419504 - 2.97052i) q^{3} +(-8.20800 - 4.73889i) q^{5} +(1.05671 + 1.83027i) q^{7} +(-8.64803 + 2.49230i) q^{9} +O(q^{10})\)	\(q+(-0.419504 - 2.97052i) q^{3} +(-8.20800 - 4.73889i) q^{5} +(1.05671 + 1.83027i) q^{7} +(-8.64803 + 2.49230i) q^{9} +(13.7064 - 7.91342i) q^{11} +(4.70337 - 8.14648i) q^{13} +(-10.6337 + 26.3701i) q^{15} -11.6027i q^{17} +12.9707 q^{19} +(4.99357 - 3.90678i) q^{21} +(-5.27427 - 3.04510i) q^{23} +(32.4142 + 56.1431i) q^{25} +(11.0313 + 24.6437i) q^{27} +(-24.7667 + 14.2991i) q^{29} +(8.75365 - 15.1618i) q^{31} +(-29.2569 - 37.3956i) q^{33} -20.0305i q^{35} -15.6207 q^{37} +(-26.1724 - 10.5540i) q^{39} +(14.8062 + 8.54836i) q^{41} +(-21.7157 - 37.6127i) q^{43} +(82.7938 + 20.5253i) q^{45} +(20.6696 - 11.9336i) q^{47} +(22.2667 - 38.5671i) q^{49} +(-34.4661 + 4.86739i) q^{51} -14.1051i q^{53} -150.003 q^{55} +(-5.44126 - 38.5297i) q^{57} +(38.5788 + 22.2735i) q^{59} +(-1.86057 - 3.22260i) q^{61} +(-13.7000 - 13.1946i) q^{63} +(-77.2105 + 44.5775i) q^{65} +(21.0090 - 36.3887i) q^{67} +(-6.83297 + 16.9448i) q^{69} +120.440i q^{71} +5.48692 q^{73} +(153.176 - 119.839i) q^{75} +(28.9674 + 16.7243i) q^{77} +(60.5480 + 104.872i) q^{79} +(68.5769 - 43.1069i) q^{81} +(46.5861 - 26.8965i) q^{83} +(-54.9840 + 95.2351i) q^{85} +(52.8655 + 67.5717i) q^{87} +102.195i q^{89} +19.8803 q^{91} +(-48.7106 - 19.6425i) q^{93} +(-106.463 - 61.4667i) q^{95} +(-58.9377 - 102.083i) q^{97} +(-98.8112 + 102.596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) \) 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9	\( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9} + 36 q^{11} + 14 q^{13} + 10 q^{15} + 4 q^{19} - 54 q^{21} - 102 q^{23} + 10 q^{25} - 20 q^{27} - 114 q^{29} - 50 q^{31} - 104 q^{33} + 120 q^{37} + 82 q^{39} + 264 q^{41} - 28 q^{43} + 206 q^{45} + 150 q^{47} + 94 q^{49} + 170 q^{51} - 244 q^{55} - 178 q^{57} - 108 q^{59} + 14 q^{61} - 210 q^{63} - 198 q^{65} - 20 q^{67} - 14 q^{69} - 76 q^{73} + 326 q^{75} + 66 q^{77} + 26 q^{79} + 194 q^{81} + 246 q^{83} - 224 q^{85} - 18 q^{87} + 108 q^{91} - 130 q^{93} - 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) \) 8 * q + 10 * q^3 - 6 * q^5 + 6 * q^7 - 22 * q^9 + 36 * q^11 + 14 * q^13 + 10 * q^15 + 4 * q^19 - 54 * q^21 - 102 * q^23 + 10 * q^25 - 20 * q^27 - 114 * q^29 - 50 * q^31 - 104 * q^33 + 120 * q^37 + 82 * q^39 + 264 * q^41 - 28 * q^43 + 206 * q^45 + 150 * q^47 + 94 * q^49 + 170 * q^51 - 244 * q^55 - 178 * q^57 - 108 * q^59 + 14 * q^61 - 210 * q^63 - 198 * q^65 - 20 * q^67 - 14 * q^69 - 76 * q^73 + 326 * q^75 + 66 * q^77 + 26 * q^79 + 194 * q^81 + 246 * q^83 - 224 * q^85 - 18 * q^87 + 108 * q^91 - 130 * q^93 - 456 * q^95 - 236 * q^97 - 634 * q^99

Introduction

L-functions

Modular forms

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Database

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