LMFDB - Embedded newform 324.3.o.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.76434 - 1.16550i) q^{3} +(-0.148228 + 0.110352i) q^{5} +(5.09912 - 3.35374i) q^{7} +(6.28320 + 6.44371i) q^{9} +O(q^{10})$	\(q+(-2.76434 - 1.16550i) q^{3} +(-0.148228 + 0.110352i) q^{5} +(5.09912 - 3.35374i) q^{7} +(6.28320 + 6.44371i) q^{9} +(-1.69174 + 14.4737i) q^{11} +(-2.59671 - 8.67360i) q^{13} +(0.538369 - 0.132290i) q^{15} +(6.34459 + 1.11872i) q^{17} +(-4.95520 - 28.1023i) q^{19} +(-18.0045 + 3.32785i) q^{21} +(24.7802 - 37.6764i) q^{23} +(-7.16029 + 23.9170i) q^{25} +(-9.85875 - 25.1357i) q^{27} +(35.2456 - 33.2525i) q^{29} +(0.345056 - 5.92438i) q^{31} +(21.5457 - 38.0387i) q^{33} +(-0.385742 + 1.05982i) q^{35} +(59.7445 - 21.7452i) q^{37} +(-2.93093 + 27.0033i) q^{39} +(-9.46893 + 39.9526i) q^{41} +(-33.4930 - 77.6454i) q^{43} +(-1.64242 - 0.261777i) q^{45} +(-8.86308 + 0.516216i) q^{47} +(-4.65449 + 10.7903i) q^{49} +(-16.2348 - 10.4872i) q^{51} +(16.9526 + 9.78756i) q^{53} +(-1.34644 - 2.33210i) q^{55} +(-19.0555 + 83.4598i) q^{57} +(-1.86108 - 15.9226i) q^{59} +(-61.9122 - 31.0935i) q^{61} +(53.6493 + 11.7850i) q^{63} +(1.34205 + 0.999121i) q^{65} +(12.7093 - 13.4711i) q^{67} +(-112.413 + 75.2692i) q^{69} +(49.6251 - 59.1408i) q^{71} +(-51.1888 + 42.9525i) q^{73} +(47.6689 - 57.7695i) q^{75} +(39.9148 + 79.4769i) q^{77} +(95.3805 - 22.6056i) q^{79} +(-2.04282 + 80.9742i) q^{81} +(35.6277 + 150.325i) q^{83} +(-1.06390 + 0.534311i) q^{85} +(-136.187 + 50.8425i) q^{87} +(64.2127 + 76.5257i) q^{89} +(-42.3299 - 35.5190i) q^{91} +(-7.85874 + 15.9749i) q^{93} +(3.83564 + 3.61874i) q^{95} +(61.2573 - 82.2829i) q^{97} +(-103.894 + 80.0403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.76434	−	1.16550i	−0.921448	−	0.388501i
$3$	−2.76434	−	1.16550i	−0.921448	−	0.388501i
$4$		0			0
$5$	−0.148228	+	0.110352i	−0.0296456	+	0.0220704i	−0.611879	−	0.790951i	$-0.709586\pi$
$5$	−0.148228	+	0.110352i	−0.0296456	+	0.0220704i	0.582234	+	0.813021i	$0.302179\pi$
$6$		0			0
$7$	5.09912	−	3.35374i	0.728445	−	0.479106i	−0.130322	−	0.991472i	$-0.541601\pi$
$7$	5.09912	−	3.35374i	0.728445	−	0.479106i	0.858767	+	0.512366i	$0.171231\pi$
$8$		0			0
$9$	6.28320	+	6.44371i	0.698133	+	0.715968i
$10$		0			0
$11$	−1.69174	+	14.4737i	−0.153794	+	1.31579i	0.667209	+	0.744871i	$0.267489\pi$
$11$	−1.69174	+	14.4737i	−0.153794	+	1.31579i	−0.821003	+	0.570924i	$0.806585\pi$
$12$		0			0
$13$	−2.59671	−	8.67360i	−0.199747	−	0.667200i	−0.997902	−	0.0647481i	$-0.979376\pi$
$13$	−2.59671	−	8.67360i	−0.199747	−	0.667200i	0.798155	−	0.602452i	$-0.205810\pi$
$14$		0			0
$15$	0.538369	−	0.132290i	0.0358913	−	0.00881932i
$16$		0			0
$17$	6.34459	+	1.11872i	0.373211	+	0.0658072i	0.357108	−	0.934063i	$-0.383763\pi$
$17$	6.34459	+	1.11872i	0.373211	+	0.0658072i	0.0161033	+	0.999870i	$0.494874\pi$
$18$		0			0
$19$	−4.95520	−	28.1023i	−0.260800	−	1.47907i	−0.780734	−	0.624863i	$-0.785155\pi$
$19$	−4.95520	−	28.1023i	−0.260800	−	1.47907i	0.519935	−	0.854206i	$-0.325956\pi$
$20$		0			0
$21$	−18.0045	+	3.32785i	−0.857358	+	0.158469i
$22$		0			0
$23$	24.7802	−	37.6764i	1.07740	−	1.63811i	0.373797	−	0.927510i	$-0.378056\pi$
$23$	24.7802	−	37.6764i	1.07740	−	1.63811i	0.703602	−	0.710595i	$-0.251574\pi$
$24$		0			0
$25$	−7.16029	+	23.9170i	−0.286411	+	0.956681i
$26$		0			0
$27$	−9.85875	−	25.1357i	−0.365139	−	0.930953i
$28$		0			0
$29$	35.2456	−	33.2525i	1.21537	−	1.14664i	0.230546	−	0.973061i	$-0.425949\pi$
$29$	35.2456	−	33.2525i	1.21537	−	1.14664i	0.984820	−	0.173578i	$-0.0555329\pi$
$30$		0			0
$31$	0.345056	−	5.92438i	0.0111308	−	0.191109i	−0.988159	−	0.153432i	$-0.950967\pi$
$31$	0.345056	−	5.92438i	0.0111308	−	0.191109i	0.999290	−	0.0376766i	$-0.0119957\pi$
$32$		0			0
$33$	21.5457	−	38.0387i	0.652901	−	1.15269i
$34$		0			0
$35$	−0.385742	+	1.05982i	−0.0110212	+	0.0302805i
$36$		0			0
$37$	59.7445	−	21.7452i	1.61472	−	0.587709i	0.632352	−	0.774681i	$-0.282090\pi$
$37$	59.7445	−	21.7452i	1.61472	−	0.587709i	0.982365	+	0.186972i	$0.0598675\pi$
$38$		0			0
$39$	−2.93093	+	27.0033i	−0.0751521	+	0.692392i
$40$		0			0
$41$	−9.46893	+	39.9526i	−0.230950	+	0.974453i	0.726800	+	0.686849i	$0.241007\pi$
$41$	−9.46893	+	39.9526i	−0.230950	+	0.974453i	−0.957749	+	0.287604i	$0.907141\pi$
$42$		0			0
$43$	−33.4930	−	77.6454i	−0.778906	−	1.80571i	−0.556714	−	0.830704i	$-0.687938\pi$
$43$	−33.4930	−	77.6454i	−0.778906	−	1.80571i	−0.222192	−	0.975003i	$-0.571321\pi$
$44$		0			0
$45$	−1.64242	−	0.261777i	−0.0364983	−	0.00581727i
$46$		0			0
$47$	−8.86308	+	0.516216i	−0.188576	+	0.0109833i	−0.152173	−	0.988354i	$-0.548627\pi$
$47$	−8.86308	+	0.516216i	−0.188576	+	0.0109833i	−0.0364032	+	0.999337i	$0.511590\pi$
$48$		0			0
$49$	−4.65449	+	10.7903i	−0.0949897	+	0.220211i
$50$		0			0
$51$	−16.2348	−	10.4872i	−0.318329	−	0.205631i
$52$		0			0
$53$	16.9526	+	9.78756i	0.319860	+	0.184671i	0.651330	−	0.758795i	$-0.274211\pi$
$53$	16.9526	+	9.78756i	0.319860	+	0.184671i	−0.331470	+	0.943466i	$0.607545\pi$
$54$		0			0
$55$	−1.34644	−	2.33210i	−0.0244807	−	0.0424019i
$56$		0			0
$57$	−19.0555	+	83.4598i	−0.334307	+	1.46421i
$58$		0			0
$59$	−1.86108	−	15.9226i	−0.0315437	−	0.269874i	−0.999802	−	0.0199203i	$-0.993659\pi$
$59$	−1.86108	−	15.9226i	−0.0315437	−	0.269874i	0.968258	−	0.249953i	$-0.0804153\pi$
$60$		0			0
$61$	−61.9122	−	31.0935i	−1.01495	−	0.509729i	−0.138065	−	0.990423i	$-0.544088\pi$
$61$	−61.9122	−	31.0935i	−1.01495	−	0.509729i	−0.876888	+	0.480694i	$0.840385\pi$
$62$		0			0
$63$	53.6493	+	11.7850i	0.851577	+	0.187064i
$64$		0			0
$65$	1.34205	+	0.999121i	0.0206470	+	0.0153711i
$66$		0			0
$67$	12.7093	−	13.4711i	0.189691	−	0.201061i	−0.625548	−	0.780186i	$-0.715124\pi$
$67$	12.7093	−	13.4711i	0.189691	−	0.201061i	0.815238	+	0.579125i	$0.196606\pi$
$68$		0			0
$69$	−112.413	+	75.2692i	−1.62917	+	1.09086i
$70$		0			0
$71$	49.6251	−	59.1408i	0.698945	−	0.832970i	−0.293462	−	0.955971i	$-0.594807\pi$
$71$	49.6251	−	59.1408i	0.698945	−	0.832970i	0.992407	+	0.123001i	$0.0392519\pi$
$72$		0			0
$73$	−51.1888	+	42.9525i	−0.701217	+	0.588391i	−0.922120	−	0.386905i	$-0.873544\pi$
$73$	−51.1888	+	42.9525i	−0.701217	+	0.588391i	0.220903	+	0.975296i	$0.429100\pi$
$74$		0			0
$75$	47.6689	−	57.7695i	0.635585	−	0.770261i
$76$		0			0
$77$	39.9148	+	79.4769i	0.518374	+	1.03217i
$78$		0			0
$79$	95.3805	−	22.6056i	1.20735	−	0.286147i	0.422805	−	0.906221i	$-0.361046\pi$
$79$	95.3805	−	22.6056i	1.20735	−	0.286147i	0.784543	+	0.620074i	$0.212898\pi$
$80$		0			0
$81$	−2.04282	+	80.9742i	−0.0252200	+	0.999682i
$82$		0			0
$83$	35.6277	+	150.325i	0.429249	+	1.81114i	0.570653	+	0.821191i	$0.306690\pi$
$83$	35.6277	+	150.325i	0.429249	+	1.81114i	−0.141404	+	0.989952i	$0.545162\pi$
$84$		0			0
$85$	−1.06390	+	0.534311i	−0.0125165	+	0.00628601i
$86$		0			0
$87$	−136.187	+	50.8425i	−1.56537	+	0.584397i
$88$		0			0
$89$	64.2127	+	76.5257i	0.721491	+	0.859840i	0.994775	−	0.102094i	$-0.0325541\pi$
$89$	64.2127	+	76.5257i	0.721491	+	0.859840i	−0.273283	+	0.961934i	$0.588110\pi$
$90$		0			0
$91$	−42.3299	−	35.5190i	−0.465164	−	0.390319i
$92$		0			0
$93$	−7.85874	+	15.9749i	−0.0845026	+	0.171773i
$94$		0			0
$95$	3.83564	+	3.61874i	0.0403752	+	0.0380920i
$96$		0			0
$97$	61.2573	−	82.2829i	0.631519	−	0.848277i	−0.365055	−	0.930986i	$-0.618950\pi$
$97$	61.2573	−	82.2829i	0.631519	−	0.848277i	0.996574	+	0.0827091i	$0.0263572\pi$
$98$		0			0
$99$	−103.894	+	80.0403i	−1.04944	+	0.808488i
$100$		0			0
$101$	−4.61707	+	9.19334i	−0.0457135	+	0.0910231i	−0.915330	−	0.402705i	$-0.868070\pi$
$101$	−4.61707	+	9.19334i	−0.0457135	+	0.0910231i	0.869616	+	0.493728i	$0.164366\pi$
$102$		0			0
$103$	−125.490	+	14.6676i	−1.21835	+	0.142404i	−0.700867	−	0.713292i	$-0.747204\pi$
$103$	−125.490	+	14.6676i	−1.21835	+	0.142404i	−0.517479	+	0.855696i	$0.673129\pi$
$104$		0			0
$105$	2.30154	−	2.48011i	0.0219195	−	0.0236201i
$106$		0			0
$107$	47.4116	−	27.3731i	0.443099	−	0.255823i	−0.261812	−	0.965119i	$-0.584320\pi$
$107$	47.4116	−	27.3731i	0.443099	−	0.255823i	0.704911	+	0.709295i	$0.250987\pi$
$108$		0			0
$109$	−12.8028	+	22.1750i	−0.117456	+	0.203441i	−0.918759	−	0.394819i	$-0.870807\pi$
$109$	−12.8028	+	22.1750i	−0.117456	+	0.203441i	0.801303	+	0.598259i	$0.204141\pi$
$110$		0			0
$111$	−190.499	−	9.52121i	−1.71620	−	0.0857766i
$112$		0			0
$113$	−6.63526	−	2.86217i	−0.0587191	−	0.0253289i	0.366518	−	0.930411i	$-0.380550\pi$
$113$	−6.63526	−	2.86217i	−0.0587191	−	0.0253289i	−0.425237	+	0.905082i	$0.639809\pi$
$114$		0			0
$115$	0.484541	+	8.31924i	0.00421340	+	0.0723413i
$116$		0			0
$117$	39.5746	−	71.2304i	0.338244	−	0.608807i
$118$		0			0
$119$	36.1037	−	15.5736i	0.303393	−	0.130871i
$120$		0			0
$121$	−88.8886	−	21.0670i	−0.734617	−	0.174107i
$122$		0			0
$123$	72.7403	−	99.4066i	0.591384	−	0.808184i
$124$		0			0
$125$	−3.15802	−	8.67659i	−0.0252642	−	0.0694127i
$126$		0			0
$127$	164.469	+	59.8617i	1.29503	+	0.471352i	0.895375	−	0.445313i	$-0.146908\pi$
$127$	164.469	+	59.8617i	1.29503	+	0.471352i	0.399655	+	0.916666i	$0.369130\pi$
$128$		0			0
$129$	2.09001	+	253.675i	0.0162016	+	1.96647i
$130$		0			0
$131$	−175.399	−	10.2158i	−1.33892	−	0.0779834i	−0.626329	−	0.779559i	$-0.715443\pi$
$131$	−175.399	−	10.2158i	−1.33892	−	0.0779834i	−0.712595	+	0.701576i	$0.752480\pi$
$132$		0			0
$133$	−119.515	−	126.679i	−0.898609	−	0.952470i
$134$		0			0
$135$	4.23512	+	2.63789i	0.0313712	+	0.0195399i
$136$		0			0
$137$	194.266	+	58.1596i	1.41800	+	0.424522i	0.901878	−	0.431991i	$-0.142189\pi$
$137$	194.266	+	58.1596i	1.41800	+	0.424522i	0.516125	+	0.856513i	$0.327374\pi$
$138$		0			0
$139$	13.6911	+	9.00481i	0.0984975	+	0.0647828i	0.597802	−	0.801644i	$-0.296041\pi$
$139$	13.6911	+	9.00481i	0.0984975	+	0.0647828i	−0.499305	+	0.866426i	$0.666411\pi$
$140$		0			0
$141$	25.1023	+	8.90296i	0.178030	+	0.0631416i
$142$		0			0
$143$	129.932	−	22.9106i	0.908618	−	0.160214i
$144$		0			0
$145$	−1.55492	+	8.81838i	−0.0107236	+	0.0608164i
$146$		0			0
$147$	25.4428	−	24.4034i	0.173080	−	0.166009i
$148$		0			0
$149$	−107.890	+	32.3001i	−0.724092	+	0.216779i	−0.627579	−	0.778553i	$-0.715954\pi$
$149$	−107.890	+	32.3001i	−0.724092	+	0.216779i	−0.0965129	+	0.995332i	$0.530769\pi$
$150$		0			0
$151$	−55.2751	−	6.46073i	−0.366060	−	0.0427863i	−0.0689252	−	0.997622i	$-0.521957\pi$
$151$	−55.2751	−	6.46073i	−0.366060	−	0.0427863i	−0.297135	+	0.954836i	$0.596031\pi$
$152$		0			0
$153$	32.6556	+	47.9119i	0.213435	+	0.313149i
$154$		0			0
$155$	0.602619	+	0.916237i	0.00388786	+	0.00591121i
$156$		0			0
$157$	−76.4112	−	102.638i	−0.486695	−	0.653746i	0.489152	−	0.872199i	$-0.337306\pi$
$157$	−76.4112	−	102.638i	−0.486695	−	0.653746i	−0.975847	+	0.218453i	$0.929899\pi$
$158$		0			0
$159$	−35.4553	−	46.8145i	−0.222989	−	0.294431i
$160$		0			0
$161$		−	275.223i		−	1.70946i
$162$		0			0
$163$	153.676			0.942799			0.471400	−	0.881920i	$-0.343749\pi$
$163$	153.676			0.942799			0.471400	+	0.881920i	$0.343749\pi$
$164$		0			0
$165$	1.00395	+	8.01601i	0.00608453	+	0.0485819i
$166$		0			0
$167$	−122.997	+	91.5682i	−0.736512	+	0.548313i	−0.898762	−	0.438437i	$-0.855532\pi$
$167$	−122.997	+	91.5682i	−0.736512	+	0.548313i	0.162250	+	0.986750i	$0.448125\pi$
$168$		0			0
$169$	72.7089	−	47.8214i	0.430230	−	0.282967i
$170$		0			0
$171$	149.949	−	208.502i	0.876893	−	1.21931i
$172$		0			0
$173$	−31.3999	+	268.643i	−0.181502	+	1.55285i	0.528672	+	0.848826i	$0.322690\pi$
$173$	−31.3999	+	268.643i	−0.181502	+	1.55285i	−0.710175	+	0.704025i	$0.751384\pi$
$174$		0			0
$175$	43.7004	+	145.969i	0.249717	+	0.834111i
$176$		0			0
$177$	−13.4131	+	46.1845i	−0.0757805	+	0.260930i
$178$		0			0
$179$	−188.199	−	33.1845i	−1.05139	−	0.185388i	−0.378856	−	0.925455i	$-0.623683\pi$
$179$	−188.199	−	33.1845i	−1.05139	−	0.185388i	−0.672533	+	0.740067i	$0.734794\pi$
$180$		0			0
$181$	−3.61813	−	20.5195i	−0.0199897	−	0.113367i	0.973180	−	0.230044i	$-0.0738870\pi$
$181$	−3.61813	−	20.5195i	−0.0199897	−	0.113367i	−0.993170	+	0.116677i	$0.962776\pi$
$182$		0			0
$183$	134.907	+	158.112i	0.737197	+	0.864000i
$184$		0			0
$185$	−6.45620	+	9.81617i	−0.0348984	+	0.0530604i
$186$		0			0
$187$	−26.9255	+	89.9374i	−0.143987	+	0.480948i
$188$		0			0
$189$	−134.570	−	95.1063i	−0.712009	−	0.503208i
$190$		0			0
$191$	−59.7436	+	56.3652i	−0.312794	+	0.295106i	−0.826588	−	0.562808i	$-0.809721\pi$
$191$	−59.7436	+	56.3652i	−0.312794	+	0.295106i	0.513794	+	0.857914i	$0.328240\pi$
$192$		0			0
$193$	1.57864	−	27.1043i	0.00817950	−	0.140437i	−0.991746	−	0.128219i	$-0.959074\pi$
$193$	1.57864	−	27.1043i	0.00817950	−	0.140437i	0.999925	−	0.0122175i	$-0.00388904\pi$
$194$		0			0
$195$	−2.54542	−	4.32608i	−0.0130534	−	0.0221850i
$196$		0			0
$197$	57.0836	−	156.836i	0.289764	−	0.796121i	−0.706335	−	0.707878i	$-0.749653\pi$
$197$	57.0836	−	156.836i	0.289764	−	0.796121i	0.996099	−	0.0882429i	$-0.0281252\pi$
$198$		0			0
$199$	83.2970	−	30.3176i	0.418578	−	0.152350i	−0.124141	−	0.992265i	$-0.539617\pi$
$199$	83.2970	−	30.3176i	0.418578	−	0.152350i	0.542718	+	0.839915i	$0.317395\pi$
$200$		0			0
$201$	−50.8334	+	22.4259i	−0.252903	+	0.111572i
$202$		0			0
$203$	68.2012	−	287.763i	0.335966	−	1.41755i
$204$		0			0
$205$	−3.00528	−	6.96701i	−0.0146599	−	0.0339854i
$206$		0			0
$207$	398.475	−	77.0522i	1.92500	−	0.372233i
$208$		0			0
$209$	415.128	−	24.1785i	1.98626	−	0.115686i
$210$		0			0
$211$	−52.4140	+	121.509i	−0.248407	+	0.575873i	−0.996106	−	0.0881652i	$-0.971900\pi$
$211$	−52.4140	+	121.509i	−0.248407	+	0.575873i	0.747698	+	0.664038i	$0.231159\pi$
$212$		0			0
$213$	−206.110	+	105.647i	−0.967651	+	0.495997i
$214$		0			0
$215$	13.5329	+	7.81323i	0.0629438	+	0.0363406i
$216$		0			0
$217$	−18.1094	−	31.3663i	−0.0834532	−	0.144545i
$218$		0			0
$219$	191.565	−	59.0748i	0.874725	−	0.269748i
$220$		0			0
$221$	−6.77168	−	57.9355i	−0.0306411	−	0.262151i
$222$		0			0
$223$	−196.257	−	98.5641i	−0.880078	−	0.441992i	−0.0494220	−	0.998778i	$-0.515738\pi$
$223$	−196.257	−	98.5641i	−0.880078	−	0.441992i	−0.830656	+	0.556786i	$0.812034\pi$
$224$		0			0
$225$	−199.104	+	104.137i	−0.884906	+	0.462829i
$226$		0			0
$227$	−98.1389	−	73.0617i	−0.432330	−	0.321858i	0.358901	−	0.933376i	$-0.383152\pi$
$227$	−98.1389	−	73.0617i	−0.432330	−	0.321858i	−0.791230	+	0.611518i	$0.790559\pi$
$228$		0			0
$229$	−160.177	+	169.778i	−0.699465	+	0.741390i	−0.975558	−	0.219741i	$-0.929479\pi$
$229$	−160.177	+	169.778i	−0.699465	+	0.741390i	0.276093	+	0.961131i	$0.410960\pi$
$230$		0			0
$231$	−17.7076	−	266.222i	−0.0766562	−	1.15248i
$232$		0			0
$233$	−35.5242	+	42.3360i	−0.152464	+	0.181700i	−0.836870	−	0.547401i	$-0.815617\pi$
$233$	−35.5242	+	42.3360i	−0.152464	+	0.181700i	0.684406	+	0.729101i	$0.260062\pi$
$234$		0			0
$235$	1.25679	−	1.05457i	0.00534806	−	0.00448755i
$236$		0			0
$237$	−290.011	−	48.6767i	−1.22368	−	0.205387i
$238$		0			0
$239$	−36.5797	−	72.8363i	−0.153053	−	0.304754i	0.804019	−	0.594604i	$-0.202691\pi$
$239$	−36.5797	−	72.8363i	−0.153053	−	0.304754i	−0.957072	+	0.289850i	$0.906395\pi$
$240$		0			0
$241$	327.819	−	77.6946i	1.36025	−	0.322384i	0.515196	−	0.857072i	$-0.327719\pi$
$241$	327.819	−	77.6946i	1.36025	−	0.322384i	0.845049	+	0.534688i	$0.179571\pi$
$242$		0			0
$243$	100.023	−	221.460i	0.411617	−	0.911357i
$244$		0			0
$245$	−0.500805	−	2.11306i	−0.00204410	−	0.00862475i
$246$		0			0
$247$	−230.881	+	115.953i	−0.934741	+	0.469445i
$248$		0			0
$249$	76.7172	−	457.074i	0.308101	−	1.83564i
$250$		0			0
$251$	−73.1008	−	87.1181i	−0.291238	−	0.347084i	0.600509	−	0.799618i	$-0.294965\pi$
$251$	−73.1008	−	87.1181i	−0.291238	−	0.347084i	−0.891747	+	0.452534i	$0.850520\pi$
$252$		0			0
$253$	503.397	+	422.400i	1.98971	+	1.66957i
$254$		0			0
$255$	3.56373	−	0.237039i	0.0139754	−	0.000929563i
$256$		0			0
$257$	6.47174	+	6.10577i	0.0251819	+	0.0237579i	0.698730	−	0.715386i	$-0.253749\pi$
$257$	6.47174	+	6.10577i	0.0251819	+	0.0237579i	−0.673548	+	0.739144i	$0.735230\pi$
$258$		0			0
$259$	231.716	−	311.249i	0.894658	−	1.20173i
$260$		0			0
$261$	435.725	+	18.1803i	1.66944	+	0.0696565i
$262$		0			0
$263$	−94.9764	+	189.114i	−0.361127	+	0.719063i	−0.998681	−	0.0513428i	$-0.983650\pi$
$263$	−94.9764	+	189.114i	−0.361127	+	0.719063i	0.637554	+	0.770405i	$0.279946\pi$
$264$		0			0
$265$	−3.59292	+	0.419952i	−0.0135582	+	0.00158473i
$266$		0			0
$267$	−88.3150	−	286.384i	−0.330768	−	1.07260i
$268$		0			0
$269$	229.643	−	132.585i	0.853692	−	0.492880i	−0.00820252	−	0.999966i	$-0.502611\pi$
$269$	229.643	−	132.585i	0.853692	−	0.492880i	0.861895	+	0.507087i	$0.169278\pi$
$270$		0			0
$271$	176.250	−	305.273i	0.650368	−	1.12647i	−0.332666	−	0.943045i	$-0.607948\pi$
$271$	176.250	−	305.273i	0.650368	−	1.12647i	0.983034	−	0.183425i	$-0.0587186\pi$
$272$		0			0
$273$	75.6169	+	147.523i	0.276985	+	0.540376i
$274$		0			0
$275$	−334.055	−	144.097i	−1.21475	−	0.523991i
$276$		0			0
$277$	−7.98803	−	137.149i	−0.0288377	−	0.495123i	−0.981545	−	0.191233i	$-0.938751\pi$
$277$	−7.98803	−	137.149i	−0.0288377	−	0.495123i	0.952707	−	0.303890i	$-0.0982857\pi$
$278$		0			0
$279$	40.3430	−	35.0006i	0.144599	−	0.125450i
$280$		0			0
$281$	−212.139	+	91.5077i	−0.754942	+	0.325650i	−0.738535	−	0.674215i	$-0.764482\pi$
$281$	−212.139	+	91.5077i	−0.754942	+	0.325650i	−0.0164068	+	0.999865i	$0.505223\pi$
$282$		0			0
$283$	304.073	+	72.0665i	1.07446	+	0.254652i	0.729511	−	0.683969i	$-0.239748\pi$
$283$	304.073	+	72.0665i	1.07446	+	0.254652i	0.344950	+	0.938621i	$0.387896\pi$
$284$		0			0
$285$	−6.38537	−	14.4739i	−0.0224048	−	0.0507856i
$286$		0			0
$287$	85.7074	+	235.479i	0.298632	+	0.820485i
$288$		0			0
$289$	−232.569	−	84.6481i	−0.804737	−	0.292900i
$290$		0			0
$291$	−265.237	+	156.062i	−0.911469	+	0.536297i
$292$		0			0
$293$	−91.7426	−	5.34340i	−0.313115	−	0.0182369i	−0.0991320	−	0.995074i	$-0.531607\pi$
$293$	−91.7426	−	5.34340i	−0.313115	−	0.0182369i	−0.213983	+	0.976837i	$0.568644\pi$
$294$		0			0
$295$	2.03295	+	2.15480i	0.00689135	+	0.00730440i
$296$		0			0
$297$	380.486	−	100.170i	1.28110	−	0.337272i
$298$		0			0
$299$	−391.137	−	117.099i	−1.30815	−	0.391635i
$300$		0			0
$301$	−431.187	−	283.596i	−1.43252	−	0.942180i
$302$		0			0
$303$	23.4780	−	20.0323i	0.0774853	−	0.0661133i
$304$		0			0
$305$	12.6084	−	2.22319i	0.0413389	−	0.00728916i
$306$		0			0
$307$	−82.4546	+	467.623i	−0.268582	+	1.52320i	0.490057	+	0.871691i	$0.336976\pi$
$307$	−82.4546	+	467.623i	−0.268582	+	1.52320i	−0.758638	+	0.651512i	$0.774135\pi$
$308$		0			0
$309$	363.992	+	105.712i	1.17797	+	0.342111i
$310$		0			0
$311$	−209.104	+	62.6017i	−0.672360	+	0.201291i	−0.604744	−	0.796420i	$-0.706725\pi$
$311$	−209.104	+	62.6017i	−0.672360	+	0.201291i	−0.0676164	+	0.997711i	$0.521539\pi$
$312$		0			0
$313$	−459.937	−	53.7590i	−1.46945	−	0.171754i	−0.656604	−	0.754235i	$-0.728008\pi$
$313$	−459.937	−	53.7590i	−1.46945	−	0.171754i	−0.812844	+	0.582481i	$0.802082\pi$
$314$		0			0
$315$	−9.25284	+	4.17343i	−0.0293741	+	0.0132490i
$316$		0			0
$317$	−256.694	−	390.284i	−0.809760	−	1.23118i	−0.969759	−	0.244063i	$-0.921520\pi$
$317$	−256.694	−	390.284i	−0.809760	−	1.23118i	0.160000	−	0.987117i	$-0.448851\pi$
$318$		0			0
$319$	421.662	+	566.390i	1.32182	+	1.77552i
$320$		0			0
$321$	−162.965	+	20.4102i	−0.507681	+	0.0635833i
$322$		0			0
$323$		−	183.841i		−	0.569168i
$324$		0			0
$325$	226.040			0.695507
$326$		0			0
$327$	61.2363	−	46.3777i	0.187267	−	0.141828i
$328$		0			0
$329$	−43.4626	+	32.3567i	−0.132105	+	0.0983487i
$330$		0			0
$331$	−433.787	+	285.306i	−1.31054	+	0.861953i	−0.996178	−	0.0873513i	$-0.972160\pi$
$331$	−433.787	+	285.306i	−1.31054	+	0.861953i	−0.314358	+	0.949304i	$0.601789\pi$
$332$		0			0
$333$	515.507	+	248.347i	1.54807	+	0.745786i
$334$		0			0
$335$	−0.397319	+	3.39928i	−0.00118603	+	0.0101471i
$336$		0			0
$337$	84.3456	+	281.734i	0.250284	+	0.836006i	0.987126	+	0.159942i	$0.0511306\pi$
$337$	84.3456	+	281.734i	0.250284	+	0.836006i	−0.736843	+	0.676064i	$0.763684\pi$
$338$		0			0
$339$	15.0063	+	15.6454i	0.0442663	+	0.0461518i
$340$		0			0
$341$	85.1641	+	15.0167i	0.249748	+	0.0440373i
$342$		0			0
$343$	64.3845	+	365.143i	0.187710	+	1.06456i
$344$		0			0
$345$	8.35668	−	23.5620i	0.0242223	−	0.0682956i
$346$		0			0
$347$	−361.424	+	549.519i	−1.04157	+	1.58363i	−0.254193	+	0.967153i	$0.581810\pi$
$347$	−361.424	+	549.519i	−1.04157	+	1.58363i	−0.787375	+	0.616474i	$0.788560\pi$
$348$		0			0
$349$	31.6683	−	105.779i	0.0907400	−	0.303093i	−0.900557	−	0.434738i	$-0.856841\pi$
$349$	31.6683	−	105.779i	0.0907400	−	0.303093i	0.991297	+	0.131645i	$0.0420260\pi$
$350$		0			0
$351$	−192.417	+	150.781i	−0.548197	+	0.429576i
$352$		0			0
$353$	50.7656	−	47.8949i	0.143812	−	0.135680i	−0.610974	−	0.791650i	$-0.709222\pi$
$353$	50.7656	−	47.8949i	0.143812	−	0.135680i	0.754786	+	0.655971i	$0.227741\pi$
$354$		0			0
$355$	−0.829534	+	14.2426i	−0.00233672	+	0.0401199i
$356$		0			0
$357$	−117.954	+	0.971817i	−0.330404	+	0.00272218i
$358$		0			0
$359$	104.050	−	285.875i	0.289833	−	0.796309i	−0.706256	−	0.707956i	$-0.749617\pi$
$359$	104.050	−	285.875i	0.289833	−	0.796309i	0.996089	−	0.0883529i	$-0.0281603\pi$
$360$		0			0
$361$	−425.957	+	155.036i	−1.17994	+	0.429462i
$362$		0			0
$363$	221.165	+	161.836i	0.609270	+	0.445830i
$364$		0			0
$365$	2.84774	−	12.0156i	0.00780202	−	0.0329193i
$366$		0			0
$367$	144.368	+	334.683i	0.393373	+	0.911942i	0.993688	+	0.112178i	$0.0357828\pi$
$367$	144.368	+	334.683i	0.393373	+	0.911942i	−0.600315	+	0.799764i	$0.704958\pi$
$368$		0			0
$369$	−316.938	+	190.015i	−0.858911	+	0.514946i
$370$		0			0
$371$	119.268	−	6.94657i	0.321477	−	0.0187239i
$372$		0			0
$373$	−287.463	+	666.414i	−0.770678	+	1.78663i	−0.172956	+	0.984929i	$0.555332\pi$
$373$	−287.463	+	666.414i	−0.770678	+	1.78663i	−0.597722	+	0.801704i	$0.703927\pi$
$374$		0			0
$375$	−1.38275	+	27.6658i	−0.00368733	+	0.0737753i
$376$		0			0
$377$	−379.942	−	219.360i	−1.00780	−	0.581856i
$378$		0			0
$379$	268.913	+	465.771i	0.709532	+	1.22895i	0.965031	+	0.262136i	$0.0844271\pi$
$379$	268.913	+	465.771i	0.709532	+	1.22895i	−0.255499	+	0.966809i	$0.582240\pi$
$380$		0			0
$381$	−384.879	−	357.168i	−1.01018	−	0.937448i
$382$		0			0
$383$	12.1868	+	104.265i	0.0318194	+	0.272232i	0.999777	+	0.0211185i	$0.00672273\pi$
$383$	12.1868	+	104.265i	0.0318194	+	0.272232i	−0.967958	+	0.251114i	$0.919203\pi$
$384$		0			0
$385$	−14.6869	−	7.37605i	−0.0381479	−	0.0191586i
$386$		0			0
$387$	289.882	−	703.680i	0.749048	−	1.81830i
$388$		0			0
$389$	385.857	+	287.260i	0.991919	+	0.738456i	0.965288	−	0.261189i	$-0.0841145\pi$
$389$	385.857	+	287.260i	0.991919	+	0.738456i	0.0266314	+	0.999645i	$0.491522\pi$
$390$		0			0
$391$	199.370	−	211.319i	0.509897	−	0.540459i
$392$		0			0
$393$	472.957	+	232.668i	1.20345	+	0.592031i
$394$		0			0
$395$	−11.6435	+	13.8762i	−0.0294772	+	0.0351296i
$396$		0			0
$397$	423.731	−	355.553i	1.06733	−	0.895599i	0.0725251	−	0.997367i	$-0.476894\pi$
$397$	423.731	−	355.553i	1.06733	−	0.895599i	0.994808	+	0.101768i	$0.0324498\pi$
$398$		0			0
$399$	182.736	+	489.478i	0.457986	+	1.22676i
$400$		0			0
$401$	75.0448	+	149.426i	0.187144	+	0.372635i	0.967566	−	0.252619i	$-0.0812919\pi$
$401$	75.0448	+	149.426i	0.187144	+	0.372635i	−0.780422	+	0.625254i	$0.784996\pi$
$402$		0			0
$403$	−52.2817	+	12.3910i	−0.129731	+	0.0307469i
$404$		0			0
$405$	−8.63285	−	12.2281i	−0.0213157	−	0.0301928i
$406$		0			0
$407$	213.663	+	901.514i	0.524970	+	2.21502i
$408$		0			0
$409$	−183.275	+	92.0444i	−0.448106	+	0.225047i	−0.658517	−	0.752566i	$-0.728816\pi$
$409$	−183.275	+	92.0444i	−0.448106	+	0.225047i	0.210411	+	0.977613i	$0.432520\pi$
$410$		0			0
$411$	−469.234	−	387.191i	−1.14169	−	0.942072i
$412$		0			0
$413$	−62.8900	−	74.9494i	−0.152276	−	0.181476i
$414$		0			0
$415$	−21.8696	−	18.3508i	−0.0526979	−	0.0442188i
$416$		0			0
$417$	−27.3519	−	40.8495i	−0.0655921	−	0.0979604i
$418$		0			0
$419$	−237.074	−	223.667i	−0.565808	−	0.533813i	0.349305	−	0.937009i	$-0.386418\pi$
$419$	−237.074	−	223.667i	−0.565808	−	0.533813i	−0.915113	+	0.403196i	$0.867899\pi$
$420$		0			0
$421$	163.489	−	219.603i	0.388334	−	0.521623i	−0.564370	−	0.825522i	$-0.690881\pi$
$421$	163.489	−	219.603i	0.388334	−	0.521623i	0.952704	+	0.303899i	$0.0982884\pi$
$422$		0			0
$423$	−59.0149	−	53.8676i	−0.139515	−	0.127347i
$424$		0			0
$425$	−72.1856	+	143.733i	−0.169849	+	0.338196i
$426$		0			0
$427$	−419.977	+	49.0883i	−0.983553	+	0.114961i
$428$		0			0
$429$	−385.880	−	88.1040i	−0.899488	−	0.205371i
$430$		0			0
$431$	−516.658	+	298.293i	−1.19874	+	0.692095i	−0.960275	−	0.279056i	$-0.909979\pi$
$431$	−516.658	+	298.293i	−1.19874	+	0.692095i	−0.238468	+	0.971150i	$0.576645\pi$
$432$		0			0
$433$	144.682	−	250.597i	0.334139	−	0.578745i	−0.649180	−	0.760635i	$-0.724888\pi$
$433$	144.682	−	250.597i	0.334139	−	0.578745i	0.983319	+	0.181889i	$0.0582213\pi$
$434$		0			0
$435$	14.5762	−	22.5648i	0.0335085	−	0.0518731i
$436$		0			0
$437$	−1181.59	−	509.686i	−2.70386	−	1.16633i
$438$		0			0
$439$	12.2298	+	209.978i	0.0278583	+	0.478309i	0.983168	+	0.182703i	$0.0584846\pi$
$439$	12.2298	+	209.978i	0.0278583	+	0.478309i	−0.955310	+	0.295606i	$0.904478\pi$
$440$		0			0
$441$	−98.7749	+	37.8056i	−0.223979	+	0.0857269i
$442$		0			0
$443$	−258.564	+	111.534i	−0.583667	+	0.251769i	−0.667376	−	0.744721i	$-0.732583\pi$
$443$	−258.564	+	111.534i	−0.583667	+	0.251769i	0.0837093	+	0.996490i	$0.473323\pi$
$444$		0			0
$445$	−17.9629	−	4.25728i	−0.0403660	−	0.00956693i
$446$		0			0
$447$	335.890	+	36.4574i	0.751432	+	0.0815603i
$448$		0			0
$449$	−112.247	−	308.396i	−0.249993	−	0.686851i	−0.999686	−	0.0250648i	$-0.992021\pi$
$449$	−112.247	−	308.396i	−0.249993	−	0.686851i	0.749692	−	0.661786i	$-0.230201\pi$
$450$		0			0
$451$	−562.244	−	204.640i	−1.24666	−	0.453747i
$452$		0			0
$453$	145.269	+	82.2830i	0.320683	+	0.181640i
$454$		0			0
$455$	10.1941	+	0.593738i	0.0224046	+	0.00130492i
$456$		0			0
$457$	105.495	+	111.819i	0.230843	+	0.244680i	0.832433	−	0.554125i	$-0.186947\pi$
$457$	105.495	+	111.819i	0.230843	+	0.244680i	−0.601590	+	0.798805i	$0.705466\pi$
$458$		0			0
$459$	−34.4298	−	170.505i	−0.0750106	−	0.371471i
$460$		0			0
$461$	557.250	+	166.830i	1.20878	+	0.361886i	0.826914	−	0.562329i	$-0.190095\pi$
$461$	557.250	+	166.830i	1.20878	+	0.361886i	0.381871	+	0.924215i	$0.375280\pi$
$462$		0			0
$463$	116.031	+	76.3146i	0.250606	+	0.164826i	0.668597	−	0.743625i	$-0.266895\pi$
$463$	116.031	+	76.3146i	0.250606	+	0.164826i	−0.417991	+	0.908451i	$0.637266\pi$
$464$		0			0
$465$	−0.597967	−	3.23515i	−0.00128595	−	0.00695731i
$466$		0			0
$467$	648.396	−	114.330i	1.38843	−	0.244818i	0.571049	−	0.820916i	$-0.306537\pi$
$467$	648.396	−	114.330i	1.38843	−	0.244818i	0.817380	+	0.576098i	$0.195426\pi$
$468$		0			0
$469$	19.6277	−	111.314i	0.0418501	−	0.237344i
$470$		0			0
$471$	91.6018	+	372.784i	0.194484	+	0.791474i
$472$		0			0
$473$	1180.48	−	353.413i	2.49573	−	0.747172i
$474$		0			0
$475$	707.604	+	82.7071i	1.48969	+	0.174120i
$476$		0			0
$477$	43.4481	+	170.735i	0.0910861	+	0.357934i
$478$		0			0
$479$	107.308	+	163.155i	0.224026	+	0.340615i	0.929959	−	0.367664i	$-0.119842\pi$
$479$	107.308	+	163.155i	0.224026	+	0.340615i	−0.705933	+	0.708279i	$0.749472\pi$
$480$		0			0
$481$	−343.748	−	461.734i	−0.714654	−	0.959947i
$482$		0			0
$483$	−320.773	+	760.811i	−0.664127	+	1.57518i
$484$		0			0
$485$			18.9565i			0.0390856i
$486$		0			0
$487$	284.987			0.585188			0.292594	−	0.956237i	$-0.405482\pi$
$487$	284.987			0.585188			0.292594	+	0.956237i	$0.405482\pi$
$488$		0			0
$489$	−424.814	−	179.110i	−0.868741	−	0.366279i
$490$		0			0
$491$	433.321	−	322.595i	0.882527	−	0.657017i	−0.0574153	−	0.998350i	$-0.518286\pi$
$491$	433.321	−	322.595i	0.882527	−	0.657017i	0.939942	+	0.341333i	$0.110878\pi$
$492$		0			0
$493$	260.820	−	171.544i	0.529046	−	0.347959i
$494$		0			0
$495$	6.56744	−	23.3291i	0.0132676	−	0.0471296i
$496$		0			0
$497$	54.7009	−	467.996i	0.110062	−	0.941642i
$498$		0			0
$499$	−259.835	−	867.908i	−0.520711	−	1.73929i	−0.662173	−	0.749351i	$-0.730366\pi$
$499$	−259.835	−	867.908i	−0.520711	−	1.73929i	0.141462	−	0.989944i	$-0.454820\pi$
$500$		0			0
$501$	446.730	−	109.772i	0.891677	−	0.219106i
$502$		0			0
$503$	−23.6992	−	4.17881i	−0.0471157	−	0.00830777i	0.150041	−	0.988680i	$-0.452060\pi$
$503$	−23.6992	−	4.17881i	−0.0471157	−	0.00830777i	−0.197156	+	0.980372i	$0.563171\pi$
$504$		0			0
$505$	−0.330122	−	1.87221i	−0.000653706	−	0.00370735i
$506$		0			0
$507$	−256.729	+	47.4523i	−0.506368	+	0.0935943i
$508$		0			0
$509$	−318.908	+	484.875i	−0.626537	+	0.952604i	0.373154	+	0.927769i	$0.378276\pi$
$509$	−318.908	+	484.875i	−0.626537	+	0.952604i	−0.999692	+	0.0248346i	$0.992094\pi$
$510$		0			0
$511$	−116.966	+	390.694i	−0.228897	+	0.764568i
$512$		0			0
$513$	−657.520	+	401.606i	−1.28172	+	0.782858i
$514$		0			0
$515$	16.9825	−	16.0222i	0.0329757	−	0.0311110i
$516$		0			0
$517$	7.52243	−	129.155i	0.0145502	−	0.249817i
$518$		0			0
$519$	399.905	−	706.026i	0.770530	−	1.36036i
$520$		0			0
$521$	8.04582	−	22.1057i	0.0154430	−	0.0424294i	−0.931732	−	0.363148i	$-0.881702\pi$
$521$	8.04582	−	22.1057i	0.0154430	−	0.0424294i	0.947175	+	0.320718i	$0.103924\pi$
$522$		0			0
$523$	417.356	−	151.905i	0.798004	−	0.290450i	0.0893450	−	0.996001i	$-0.471523\pi$
$523$	417.356	−	151.905i	0.798004	−	0.290450i	0.708659	+	0.705551i	$0.249300\pi$
$524$		0			0
$525$	49.3251	−	454.443i	0.0939526	−	0.865606i
$526$		0			0
$527$	8.81697	−	37.2017i	0.0167305	−	0.0705915i
$528$		0			0
$529$	−595.930	−	1381.52i	−1.12652	−	2.61157i
$530$		0			0
$531$	90.9068	−	112.037i	0.171199	−	0.210992i
$532$		0			0
$533$	371.121	−	21.6153i	0.696287	−	0.0405541i
$534$		0			0
$535$	−4.00706	+	9.28942i	−0.00748984	+	0.0173634i
$536$		0			0
$537$	481.569	+	311.080i	0.896777	+	0.579292i
$538$		0			0
$539$	−148.302	−	85.6223i	−0.275143	−	0.158854i
$540$		0			0
$541$	94.2767	+	163.292i	0.174264	+	0.301834i	0.939906	−	0.341433i	$-0.110912\pi$
$541$	94.2767	+	163.292i	0.174264	+	0.301834i	−0.765642	+	0.643266i	$0.777579\pi$
$542$		0			0
$543$	−13.9138	+	60.9398i	−0.0256239	+	0.112228i
$544$		0			0
$545$	−0.549324	−	4.69977i	−0.00100793	−	0.00862343i
$546$		0			0
$547$	−139.195	−	69.9063i	−0.254470	−	0.127799i	0.316992	−	0.948428i	$-0.397327\pi$
$547$	−139.195	−	69.9063i	−0.254470	−	0.127799i	−0.571462	+	0.820629i	$0.693623\pi$
$548$		0			0
$549$	−188.649	−	594.311i	−0.343623	−	1.08253i
$550$		0			0
$551$	−1109.12	−	825.711i	−2.01293	−	1.49857i
$552$		0			0
$553$	410.543	−	435.150i	0.742392	−	0.786890i
$554$		0			0
$555$	29.2879	−	19.6106i	0.0527711	−	0.0353343i
$556$		0			0
$557$	−257.459	+	306.827i	−0.462224	+	0.550857i	−0.945929	−	0.324374i	$-0.894846\pi$
$557$	−257.459	+	306.827i	−0.462224	+	0.550857i	0.483705	+	0.875231i	$0.339291\pi$
$558$		0			0
$559$	−586.494	+	492.127i	−1.04918	+	0.880370i
$560$		0			0
$561$	179.254	−	217.236i	0.319525	−	0.387230i
$562$		0			0
$563$	160.112	+	318.808i	0.284390	+	0.566267i	0.989788	−	0.142544i	$-0.0455282\pi$
$563$	160.112	+	318.808i	0.284390	+	0.566267i	−0.705399	+	0.708811i	$0.749232\pi$
$564$		0			0
$565$	1.29938	−	0.307958i	0.00229978	−	0.000545059i
$566$		0			0
$567$	261.150	+	419.748i	0.460582	+	0.740297i
$568$		0			0
$569$	70.6356	+	298.035i	0.124140	+	0.523787i	0.999208	+	0.0397879i	$0.0126682\pi$
$569$	70.6356	+	298.035i	0.124140	+	0.523787i	−0.875068	+	0.484000i	$0.839184\pi$
$570$		0			0
$571$	176.526	−	88.6548i	0.309153	−	0.155262i	−0.287458	−	0.957793i	$-0.592810\pi$
$571$	176.526	−	88.6548i	0.309153	−	0.155262i	0.596610	+	0.802531i	$0.296514\pi$
$572$		0			0
$573$	230.846	−	86.1814i	0.402872	−	0.150404i
$574$		0			0
$575$	723.675	+	862.442i	1.25856	+	1.49990i
$576$		0			0
$577$	109.656	+	92.0120i	0.190044	+	0.159466i	0.732846	−	0.680395i	$-0.238192\pi$
$577$	109.656	+	92.0120i	0.190044	+	0.159466i	−0.542801	+	0.839861i	$0.682636\pi$
$578$		0			0
$579$	−35.9541	+	73.0856i	−0.0620968	+	0.126227i
$580$		0			0
$581$	685.821	+	647.038i	1.18041	+	1.11366i
$582$		0			0
$583$	−170.342	+	228.809i	−0.292182	+	0.392468i
$584$		0			0
$585$	1.99434	+	14.9255i	0.00340912	+	0.0255136i
$586$		0			0
$587$	395.206	−	786.920i	0.673264	−	1.34058i	−0.254376	−	0.967105i	$-0.581870\pi$
$587$	395.206	−	786.920i	0.673264	−	1.34058i	0.927641	−	0.373474i	$-0.121834\pi$
$588$		0			0
$589$	−168.198	+	19.6596i	−0.285566	+	0.0333779i
$590$		0			0
$591$	−340.592	+	367.017i	−0.576297	+	0.621010i
$592$		0			0
$593$	796.616	−	459.926i	1.34337	−	0.775592i	0.356065	−	0.934461i	$-0.384118\pi$
$593$	796.616	−	459.926i	1.34337	−	0.775592i	0.987300	+	0.158869i	$0.0507847\pi$
$594$		0			0
$595$	−3.63301	+	6.29256i	−0.00610590	+	0.0105757i
$596$		0			0
$597$	−265.597	−	13.2746i	−0.444886	−	0.0222356i
$598$		0			0
$599$	−429.366	−	185.210i	−0.716804	−	0.309199i	0.00625952	−	0.999980i	$-0.498008\pi$
$599$	−429.366	−	185.210i	−0.716804	−	0.309199i	−0.723064	+	0.690781i	$0.757267\pi$
$600$		0			0
$601$	−8.36225	−	143.574i	−0.0139139	−	0.238892i	−0.998094	−	0.0617190i	$-0.980342\pi$
$601$	−8.36225	−	143.574i	−0.0139139	−	0.238892i	0.984180	−	0.177173i	$-0.0566953\pi$
$602$		0			0
$603$	166.659	−	2.74636i	0.276382	−	0.00455450i
$604$		0			0
$605$	15.5006	−	6.68630i	0.0256208	−	0.0110517i
$606$		0			0
$607$	660.131	+	156.454i	1.08753	+	0.257750i	0.735011	−	0.678055i	$-0.237177\pi$
$607$	660.131	+	156.454i	1.08753	+	0.257750i	0.352520	+	0.935804i	$0.385325\pi$
$608$		0			0
$609$	−523.921	+	715.988i	−0.860297	+	1.17568i
$610$		0			0
$611$	27.4923	+	75.5344i	0.0449955	+	0.123624i
$612$		0			0
$613$	−374.930	−	136.463i	−0.611631	−	0.222616i	0.0175855	−	0.999845i	$-0.494402\pi$
$613$	−374.930	−	136.463i	−0.611631	−	0.222616i	−0.629217	+	0.777230i	$0.716624\pi$
$614$		0			0
$615$	0.187533	+	22.7619i	0.000304932	+	0.0370112i
$616$		0			0
$617$	117.178	+	6.82482i	0.189915	+	0.0110613i	0.152839	−	0.988251i	$-0.451158\pi$
$617$	117.178	+	6.82482i	0.189915	+	0.0110613i	0.0370763	+	0.999312i	$0.488196\pi$
$618$		0			0
$619$	641.919	+	680.395i	1.03703	+	1.09918i	0.994981	+	0.100068i	$0.0319060\pi$
$619$	641.919	+	680.395i	1.03703	+	1.09918i	0.0420456	+	0.999116i	$0.486613\pi$
$620$		0			0
$621$	−1191.33	−	251.425i	−1.91840	−	0.404872i
$622$		0			0
$623$	584.076	+	174.861i	0.937522	+	0.280676i
$624$		0			0
$625$	−520.041	−	342.036i	−0.832066	−	0.547258i
$626$		0			0
$627$	−1175.74	−	416.996i	−1.87518	−	0.665066i
$628$		0			0
$629$	403.382	−	71.1270i	0.641306	−	0.113080i
$630$		0			0
$631$	−62.4220	+	354.013i	−0.0989255	+	0.561034i	0.894548	+	0.446972i	$0.147498\pi$
$631$	−62.4220	+	354.013i	−0.0989255	+	0.561034i	−0.993474	+	0.114063i	$0.963614\pi$
$632$		0			0
$633$	286.510	−	274.805i	0.452622	−	0.434131i
$634$		0			0
$635$	−30.9848	+	9.27623i	−0.0487949	+	0.0146082i
$636$		0			0
$637$	105.677	+	12.3519i	0.165899	+	0.0193908i
$638$		0			0
$639$	692.891	−	51.8242i	1.08434	−	0.0811020i
$640$		0			0
$641$	−217.294	−	330.379i	−0.338992	−	0.515412i	0.625254	−	0.780421i	$-0.284995\pi$
$641$	−217.294	−	330.379i	−0.338992	−	0.515412i	−0.964246	+	0.265009i	$0.914625\pi$
$642$		0			0
$643$	249.878	+	335.645i	0.388613	+	0.521998i	0.952779	−	0.303663i	$-0.0982098\pi$
$643$	249.878	+	335.645i	0.388613	+	0.521998i	−0.564167	+	0.825661i	$0.690802\pi$
$644$		0			0
$645$	−28.3033	−	37.3711i	−0.0438810	−	0.0579397i
$646$		0			0
$647$		−	928.853i		−	1.43563i	−0.696234	−	0.717815i	$-0.745142\pi$
$647$		−	928.853i		−	1.43563i	0.696234	−	0.717815i	$-0.254858\pi$
$648$		0			0
$649$	233.607			0.359950
$650$		0			0
$651$	13.5029	+	107.814i	0.0207418	+	0.165613i
$652$		0			0
$653$	279.299	−	207.931i	0.427717	−	0.318424i	−0.361685	−	0.932301i	$-0.617798\pi$
$653$	279.299	−	207.931i	0.427717	−	0.318424i	0.789402	+	0.613877i	$0.210391\pi$
$654$		0			0
$655$	27.1264	−	17.8413i	0.0414144	−	0.0272387i
$656$		0			0
$657$	−598.403	−	59.9667i	−0.910812	−	0.0912736i
$658$		0			0
$659$	−138.049	+	1181.08i	−0.209482	+	1.79223i	0.323625	+	0.946185i	$0.395098\pi$
$659$	−138.049	+	1181.08i	−0.209482	+	1.79223i	−0.533107	+	0.846048i	$0.678976\pi$
$660$		0			0
$661$	107.407	+	358.764i	0.162491	+	0.542759i	0.999993	−	0.00367540i	$-0.00116992\pi$
$661$	107.407	+	358.764i	0.162491	+	0.542759i	−0.837502	+	0.546435i	$0.815985\pi$
$662$		0			0
$663$	−48.8048	+	168.046i	−0.0736120	+	0.253463i
$664$		0			0
$665$	31.6947	+	5.58863i	0.0476612	+	0.00840396i
$666$		0			0
$667$	−379.444	−	2151.93i	−0.568881	−	3.22629i
$668$		0			0
$669$	427.646	+	501.204i	0.639232	+	0.749184i
$670$		0			0
$671$	554.778	−	843.499i	0.826792	−	1.25708i
$672$		0			0
$673$	101.898	−	340.363i	0.151409	−	0.505741i	−0.848309	−	0.529502i	$-0.822379\pi$
$673$	101.898	−	340.363i	0.151409	−	0.505741i	0.999718	+	0.0237612i	$0.00756412\pi$
$674$		0			0
$675$	671.763	−	55.8130i	0.995205	−	0.0826859i
$676$		0			0
$677$	436.430	−	411.750i	0.644652	−	0.608198i	−0.292858	−	0.956156i	$-0.594606\pi$
$677$	436.430	−	411.750i	0.644652	−	0.608198i	0.937510	+	0.347958i	$0.113125\pi$
$678$		0			0
$679$	36.4028	−	625.011i	0.0536123	−	0.920488i
$680$		0			0
$681$	186.136	+	316.349i	0.273327	+	0.464536i
$682$		0			0
$683$	−315.507	+	866.849i	−0.461943	+	1.26918i	0.462078	+	0.886839i	$0.347104\pi$
$683$	−315.507	+	866.849i	−0.461943	+	1.26918i	−0.924022	+	0.382340i	$0.875118\pi$
$684$		0			0
$685$	−35.2138	+	12.8168i	−0.0514070	+	0.0187106i
$686$		0			0
$687$	640.663	−	282.638i	0.932552	−	0.411409i
$688$		0			0
$689$	40.8726	−	172.455i	0.0593217	−	0.250298i
$690$		0			0
$691$	−360.092	−	834.788i	−0.521118	−	1.20809i	−0.952117	−	0.305734i	$-0.901098\pi$
$691$	−360.092	−	834.788i	−0.521118	−	1.20809i	0.430999	−	0.902352i	$-0.358161\pi$
$692$		0			0
$693$	−261.334	+	756.569i	−0.377105	+	1.09173i
$694$		0			0
$695$	−3.02311	+	0.176076i	−0.00434980	+	0.000253347i
$696$		0			0
$697$	−104.772	+	242.890i	−0.150319	+	0.348479i
$698$		0			0
$699$	147.544	−	75.6278i	0.211078	−	0.108194i
$700$		0			0
$701$	−619.626	−	357.741i	−0.883917	−	0.510330i	−0.0119692	−	0.999928i	$-0.503810\pi$
$701$	−619.626	−	357.741i	−0.883917	−	0.510330i	−0.871948	+	0.489599i	$0.837143\pi$
$702$		0			0
$703$	−907.137	−	1571.21i	−1.29038	−	2.23500i
$704$		0			0
$705$	−4.70332	+	1.45041i	−0.00667138	+	0.00205732i
$706$		0			0
$707$	7.28911	+	62.3624i	0.0103099	+	0.0882070i
$708$		0			0
$709$	−381.413	−	191.553i	−0.537959	−	0.270173i	0.159007	−	0.987277i	$-0.449171\pi$
$709$	−381.413	−	191.553i	−0.537959	−	0.270173i	−0.696966	+	0.717104i	$0.745467\pi$
$710$		0			0
$711$	744.958	+	472.569i	1.04776	+	0.664654i
$712$		0			0
$713$	−214.659	−	159.808i	−0.301064	−	0.224134i
$714$		0			0
$715$	−16.7314	+	17.7343i	−0.0234006	+	0.0248032i
$716$		0			0
$717$	16.2280	+	243.978i	0.0226332	+	0.340277i
$718$		0			0
$719$	−886.267	+	1056.21i	−1.23264	+	1.46900i	−0.398759	+	0.917056i	$0.630559\pi$
$719$	−886.267	+	1056.21i	−1.23264	+	1.46900i	−0.833880	+	0.551946i	$0.813885\pi$
$720$		0			0
$721$	−590.695	+	495.652i	−0.819272	+	0.687451i
$722$		0			0
$723$	−996.758	−	167.300i	−1.37864	−	0.231397i
$724$		0			0
$725$	542.933	+	1081.07i	0.748873	+	1.49113i
$726$		0			0
$727$	−468.329	+	110.996i	−0.644194	+	0.152677i	−0.539712	−	0.841850i	$-0.681467\pi$
$727$	−468.329	+	110.996i	−0.644194	+	0.152677i	−0.104482	+	0.994527i	$0.533319\pi$
$728$		0			0
$729$	−534.610	+	495.614i	−0.733347	+	0.679854i
$730$		0			0
$731$	−125.635	−	530.098i	−0.171868	−	0.725168i
$732$		0			0
$733$	688.942	−	346.000i	0.939894	−	0.472033i	0.0882181	−	0.996101i	$-0.471883\pi$
$733$	688.942	−	346.000i	0.939894	−	0.472033i	0.851676	+	0.524069i	$0.175586\pi$
$734$		0			0
$735$	−1.07839	+	6.42493i	−0.00146719	+	0.00874140i
$736$		0			0
$737$	173.476	+	206.740i	0.235381	+	0.280516i
$738$		0			0
$739$	19.5958	+	16.4429i	0.0265167	+	0.0222501i	0.655950	−	0.754805i	$-0.272268\pi$
$739$	19.5958	+	16.4429i	0.0265167	+	0.0222501i	−0.629433	+	0.777055i	$0.716713\pi$
$740$		0			0
$741$	773.378	−	51.4407i	1.04370	−	0.0694206i
$742$		0			0
$743$	659.369	+	622.083i	0.887442	+	0.837258i	0.987483	−	0.157725i	$-0.0504159\pi$
$743$	659.369	+	622.083i	0.887442	+	0.837258i	−0.100041	+	0.994983i	$0.531897\pi$
$744$		0			0
$745$	12.4279	−	16.6936i	0.0166818	−	0.0224075i
$746$		0			0
$747$	−744.795	+	1174.10i	−0.997048	+	1.57175i
$748$		0			0
$749$	149.955	−	298.585i	0.200207	−	0.398645i
$750$		0			0
$751$	861.679	−	100.716i	1.14738	−	0.134109i	0.478918	−	0.877859i	$-0.341029\pi$
$751$	861.679	−	100.716i	1.14738	−	0.134109i	0.668457	+	0.743751i	$0.266955\pi$
$752$		0			0
$753$	100.539	+	326.024i	0.133518	+	0.432966i
$754$		0			0
$755$	8.90628	−	5.14204i	0.0117964	−	0.00681065i
$756$		0			0
$757$	391.491	−	678.081i	0.517161	−	0.895748i	−0.482641	−	0.875818i	$-0.660322\pi$
$757$	391.491	−	678.081i	0.517161	−	0.895748i	0.999801	−	0.0199300i	$-0.00634432\pi$
$758$		0			0
$759$	−899.253	−	1754.37i	−1.18479	−	2.31142i
$760$		0			0
$761$	468.294	+	202.002i	0.615366	+	0.265443i	0.680864	−	0.732410i	$-0.261604\pi$
$761$	468.294	+	202.002i	0.615366	+	0.265443i	−0.0654980	+	0.997853i	$0.520864\pi$
$762$		0			0
$763$	9.08656	+	156.010i	0.0119090	+	0.204469i
$764$		0			0
$765$	−10.1276	−	3.49829i	−0.0132387	−	0.00457292i
$766$		0			0
$767$	−133.273	+	57.4885i	−0.173759	+	0.0749524i
$768$		0			0
$769$	706.113	+	167.352i	0.918223	+	0.217623i	0.662443	−	0.749112i	$-0.269520\pi$
$769$	706.113	+	167.352i	0.918223	+	0.217623i	0.255780	+	0.966735i	$0.417668\pi$
$770$		0			0
$771$	−10.7738	−	24.4213i	−0.0139738	−	0.0316748i
$772$		0			0
$773$	311.464	+	855.741i	0.402929	+	1.10704i	0.960832	+	0.277133i	$0.0893841\pi$
$773$	311.464	+	855.741i	0.402929	+	1.10704i	−0.557902	+	0.829907i	$0.688394\pi$
$774$		0			0
$775$	139.223	+	50.6729i	0.179642	+	0.0653844i
$776$		0			0
$777$	−1003.31	+	590.334i	−1.29126	+	0.759760i
$778$		0			0
$779$	1169.68	+	68.1261i	1.50151	+	0.0874533i
$780$		0			0
$781$	772.036	+	818.311i	0.988523	+	1.04777i
$782$		0			0
$783$	−1183.30	−	558.096i	−1.51125	−	0.712767i
$784$		0			0
$785$	22.6526	+	6.78174i	0.0288568	+	0.00863916i
$786$		0			0
$787$	−572.616	−	376.616i	−0.727594	−	0.478546i	0.130883	−	0.991398i	$-0.458219\pi$
$787$	−572.616	−	376.616i	−0.727594	−	0.478546i	−0.858477	+	0.512852i	$0.828589\pi$
$788$		0			0
$789$	482.960	−	412.079i	0.612117	−	0.522281i
$790$		0			0
$791$	−43.4329	+	7.65840i	−0.0549089	+	0.00968192i
$792$		0			0
$793$	−108.925	+	617.742i	−0.137358	+	0.778994i
$794$		0			0
$795$	10.4215	+	3.02667i	0.0131088	+	0.00380714i
$796$		0			0
$797$	−916.571	+	274.403i	−1.15003	+	0.344295i	−0.804406	−	0.594080i	$-0.797516\pi$
$797$	−916.571	+	274.403i	−1.15003	+	0.344295i	−0.345620	+	0.938375i	$0.612331\pi$
$798$		0			0
$799$	−56.8101	−	6.64015i	−0.0711015	−	0.00831058i
$800$		0			0
$801$	−89.6485	+	894.595i	−0.111921	+	1.11685i
$802$		0			0
$803$	−535.085	−	813.558i	−0.666358	−	1.01315i
$804$		0			0
$805$	30.3713	+	40.7958i	0.0377284	+	0.0506780i
$806$		0			0
$807$	−789.341	+	98.8593i	−0.978118	+	0.122502i
$808$		0			0
$809$			631.480i			0.780568i	0.920695	+	0.390284i	$0.127623\pi$
$809$			631.480i			0.780568i	−0.920695	+	0.390284i	$0.872377\pi$
$810$		0			0
$811$	−156.202			−0.192604			−0.0963022	−	0.995352i	$-0.530702\pi$
$811$	−156.202			−0.192604			−0.0963022	+	0.995352i	$0.530702\pi$
$812$		0			0
$813$	−843.012	+	638.461i	−1.03692	+	0.785315i
$814$		0			0
$815$	−22.7792	+	16.9585i	−0.0279499	+	0.0208079i
$816$		0			0
$817$	−2016.05	+	1325.98i	−2.46763	+	1.62298i
$818$		0			0
$819$	−37.0930	−	495.935i	−0.0452906	−	0.605537i
$820$		0			0
$821$	9.43926	−	80.7580i	0.0114973	−	0.0983655i	−0.986271	−	0.165133i	$-0.947195\pi$
$821$	9.43926	−	80.7580i	0.0114973	−	0.0983655i	0.997769	+	0.0667678i	$0.0212687\pi$
$822$		0			0
$823$	252.374	+	842.989i	0.306652	+	1.02429i	0.962926	+	0.269766i	$0.0869462\pi$
$823$	252.374	+	842.989i	0.306652	+	1.02429i	−0.656274	+	0.754522i	$0.727869\pi$
$824$		0			0
$825$	755.498	+	787.678i	0.915755	+	0.954761i
$826$		0			0
$827$	646.398	+	113.977i	0.781618	+	0.137820i	0.550199	−	0.835034i	$-0.314552\pi$
$827$	646.398	+	113.977i	0.781618	+	0.137820i	0.231419	+	0.972854i	$0.425663\pi$
$828$		0			0
$829$	162.765	+	923.089i	0.196340	+	1.11350i	0.910498	+	0.413513i	$0.135698\pi$
$829$	162.765	+	923.089i	0.196340	+	1.11350i	−0.714159	+	0.699984i	$0.753190\pi$
$830$		0			0
$831$	−137.766	+	388.438i	−0.165784	+	0.467434i
$832$		0			0
$833$	−41.6023	+	63.2532i	−0.0499427	+	0.0759342i
$834$		0			0
$835$	8.12697	−	27.1460i	0.00973290	−	0.0325102i
$836$		0			0
$837$	−152.315	+	49.7337i	−0.181978	+	0.0594190i
$838$		0			0
$839$	−962.306	+	907.889i	−1.14697	+	1.08211i	−0.151361	+	0.988479i	$0.548366\pi$
$839$	−962.306	+	907.889i	−1.14697	+	1.08211i	−0.995607	+	0.0936297i	$0.970153\pi$
$840$		0			0
$841$	87.6234	−	1504.44i	0.104190	−	1.78887i
$842$		0			0
$843$	693.077	−	5.71021i	0.822155	−	0.00677368i
$844$		0			0
$845$	−5.50033	+	15.1120i	−0.00650927	+	0.0178841i
$846$		0			0
$847$	−523.907	+	190.686i	−0.618544	+	0.225132i
$848$		0			0
$849$	−756.568	−	553.615i	−0.891128	−	0.652079i
$850$		0			0
$851$	661.197	−	2789.81i	0.776965	−	3.27827i
$852$		0			0
$853$	304.768	+	706.533i	0.357290	+	0.828292i	0.998160	+	0.0606417i	$0.0193147\pi$
$853$	304.768	+	706.533i	0.357290	+	0.828292i	−0.640870	+	0.767650i	$0.721426\pi$
$854$		0			0
$855$	0.781977	+	47.4530i	0.000914593	+	0.0555006i
$856$		0			0
$857$	−111.117	+	6.47181i	−0.129658	+	0.00755171i	−0.122851	−	0.992425i	$-0.539204\pi$
$857$	−111.117	+	6.47181i	−0.129658	+	0.00755171i	−0.00680679	+	0.999977i	$0.502167\pi$
$858$		0			0
$859$	124.070	−	287.626i	0.144435	−	0.334838i	−0.830607	−	0.556859i	$-0.812006\pi$
$859$	124.070	−	287.626i	0.144435	−	0.334838i	0.975042	+	0.222021i	$0.0712654\pi$
$860$		0			0
$861$	37.5272	−	750.838i	0.0435856	−	0.872054i
$862$		0			0
$863$	549.662	+	317.347i	0.636920	+	0.367726i	0.783427	−	0.621484i	$-0.213470\pi$
$863$	549.662	+	317.347i	0.636920	+	0.367726i	−0.146507	+	0.989210i	$0.546803\pi$
$864$		0			0
$865$	−24.9909	−	43.2855i	−0.0288912	−	0.0500411i
$866$		0			0
$867$	544.243	+	505.057i	0.627731	+	0.582534i
$868$		0			0
$869$	165.829	+	1418.75i	0.190827	+	1.63263i
$870$		0			0
$871$	−149.845	−	75.2549i	−0.172038	−	0.0864006i
$872$		0			0
$873$	915.099	−	122.275i	1.04822	−	0.140063i
$874$		0			0
$875$	−45.2021	−	33.6518i	−0.0516596	−	0.0384591i
$876$		0			0
$877$	329.599	−	349.354i	0.375825	−	0.398352i	−0.511660	−	0.859188i	$-0.670969\pi$
$877$	329.599	−	349.354i	0.375825	−	0.398352i	0.887485	+	0.460837i	$0.152451\pi$
$878$		0			0
$879$	247.380	+	121.697i	0.281434	+	0.138450i
$880$		0			0
$881$	−600.155	+	715.237i	−0.681220	+	0.811846i	−0.990264	−	0.139201i	$-0.955546\pi$
$881$	−600.155	+	715.237i	−0.681220	+	0.811846i	0.309044	+	0.951048i	$0.399991\pi$
$882$		0			0
$883$	−788.807	+	661.888i	−0.893326	+	0.749590i	−0.968874	−	0.247553i	$-0.920374\pi$
$883$	−788.807	+	661.888i	−0.893326	+	0.749590i	0.0755484	+	0.997142i	$0.475929\pi$
$884$		0			0
$885$	−3.10834	−	8.32601i	−0.00351225	−	0.00940792i
$886$		0			0
$887$	219.617	+	437.293i	0.247595	+	0.493002i	0.982760	−	0.184886i	$-0.0591916\pi$
$887$	219.617	+	437.293i	0.247595	+	0.493002i	−0.735165	+	0.677888i	$0.762895\pi$
$888$		0			0
$889$	1039.41	−	246.344i	1.16919	−	0.277102i
$890$		0			0
$891$	−1168.54	−	166.554i	−1.31150	−	0.186930i
$892$		0			0
$893$	58.4252	+	246.515i	0.0654257	+	0.276053i
$894$		0			0
$895$	31.5583	−	15.8492i	0.0352607	−	0.0177086i
$896$		0			0
$897$	944.759	+	779.573i	1.05324	+	0.869090i
$898$		0			0
$899$	−184.839	−	220.282i	−0.205605	−	0.245030i
$900$		0			0
$901$	96.6075	+	81.0633i	0.107222	+	0.0899704i
$902$		0			0
$903$	861.417	+	1286.51i	0.953950	+	1.42470i
$904$		0			0
$905$	2.80067	+	2.64229i	0.00309466	+	0.00291966i
$906$		0			0
$907$	74.4405	−	99.9909i	0.0820733	−	0.110244i	−0.759190	−	0.650869i	$-0.774405\pi$
$907$	74.4405	−	99.9909i	0.0820733	−	0.110244i	0.841264	+	0.540625i	$0.181812\pi$
$908$		0			0
$909$	−88.2492	+	28.0125i	−0.0970838	+	0.0308169i
$910$		0			0
$911$	437.519	−	871.173i	0.480263	−	0.956282i	−0.514826	−	0.857295i	$-0.672143\pi$
$911$	437.519	−	871.173i	0.480263	−	0.956282i	0.995089	−	0.0989871i	$-0.0315603\pi$
$912$		0			0
$913$	−2236.04	+	261.355i	−2.44911	+	0.286260i
$914$		0			0
$915$	−37.4450	−	8.54942i	−0.0409235	−	0.00934363i
$916$		0			0
$917$	−928.641	+	536.151i	−1.01269	+	0.584680i
$918$		0			0
$919$	256.455	−	444.194i	0.279059	−	0.483345i	−0.692092	−	0.721809i	$-0.743311\pi$
$919$	256.455	−	444.194i	0.279059	−	0.483345i	0.971151	+	0.238465i	$0.0766441\pi$
$920$		0			0
$921$	772.950	−	1196.57i	0.839251	−	1.29921i
$922$		0			0
$923$	−641.826	−	276.857i	−0.695369	−	0.299953i
$924$		0			0
$925$	92.2932	+	1584.61i	0.0997765	+	1.71310i
$926$		0			0
$927$	−882.991	−	716.460i	−0.952525	−	0.772880i
$928$		0			0
$929$	−630.649	+	272.035i	−0.678847	+	0.292826i	−0.707449	−	0.706765i	$-0.750154\pi$
$929$	−630.649	+	272.035i	−0.678847	+	0.292826i	0.0286014	+	0.999591i	$0.490895\pi$
$930$		0			0
$931$	326.297	+	77.3339i	0.350480	+	0.0830654i
$932$		0			0
$933$	650.998	+	70.6592i	0.697747	+	0.0757333i
$934$		0			0
$935$	−5.93363	−	16.3025i	−0.00634613	−	0.0174359i
$936$		0			0
$937$	−445.058	−	161.988i	−0.474982	−	0.172879i	0.0934260	−	0.995626i	$-0.470218\pi$
$937$	−445.058	−	161.988i	−0.474982	−	0.172879i	−0.568408	+	0.822747i	$0.692440\pi$
$938$		0			0
$939$	1208.77	+	684.667i	1.28729	+	0.729145i
$940$		0			0
$941$	−1681.41	−	97.9308i	−1.78683	−	0.104071i	−0.867470	−	0.497490i	$-0.834255\pi$
$941$	−1681.41	−	97.9308i	−1.78683	−	0.104071i	−0.919359	+	0.393419i	$0.871292\pi$
$942$		0			0
$943$	1270.63	+	1346.79i	1.34743	+	1.42819i
$944$		0			0
$945$	30.4422	−	0.752569i	0.0322139	−	0.000796369i
$946$		0			0
$947$	330.954	+	99.0811i	0.349476	+	0.104626i	0.456730	−	0.889605i	$-0.349021\pi$
$947$	330.954	+	99.0811i	0.349476	+	0.104626i	−0.107254	+	0.994232i	$0.534206\pi$
$948$		0			0
$949$	505.475	+	332.456i	0.532640	+	0.350323i
$950$		0			0
$951$	254.712	+	1378.06i	0.267836	+	1.44906i
$952$		0			0
$953$	463.774	−	81.7759i	0.486647	−	0.0858089i	0.0750590	−	0.997179i	$-0.476085\pi$
$953$	463.774	−	81.7759i	0.486647	−	0.0858089i	0.411588	+	0.911370i	$0.364974\pi$
$954$		0			0
$955$	2.63569	−	14.9477i	0.00275988	−	0.0156521i
$956$		0			0
$957$	−505.489	−	2057.15i	−0.528201	−	2.14958i
$958$		0			0
$959$	1185.64	−	354.957i	1.23633	−	0.370133i
$960$		0			0
$961$	919.523	+	107.477i	0.956840	+	0.111839i
$962$		0			0
$963$	474.281	+	133.516i	0.492503	+	0.138646i
$964$		0			0
$965$	2.75700	+	4.19182i	0.00285700	+	0.00434386i
$966$		0			0
$967$	−269.041	−	361.385i	−0.278222	−	0.373717i	0.640944	−	0.767588i	$-0.278543\pi$
$967$	−269.041	−	361.385i	−0.278222	−	0.373717i	−0.919166	+	0.393871i	$0.871136\pi$
$968$		0			0
$969$	−214.268	+	508.200i	−0.221123	+	0.524459i
$970$		0			0
$971$			286.503i			0.295060i	0.989058	+	0.147530i	$0.0471323\pi$
$971$			286.503i			0.295060i	−0.989058	+	0.147530i	$0.952868\pi$
$972$		0			0
$973$	100.013			0.102788
$974$		0			0
$975$	−624.852	−	263.451i	−0.640874	−	0.270206i
$976$		0			0
$977$	1022.28	−	761.062i	1.04635	−	0.778978i	0.0705196	−	0.997510i	$-0.477534\pi$
$977$	1022.28	−	761.062i	1.04635	−	0.778978i	0.975830	+	0.218532i	$0.0701269\pi$
$978$		0			0
$979$	−1216.24	+	799.937i	−1.24233	+	0.817096i
$980$		0			0
$981$	−223.332	+	56.8328i	−0.227657	+	0.0579336i
$982$		0			0
$983$	108.701	−	929.993i	0.110580	−	0.946076i	−0.818070	−	0.575119i	$-0.804956\pi$
$983$	108.701	−	929.993i	0.110580	−	0.946076i	0.928650	−	0.370957i	$-0.120970\pi$
$984$		0			0
$985$	8.84572	+	29.5468i	0.00898043	+	0.0299967i
$986$		0			0
$987$	157.858	−	38.7893i	0.159937	−	0.0393002i
$988$		0			0
$989$	−3755.36	−	662.172i	−3.79713	−	0.669537i
$990$		0			0
$991$	−140.896	−	799.059i	−0.142175	−	0.806316i	−0.969592	−	0.244728i	$-0.921301\pi$
$991$	−140.896	−	799.059i	−0.142175	−	0.806316i	0.827417	−	0.561589i	$-0.189810\pi$
$992$		0			0
$993$	1531.66	−	283.104i	1.54246	−	0.285100i
$994$		0			0
$995$	−9.00135	+	13.6859i	−0.00904659	+	0.0137547i
$996$		0			0
$997$	270.842	−	904.674i	0.271657	−	0.907397i	−0.707914	−	0.706298i	$-0.750364\pi$
$997$	270.842	−	904.674i	0.271657	−	0.907397i	0.979571	−	0.201098i	$-0.0644511\pi$
$998$		0			0
$999$	−1135.59	−	1287.34i	−1.13673	−	1.28863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.4	✓	324
81.65	odd	54	inner	324.3.o.a.65.4	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.4	✓	324	1.1	even	1	trivial
324.3.o.a.65.4	yes	324	81.65	odd	54	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.76434 - 1.16550i) q^{3} +(-0.148228 + 0.110352i) q^{5} +(5.09912 - 3.35374i) q^{7} +(6.28320 + 6.44371i) q^{9} +O(q^{10})\)	\(q+(-2.76434 - 1.16550i) q^{3} +(-0.148228 + 0.110352i) q^{5} +(5.09912 - 3.35374i) q^{7} +(6.28320 + 6.44371i) q^{9} +(-1.69174 + 14.4737i) q^{11} +(-2.59671 - 8.67360i) q^{13} +(0.538369 - 0.132290i) q^{15} +(6.34459 + 1.11872i) q^{17} +(-4.95520 - 28.1023i) q^{19} +(-18.0045 + 3.32785i) q^{21} +(24.7802 - 37.6764i) q^{23} +(-7.16029 + 23.9170i) q^{25} +(-9.85875 - 25.1357i) q^{27} +(35.2456 - 33.2525i) q^{29} +(0.345056 - 5.92438i) q^{31} +(21.5457 - 38.0387i) q^{33} +(-0.385742 + 1.05982i) q^{35} +(59.7445 - 21.7452i) q^{37} +(-2.93093 + 27.0033i) q^{39} +(-9.46893 + 39.9526i) q^{41} +(-33.4930 - 77.6454i) q^{43} +(-1.64242 - 0.261777i) q^{45} +(-8.86308 + 0.516216i) q^{47} +(-4.65449 + 10.7903i) q^{49} +(-16.2348 - 10.4872i) q^{51} +(16.9526 + 9.78756i) q^{53} +(-1.34644 - 2.33210i) q^{55} +(-19.0555 + 83.4598i) q^{57} +(-1.86108 - 15.9226i) q^{59} +(-61.9122 - 31.0935i) q^{61} +(53.6493 + 11.7850i) q^{63} +(1.34205 + 0.999121i) q^{65} +(12.7093 - 13.4711i) q^{67} +(-112.413 + 75.2692i) q^{69} +(49.6251 - 59.1408i) q^{71} +(-51.1888 + 42.9525i) q^{73} +(47.6689 - 57.7695i) q^{75} +(39.9148 + 79.4769i) q^{77} +(95.3805 - 22.6056i) q^{79} +(-2.04282 + 80.9742i) q^{81} +(35.6277 + 150.325i) q^{83} +(-1.06390 + 0.534311i) q^{85} +(-136.187 + 50.8425i) q^{87} +(64.2127 + 76.5257i) q^{89} +(-42.3299 - 35.5190i) q^{91} +(-7.85874 + 15.9749i) q^{93} +(3.83564 + 3.61874i) q^{95} +(61.2573 - 82.2829i) q^{97} +(-103.894 + 80.0403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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